See typed list
of tables in
side this cover
1916, 1930, 1951, 1934, and 1956 editions of
(tables in back of book)
(1916)
fable So. litle
% Traverse table, degrees
Conversion of departure into differ-
531
621
634
755
772
817
5
5B
42
44
45
not in these editions - refer to
1958 edition, Table 4, pace 106)
Meridional parts
Distance of an object by tso bear
ings, degrees
tables
(not in these editions - refer to
1988 edition, Table l?JLj^ise_140>
Logarittes of numbers
Logarithms of trigonometric func
tions, degrees
Logarithmic and natural haversines
i
No. 9
American Practical Navigator
An Epitome of Navigation and
Nautical Astronomy
ORIGINALLY BY
NATHANIEL BOWDITCH, LL. D.
PUBLISHED BY THE
UNITED STATES HYDROGRAPHIC OFFICE
UNDER THE AUTHORITY OF
THE SECRETARY OF THE NAVY
WASHINGTON
GOVERNMENT PRINTING OFFICE
1916
y /
/
Mtton.
STATUTES OF AUTHOKIZATION.
There shall be a Hydrographic Office attached to the Bur.eau of Navigation in
the Navy Department, for the improvement of the means for navigating safely
the vessels of the Navy and of the mercantile marine, by providing, under the
authority of the Secretary of the Navy, accurate and cheap nautical charts, sailing
directions, navigators, and manuals of instructions for the use of all vessels of the
United States, and for the benefit and use of navigators generally. (R. S. 431.)
The Secretary of the Navy is authorized to cause to be prepared, at the Hydro-
graphic Office attached to the Bureau of Navigation in the Navy Department,
maps, charts, and nautical books relating to and required in navigation, and to
publish and furnish them to navigators at the cost of printing and paper, and to
purchase the plates and copyrights of such existing maps, charts, navigators, sail
ing directions, and instructions, as he may consider necessary, and when he may
deem it expedient to do so, and under such regulations and instructions as he may
prescribe. (R. S. 432.)
2
r
TEXT AND APPENDICES.
.300861
NOTE ON REPRINT OF 1916. — This reprint is the same as the 1914 edition, except
that the examples worked out in the text have been brought up to date to accord with
the form of the American Nautical Almanac as now published.
CONTENTS OF F^RT I.
Page.
Abbreviations
Chapter I. Definitions relating to Navigation 9
II. Instruments and Accessories in Navigation 11
III. The Compass Error 36
IV. Piloting 56
V. The Sailings 72
VI. Dead Reckoning 84
VII. Definitions relating to Nautical Astronomy 87
VIII. Instruments employed in Nautical Astronomy 91
IX. Time and the Nautical Almanac 102
X. Correction of Observed Altitudes 115
XI. The Chronometer Error 121
XII. Latitude 126
XIII. Longitude 140
XIV. Azimuth 144
XV. The Sumner Line 150
XVI. The Practice of Navigation at Sea 169
XVII. Marine Surveying 189
XVIII. Winds 206
XIX. Cyclonic Storms 212
XX. Tides 225
XXI. Ocean Currents 232
XXII. Ice and its Movements in the North Atlantic Ocean 238
Appendix I. Extracts from the American Ephemeris and Nautical Almanac for the year 1916
which have reference to examples for that year given in this work 248
II. A collection of Forms for working Dead Reckoning and various Astronomical Sights,
with notes explaining their application under all circumstances 254
III. Explanation of certain Rules and Principles of Mathematics of use in the Solution
of Problems in Navigation 266
IV. Maritime Positions and Tidal Data ; 278
Index.. 358
ABBREVIATIONS USED IN THIS WORK.
Alt. (or ft) Altitude.
a. m Ante meridian.
Amp Amplitude.
App Apparent.
App. t Apparent time.
Ast Astronomical.
Ast. t Astronomical time.
Aug Augmentation.
Az. (orZ) Azimuth.
C Course.
C. C Chronometer correction.
C — W Chronometer minus watch.
Chro. t Chronometer time.
Co. L Co. latitude.
Col Column.
Corr Correction.
Cos Cosine.
Cosec Cosecant.
Cot Cotangent.
d (or Dec.) Declination.
D (or D.Lo) Difference longitude.
Dep Departure.
Dev Deviation.
Diff Difference.
Dist Distance.
DL Difference latitude.
D. R Dead reckoning.
E., Ely East, easterly.
Elap. t Elapsed time.
Eq. t Equation of time.
F Longitude factor.
/ Latitude factor.
G. (or Gr.) Greenwich.
G. A. T Greenwich apparent time.
G. M. T Greenwich mean time.
G. S. T Greenwich sidereal time.
ft Altitude.
H Meridian altitude.
H. A. (or t) Hour angle.
Hav Haversine.
H. D Hourly difference.
H. P. (or Hor. par.). .Horizontal parallax.
Hr-s Hour-s.
H. W High water.
I. C Index correction.
L. (or Lat.) Latitude.
L. A. T Local apparent time.
L. M. T Local mean time.
L. S. T Local sidereal time.
Lo. (or Long.) Longitude.
Log Logarithm.
Lun. Int Lunitidal interval.
L. W Low water.
A Longitude.
m Meridional difference.
Merid Meridian or noon.
Mag Magnetic.
M. D Minute's difference.
Mid Middle.
Mid. L Middle latitude.
M. T Meantime.
nat Natural.
N., Nly North, northerly.
N. A. (orNaut. Aim.) Nautical Almanac.
Np Neap .
Obs Observation.
p (or P. D.) Polar distance.
p. c Per compass.
JP. D. (or p) Polar distance.
P. L. (or Prop. Log.). Proportional logarithm.
p. m Post meridian.
p, & r Parallax and refraction.
rar Parallax.
R. A Right ascension.
R. A. M. S Right ascension mean sun.
Red Reduction.
Ref Refraction.
S., Sly South, southerly.
S. D Semidiameter.
Sec Secant.
Sid Sidereal.
Sin Sine.
Spg Spring.
t Hour angle.
T Time.
Tab Table.
Tan Tangent.
Tr. (or Trans. ) Transit.
Var Variation.
Vert Vertex or vertical.
W., Wly West, westerly.
W. T Watch time.
z Zenith distance.
Z Azimuth.
6 Auxiliary angle.
X Difference longitude in time.
SYMBOLS.
The Sun.
The Moon.
* _ A Star or Planet.
"Q (C Alt. upper limb.
LQ ([_ Alt. lower limb.
(J) |3 Azimuthal angle.
A a ..Alpha.
£/? ..Beta.
F Y ..Gamma.
Ad.. Delta.
E e . .Epsilon.
Z C -.Zeta.
Hr) ..Eta.
8 d ..Theta.
Iota.
Kappa.
Lambda.
u.
GREEK LETTERS.
f.
I
K K
A X
M it
Degrees.
Minutes of Arc.
Seconds of Arc.
Hours.
Minutes of Time.
Seconds of Time.
N v Nu.
s e xi.
0 o Omicron.
n 7i Pi.
, P p Rho.
1 a (r)... Sigma.
T T Tau.
T y Upsilon.
0 <j> Phi.
X x Chi.
¥</> Psi.
Q a> Omega .
CHAPTER I.
DEFINITIONS KELATING TO NAVIGATION,
1. That science, generally termed Navigation, which affords the knowledge
necessary to conduct a ship from point to point upon the earth, enabling the mariner
to determine, with a sufficient degree of accuracy, the position of his vessel at any
tune, is properly divided into two branches : Navigation and Nautical Astronomy.
2. Navigation, in its limited sense, is that branch which treats of the determina
tion of the position of the ship by reference to the earth, or to objects thereon. It
comprises (a) Piloting, in which the position is ascertained from visible objects
upon the earth, or from soundings of the depth of the sea, and (b) Dead Reckoning,
in which the position at any moment is deduced from the direction and amount of
a vessel's progress from a known point of departure.
3. Nautical Astronomy is that branch of the science which treats of the deter
mination of the vessel's place by the aid of celestial objects — the sun, moon, planets,
or stars.
4. Navigation and Nautical Astronomy have been respectively termed Geo-
Navigation and Celo- Navigation, to indicate the processes upon which they depend.
5. As the method of piloting can not be employed excepting near land or in
moderate depths of water, the navigator at sea
must fix his position either by dead reckoning or by
observation of celestial objects; the latter method is
more exact, but as it is not always available, the
former must often be depended upon.
6. THE EARTH. — The Earth is an oblate
spheroid, being a nearly spherical, body slightly
flattened at the poles; its longer or equatorial
axis measures about 7,927 statute miles, and its E
shorter axis, around which it rotates, about 7,900
statute miles.
The Earth (assumed for purposes of illustra
tion to be a sphere) is represented in figure 1.
The Axis of Rotation, usually spoken of simply
as the Axis, is PP'.
The Poles are the points, P and P', in which
the axis intersects the surface, and are designated,
respectively, as the North Pole and the South Pole.
The Equator is the great circle EQMW, formed by the intersection with the
earth's surface of a plane perpendicular to the axis ; the equator is equidistant from
the poles, every point upon it being^90° from each pole.
Meridians are the great circles rQP', PMP', PM'P', formed by the intersection
with the earth's surface of planes secondary to the equator (that is, passing through
its poles and therefore perpendicular to its plane).
Parallels of Latitude are small circles NTn, N'n'T', formed by the intersection
with the earth's surface of planes passed parallel to the equator.
The Latitude of a place on the surface of the earth is the arc of the meridian
intercepted between the equator and that place. Latitude is reckoned North and
South, from the equator as an origin, through 90° to the poles; thus, the latitude
of the point T is MT, north, and of the point T', MT, north. The Difference of
Latitude between any two places is the arc of a meridian intercepted between their
parallels of latitude, and is called North or South, according to direction; tnus, the
difference of latitude between T and T' is Tnf or T'n, north from T or south from T'.
The Longitude of a place on the surface of the earth is the arc of the equator inter
cepted between its meridian and that of some place from which the longitude is
9
FIG. l.
10 ... fc.. DEFINITION RELATING TO NAVIGATION.
reckoned. Longitude is measured East or West through 180° from the meridian of
a designated- place, such meridian being termed the Prime Meridian; the prime
meridian used by most nations, including the United States, is that of Greenwich,
England. If, in the figure, the prime meridian be PGQP', then the longitude of the
point T is QM, east, and of T', QM', east. The Difference of Longitude between any
two places is the arc of the equator intercepted between their meridians, and is called
East or West, according to direction ; thus, the difference of longitude between T and
T' is MM', east from M or west from M'. The Departure is the linear distance,
measured on a parallel of latitude, between two meridians; unlike the various quanti
ties previously defined, departure is reckoned in miles; the departure between two
meridians varies with the parallel of latitude upon which it is measured; thus, the
departure between the meridians of T and T' is the number of miles corresponding
to the distance Tn in the latitude of T, or to n'T' in the latitude of T'.
The curved line which joins any two places on the earth's surface, cutting all the
meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equian
gular Spiral. In the figure this line is represented by TYT'. The constant angle
which this line makes with the meridians is called the Course; and the length of the
line between any two places is called the Distance between those places;
The unit of linear measure employed by navigators is the Nautical or Sea Mile,
or Knot. This unit is defined in the United States of America as being 6,080.27
feet in length and equal to one-sixtieth part of a degree of a great circle ot a sphere
whose surface is equal in area to the area of the surface of the earth.
The nautical mile is not exactly the same in all countries, but, from the navi
gator's standpoint, the various lengths adopted do not differ materially.
Since, upon the ocean, latitude has been capable of easier and more accurate
determination than longitude, it might naturally be expected that there exists an
intimate fixed relation between the nautical mile and the minute of latitude (or the
length of that portion of a meridian which subtends at the earth's center the angular
measure of one minute); but on account of the fact that the earth is not a perfect
sphere, a fixed relation does not exist, and the arc of a meridian that subtends an
angle of 1' at the center of the earth varies slightly in length from the Equator to
the poles, being 6,045.95 feet at the Equator and 6,107.85 feet at the poles. Its
average length is 1,852.201 meters, or 6,076.82 feet. Accordingly in France,
Germany, and Austria the nautical mile is 1,852 meters, 2,025.41 yards, or 6,076.23
feet.
For purposes of navigation the nautical mile is assumed to be equal to a minute
of latitude in all parts of the world; and, hence, when a vessel changes her position
to the north or south by 1 nautical mile, it may always be considered that the latitude
has changed 1'. Owing to the fact that the meridians converge toward the poles,
the difference of longitude produced by a change of position ol 1 mile to the east
or west will vary with the latitude ; thus, a departure of 1 mile will equal a difference of
longitude of 1' at the Equator, but of more than 1' at any higher latitude, being in
fact equal to I'.l of longitude in latitude 30° and to 2' of longitude in latitude 60°.
In England the nautical mile, corresponding to the Admiralty knot, is regarded
as having a length of 6,080 feet.
The statute mile of 5,280 feet, which is employed in land measurements, is
commonly used in navigating river and lake vessels. This is notably the case on the
Great Lakes of America, but with the recognition of the advantages to be gamed by
the nractice of nautical astronomy in the navigation of these vessels, the use of the
nautical mile is extending.
The Great Circle Track or Course between any two places is the route between
those places along the circumference of the great circle which joins them. In the
figure this line is represented by T/T . From the properties of a great circle (which is a
circle upon the earth's surface formed by the intersection of a plane passed through
its center) the distance between two points measured on a great circle track is shorter
than the distance upon any other line which joins them. Except when the two
points are on the same meridian or when both lie upon the equator, the great circle
track will always differ from the rhumb line, and the great circle track wul intersect
each intervening meridian at a different angle.
CHAPTER II.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION,
DIVIDERS OB COMPASSES.
7. This instrument consists of two legs movable about a joint, so that the
points at the extremities of the legs may be set at any required distance from each
other. It is used to take and transfer distances and to describe arcs and circles.
When used for the former purpose it is termed dividers, and the extremities of both
legs are metal points; when used for describing arcs or circles, it is called a compass,
and one of the metal points is replaced by a pencil or pen.
PARALLEL RULERS.
8. Parallel rulers are used for drawing lines parallel to each other in any direc
tion, and are particularly useful in transferring the rhumb-line on the chart to the
nearest compass-rose to ascertain the course, or to lay off bearings and courses.
PROTRACTOR.
9. This is an instrument used for the measurement of angles upon paper;
there is a wide variation in the material, size, and shape in which it may be made.
(For a description of the Three Armed Protractor, see art. 428, Chap. XVII.)
THE CHIP LOG.
10. This instrument, for measuring the rate of sailing, consists of three parts;
viz, the log-chip, the log-line, and the log-glass. A light substance thrown from the
ship ceases to partake of the motion 01 the vessel as soon as it strikes the water,
and will be left behind on the surface; after a certain interval, if the distance of the
ship from this stationary object be measured, the approximate rate of sailing will
be given. The log-chip is the float, the log-line is the measure of the distance, and
the log-glass defines the interval of tune.
The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with
lead on the circular edge sufficiently to make it float upright in the water. There
is a hole in each corner of the log-chip, and the log-line is knotted in the one at the
apex; at about 8 inches from the end there is seized a wooden socket; a piece of
line of proper length, being knotted in the other holes, has seized into its bight a
wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as
the line is checked this peg pulls out, thus allowing the log-chip to be hauled in
with the least resistance.
The log-line is about 150 fathoms in length, one end made fast to the log-chip,
the other to a reel upon which it is wound. At a distance of from 15 to 20 fathoms
from the log-chip a permanent mark of red bunting about 6 inches long is placed
to allow sufficient stray line for the log-chip to clear the vessel's eddy or wake. The
rest of the fine is divided into lengths of 47 feet 3 inches called Jcnots, by pieces of
fish-fine thrust through the strands, with one, two, three, etc., knots, according to
the number from stray-fine mark; each knot is further subdivided into five equal
lengths of two-tenths of a knot each, marked by pieces of white rag.
The length of a knot depends upon the number of seconds which the log-glass
measures; the length of each knot must bear the same ratio to the nautical mile
(-gV of a degree of a great circle of the earth, or 6,080 feet) that the time of the glass
does to an hour.
11
12 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
In the United States Navy all log-lines are marked for log-glasses of 28 seconds,
for which the proportion is :
3600 : 6080 = 28s : x,
x being the length of the knot.
Hence,
z = 47ft.29, or47ft3in.
The speed of the ship is estimated in knots and tenths of a knot.
The log-glass is a sand glass of the same shape and construction as the old hour
glass. Two glasses are used, one of 28 seconds and one of 14 seconds; the latter is
employed when the ship is going at a high rate of speed, the number of knots indi
cated on a line marked for a 28-second glass being doubled to obtain the true rate
of speed.
11. The log in all its parts should be frequently examined and adjusted; the
Eeg must be found to fit sufficiently tight to keep the log-chip upright; the log-
ne shrinks and stretches and should often be verified; the log-glass should be
compared with a watch. One end of the glass is stopped with a cork, by removing
which the sand may be dried or its quantity corrected.
12. A ground log consists of an ordinary log-line, with a lead attached instead
of a chip; in shoal water, where there are no well-defined objects available for fixing
the position of the vessel and the course and speed are influenced by a tidal or other
current, this log is sometimes used, its advantage being that the lead marks a sta
tionary point to which motion may be referred, whereas the chip would drift with
the stream. The speed, which is marked in the usual manner, is the speed over
the ground, and the trend of the line gives the course actually made good by the
vessel.
THE PATENT LOG.
13. This is a mechanical contrivance for registering the distance actually run
by a vessel through the water. There are various types of patent logs, but for the
most part they act upon the same principle, consisting of a registering device, a fly
or rotator, and a log or towline; the rotator is a small spino3e with a number of
blades extending radially in such manner as to form a spiral, and, when drawn through
the water in the direction of its axis, rotates about that axis after the manner of a
screw propeller; the rotator is towed from the vessel by means of a log or towline
from 30 to 100 fathoms in length, made fast at its apex, the line being of special
make, so that the turns of the rotator are transmitted through it to. the worm shaft
of the register, to which the inboard end of the line is attached; the registering
device is so constructed as to show upon a dial face the distance run, according to
the number of turns of its worm shaft due to the motion of the rotator; the register
is carried at some convenient point on the vessel's quarter; it is frequently found
expedient to rig it out upon a small boom, so that the rotator will be towed clear
of the wake.
14. Though not a perfect instrument, the patent log affords a means of deter
mining the vessel's speed through the water. It will usually be found that the
indications of the log are in error by a constant percentage, and the amount of this
error should be determined by careful experiment and applied to all readings.
Various causes may operate to produce inaccuracy of working in the patent
log, such as the bending of the blades of the rotator by accidental blows, fouling of
the rotator by seaweed or refuse from the ship, or mechanical wear of parts of the
register. The length of the towline has much to do with the working of the log,
and by varying the length the indications of the instrument may sometimes be
adjusted when the percentage of error is small; it is particularly important that the
line shall not be too short. The readings of the patent log can not be depended upon
for accuracy at low speeds, when the rotator does not tow horizontally, nor in a head
or a following sea, when the effect depends upon the wave motion as well as upon
the speed of the vessel.
15. Electrical registers for patent logs are in use, the distance recorded by the
mechanical register being communicated electrically to some point of the vessel
which is most convenient for the purposes of those charged with the navigation.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
13
17 fathoms from the lead, same as at 7 fathoms.
20 fathoms from the lead, with 2 knots.
25 fathoms from the lead, with 1 knot.
30 fathoms from the lead, with 3 knots.
35 fathoms from the lead, with 1 knot.
40 fathoms from the lead, with 4 knots.
And so on.
16. A number of instruments based upon different physical principles have
been devised for recording the speed of a vessel through the water and have been
used with varying degrees of success. Of these the hydraulic speed indicator, known
as the Nicholson Ship Log, affords an instance.
17. The revolutions of the screw propeller afford in a steamer the most valuable
means of determining a vessel's speed through the water. The number of revolu
tions per knot must be carefully determined for the vessel by experiment under
varying conditions of speed, draft, and foulness of bottom.
THE LEAD.
18. This device, for ascertaining the depth of water, consists essentially of a
suitably marked line, having a lead attached to one of its ends. It is an invaluable
aid to the navigator in shallow water, particularly in thick or foggy weather, and is
often of service when the vessel is out of sight of land.
Two leads are used for soundings — the Tiand-lead, weighing from 7 to 14 pounds,
with a line marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to
100 pounds, the line being 100 fathoms or upward in length.
Lines are generally marked as follows :
2 fathoms from the lead, with 2 strips of leather.
3 fathoms from the lead, with 3 strips of leather.
5 fathoms from the lead, with a white rag.
7 fathoms from the lead, with a red rag.
10 fathoms from the lead, with leather having a
hole in it.
13 fathoms from the lead, same as at 3 fathoms.
15 fathoms from the lead, same as at 5 fathoms.
Fathoms which correspond with the depths marked are called marks; the inter
mediate fathoms are called deeps; the only fractions of a fathom used are a half
and a quarter.
A practice sometimes followed is to mark the hand-lead line in feet around the
critical depths of the vessel by which it is to be used.
Lead lines should be measured frequently while wet and the correctness of the
marking verified. The distance from the leadsman's hand to the water's edge should
be ascertained in order that proper allowance may be made therefor in taking
soundings at night.
19. The deep-sea lead may be armed by filling with tallow a hole hollowed out
in its lower end, by which means a sample of the bottom is brought up.
THE SOUNDING MACHINE.
20. This machine possesses advantages over the deep-sea lead, for which it is
a substitute, in that soundings may be obtained at great depths and with rapidity
and accuracy without stopping the ship. It consists essentially of a stand holding
a reel upon which is wound the sounding wire, and which is controlled by a suitable
brake. Crank handles are provided for reeling in the wire after the sounding has
been taken. Attached to the outer end of the wire is the lead, which has a cavity
at its lower end for the reception of the tallow for arming. Above the lead is a
cylindrical case containing the depth-registering mechanism; various devices are in
use for this purpose, all depending, however, upon the increasing pressure of the
water with increasing depths.
21. In the Lord Kelvin machine a slender glass tube is used, sealed at one end
and open at the other, and coated inside with a chemical substance which changes
color upon contact with sea water; this tube is placed, closed end up, in the metal
cylinder; as it sinks the water rises in the tube, the contained air being compressed
with a force dependent upon the depth. The limit of discoloration is marked by a
clearly defined line, and the depth of the sounoling corresponding to this line is read
off from a scale. Tubes that have been used in comparatively shallow water may
be used again where the water is known to be deeper.
22. A tube whose inner surface is ground has been substituted for the chemical-
coated lube, ground glass, when wet, showing clear. The advantage of these tubes
14
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
is that they may be used an indefinite number of times if thoroughly dried. To
facilitate drying, a rubber cap is fitted to the upper end, which, when removed,
admits of a circulation of the air through the tube.
23. As a substitute for the glass tubes a mechanical depth recorder contained in a
suitable case has been used. In this device the pressure of the water acts upon a
piston against the tension of a spring. A scale with an index pointer records the
depth reached. The index pointer must be set at zero before each sounding.
24. Since the action of the sounding machine, when glass tubes are used,
depends upon the compression of the air, the barometric pressure of the atmosphere
must be taken into account when accurate results are required. The correction
consists in increasing the indicated depth by a fractional amount according to the
following table :
Bar. reading.
Increase.
29.75
One-fortieth.
30.00
One-thirtieth.
30.50
One- twentieth.
30.75
One-fifteenth.
THE MARINER'S COMPASS.
25. The Mariner's Compass is an instrument consisting either of a single
magnet, or, more usually, of a group of magnets, which, being attached to a graduated
circle pivoted at the center and allowed to swing freely in a horizontal plane, has a
tendency, when not affected by disturbing magnetic features within the ship, to lie
with its magnetic axis in the plane of the earth's magnetic meridian, thus affording a
means of determining the azimuth, or horizontal angular distance from that meridian,
of the ship's course and of all visible objects, terrestrial or celestial.
26. The circular card of the compass is divided on its periphery into 360°,
frequently numbered from 0° at North and South to 90° at East and West; also
into thirty-two divisions of 11J° each, called points, the latter being further divided
into naif-points and quarter-points; still finer subdivisions, eighth-points, are some-
tunes used, though not indicated on the card. A system of numbering the degrees
from 0° to 360°, always increasing toward the right, is shown in figure 2. This
system is in use in the United States Navy and by the mariners of some foreign
nations, and its general adoption would carry with it certain undoubted advantages.
27. Boxing the Compass is the process of naming the points in their order, and is
one of the first things to be learned by the young mariner. The four principal points
are called cardinal points and are named North, South, East, and West; each differs
in direction from the adjacent one by 90°, or 8 points. Midway between the cardinal
points, at an angular distance of 45°, or 4 points, are the inter-cardinal points, named
according to their position Northeast, Southeast, etc. Midway between each
cardinal and inter-cardinal point, at an angular distance of 22£°, or 2 points, is a
point whose name is made up of a combination of that of the cardinal with that of
the inter-cardinal point: North-Northeast, East-Northeast, East-Southeast, etc. At
an angular distance of 1 point, or 11J°, from each cardinal and inter-cardinal point
(and therefore midway between it and the 22£°-division last described), is a point
which bears the name of that cardinal or inter-cardinal point joined by the word by
to that of the cardinal point in the direction of which it lies : North by East, Northeast
by North, Northeast by East, etc.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
15
In boxing by fractional points, it is evident that each division may be referred to
either of the whole points to which it is adjacent; for instance, NE. by N. £ N. and
NNE. £ E. would describe the same division. It is the custom in the United States
Navy to box from North and South toward East and West, excepting that divisions
adjacent to a cardinal or inter-cardinal point are always referred to that point; as
No. 1742
JUNE 1908
FIG. 2.
N. i E., N. by E. £ E., NNE. $ E., NE. £ N., etc. Some mariners, however, make it a
practice to box from each cardinal and inter-cardinal point toward a 22 J°-point (NNE.,
ENE., etc.); as N. * E., N. by E. J E., NE. by N. * N., NE. i N., etc.
The names of the whole points, together with fractional points (according to the
nomenclature of the United States Navy), are given in the following table, which
16
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
shows also the degrees, minutes, and seconds from North or South to which each
division corresponds:
Points.
Angular
measure.
Points.
Angular
measure.
NORTH TO EAST.
Nnrlh-
0 / //
EAST TO SOUTH.
East.
8
90 00 00
N 1 E
1
2 48 45
E.-JS
8J
92 48 45
N | E
5 37 30
E. IS
8J
95 57 30
N £ E
1
8 26 15
E. f S
8|
98 26 15
N bv E
1
11 15 00
E. byS...
9
101 15 00
N hv E 4 E
14 03 45
ESE. f E . .
91
104 03 45
N byE }E
14
16 52 30
ESE.iE
91
106 52 30
N by E £ E
if
19 41 15
ESE. IE
9|
109 41 15
NNE
2
22 30 00
ESE
10
112 30 00
NNE £E
21
25 18 45
SE. byE. fE
101
115 18 45
NNE $ E
2*
28 07 30
SE. byE. |E
101
118 07 30
NNE f E
2i
30 56 15
SE. byE. IE...
id
320 56 15
NE by N
3
33 45 00
SE. by E
11
123 45 00
NE. f N
31
36 33 45
SE. |E
111
126 33 45
NE. 1 N
3f
39 22 30
SE.^E
111
129 22 30
NE 1 N
3J
42 11 15
SE. IE
llf
13^ 11 15
NE
4
45 00 00
SE
12
135 00 00
NE £ E
41
47 48 45
SE 1 S
121
137 48 45
NE A E
41
50 37 30
SE £ S
12i
140 37 30
NE f E
4J
53 26 15
SE | S
12£
143 26 15
NE byE
5
56 15 00
SE by S
13
146 15 00
NE by E 1 E
51
59 03 45
SSE £ E
131
149 03 45
NE byE. IE
5A
61 52 30
SSE. * E .
m
151 52 30
NE byE. IE
53
64 41 15
SSE. 1 E .
13f
154 41 15
ENE
6
67 30 00
SSE
14
157 30 00
ENE i E
61
70 18 45
S by E f E
141
160 18 45
ENE i E
6f
73 07 30
S by E ^ E
14!
163 07 30
ENE. IE..
S|
75 56 15
S by E IE
LUZ
14 1
165 56 15
E.byN
7
78 45 00
S byE
15
168 45 00
E £ N
71
81 33 45
S 4 E
151
171 33 45
E $N
71
84 2? 30
S i E
151
174 " 30
E JN
7i
87 11 15
S i E
15?
177 11 15
SOUTH TO WEST.
WEST TO NORTH.
West
24
270 00 00
South
16
180 00 00
WIN
241
272 48 45
S.I W
161
182 48 45
W £N
241
275 37 30
S. * W
161
185 37 30
W f N
24J
278 96 15
S.fW
16J
188 26 15
W by N
25
281 15 00
S. byW
17
191 15 00
WNW £ W
251
284 03 45
S.byW.JW
171
194 03 45
WNW ^W
251
286 52 30
S. byW. *W
17*
196 52 30
WNW 1 W
25J
289 41 15
S.byW.fW..,
17|
199 41 15
WNW
26
292 30 00
ssw
18
202 30 00
NW by W f W
9fil
295 IS 4^
SSW. -JW
181
205 18 45
NW by W \ W
*'U4
261
298 07 30
ssw. ^w
18*
208 07 30
NW byW 1W
262
300 56 15
ssw. * w....
181
210 56 15
NW byW
27
303 45 00
SW. byS
19
213 45 00
NW £ W
271
306 33 45
SW.f S
191
216 33 45
NW £ W
27^
309 22 30
SW. *S
191
219 22 30
NW 1 W
27J
311 11 15
SW.-fcS
19|
222 11 15
NW
28
315 00 00
SW
20
225 00 00
NW 1 N
281
317 48 45
SW. 1W
201
227 48 45
NW 1 N
981
320 37 30
SW. *W
201
230 37 30
NW £ N
98f
393 26 15
SW. | W
201
233 26 15
NW by N
99
326 15 00
SW. byW...
21
2o6 15 00
NNW £ W
291
329 03 45
Sw.byW.iW..
211
2o9 03 45
NNW 1 W
291
331 52 30
SW. by W. £W
21*
241 52 30
NNW 1 W
29$
334 41 15
SW. by W. 2 W
21|
244 41 15
NNW
30
337 30 00
WSW
22
247 30 00
NV>v W 3. W
cmi
340 1^4^
WSW.iW....
22J
250 18 45
N by W 1 W
Qfii
343 07 30
WSW. *W
22i
253 07 30
N "by W 1 W
30f
345 5(j 15
WSW. £ W..
22|
255 56 15
N byW
31
348 45 00
W.bvS
23
258 45 00
N £ W
311
351 33 45
W.f S
231
261 33 45
N 4 W
311
354 " 30
W.-fcS
Oof
23*,
264 '22 30
N 1 W
Qli
357 n 15
W.-JS
23£
267 11 15
North
39
3fiO 00 00
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 17
28. The compass card is mounted in a bowl which is carried in gimbals, thus
enabling the card to retain a horizontal position while the ship is pitching and rolling.
A vertical black line called the lubber's line is marked on the inner surface of the bowl,
and the compass is so mounted that a line joining its pivot with the lubber's fine is
parallel to the keel line of the vessel; thus the lubber's line always indicates the com
pass direction of the ship's head.
29. According to the purpose which it is designed to fulfill, a compass is desig
nated as a Standard, Steering, Check, or Boat Compass. On United States naval ves
sels additional compasses are designated as follows: Maneuvering, battle, auxiliary
battle, top, and conning-tower compasses.
30. There are two types of magnetic compass in use, the liquid or wet and the
dry; in the former the bowl is filled with liquid, the card being thus partially buoyed
with consequent increased ease of working on the pivot, and the liquid further serving
to decrease the vibrations of the card when deflected by reason 01 the motion of the
vessel or other cause. On account of its advantages the liquid compass is used in
the United States Navy.
31. THE NAVY SERVICE T^-INCH LIQUID COMPASS. — This consists of a skeleton
card 7i inches in diameter, made of tinned brass, resting on a pivot in liquid, with
provisions for two pairs of magnets symmetrically placed.
The magnet system of the card consists of four cylindrical bundles of steel wires;
these wires are laid side by side and magnetized as a bundle between the poles of a
powerful electro-magnet. They are afterwards placed in a cylindrical case, sealed,
and secured to the card. Steel wires made up into a bundle were adopted because
they are more homogeneous, can be more perfectly tempered, and for the same weight
give greater magnetic power than a solid steel bar.
Two of the magnets are placed parallel to the north and south diameter of the
card, and on the chords of 15° (nearly) of a circle passing through their extremities.
These magnets penetrate the air vessel, to which they are soldered, and are further
secured to the bottom of the ring of the card. The other two magnets of the system
are placed parallel to the longer magnets on the chords of 45° (nearly) of a circle
passing through their extremities and are secured to the bottom of the ring of the card.
The card is of a curved annular type, the outer ring being convex on the upper
and inner side, and is graduated to read to one-quarter point, a card circle being
adjusted to its outer edge and divided to half degrees, with legible figures at each
3°, for use in reading bearings by an azimuth circle or in laving the course to degrees.
The card is provided with a concentric spheroidal air vessel, to buoy its own
weight and that of the magnets, allowing a pressure of between 60 and 90 grains on
the pivot at 60° F.; the weight of the card in air is 3,060 grains. The air vessel has
within it a hollow cone, open at its lower end, and provided with the pivot bearing
or cap, containing a sapphire, which rests upon the pivot and thus supports the
card; the cap is provided with adjusting screws for accurately centering the card.
The pivot is fastened to the center of the bottom of the bowl by a flanged plate and
screws. Through this plate and the bottom of the bowl are two small holes which
communicate with the expansion chamber and admit of a circulation of the liquid
between it and the bowl. The pivot is of gun metal with an iridium cap.
The card is mounted in a bowl of cast bronze, the glass cover of which is closely
packed with rubber, preventing the evaporation or leakage of the liquid, which entirely
nils the bowl. This liquid is composed of 45 per cent pure alcohol and 55 per cent
distilled water, and remains liquid below —10° F.
The lubber's line is a fine line drawn on an enameled plate on the inside of the
bowl, the inner surface of the latter being covered with an insoluble white paint.
Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal,
by means of which the bowl is kept constantly full without the show of bubbles or the
development of undue pressure caused by the change in volume of the liquid due
to changes of temperature.
The rim of the compass bowl is made rigid and its outer edge turned strictly
to gauge to receive the azimuth circle.
32. THE DRY COMPASS. — The Lord Kelvin Compass, which may be regarded
as the standard for the dry type, consists of a strong paper card with the
central parts cut away and its outer edge stiffened by a thin aluminum ring. The
61828°—]
20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
standard compass being located, all peloruses may be oriented from it by any one
of the following methods :
(a) By making the azimuth of a celestial body, taken by the pelorus, coincide
with the simultaneous azimuth of the same body taken by the standard compass.
(b) By a similar process with distant objects; and the parallax may be entirely
eliminated in an apparently near object, in view of the moderate distance that
usually separates the two instruments on board ship.
(c) By reciprocal bearings between the correct instrument and the instrument
to be established; it is evident that if the lubber lines of the two instruments are
both in the direction of the keel line, the bearing of the sight vane of each from the
other (one being reversed) should coincide.
(d) By computing the angle subtended at the pelorus by the fore-and-aft line
through the pelorus and the line drawn through the pelorus to the jack staff, and
setting the pelorus at this angle and sighting on the jack staff.
THE CHART.
37. A nautical chart is a miniature representation upon a plane surface, in
accordance with a definite system of projection or development, 01 a portion of the
navigable waters of the world. It generally includes the outline of the adjacent
land, together with the surface forms and artificial features that are useful as aids
to navigation, and sets forth the depths of water, especially in the near approaches
to the land, by soundings that are fixed in position by accurate determinations.
Except in charts of harbors or other localities so limited that the curvature of the
earth is inappreciable on the scale of construction, a nautical chart is always framed
over with a network of parallels of latitude and meridians of longitude in relation
to which the features to be depicted on the chart are located and drawn; and the
mathematical relation between the meridians and parallels of the chart and those
of the terrestrial sphere determines the method of measurement that is to be employed
on the chart and the special uses to which it is adapted.
38. There are three principal systems of projection in use: (a) the Mercator,
(b) the poly conic, and (c) the gnomonic; of these the Mercator is byf ar the most generally
used for purposes of navigation proper, while the polyconic and the gnomonic charts
are employed for nautical purposes in a more restricted manner, as for plotting
surveys or for facilitating great circle sailing.
39. THE MERCATOR PROJECTION. — The Mercator Projection, so called, may be
said to result from the development, upon a plane surface, of a cylinder which is
tangent to the earth at the equator, the various points of the earth's surface having
been projected upon the cylinder in such manner that the loxodromic curve or
rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of
bearing with respect to the intersected meridians as does the ship's track.
In order to realize this condition, the line of tangency, which coincides with the
earth's equator, being the circumference of a right section of the cylinder, will appear
as a right ^line on the development; while the series of elements of the cylinder
corresponding to the projected terrestrial meridians will appear as equidistant right
lines, parallel to each other and perpendicular to the equator of the chart, main
taining the same relative positions and the same distance apart on that equator as
the meridians have on the terrestrial spheroid. The series of terrestrial parallels
will also appear as a system of right lines parallel to each other and to the equator,
and will so^intersect the meridians as to form a system of rectangles whose altitudes,
for successive intervals of latitude, must be variable, increasing from the equator in
such manner that the angles made by the rhumb line with the meridian on the chart
may maintain the required equality with the corresponding angles on the spheroid.
, 40. MERIDIONAL PARTS. — At the equator a degree of longitude is equal to a
degree of latitude^ but in receding from the equator and approaching the pole, while
the degrees of latitude remain always of the same length (save for a slight change
due to the fact that the earth is not a perfect sphere), the degrees of longitude become
less and less.
Since, in the Mercator projection, the degrees of longitude are made to appear
everywhere of the same length, it becomes necessary, in order to preserve the propor-
INSTRUMENTS AND ACCESSOKIES IN NAVIGATION. 21
tion that exists at different parts of the earth's surface between degrees of latitude
and degrees of longitude, that the former be increased from their natural lengths,
and such increase must become greater and greater the higher the latitude.
The length of the meridian, as thus increased, between the equator and any
given latitude, expressed in minutes at the equator as a unit, constitutes the number
of Meridional Parts corresponding to that latitude. The Table of Meridional Parts
or Increased Latitudes (Table 3), computed for every minute of latitude between 0°
and 80°, affords facilities for constructing charts on "the Mercator projection and for
solving problems in Mercator sailing.
41. To CONSTRUCT A MERCATOR CHARTS — If the chart for which a projection
is to be made includes the equator, the values to be measured off are given directly
by Table 3. If the equator does not come upon the chart, then the parallels of
latitude to be laid down should be referred to a principal parallel, preferably the lowest
parallel to be drawTi on the chart. The distance of any other parallel of latitude
from the principal parallel is then the difference of the values for the two taken from
Table 3.
The values so found may either be measured off, without previous numerical
conversion, by means of a diagonal scale constructed on the chart, or they may be
laid dowTi on the chart by means of any properly divided scale of yards, meters, feet,
or miles, after having been reduced to the scale of proportions adopted for the chart.
If, for example, it be required to construct a chart on a scale of one-quarter of an
inch to five minutes of arc on the equator, a diagonal scale may first be constructed,
on which ten meridional parts, or ten minutes of arc on the equator, have a length
of half an inch.
It may often be desirable to adapt the scale to a certain allotment of paper. In
this case, the lowest and the highest parallels of latitude may first be drawn on the
sheet on which the transfer is to be made. The distance oetween these parallels
may then be measured, and the number of meridional parts between them ascertained.
Dividing the distance by this number will then give the length of one meridional
part, or the quantity by which all the meridional parts taken from Table 3 must be
multiplied. This quantity will represent the scale of the chart. If it occurs that the
limits of longitude are a governing consideration, the case may be similarly treated.
EXAMPLE: Let a projection be required for a chart of 14° extent in longitude
between the parallels of latitude 20° 30' and 30° 25', and let the space allowable on
the paper between these parallels measure 10 inches.
Entering the column in Table 3 headed 20°, and running down to the line marked
30' in the side column, will be found 1248.9; then, entering the column 30°, and
running dowTi to the line 25', will be found 1905.5. The difference, or 1905.5 —
1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which
1' of arc of the equator is taken as the unit. On the intended projection, therefore,
10in
I7 of arc of longitude will measure .,. ' =0.0152 inch, which will be the scale of the
o5o.b
chart. For the sake of brevity call it 0.015. By this quantity all the values derived
from Table 3 will have to be multiplied before laying them down on the projection, if
they are to be measured on a diagonal scale of one inch.
Draw in the center of the sheet a straight line, and assume it to be the middle
meridian of the chart. Construct very carefully on this line a perpendicular near
the lower border of the sheet, and assume this perpendicular to be the parallel of
latitude 20° 30'; this will be the southern inner neat line of the chart. From the
intersection of the lines lay off on the parallel, on each side of the middle meridian,
seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches;
and through the points thus obtained draw lines parallel to the middle meridian,
and these will be the eastern and western neat lines of the chart.
In order to construct the parallel of latitude for 21° 00', find, in Table 3, the
meridional parts for 21° 00', which are 1280.8. Subtracting from this number the
number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inch,
which is the distance on the chart between 20° 30' and 21° 00'. On the meridians
a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is
made of the Position Plotting Sheets published by the Hydrographic Office.
20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
standard compass being located, all peloruses may be oriented from it by any one
of the following methods :
(a) By making the azimuth of a celestial body, taken by the pelorus, coincide
with the simultaneous azimuth of the same body taken by the standard compass.
(&) By a similar process with distant objects; and the parallax may be entirely
eliminated in an apparently near object, in view of the moderate distance that
usually separates the two instruments on board ship.^
(c) By reciprocal bearings between the correct instrument and the instrument
to be established; it is evident that if the lubber lines of the two instruments are
both in the direction of the keel line, the bearing of the sight vane of each from the
other (one being reversed) should coincide.
(d) By computing the angle subtended at the pelorus by the fore-and-aft line
through the pelorus and the line drawn through the pelorus to the jack staff, and
setting the pelorus at this angle and sighting on the jack staff.
THE CHART.
37. A nautical chart is a miniature representation upon a plane surface, in
accordance with a definite system of projection or development, of a portion of the
navigable waters of the world. It generally includes the outline of the adjacent
land, together with the surface forms and artificial features that are useful as aids
to navigation, and sets forth the depths of water, especially in the near approaches
to the land, by soundings that are fixed in position by accurate determinations.
Except in charts of harbors or other localities so limited that the curvature of the
earth is inappreciable on the scale of construction, a nautical chart is always framed
over with a network of parallels of latitude and meridians of longitude in relation
to which the features to be depicted on the chart are located and drawn; and the
mathematical relation between the meridians and parallels of the chart and those
of the terrestrial sphere determines the method of measurement that is to be employed
on the chart and the special uses to which it is adapted.
38. There are three principal systems of projection in use: (a) the Mercator,
(&) the poly conic, and (c) the gnomonic; of these the Mercator is byf ar the most generally
used for purposes of navigation proper, while the polyconic and the gnomonic charts
are employed for nautical purposes in a more restricted manner, as for plotting
surveys or for facilitating great circle sailing.
39. THE MERCATOR PROJECTION. — The Mercator Projection, so called, may be
said to result from the development, upon a plane surface, of a cylinder which is
tangent to the earth at the equator, the various points of the earth's surface having
been projected upon the cylinder in such manner that the loxodromic curve or
rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of
bearing with respect to the intersected meridians as does the ship's track.
In order to realize this condition, the line of tangency, which coincides with the
earth's equator, being the circumference of a right section of the cylinder, will appear
as a right line on the development; while the series of elements of the cylinder
corresponding to the projected terrestrial meridians will appear as equidistant right
lines, parallel to each other and perpendicular to the equator of the chart, main
taining the same relative positions and the same distance apart on that equator as
the meridians have on the terrestrial spheroid. The series of terrestrial parallels
will also appear as a system of right lines parallel to each other and to the equator,
and will so^intersect the meridians as to form a system of rectangles whose altitudes,
for successive intervals of latitude, must be variable, increasing from the equator in
such manner that the angles made by the rhumb line with the meridian on the chart
may maintain the required equality with the corresponding angles on the spheroid.
, 40. MERIDIONAL PARTS. — At the equator a degree of longitude is equal to a
degree of latitude^ but in receding from the equator and approaching the pole, while
the degrees of latitude remain always of the same length (save for a slight change
due to the fact that the earth is not a perfect sphere), the degrees of longitude become
less and less.
Since, in the Mercator projection, the degrees of longitude are made to appear
everywhere of the same length, it becomes necessary, in order to preserve the propor-
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 21
tion that exists at different parts of the earth's surface between degrees of latitude
and degrees of longitude, that the former be increased from their natural lengths,
and such increase must become greater and greater the higher the latitude.
The length of the meridian, as thus increased, between the equator and any
given latitude, expressed in minutes at the equator as a unit, constitutes the number
of Meridional Parts corresponding to that latitude. The Table of Meridional Parts
or Increased Latitudes (Table 3), computed for every minute of latitude between 0°
and 80°, affords facilities for constructing charts on the Mercator projection and for
solving problems in Mercator sailing.
41. To CONSTRUCT A MERCATOR CHART.® — If the chart for which a projection
is to be made includes the equator, the values to be measured off are given directly
by Table 3. If the equator does not come upon the chart, then the parallels of
latitude to be laid down should be referred to a principal parallel, preferably the lowest
Earallel to be drawn on the chart. The distance of any other parallel of latitude
*om the principal parallel is then the difference of the values for the two taken from
Table 3.
The values so found may either be measured off, without previous numerical
conversion, by means of a diagonal scale constructed on the chart, or they may be
laid down on the chart by means of any properly divided scale of yards, meters, feet,
or miles, after having been reduced to the scale of proportions adopted for the chart.
If, for example, it be required to construct a chart on a scale of one-quarter of an
inch to five minutes of arc on the equator, a diagonal scale may first be constructed,
on which ten meridional parts, or ten minutes of arc on the equator, have a length
of half an inch.
It may often be desirable to adapt the scale to a certain allotment of paper. In
this case, the lowest and the highest parallels of latitude may first be drawn on the
sheet on which the transfer is to be made. The distance between these parallels
may then be measured, and the number of meridional parts between them ascertained.
Dividing the distance by this number will then give the length of one meridional
part, or the quantity by which all the meridional parts taken from Table 3 must be
multiplied. This quantity will represent the scale of the chart. If it occurs that the
limit.fi of longitude are a governing consideration, the case may be similarly treated.
EXAMPLE: Let a projection be required for a chart of 14° extent in longitude
between the parallels of latitude 20° 30' and 30° 25', and let the space allowable on
the paper between these parallels measure 10 inches.
Entering the column in Table 3 headed 20°, and running down to the line marked
30' in the side column, will be found 1248.9; then, entering the column 30°, and
running down to the line 25', will be found 1905.5. The difference, or 1905.5 —
1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which
I' of arc of the equator is taken as the unit. On the intended projection, therefore,
10in
1' of arc of longitude will measure -_„ ' =0.0152 inch, which will be the scale of the
DOO.D
chart. For the sake of brevity call it 0.015. By this quantity all the values derived
from Table 3 will have to be multiplied before laying them down on the projection, if
they are to be measured on a diagonal scale of one inch.
Draw in the center of the sheet a straight line, and assume it to be the middle
meridian of the chart. Construct very carefully on this line a perpendicular near
the lower border of the sheet, and assume this perpendicular to be the parallel of
latitude 20° 30'; this will be the southern inner neat line of the chart. From the
intersection of the lines lay off on the parallel, on each side of the middle meridian,
seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches;
and through the points thus obtained draw lines parallel to the middle meridian,
and these will be the eastern and western neat lines of the chart.
In order to construct the parallel of latitude for 21° 00', find, in Table 3, the
meridional parts for 21° 00', which are 1280.8. Subtracting from this number the
number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inch,
which is the distance on the chart between 20° 30' and 21° 00'. On the meridians
a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is
made of the Position Plotting Sheets published by the Hydrographic Office.
22 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
lay off distances equal to 0.478 inch, and through the three points thus obtained
draw a straight line, which will be the parallel of 21° 00'.
Proceed in the same manner to lay down all the parallels answering to full
degrees of latitude; the distances will be respectively:
Oin.015X (1344.9- 1248.9) = 1.440 inches.
Oin.015 X (1409.5 - 1248.9) = 2.409 inches.
Oin. 105 X (1474.5 -1248.9) =3.384 inches, etc.
Thus will be shown the parallels of latitude 22° 00', 23° 0<X, 24° 00', etc. FinaUy,
lay down in the same way the parallel of latitude 30° 25', which will be the northern
inner neat line of the chart.
A degree of longitude will measure on this chart Oin.015X60 = Oin.9. Lay off,
therefore, on the lowest parallel of latitude drawn on the chart, on a middle one, and
on the highest parallel, measuring from the middle meridian toward each side, the
distances of Oin.9, lin.8, 2in.7, 3in.6, etc., in order to determine the points where
meridians answering to full degrees cross the parallels drawn on the chart. Through
the points thus found draw the meridians. Draw then the outer neat lines of the
chart at a convenient distance outside of the inner neat lines, and extend to them the
meridians and parallels. Between the inner and outer neat lines of the chart sub
divide the degrees of latitude and longitude as minutely as the scale of the chart will
permit, the subdivisions of the degrees of longitude being found by dividing the
degrees into equal parts, and the subdivisions of the degrees of latitude being accu
rately found in the same manner as the full degrees of latitude previously described,
though it will generally be found sufficiently exact to make even subdivisions of the
degrees, as in the case of the longitude.
The subdivisions between the two eastern as well as those between the two
western neat lines will serve for measuring or estimating terrestrial distances. Dis
tances between points bearing North and South of each other may be ascertained
by referring them to the subdivisions between the same parallels. Distances repre
sented by fines at an angle to the meridians (loxodromic lines) may be measured
by taking between the dividers a small number of the subdivisions near the middle
latitude of the line to be measured, and stepping them off on that line. If, for
instance, the terrestrial length of a line running at an angle to the meridians between
the parallels of latitude of 24° 00' and 29° 00' be required, the distance shown on the
neat space between 26° 15' and 26° 45' ( = 30 nautical miles) may be taken between
the dividers and stepped off on that line.
42. Coast lines and other positions are plotted on the chart by their latitude
and longitude. A chart may be transferred from any other projection to that of
Mercator by drawing a system of corresponding parallels of latitude and meridians
over both charts so close to each other as to form minute squares, and then the lines
and characters contained in each square of the map to be transferred may be copied
by the eye in the corresponding squares of the Mercator projection.
Since the unit of measure, the mile or minute of latitude, has a different value
in every latitude, there is an appearance of distortion in a Mercator chart that covers
any large extent of surface; for instance, an island near the pole will be represented
as being much larger than one of the same size near the equator, due to the different
scale used to preserve the character of the projection.
43. THE POLYCONIC PROJECTION. — This projection is based upon the develop
ment of the earth's surface on a series of cones, a different one for each parallel of
latitude, each one having the parallel as its base, and its vertex in the point where a
tangent to the earth at that latitude intersects the earth's axis. The degrees of
latitude and longitude on this chart are projected in their true length, and the general
distortion of the figure is less than in any other method of projection, the relative
magnitudes being closely preserved.
A straight line on the polyconic chart represents a near approach to a great
circle, making a slightly different angle with each successive meridian as the meridians
converge toward the pole and are theoretically curved lines; but it is only on charts
of large extent that this curvature is apparent; the parallels are also curved, this
fact being apparent to the eye upon all excepting the largest scale charts.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
23
This method of projection is especially adapted to the plotting of surveys; it
is also employed to some extent in the charts of the United States Coast and Geodetic
Survey.
44. GXOMONIC PROJECTION. — This is based upon a system in which the plane
of projection is tangent to the earth at some given point; the eye of the spectator
is situated at the center of the sphere, where, being at once in the plane of every great
circle, it will see all such circles projected as straight lines where the visual rays
passing through them intersect tie plane of projection. In a gnomonic chart, tne
straight line between any two points represents the arc of a great circle, and is there
fore the shortest line between those points.
Excepting in the polar regions, for which latitudes the Mercator projection can
not be constructed, the gnomonic charts are not used for general navigating purposes.
Their greatest application is to afford a ready means of finding the course and distance
at any time in great circle sailing, the method of doing which will be explained in
Chapter V.
45. MERIDIANS ADOPTED IN THE CONSTRUCTION OF CHARTS. — The nautical
charts published by the United States are based upon the meridian of Greenwich,
and this meridian is also the origin of longitudes in use on the nautical charts pub
lished by the Governments of Argentina, Austria, Belgium, Brazil, Chile, Denmark,
France, Germany, Great Britain, Holland (for all charts published at Batavia and
for some published at The Hague), Italy, Japan, Norway, Kussia, and Sweden.
In addition to the meridian of Greenwich, the meridian of Pulkowa Observatory,
at St. Petersburg, in longitude 30° 19' 40" east of Greenwich, is sometimes referred
to in the Kussian charts. At one time the Royal Observatory at Naples, in longitude
14° 15' 26" east of Greenwich, was referred to in the Italian charts, and the observatory
at Christiania, in longitude 10° 43' 23" east of Greenwich, was referred to in the
Norwegian charts.
The French charts are based both upon the meridian of Greenwich and of the
Observatory at Paris, which has been determined to be in longitude 2° 20' 14.6" east
of Greenwich. The longitudes of a few Dutch charts published at The Hague are
reckoned from the meridian of the west tower of the cathedral at Amsterdam, which
is hi longitude 4° 53' 01.5" east of Greenwich. Portuguese charts refer to the meridian
of the observatory of Lisbon Castle, which is 9° 07' 54.86" west of Greenwich, and
to the meridian of Greenwich. In Spain the meridian of San Fernando Observatory,
at Cadiz, which is in longitude 6° 12' 20" west of Greenwich, and also the meridian
of Greenwich, are used.
46. QUALITY OF BOTTOM. — The following table shows the qualities of the
bottom, as expressed on charts of various nations:
United States.
English.
French.
Italian.
Spanish.
German.
Clay C.
Clay cl.
Argile A.
Argila arg.
Arcillo or Barro.arc.
Lehm L.
Coral Co.
Coral crl
Corail Cor
Corallo crl
Coral cl
KoT"allen Kor.
Gravel G
Gravel g
Gravier Gr
Rena or Ghia'a gh
Cases' jo Co
Ivies k
Mud. M
Mud m
Vase V
Fango f
Fango or Luno F
RnhlamTn Schl.
Rocky rky.
Rock rk.
Roche... R.
Roccia r.
PiedraorRoca P.orr.
Felsig Fls.
Sand S
Sand s
Sable S
Sfibbiaor Vena s
\rpna -V
Sand Sd.
Shells Sh
Shells • sh
Coquille Coq
Muscheln M
Stone St
Stones st
Pierre P
Pietre p
Piedra P
Stein St.
Weed Wd
Weed wd
Kerb II
Alga V
Gras Grs
Fine fne
Fine f
Fin fir.
Fino
Fina f
Fein f.
Coarse crs.
Coarse c
Gros g
Grosso
Gruesa ™
Grob . gb.
Stiff stf.
Stiff stf.
Dure.. d.
Tenace.
Tena?
Schlick sk.
Soft sft.
Soft sff
Voile ni
Molle
Blando bclo
Welch Wch.
Black.. bk
Black blk
Nero
Schwarz sch\v.
Red rd.
Red. rd
Rou^e r
Rosse
Rojo r
Roth r.
Yellow... yl
Yellow v
Jaune j
Giallo
\marillo am
Gelb.... g.
Gray . . ev
24
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
47. MEASURES OF DEPTH. — The following table shows the units of measure
employed in expressing the soundings in the more modern nautical charts of foreign
nations together with their equivalents in the units of measure used in the charts
published by the United States :
Nationality of
chart.
Unit of soundings.
Equivalent in United
States units.
Nationality of
chart.
Unit of soundings.
Equivalent in United
States units.
Feet.
3.281
3.281
6.223
3. 281
3.281
6.176
5.905
3.281
3.281
3.281
3.281
Fathoms.
Feet.
Fathoms.
Argentine...
Austrian
Belgian
Metro
0.547
0.547
1.037
0.547
0.547
1.029
0.984
0.547
0.547
0.547
0.547
Japanese
Norwegian
Fathom
6.000
3.281
6.176
3.281
6.000
3.281
5.492
3.281
5.844
6.000
1.000
0.547
1.029
0.547
1.000
0.547
0.914
0.547
0.974
1.000
Metro
Metre
or faden
Portuguese. .
Russian
or favn
Metre
Metro
Metro .
Chilean
Danish.
Dutch
Sajene
favn
vadem
Spanish
Metro
Swedish. . .
or braza
French
or metre
Metre
Metre
British
or famn
Fathom..
German .
do..
Italian
1
Metro
THE BAROMETER.
48. The barometer is an instrument for measuring the pres
sure of the atmosphere, and is of great service to the mariner
in affording a knowledge of existing meteorological conditions
and of the probable changes therein. There are two classes of
barometer — mercurial and aneroid.
49. THE MERCURIAL BAROMETER. — This instrument, in
vented by Torricelli in 1643, indicates the pressure of the atmos
phere by the height of a column of mercury.
If a glass tube of uniform internal diameter somewhat
more than 30 inches in length and closed at one end be com
pletely^ filled with pure mercury, and then placed, open end
down, in a cup of mercury (the open end having been tempo
rarily sealed to retain the liquid during the process of inverting),
it will be found that the mercury in the tube will fall until the
top of the column is about 30 inches above the level of that
which is in the cup, leaving in the upper part of the tube a
vacuum. Since the weight of the column of mercury thus left
standing in the tube is equal to the pressure by which it is held
WISP! HI *n Pos^on — namely, that of the atmospheric air — it follows that
the height of the column is subject to variation upon variation of
that pressure; hence the mercury falls as the pressure of the
atmosphere decreases and rises as that pressure increases. The
mean pressure of the atmosphere is equal to nearly 15 pounds
to the square inch; the mean height of the barometer is about
30 inches.
50. In the practical construction of the barometer the glass
tube which contains the mercury is encased in a brass tube, the
latter terminating at the top in a ring to be used for suspension,
and at the bottom in a flange, to which the several parts form
ing the cistern are attached. The upper part of the brass
tube is partially cut away to expose the mercurial column for
observation; abreast this opening is fitted a scale for measur
ing the height, and along the scale travels a vernier for exact
reading; the motion of the vernier is controlled by a rack and
pinion, the latter having a milled head accessible to the observer,
FIG. 3. by which the adjustment is made. In the middle of the brass FIG. 4.
tube is fixed a thermometer, the bulb of which is covered from
the outside but open toward the mercury, and which, being nearly in contact with
the glass tube, indicates the temperature of the mercury and not that of the external
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
25
air; the central position of the column is selected in order that the mean temperature
may be obtained — a matter of importance, as the temperature of the mercurial
column must be taken into account in every accurate application of its reading.
51. In the arrangement of further details mercurial barometers are divided
into two classes, according as they are to be used, as Standards (fig. 4) on shore, or
as Sea Barometers (fig. 3) on shipboard.
In the Standard Barometer the scale and vernier are so graduated as to enable
an observer to read the height of the mercurial column to the nearest 0.002 inch,
while in the Sea Barometer the reading can not be made closer than 0.01 inch.
The instruments also differ in the method of obtaining the true height of the
mercurial column at varying levels of _ the liquid in the cistern. It is evident that
as the mercury in the tube rises, upon increase of atmospheric pressure, the mercury
in the cistern must fall; and, conversely, when the mercurial column falls the amount
of fluid in the cistern will thereby be increased and a rise of level will occur. As the
height of the mercurial column is required above the existing level in the cistern,
some means must be adopted to obtain the true height under varying conditions.
In the Standard Barometer the mercury of the cistern is contained in a leather bag,
against the bottom of which presses the point of a vertical screw, the milled head
of the screw projecting from the bottom of the instrument and thus placing it under
control of the observer. By this means the surface of the mercury in the cistern
(which is visible through a glass casing) may be raised or lowered until it exactly
coincides with that level which is chosen as the zero of the scale, and which is indicated
by an ivory pointer in plain view.
In the Sea Barometer there is no provision for adjusting the level of the cistern
to a fixed point, but compensation for the variable level is made in the scale gradu
ations ; a division representing an inch on the scale is a certain fraction short of the
true inch, proper allowance being thus made for the rise in level which occurs with
a fall of the column, and for the reverse condition.
Further modification is made in the Sea Barometer to adapt it to the special
use for which intended. The tube toward its lower end is much contracted to prevent
the oscillation of the mercurial column known as "pumping," which arises from the
motion of the ship ; and just below this point is a trap to arrest anv small bubbles
of air from finding their way upward. The instrument aboard ship is suspended in
a revolving center ring, in gimbals, supported on a horizontal brass arm which is
screwed to the bulkhead; a vertical position is thus maintained by the tube at all
times.
52. The vernier is an attachment for facilitating the exact reading of the scale
of the barometer, and is also applied to many other instruments of precision, as, for
example, the sextant and theodolite. It consists of a metal scale similar
in general construction to that of the instrument to which it is fitted, and
arranged to move alongside of and in contact with the main scale.
The general principle of the vernier requires that its scale shall have
a total length exactly equal to some whole number of divisions of the scale
of the instrument and tnat this length shall be subdivided into a number
of parts equal to 1 more or 1 less than the number of divisions of the
instrument scale which are covered; thus, if a space of 9 divisions of the
main scale be designated as the length of the vernier, the vernier scale
would be divided into either 8 or 10 parts.
Suppose that a barometer scale be divided into tenths of an inch and
that ^ a length of 9 divisions of such a scale be divided into 10 parts for a
vernier (fig. 5) ; and suppose that the divisions of the vernier be numbered
consecutively from zero at the origin to 10 at the upper extremity^. If, now,
by means of the movable rack and pinion, the.bottom or zero division of the
vernier be brought level with the top of the mercurial column, and that
division falls into exact coincidence with a division of the main scale, then
the height of the column will correspond with the scale reading indicated.
In such a case the top of the vernier will also exactly coincide with a
scale division, but none of the intermediate divisions will be evenly abreast FIG. 5.
of such a division; the division marked "I" will fall short of a scale
division by one-tenth of 1 division of the scale, or by 0.01 inch ; that marked "2" by
two-tenths of a division, or 0.02 inch; and so on. If the vernier, instead of having
26
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
the zero coincide with a scale division, has the division " 1 " in such coincidence,
it follows that the mercurial column stands at 0.01 inch above that scale division
which is next below the zero; for the division "2," at 0.02 inch; and similarly for
the others. In the case portrayed in figure 5, the reading of the^column is 29.81
inches, the scale division next below the zero being 29.80 inches, while the fact that
the first division is abreast a mark of the scale shows that 0.01 inch must be added
to this to obtain the exact reading.
Had an example been chosen in which 8 vernier divisions covered 9 scale
divisions — that is, where the number of vernier divisions was 1 ^less than the number
of scale divisions covered — the principle would still have applied. But, instead of
the length of 1 division of the vernier falling short of a division of the scale by one-
tenth the length of the latter, it would have fallen beyond by one-eighth. To read in
such a case it would therefore be necessary to number the vernier divisions from
up downward and to regard the subdivisions as -fo instead of 0.01 inch.
It is a general rule that the smallest measure to which a vernier reads is equal
to the length of 1 division of the scale divided by the number of divisions of the
vernier; hence, by varying either the scale or the vernier, we may arrive at any
subdivision that may be desired.
53. The Sea Barometer is arranged as described for the instrument assumed in
the illustration; the scale divisions are tenths of an inch, and the vernier has 10
divisions, whence it reads to 0.01 inch. It is not necessary to seek a closer reading,
as complete accuracy is not attainable in observing the height of a barometer on a
vessel at sea, nor is it essential. The Standard Barometer on shore, however, is
capable of very exact reading; hence each scale division is made equal to half a
tenth, or 0.05 inch, while a vernier covering 24 such divisions is divided into 25 parts;
hence the column may be read to 0.002 inch.
54. To adjust the vernier for reading the height of the mercurial column the
eye should be brought exactly on a level with the top of the column; that is, the line
of sight should be at right angles to the scale. When properly set, the front and
rear edges of the vernier and the uppermost point of the mercury should all be in
the line of sight. A piece of white paper, held at the back of the tube so as to reflect
the light, assists in accurately setting the vernier by day, while a small bull's-eye
lamp held behind the instrument enables the observer to get a correct reading at
niojht. When observing the barometer it should hang freely, not being inclined by
holding or even by touch, because any inclination wm cause the column to rise in
the tube.
55. Other things being equal, the mercury will stand higher in the tube when
it is warm than when it is cold, owing to expansion. For the purposes of comparison,
all barometric observations are reduced to a standard which assumes 32° F. as the
temperature of the mercurial column, and 62° F. as that of the metal scale; it is
therefore important to make this reduction, as well as that for instrumental error
(art. 57), in order to be enabled to compare the true barometric pressure with the
normal that may be expected for any locality. The following table gives the value
of this correction for each 2° F., the plus sign showing that the correction is to be
added to the reading of the ship's barometer and the minus sign that it is to be
subtracted:
Tempera
ture.
Correction.
Tempera
ture.
Correction.
Tempera
ture.
Correction.
Tempera
ture.
Correction.
0
Inch.
0
Inch..
o
Inch.
0
Inch.
20
+0.02
40
-0.03
60
-0.09
80
-0. 14
22
+0.02
42
-0.04
62
-0.09
82
-0. 14
24
+0.01
44
-0.04
64
-0.09
84
-0.15
26
+0.01
46
-0.05
66
-0. 10
86
-0. 15
28
0. 00
48
-0. 05
68
-0. 10
88
-0. 16
30
0.00
50
-0.06
70
-0. 11
90
-0.16
32
-0. 01
52
-0.06
72
-0. 12
92
-0.17
34
-0. 02
54
-0. 07
74
-0. 12
94
-0. 17
36
-0.02
56
-0. 07
76
-0. 13
96
-0. 18
38
-0.03
58
-0.08
78
-0.13
98
-0. 18
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 27
As an example, let the observed reading of the mercurial barometer be 29.95
inches, and the temperature as given by the attached thermometer 74°; then we have:
//
Observed height of the mercury 29. 95
Correction for temperature (74°) — 0. 12
Height of the mercury at standard temperature 29. 83
56. THE ANEROID BAROMETER. — This is an instrument in which the pressure
of the air is measured by means of the elasticity of a plate of metal. It consists of a
cylindrical brass box, the metal in the sides being very thin; the contained air having
been partially, though not completely, exhausted, the box is hermetically sealed.
When the pressure of the atmosphere increases the inclosed air is compressed, the
capacity of the box is diminished, and the two flat ends approach each other; when
the pressure of the atmosphere decreases, the ends recede from one another in conse
quence of the expansion of the inclosed air. By means of a combination of levers,
this motion of the ends of the box is communicated to an index pointer which travels
over a graduated dial plate, the mechanical arrangement being such that the motion
of the ends of the box is magnified many times, a very minute movement of the box
making a considerable difference in the indication of the pointer. The graduations
of the aneroid scale are obtained by comparison with the correct readings of a standard
mercurial barometer under normal and reduced atmospheric pressure.
The thermometer attached to the aneroid barometer is merely for convenience
in indicating the temperature of the air, but as regards the instrument itself no cor
rection for temperature can be applied with certainty. Aneroids, as now manufac
tured, are almost perfectly compensated for temperature by the use of different
metals having unequal coefficients of expansion; they ought, therefore, to show the
same pressure at all temperatures.
The aneroid barometer, from its small size and the ease with which it may be trans
ported, can often be usefully employed under circumstances where a mercurial
barometer would not be available. It also has an advantage over the mercurial
instrument in its greater sensitiveness, and the fact that it gives earlier indications
of change of pressure. It can, however, be relied upon only when frequently com
pared with a standard mercurial barometer; moreover, considerable care is required
in its handling; while slight shocks will not ordinarily affect it, a severe jar or knock
may change its indications by a large amount.
When in use the aneroid barometer may be suspended vertically or placed flat,
but changing from one position to another ordinarily makes a sensible change in the
readings; the instrument should always, therefore, be kept in the same position, and
the errors determined by comparisons made while occupying its customary place.
57. COMPARISON OF BAROMETERS. — To determine the reliability of the ship's
barometer, whether mercurial or aneroid, comparisons should from time to time be
made with a standard barometer. Nearly all instruments read either too high or too
low by a small amount. These errors arise, in a mercurial barometer, from the
improper placing of the scale, lack of uniformity of caliber of the glass tube, or
similar causes ; in an aneroid, which is less accurate and in which there is even more
necessity for frequent comparisons, errors may be due to derangement of any of the
various mechanical features upon which its working depends. The errors of the
barometer should be determined for various heights, as they are seldom the same at
all parts of the scale.
In the principal ports of the world standard barometers are observed at specified
times each day, and the readings, reduced to zero and to sea level, are published.
It is therefore only necessary to read the barometer on shipboard at those times
and, if a mercurial instrument is used, to note the attached thermometer and apply
the correction for temperature (art. 55). It is evident that a comparison of the
heights by reduced standard and by the ship's barometer will give the correction to
be applied to the latter, including the instrumental error, the reduction to sea level,
and the personal error of the observer. In the United States, standard barometer
readings are made by the Weather Bureau.
Aneroid Barometers may be adjusted for instrumental error by moving the index
hand, but this is usually done only in the case of errors of considerable magnitude.
28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
58. DETERMINATION OF HEIGHTS BY BAROMETER. — The barometer may be
used to determine the difference in heights between any two stations by means of
the difference in atmospheric pressure between them. An approximate rule is to
allow 0.0011 inch for each difference in level of 1 foot, or, more roughly, 0.01 inch
for every 9 feet.
A very exact method is afforded by Babinet's formula. If B0 and B represent
the barometric pressure (corrected for all sources of instrumental error) at the lower
and at the upper stations respectively, and t0 and t the corresponding temperatures of
the air; then,
Diff . in height = C X
if the temperatures be taken by a Fahrenheit thermometer,
C (in feet) =52, 494 (l +
if a centigrade thermometer is used,
C (in meters) = 16,000^1
THE THERMOMETER.
59. The TJiermometer is an instrument for indicating temperature. In its
construction advantage is taken of the fact that bodies are expanded by heat and
contracted by cold. In its most usual form the thermometer consists of a bulb filled
with mercury, connected with a tube of very fine cross-sectional area, the liquid
column rising or falling in the tube according to the volume of the mercury due to the
actual degree of heat, and the height of the mercury indicating upon a scale the
temperature; the mercury contained in the tube moves in a vacuum produced by
the expulsion of the air through boiling the mercury and then closing the top of the
tube by means of the blowpipe.
There are three classes of thermometer, distinguished according to the method
of graduating the scale as follows: the Fahrenheit, in which the freezing point of
water is placed at 32° and its boiling point (under normal atmospheric pressure) at
212°; the Centigrade, in which the freezing point is at 0° and the boiling point at
100°; and the Reaumur, in which these points are at 0° and 80°, respectively. The
Fahrenheit thermometer is generally used in the United States and England. Tables
will be found in this work for the interconversion of the various scale readings
(Table 31).
60. The thermometer is a valuable instrument for the mariner, not only by
reason of the aid it affords him in judging meteorological conditions from the tem
perature of the air and the amount of moisture it contains, but also for the evidences
it furnishes at times, through the temperature of the sea water, of the ship's position
and the probable current that is being encountered.
61. The thermometers employed in determining the temperature of the air
(wet and dry bulb) and of the water at the surface, should be mercurial, and of some
standard make, with the graduation etched upon the glass stem; they should be
compared with accurate standards, and not accepted ii their readings vary more
than 1° from the true at any point of the scale.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
29
62. The dry-bulb thermometer gives the temperature of the free air. The
wet-bulb thermometer, an exactly similar instrument, the bulb of \vhich is surrounded
by an envelope of moistened cloth, gives what is known as the temperature of evapora
tion, which is always somewhat less than the temperature of the free air. From the
difference of these two temperatures the observer may determine the proximity of
the air to saturation; that is, how near the air is to that point at which it will be
obliged to precipitate some of its moisture (water vapor) in the form of liquid. With
the envelope of the wet bulb removed, the two thermometers should read precisely
the same; otherwise they are practically useless.
The two thermometers, the wet and the dry bulb, should be hung within a few
inches of each other, and the surroundings should be as far as possible identical. In
practice the two thermometers0 are gener
ally inclosed within a small lattice case, such
as that shown in figure 6 ; the case should be
placed in a position on deck remote from any
source of artificial heat, sheltered from the
direct rays of the sun, and from the rain and
spray, but freely exposed to the circulation
of the air; the door should be kept closed
except during the process of reading. The
cloth envelope of the wet bulb should be
a single thickness of fine muslin, tightly
stretched over the bulb, and tied with a fine
thread. The wick which serves to carry the
water from the cistern to the bulb should
consist of a few threads of lamp cotton, and
should be of sufficient length to admit of two
or three inches being coiled in the cistern.
The muslin envelope of the wet bulb should
be at all times thoroughly moist, but not
dripping.
When the temperature of the air falls
to 32° F. the water in the wick freezes, the
capillary action is at an end, the bulb in
consequence soon becomes quite dry, and
the thermometer no longer shows the tem
perature of evaporation. At such times the
bulb should be thoroughly wetted with ice-
cold water shortly before the time of observation, using for this purpose a camel's
hair brush or feather; by this process the temperature of the wet bulb is temporarily
raised above that of the dry, but only for a brief time, as the water quickly freezes;
and inasmuch as evaporation takes place from the surface of the ice thus formed
precisely as from the surface of the wrater, the thermometer will act in the same way
as if it nad a damp bulb. The wet-bulb thermometer can not properly read higher
than the dry, and if the reading of the wet bulb should be the higher, it may always
be attributed to imperfections in the instruments.
o Called a psychrometer.
FIG. G.
30
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
63. Knowing the temperature of the wet and dry bulbs, the relative humidity
of the atmosphere at the time of observation may be found from the following table :
Tempera
ture of the
Difference between dry-bulb and wet-bulb readings.
i
10°
mometer.
1°
0
PC r ct.
Per ct.
Per ct.
Per ct.
Per ct.
Per ct. Per ct.
Per ct. \ Per ct.
Per ct.
24
87
75
62
50
38
26
26
88
76
65
53
42
30
'
28
89
78
67
56
45
34
24
30
90
79
68
58
48
38
28
32
90
80
70
61
51
41
32
23
34
90
81
72
63
53
44
35
27
36
91
82
73
64
55
47
38
30
22
38
92
83
75
66
57
50
42
34
26
40
92
84
76
68
59
52
44
37
30
22
42
92
84
77
69
61
54
47
40
33
26
44
92
85
78
70
63
56
49
43
36
29
46
93
85
79
72
65
58
51
45
38
32
48
93
80
79
73
66
60
53
47
41
35
50
93
87
80
74
67
61
55
49
43
37
52
94
87
81
75
69
63
57
51
46
40
54
94
88
82
76
70
64
59
53
48
42
56
94
88
82
77
71
65
60
55
50
44
58
94
89
83
78
72
67
61
56
51
46
60
94
89
84
78
73
68
63
58
53
48
62
95
89
84
79
74
69
64
59
54
50
64
95
90
85
79
74
70
65
60
56
51
66
95
90
85
80
75
71
66
61
57
53
68
95
90
85
81
76
71
67
63
58
54
70
95
90
86
81
77
72
68
64
60
55
72
95
91
86
82
77
73
69
65
61
57
74
95
91
86
82
78
74
70
66
62
58
76
95
91
87
82
78
74
70
66
63
59
78
96
91
87
83
79
75
71
67
63
60
80
96
92
87
83
79
75
72
68
64
61
82
96
92
88
84
80
76
72
69
65
62
84
96
92
88
84
80
77
73
69
66
63
86
96
92
88
84
81
77
73
70
67
63
88
96
92
88
85
81
77
74
71
67
64
90
96
92
88
85
81
78
74
71
68
65
The table may be readily understood. For example, if the temperature of the
air (dry bulb) be 60°, and the temperature of evaporation (wet bulb) be 56°, the
difference being 4°, look in the column headed " Temperature of the air7' for 60°,
and for the figures on the same line in column headed 4°; here 78 wiU be found,
which means that the air is 78 per cent saturated with water vapor; that is, that the
amount of water vapor present in the atmosphere is 78 per cent of the total amount
that it could carry at the given temperature (60°). This total amount, or saturation,
is thus represented by 100, and if there occurred any increase of the quantity ^of
vapor beyond this point, the excess would be precipitated in the form of liquid.
Over the ocean's surface the relative humidity is generally about 90 per cent, or even
higher in the doldrums; over the land in dry winter weather it may fall as low as
40 per cent.
64. The sea water of which the temperature is to be taken should be drawn from
a depth of 3 feet below the surface, the bucket used being weighted in order to sink
it. The bulb of the thermometer should remain immersed in the water at least
three minutes before reading, and the reading should be made with the bulb
immersed.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 31
THE LOG BOOK.
65. The Log Book is a record of the ship's cruise, and, as such, an important
accessory in the navigation. It should afford all the data from which the position
of the snip is established by the method of dead reckoning; it should also comprise
a record of meteorological observations, which should be made not only for the purpose
of foretelling the weather during the voyage, but also for contribution to the general
fund of knowledge of marine meteorology.
66. A convenient form for recording the data, which is employed for the log
books of United States naval vessels, is shown on page 32 ; beside the tabulated matter
thus arranged, to which one page of the book is devoted, a narrative of the miscella
neous events of the day, written and signed by the proper officers, appears upon the
opposite page.
32
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
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INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
33
67. For the most part, the nature of the information called for, with the method
of recording it, will be apparent. A brief explanation is here given of such points
as seem to require it.
68. THE WIND. — In recording the force of the wind the scale devised by the
late Admiral Sir F. Beaufort is employed. According to this scale the wind varies
from 0, a calm, to 12, a hurricane, the greatest velocity it ever attains. In the lower
grades of the scale the force of the wind is estimated from the speed imparted to a
man-of-war of the early part of the nineteenth century sailing full and by; in the
higher grades, from the amount of sail which the same vessel could carry when
close-hauled. The scale, with the estimated velocity of the wind in both statute and
nautical miles per hour, is as follows :
Force of -wind.
Conditions.
•Velocity.
Mean pressure
in pounds
per square
foot.
Statute miles per Nautical miles per
hour. ' hour.
0 — Calm
Full-rigged ship, all sails set, no headway. .
Just sufficient to give steerage wav
0 to 3
8
13
18
23
28
34
40
48
56
65
75
90 and over.
0 to ' 2.G
6.9
11.3
15.6
20.0
24.3
29.5
34.7
41.6
48.6
56.4
65.1
78. 1 and over.
O.C3
0.23
0.62
1.2
1.9
2.9
4.2
5.9
S.4
11.5
15.5
20.6
29.6
1 Light air
2 Light breeze
Speed of 1 or 2 knots, " full and by "
3 — Gentle breeze
Speed of 3 or 4 knots, "full and by"...
4. — Moderate breeze . . .
5 Fresh breeze
Speed of 5 or 6 knots, "full and by "
All plain sail "full and by "..
6 —Strong breeze
7. — Moderate gale
8.— Fresh gale
T opgallant sails over single-reefed topsails. .
Double-reefed topsails
Treble-reefed topsails (or reefed upper
topsails and courses).
Close-reefed topsails and courses (or lower
topsails and courses).
Close-reefed main topsail and reefed fore
sail (or lower main topsail and reefed
foresail).
Storm staysails
9. — Strong gale
10 — Whole gale
11. — Storm
12. — Hurricane
Under bare poles
69. When steaming or sailing with any considerable speed, the apparent direc
tion and force of the wind, as determined from a vane flag, or pennant aboard ship,
may differ materially from the true direction and force, the reason being that the
air appears to come from a direction and with a force dependent, not only upon the
wind itself, but also upon the motion of the vessel. For instance, suppose that the
wind has a velocity of 20 knots an hour (force 4), and take the case 01 two vessels,
eachsteaming 20 knots, the first with the wind dead aft, the second with the wind dead
ahead. The former vessel will be moving with the same velocity as the ah" and in
the same direction; the velocity of the wind relatively to the ship will thus be zero;
on the vessel an apparent calm will prevail and the pennant will hang up and down.
The latter vessel will be moving with the same velocity as the air, but in the opposite
direction; the relative velocity of the two will thus be the sum of the two velocities,
or 40 knots an hour, and on the second vessel the wind will apparently have the
velocity corresponding very nearly with a fresh gale. Again, it might be shown that
in the case of a vessel steaming west at the rate of 20 knots, with the wind blowing
from north with the velocity of 20 knots an hour, the velocity with which the air
strikes the ship as a result of the combined motion will be 23 knots an hour, and the
direction from which it comes will be IN W. If, therefore, the effect of the speed of
the ship is neglected the wind will be recorded as ]STW., force 6, when in reality it is
north, force 4.
In order to make a proper allowance for this error and arrive at the true direction
and force of the wind, Table 32 may be entered with the ship's speed and the apparent
direction and force of the wind as arguments, and the true direction and force will
be found.
61828°— 16 3
34 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
70. WEATHER. — To designate the weather a series of symbols devised by the
late Admiral Beaufort is employed. The system employed in the United States Navy
is as follows :
&.— Clear blue sky. p.— Passing showers of rain.
c.— Clouds. 5.— Squally weather.
d. — Drizzling, or light rain. r. — Rainy weather, or continuous rain.
/. — Fog, or foggy weather. s. — Snow, snowy weather, or snow falling.
f. — Gloomy, or dark, stormy-looking weather. t. — Thunder.
. — Hail. u. — Ugly appearances, or threatening weather.
1. — Lightning. v. — Variable weather.
m— Misty weather. w— Wet, or heavy dew.
o. — Overcast. 2. — Hazy weather.
To indicate great intensity of any feature, its symbol may be underlined; thus:
r., heavy rain.
71. CLOUDS. — The following are the principal forms of clouds, named in the
order of the altitude above the earth at which they usually occur, beginning with the
most elevated. The symbols by which each is designated follows its name:
1. CIRRUS (Ci.). — Detached clouds, delicate and fibrous looking, taking the
form of feathers, generally of a white color, sometimes arranged in belts which cross
a portion of the sky in great circles, and, by an effect of perspective, converging toward
one or two opposite points of the horizon.
2. CIRRO-STRATUS (Ci.-S.). — A thin, whitish sheet, sometimes completely cover
ing the sky and only giving it a whitish appearance, or at others presenting, more or
less distinctly, a formation like a tangled web. This sheet often produces halos
around the sun and moon.
3. CIRRO-CUMULUS (Ci.-Cu.). — Small globular masses or white flakes, having
no shadows, or only very slight shadows, arranged in groups and often in lines.
4. ALTO-CUMULUS (A.-Cu.). — Rather large globular masses, white or grayish,
partially shaded, arranged in groups or lines, and often so closely packed that their
edges appear confused. The detached masses are generally larger and more compact
at the center of the group; at the margin they form into finer flakes. They often
spread themselves out in lines in one or two directions.
5. ALTO-STRATUS (A.-S.). — A thick sheet of a gray or bluish color, showing a
brilliant patch in the neighborhood of the sun or moon, and which, without causing
halos, may give rise to coronse. This form goes through all the changes like the
Cirro-Stratus, but its altitude is only half so great.
6. STRATO-CUMULUS (S.-Cu.). — Large globular masses or rolls of dark cloud,
frequently covering the whole sky, especially in winter, and occasionally giving it
a wavy appearance. The layer of Strato-Cumulus is not, as a rule, very thick, and
patches of blue sky are often visible through the intervening spaces. All sorts of
transitions between this form and the Alto-Cumulus are noticeable. It may be
distinguished from Nimbus by its globular or rolled appearance and also because it
does not bring rain.
7. NIMBUS (N.). — Rain clouds; a thick layer of dark clouds, without shape and
with ragged edges, from which continued rain or snow generally falls. Through the
openings of these clouds an upper layer of Cirro-Stratus or Alto-Stratus may almost
invariably be seen. If the layer of Nimbus separates into shreds or if small loose
clouds are visible floating at a low level underneath a large nimbus, they may be
described as Fracto-Nimbus (Fr.-N.), the "scud" of sailors.
8. CUMULUS (Cu.).— Wool-pack clouds; thick clouds of which the upper surface
is dome-shaped and exhibits protuberances, while the base is horizontal. When
these clouds are opposite the sun the surfaces usually presented to the observer have
a greater brilliance than the margins of the protuberances. When the light falls
aslant, they give deep shadows; when, on the contrary, the clouds are on the same
side as the sun, they appear dark, with bright edges. The true Cumulus has clear
superior and inferior limits. It is often broken up by strong winds, and the detached
portions undergo continual changes. These may be distinguished by the name of
Fracto-Cumulus (Fr.-Ou,.). '
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 35
9. CUMULO-NIMBUS (Cu.-N.). — The thunder-cloud or shower-cloud; heavy
masses of clouds rising in the form of mountains, turrets, or anvils, generally having
a sheet or screen of fibrous appearance above, and a mass of clouds similar to Nimbus
underneath. From the base there usually fall local showers of rain or of snow
(occasionally hail or soft hail).
10. STRATUS (£.). — A horizontal sheet of lifted fog; when this sheet is broken
up into irregular shreds by the wind or by the summits of mountains, it may be
distinguished by the name of Fracto-Stratus (Fr.-S.).
72. In the scale for the amount of clouds 0 represents a sky which is cloudless
and 10 a sky which is completely overcast.
73. STATE OF SEA. — The state of the sea is expressed by the following system
of symbols :
B. — Broken or irregular sea. M. — Moderate sea or swell.
C. — Chopping, short, or cross sea. R. — Rough sea.
G. — Ground swell. S. — Smooth sea.
H. — Heavy sea. T. — Tide-rips.
L. — Long rolling sea.
NOTE. — There are various publications issued by the Hydrographic Office
dealing with special features of navigation, which should be regularly consulted.
Among the most important of these are:
Pilot charts of the various oceans furnish information regarding the drift of
derelicts, ice, and float ing obstructions, the tracks of storms, average conditions of
wind and weather, ocean currents, magnetic variation, etc.
Hydrographic Bulletin, weekly, gives more detailed facts than the Pilot Charts
regarding ice, wrecks, and derelicts; also items on port facilities, use of oil
to calm the sea, and miscellaneous items of use and interest to mariners.
Daily Memorandum, published at the main office at Washington, also makes
public these items through the Branch Hydrographic Offices.
Notice to Mariners, weekly, gives changes in aids to navigation (lights, buoyage,
harbor constructions), dangers to navigation (rocks, shoals, banks, bars), important
new soundings, and, in general, all such facts as affect mariners' charts, manuals, and
pilots or sailing directions.
CHAPTER III.
THE COMPASS EEEOE,
CAUSES OF THE ERROR.
74. The properties of magnets are such that when two magnets are near enough
together to exert a mutual influence, those poles which possess like magnetism repel
each other, and those which possess unlike magnetism attract each other.
The earth is a magnetized body, and acts like a great spherical magnet with
poles of unlike magnetism situated within the Arctic and Antarctic circles close to
longitudes 97° west and 155° east of Greenwich, respectively. In common with
magnets, the earth is surrounded by a region in which magnetic influence is exercised
upon the compass, giving the magnetic needle a definite direction in each locality
and causing the end which we name the north pole of the compass to be directed in
general toward the region of the magnetic pole in the geographical north and the
south end toward the region of the magnetic pole in the geographical south.
The north end of the compass — north-seeking, as it is sometimes designated for
clearness — will be that end which has opposite polarity to the earth's north magnetic
pole, or, otherwise stated, which possesses like magnetism with the earth's south
magnetic pole.
75. By reason of the fact that the magnetic pole in each hemisphere differs in
geographical position by a large and unequal amount from the geographical pole,
we are made aware that the earth is not magnetized symmetrically with reference
to the geographical poles. Hence the directive influence of the earth's magnetism
will not in general cause the compass needle to point in the direction of the true
meridian, but each compass point will differ from the corresponding true point by
an amount varying according to the geographical locality. The angle representing
this difference is the Variation of ike Compass , sometimes also called the Magnetic
Declination. It is the angle between the plane of the true meridian and a vertical
plane passing through a freely suspended magnetic needle influenced solely by the
earth's magnetism.
The variation not only changes as one travels from place to place on the earth,
being different in different localities, but in every locality, besides the minor periodic
movements of the needle known as the diurnal, monthly, and annual variations,
which are not of material concern to the mariner, there is a progressive change
which extends through centuries of time and amounts to large alterations in the
pointing of the compass. ^ In taking account of the effect produced by the variation
of the compass, the navigator must therefore be sure that the variation used is
correct not only for the place, but also for the time under consideration.
Occasionally the magnetic needle is subject to spasmodic fluctuations of the
earth's ^ magnetism lasting from a brief period to several days. These are called
magnetic ^ storms, and are due to sudden changes in the electric currents which cir
culate within the earth and in the region surrounding the earth. They come appar
ently at random, and^ may occur nearly simultaneously over the whole world or be
restricted to a certain region. The range of their effect upon the compass does
not often exceed the half of a degree in the lower latitudes, and hence the navigator
need only be concerned with them in the higher latitudes where he may look to the
aurora as an indication of their occurrence.
76. Besides the error thus produced in the indications of the compass, a further
one, due to Local Attraction, .may arise from extraneous influences due to natural
magnetic attraction in the vicinity of the vessel. Instances of this are quite common
36
THE COMPASS ERROR.
37
when a ship is in port, as she may be in close proximity to vessels, docks, machinery,
or other masses of iron or steel. It is also encountered in the shallow waters of the
sea in localities where the mineral substances in the earth itself possess magnetic
qualities — as, for example, at certain places in Lake Superior and at others off the
coast of Australia. When due to the last-named cause, it may be a source of great
danger to the mariner, but, fortunately, the number of localities subject to local
attraction is limited. ^ The amount of this error can seldom be determined except
by survey; if known, it might properly be included with the variation and treated
as a part" thereof.
77. In addition to the variation, the compass ordinarily has a still further
error in its indications, which arises from the effect exerted upon it by masses of
magnetic metal within the shij) itself. This is known as the Deviation of the Compass.
For reasons that will be explained later, it differs in amount for each heading of the
ship, and, further, the character of the deviations undergoes modification as a vessel
proceeds from one geographical locality to another.
APPLYING THE COMPASS ERROR.
78. From what has been explained, it may be seen that there are three methods
by which bearings or courses may be expressed: (a) true, when they refer to the
angular distance from the earth's geographical meridian; (b) magnetic, when they
refer to the angular distance from the earth's magnetic meridian, and must be cor
rected for variation to be converted into true; and (c) by compass, when they refer
to the angular distance from the north indicated by the compass on a given heading
of the ship), and must be corrected for the deviation on that heading for conversion
to magnetic, and for both deviation and variation for conversion to true bearings or
courses. The process of applying the errors under all circumstances is one of which
the navigator must make himself a thorough master; the various problems of con
version are constantly arising; no course can be set nor bearing plotted without
involving the application of this problem, and a mistake in its solution may produce
serious consequences. The student is therefore urged to give it his most careful
attention.
79. When the effect of a compass error, whether arising from variation or from
deviation, is to draw the north end of the compass needle to the right, or eastward,
the error is named east, or is marked + ; when its effect is to draw the north end of
the needle to the left or westward, it is named west, or marked — .
Figures 7 and 8 represent, respectively, examples of easterly and westerly errors.
In^botn cases consider that the circles represent the observer's horizon, N and S
being the correct north and south points in each case. If N' and S' represent the
corresponding points indicated by a compass whose needle is deflected by a compass
error, then in the first case, the north end of the needle being drawn to the right or
east, the error will be easterly or positive, and in the second case, the north end of the
needle being drawn to the left or west, the compass error will be westerly or negative.
38 THE COMPASS ERROR.
Considering figure 7, if we assume the easterly error to amount to one point,
it will be seen that if a direction of N. by W. is indicated by the compass, the correct
direction should be north, or one point farther to the right. If the compass indicates
north, the correct bearing is N. by E.; that is, still one point to the right. If we
follow around the whole card, the same relation will be found in every case, the
corrected bearing being always one point, to the right of the compass bearing.
Conversely, if we regard figure 8, assuming the same amount of westerly error, a
compass bearing of N. by E. is the equivalent of a correct bearing of north, which is
one point to the left; and this rule is general throughout the circle, the corrected
direction being always to the left of that shown by the compass.
80. Having once satisfied himself that the general rule holds, the navigator
may save the necessity of reasoning out in each case the direction in which the error
must be applied, and need only charge his mind with some single formula which will
cover all cases. Such a one is the following:
When the CORRECT direction is to the RIGHT, the error is EAST.
The words correct-right-east, in such a case, would be the key to all of his solutions.
With easterly error, if he had a compass course to change to a corrected one, he
would know that to obtain the result the error must be applied to the right; and,
if it were desired to change a correct course to one indicated by compass, the error
would be applied to the left. If a correct bearing is to be compared with a compass
bearing to find the compass error, when the correct bearing is to the right, the
error is easterly; and when the correct bearing is to the left, the error is westerly.
81. It must be remembered that the word east is equivalent to right in dealing
with the compass error, and west to left, even though they involve an apparent
departure from the usual rules. If a vessel steers NE. by compass with one point
easterly error, her corrected course is NE. by E.; but if she steers SE., the corrected
course is not SE. by E., but SE. by S. Another caution may be necessary to avoid
confusion; the navigator should always regard himself as facing the point under
consideration when he applies an error; one point westerly error on South will bring
a corrected direction to S. by E.; but if we applied one point to the left of South
while looking at the compass card in the usual way — north end up — S. by W. would
be the point arrived at, and a mistake of two points would be the result.
82. In the foregoing explanation reference has been made to i 'correct " directions
and "compass errors'' without specifying "magnetic" and "true" or "variation"
and "deviation." This has been done in order to make the statements apply to all
cases and to enable the student to grasp the subject in its general bearing without
confusion of details.
Actually, as has already been pointed out, directions given may be true, magnetic,
or by compass. By applying variation to a magnetic bearing we correct it and make
it true, by applying a deviation to a compass bearing we correct it to magnetic, and
by applying to it the combined deviation and variation we correct it to true. Which
ever of these operations is undertaken, and whichever of the errors is considered, the
process of correction remains the same; the correct direction is always to the right,
when the error is east, by the amount of that error.
Careful study of the following examples will aid in making the subject clear:
EXAMPLES: A bearing taken by a compass free from deviation is 76°; variation,
5° W.; required the true bearing. 71°.
A bearing taken by a similar compass is NW. by W. J W.; variation, J pt. W.;
required the true bearing. NW. by W. f W.
A vessel steers 153° by compass; deviation on that heading, 3° W.; variation
in the locality, 12° E.; required the true course. 162°.
A vessel steers S. by W. JW.: deviation, \ pt. W.; variation, 1 pt, E.: required
the true course. SSW. J W.
It is desired to steer the magnetic course 322°; deviation, 4° E.; required the
course by compass. 318°.
The true course between two points is found to be W. } N.; variation, 1J pt.
E.; no deviation; required the compass course. W. f S.
True course to be made, 55°; deviation, 7° E.; variation, 14° W.; required the
course by compass. 62°.
THE COMPASS ERROR. 39
A vessel passing a range whose direction is known to be 200°, magnetic, observes
the bearing by compass to be 178°; required the deviation. 22° E.
The sun's observed bearing by compass is 91°; it is found by calculation to be
84° (true); variation, 8° W.; required the deviation. 1° E.
FINDING THE COMPASS ERROR.
83. The variation of the compass for any given locality is found from the
charts. A nautical chart always contains information from which the navigator is
enabled to ascertain the variation for any place within the region embraced and
for any year. Beside the information thus to be acquired from local charts, special
charts are published showing the variation at all points on the earth's surface.
84. The deviation of the compass, varying as it does for every ship, for every
heading, and for every geographical locality, must be determined by the navigator,
for which purpose various methods are available.
Whatever method is used, the ship must be swung in azimuth and an observa
tion made on each of the headings upon which the deviation is required to be known.
If a new iron or steel ship is being swung for the first time, observations should be
made on each of the twenty-four 15° rhumbs into which the compass card is divided.
At later swings, especially after correctors have been applied, or in the case of wooden
ships, twelve 15° rhumbs wiU suffice — or, indeed, only six. In case it is not prac
ticable to make observations on exact 15° rhumbs, they should be made as near
thereto as practicable and plotted on the Napier diagram (to be explained hereafter),
whence the deviations on exact 15° rhumbs may be found.
85. In swinging ship for deviations the vessel should be on an even keel and all
movable masses of iron in the vicinity of the compass secured as for sea, and the com
pass accurately centered in the binnacle. The vessel, upon being placed on any head
ing, should be steadied there for three or four minutes before the observation is made,
in order that the compass card may come to rest and the magnetic conditions assume
a settled state. To assure the greatest accuracy the ship should first be swung to
starboard, then to port, and the mean of the two deviations on each course taken.
Ships may be swung under their own steam, or with the assistance of a tug, or at
ancnor, where the action of the tide tends to turn them in azimuth (though in this
case it is difficult to get them steadied for the requisite time on each heading), or at
anchor, by means of springs and hawsers.
86. The deviation of all compasses on the ship may be obtained from the same
swing, it being required to make observations with me standard only. To accomplish
this it is necessary to record the ship's head by all compasses at the time of steadying
on each even rhumb of the standard; applying the deviation, as ascertained, to the
heading by standard, gives' the magnetic heads, with which the direction of the ship's
head by each other compass may be compared, and the deviation thus obtained.
Then a complete table of deviations may be constructed as explained in article 94.
87. There are four methods for ascertaining the deviations from swinging;
namely, by reciprocal bearings, by bearings of the sun, by ranges, and by a distant
object"
88. RECIPROCAL BEARINGS. — One observer is stationed on shore with a spare
compass placed in a position free from disturbing magnetic influences; a second
observer is at the standard compass on board ship. At the instant when ready for
observation a signal is made, and each notes the bearing of the other. The bearing
by the shore compass, reversed, is the magnetic bearing of the shore station from the
ship, and the difference between this and the bearing by the ship's standard compass
represents the deviation of the latter.
In determining the deviations of compasses placed 011 the fore-and-aft amidship
line, when the distribution of magnetic metal to starboard and port is symmetrical,
the shore compass may be replaced by a dumb compass, or pelorus, or by a theodolite
in which, for convenience, the zero of the horizontal graduated circle may be termed
north; the reading of the shore instrument will, of course, not represent magnetic
directions, but by assuming that they do we obtain a series of fictitious deviations,
the mean value of which is the error common to all. Upon deducting this error
from each of the fictitious deviations, we obtain the correct values.
40 THE COMPASS ERROR.
If ship and shore observers are provided with watches which have been com
pared with one another, the times may be noted at^ each observation, and thus
afford a means of locating errors due to misunderstanding of signals.
89. BEARINGS OF THE SUN. — In this method it is required that on each heading
a bearing of the sun be observed by compass and the time noted at the same moment
by a chronometer or watch. By means which will be explained in Chapter XIV, the
true bearing of the sun may be ascertained from the known data, and this, compared
with the compass bearing, gives the total compass error; deducting from the compass
error the variation, there remains the deviation. The variation used may be that
given by the chart, or, in the case of a compass affected only by symmetrically placed
iron or steel, may be considered equal to the mean of all the total errors. Other
celestial bodies may be observed for this purpose in the same manner as the sun.
This method is important as being the most convenient one available for deter
mining the compass error at sea. When adjusting compasses much time will be
saved by this simple modification of a detail:
Instead of tabulating magnetic azimuths for given stated times in advance, draw
on cross-section paper a curve whose ordinates are minutes of local apparent time and
whose abscissae are degrees of magnetic azimuth, that is, true azimuth corrected for
variation. Then for any given instant (the navigator's watch being set to local
apparent time) the magnetic azimuth may be read directly from the curve. The
difference between the magnetic azimuth of the sun and its compass bearing is, of
course, the deviation of the compass on that particular heading.
90. RANGES. — In many localities there are to be found natural or artificial
range marks which are clearly distinguishable, and which when in line lie on a known
magnetic bearing. By steaming about on different headings and noting the compass
bearing of the ranges each time of crossing the line that they mark, a series of devia
tions may be obtained, the deviation of each heading being equal to the difference
between the compass and the magnetic bearing.
91. DISTANT OBJECT. — A conspicuous object is selected which must be at a con
siderable distance from the ship and upon which there should be some clearly defined
point for taking bearings. The direction of this object by compass is observed on
successive headings. Its true or magnetic bearing is then found and compared with
the compass bearings, whence the deviation is obtained.
The true or the magnetic bearing may be taken from the chart. The magnetic
bearing may also be found by setting up a compass ashore, free from foreign magnetic
disturbance, in range with the object and the ship, and observing the bearing of the
object; or the magnetic bearing may be assumed to be the mean of the compass
bearings.
In choosing an object for use in this method care must be taken that it is at such
a distance that its bearing from the ship does not practically differ as the vessel
swings in azimuth. If the ship is swung at anchor, the distance should be not less
than 6 miles. If swung under way, the object must be so far that the parallax
(the tangent of which may be considered equal to half the diameter of swinging
divided by the distance) shall not exceed about 30'.
92. In all of the methods described it will be found convenient to arrange the
results in tabular form. In one column record the ship's head by standard compass,
and abreast it in successive columns the observations from which the deviation is
determined on that heading, and finally write the deviation itself. When tha result
of the swing has been worked up, another table is constructed showing simply the
headings and the corresponding deviations. This is known as the Deviation Table
of the^compass. If compensation is to be attempted, this table is the basis of the
operation; if not, the deviation tables of the standard and steering compass should
be posted in such place as to be accessible to all persons concerned with the naviga
tion of the ship.
THE COMPASS ERROR.
41
93. Let it be assumed that a deviation table has been found ancl that the values
are as follows:
Deviation table.
Ship's head by standard compass
Deviation.
Ship's head by standard compass.
Deviation.
North
0
-15 29
South
0
180
+ 17 5°
Bra
15
30
45
-14 53
-13 16
— 11 19
SW
195
210
225
+23 47
+27 07
+95 35
Ea^t
60
75
90
- 9 59
- 9 42
- 9 06
West
240
255
270
+21 57
+15 54
+ 9 56
SE
105
120
135
- 9 01
- 7 51
- 5 54
xw
285
300
.315
+ 1 56
- 4 09
-10 20
150
165
- 2 16
+ 8 29
330
345
-13 37
-16 01
We have from the table the amount of deviation on each compass heading;
therefore, knowing the ship's head by compass, it is easy to pick out the corresponding
deviation and thus to obtain the magnetic neading. But if we are given the magnetic
direction in which it is desired to steer and have to find the corresponding compass
course, the problem is not so simple, for we are not given deviations on magnetic
heads, and where the errors are large it may not be assumed that they are the same
as on the corresponding compass headings. For example, with the deviation table
just given, suppose it is required to determine the compass heading corresponding
to 165°, magnetic.
The deviation corresponding to 165°, per compass, is + 84-°. If we apply this
to 165°, magnetic, we have 156£° as the compass course. But, consulting the table,
it may be seen that the deviation corresponding to 156^°, per compass, is + 2J°, and
therefore if we steer that course the magnetic direction will be 159°, and not 165°,
as desired.
A way of arriving at the correct result is to make a series of trials until a course
is arrived at which fulfills the conditions. Thus, in the example given:
First trial.
Mag. course desired ...................... 165°
Try dev. on 165° ....................... 8i° E.
Trial comp. course
Dev. o
E.
Mag. course made good .................. 159°
Since this assumption carries the course 6° too far
to the left, assume next a deviation on a course 3^°
farther to the right than the one used here.
Second trial.
.Mag. course desired 165°
Trvdev. on 160°... 5° E.
Trial comp. course 160C
Dev. on 160° 5C
Mag. course made good 165°
This happens to be exactly the compass course
required. But it often occurs that further trials
may be necessary.
94. THE NAPIER DIAGRAM. — A much more expeditious method for the solution
of this problem is afforded by the Napier Diagram, and as that diagram also facilitates
a number of other operations connected with compass work it should be clearly
understood by the navigator. This admits of a graphic representation of the table
of deviations of the compass by means of a curve; besides furnishing a ready means
of converting compass into magnetic courses and the reverse, one of its chief
merits is that if the deviation has been determined on a certain number of head
ings it enables one to obtain the most probable value of the deviation on any
other course that the ship may head. The last-named feature renders it useful in
making a table of deviations of compasses other than the standard when their errors
are found as described in article 86.
95. The Napier diagram (fig. 9) represents the margin of a compass card cut
at the north point and straightened into a vertical line; for convenience, it is usually
divided into two sections, representing, respectively, the eastern and western semi
circles. The vertical line is of a convenient length and divided into twenty-four
equal parts corresponding to the 15° rhumbs of the compass, beginning at the top
42
THE COMPASS ERROR.
with North and continuing around to the right; it is also divided into 360 degrees,
which are appropriately marked.
To obtain a complete curve, a sufficient number of observations should be taken
while the ship swings through an entire circle. Generally, observations on every
alternate 15° rhumb are enough to establish a good curve, but in cases where the
maximum deviation reaches 40° it is preferable to observe on every 15° rhumb.
Compass courses on dotted tines.
Magnetic courses on solid linos.
FROM 0° NORTH TO 180° SOUTH
DEVIATION DEVIATION
WEST NORTH EAST
FROM 180° SOUTH TO 360° NORTH
DEVIATION DEVIATION
WEST SOOTH EAST
of Total Deviation
of Semicircular Component
of Quadrjjm-tal Component
FIG. 9.
The curve shown in the full line on figure 9 corresponds to the table of deviations
given in article 93.
From a given^ compass course to find the corresponding magnetic course, through the
point of the vertical fine representing the given compass course draw a line parallel
to the dotted lines until the curve is intersected, and from the point of intersection
draw another line parallel to the plain lines; the point on the scale where this last
THE COMPASS ERROR.
43
line cuts the vertical line is the magnetic course sought. The correctness of this
solution will be apparent when we consider that the 60° triangles are equilateral, and
therefore the distance measured along the vertical side will equal the distance meas
ured along the inclined sides — that is, the deviation; and the direction will be correct,
for the construction is such that magnetic directions will be to the right of compass
directions when the deviation is easterly and to the left if westerly.
From a given magnetic course to find the corresponding compass course, the process
is the same, excepting that the first line drawn should follow, or be parallel to, the
plain lines, and the second, or return line, should be parallel to the dotted; and a
proof similar to that previously employed will show the correctness of the result.
As an example, the problem given in article 93 may be solved by the diagram, and
the result will be found to accord with the solution previously given.
The vertical line is intersected at each 15° rhumb by two lines inclined to it at
an angle of 60°, that line which is inclined upward to the right being drawn plain
and the other dotted.
To plot a curve on the Napier diagram, if the deviation has been observed with
the ship's head on given compass courses (as is usually the case with the standard
compass), measure off on the vertical scale the number of degrees corresponding to
the deviation and lay it down — to the right if easterly and to the left if westerly—
on the dotted line passing through the point representing the ship's head; or, if the
observation was not made on an even 15° rhumb, then lay it down on a line drawn
parallel to the dotted ones through that division of the vertical line which represents
the compass heading; if the deviation has been observed with the ship on given
magnetic courses (as when deviations by steering compass are obtained by noting
the ship's head during a swing on even 15° rhumbs of the standard), proceed in the
same way, excepting that the deviation must be laid down on a plain line or a line
parallel thereto. Mark each point thus obtained with a dot or small circle, and draw
a free curve passing, as nearly as possible, through all the points.
THE THEORY OF DEVIATION."
96. FEATURES OF THE EARTH'S MAGNETISM. — It has already been stated that
the earth acts like a great spherical magnet, with a pole in each hemisphere which is
not coincident with the geographical pole; it has
also a magnetic equator which lies close to, but
not coincident with, the geographical equator.
A magnetic needle freely suspended at a
point on the earth's surface, and undisturbed by
any other than the earth's magnetic influence,
will lie in the plane of the magnetic meridian
and at an angle with the horizon depending upon
the geographical position.
The magnetic elements of the earth which
must be considered are shown in figure 10.
The earth's total force is represented in direction
and intensity by the line AB. Since compass
needles are mechanical! v arranged to move only
in a horizontal plane, it Tbecomes necessary, when
investigating the effect of the earth's magnetism
upon them, to resolve the total force into two
components which in the figure are represented
by AC and AD. These are known, respectively,
as the horizontal and vertical components of the
earth's total force, and are usually designated as
H and Z. The angle CAB, which the line of direction makes with the plane of
the horizon, is called the magnetic inclination or dip, and denoted by 0.
It is clear that the horizontal component will reduce to zero at the magnetic
poles, where the needle points directly downward, and that it will reach a maximum
a As it is probable that the student will not have practical need of a knowledge of the theory of deviation and the compensation
of the compass until after he has mastered all other subjects pertaining to Navigation and Nautical Astronomy, it may be considered
preferable to omit the remainder of this chapter at first and return to it later.
FIG. 10.
44 THE COMPASS ERROR.
at the magnetic equator, where the free needle hangs in a horizontal direction. The
reverse is true of the vertical component and of the angle of dip.
Values representing these different terms may be found from special charts.
97. INDUCTION; HARD AND SOFT IRON.— -When a piece of unmagnetized iron
or steel is brought within the influence of a magnet, certain magnetic properties are
immediately imparted to the former, which itself becomes magnetic and continues to
remain so as long as it is within the sphere of influence of the permanent magnet;
the magnetism that it acquires under these circumstances is saia to be induced, and
the properties of induction are such that that end or region which is nearest the pole
of the influencing magnet will take up a polarity opposite thereto. If the magnet is
withdrawn, the induced magnetism is soon dissipated. If the magnet is brought into
proximity again, but with its opposite pole nearer, magnetism will again be induced,
but this time its polarity will be reversed. A further property is that if a piece of iron
or steel, while temporarily possessed of magnetic qualities through induction, be
subjected to blows, twisting, or mechanical violence of any sort, the magnetism is
thus made to acquire a permanent nature.
The softer the metal, from a physical point of view, the more quickly and thor
oughly will induced magnetism be dissipated when the source of influence is with
drawn; hard metal, on the contrary, is slow to lose the effect of magnetism imparted
to it in any way. Hence, in regarding the different features which affect deviation,
it is usual to denominate as hard iron that which possesses retained magnetism of a
stable nature, and as soft iron that which rapidly acquires and parts with its mag
netic qualities under the varying influences to which it is subjected.
98. MAGNETIC PROPERTIES ACQUIRED BY AN IRON OR STEEL VESSEL IN
BUILDING. — The inductive action of the earth's magnetism affects all iron or steel
within its influence, and the amount and permanency of the magnetism so induced
depends upon thd position of the metal with reference to tha earth's total force,
upon its character, and upon the degree of hammering, bending, and twisting that it
undergoes.
An iron bar held in the line of the earth's total force instantly becomes magnetic;
if held at an angle thereto it would acquire magnetic properties dependent for their
amount upon its inclination to the line of total force; when held at right angles to
the line there would be no effect, as each extremity would be equally near the proles
of the earth and all influence would be neutralized. If, while such a bar is in a
magnetic state through inductive action, it should be hammered or twisted, a certain
magnetism of a permanent character is impressed upon it, which is never entirely
lost unless the bar is subjected to causes equal and opposite to those that produced
the first effect.
A sheet of iron is affected by induction in a similar way, the magnetism induced
by the earth diffusing itself over the entire plate and separating itself into regions
of opposite polarity divided by a neutral area at right angles to the earth's line of
total force. If the plate is hammered or bent, this magnetism takes up a permanent
character.
^ If the magnetic mass has a third dimension, and assumes the form of a ship, a
similar condition prevails. The whole takes up a magnetic character; there is a
magnetic axis in the direction of the line of total force, with poles at its extremities
and a zone of no magnetism perpendicular to it. The distribution of magnetism
will depend upon the horizontal and vertical components of the earth's force in the
locality and upon the direction of the keel in building; its permanency will depend
upon the amount of mechanical violence to which the metal has been subjected by
the riveting and other incidents of construction, and upon the nature of the metal
employed.
99. CAUSES THAT PRODUCE DEVIATION. — There are three influences that
operate to produce deviation; namely, (a) subpermanent magnetism; (b) transient
magnetism induced in vertical soft iron, and (c) transient magnetism induced in hori
zontal soft iron. Their effect will be explained.
Subpermanent magnetism is the name given to that magnetic force which origi
nates in the ship while building, through the process explained in the preceding
article; after the vessel is launched and has an opportunity to swing in azimuth,
the magnetism thus induced will suffer material diminution until, after the lapse of
THE COMPASS ERROR. 45
a certain time, it will settle down to a condition that continues practically unchanged;
the magnetism that remains is denominated subpermanent. The vessel will then
approximate to a permanent magnet, in which the north polarity will lie in that
region which was north in building and the south polarity (that which exerts an
attracting influence on the north pole of the compass needle) in the region which
was south in building.
Transient magnetism induced in vertical soft iron is that developed in the soft
iron of a vessel through the inductive action of the vertical component only of the
earth's total force, and is transient in nature. Its value or force in any given mass
varies with and depends upon the value of the vertical component at the place,
and is proportional to the sine of the dip, being a maximum at the magnetic pole
and zero at the magnetic equator.
Transient magnetism induced in horizontal soft iron is that developed in the soft
iron of a vessel through the inductive action of the horizontal component only of
the earth's total force, and is transient in nature. Its value or force in any given
mass varies with and depends upon the value of the horizontal component at the
place, and is proportional to the cosine of the dip, being a maximum at the magnetic
equator and reducing to zero at the magnetic pole.
The needle of a compass in any position on board ship will therefore be acted
upon by the earth's total force, together with the three forces just described. The
poles of these forces do not usually lie in the horizontal plane of the compass needle,
but as this needle is constrained to act in a horizontal plane, its movements will be
affected solely by the horizontal components of these forces, and its direction will
be determined by the resultant of those components.
The earth's force operates to retain the compass needle in the plane of the
magnetic meridian, but the resultant of the three remaining forces, wnen without
this plane, deflects the needle, and the amount of such deflection constitutes the
deviation.
100. CLASSES OF DEVIATION. — Investigation has developed the fact that the
deviation produced as described is made up of three parts, which are known respec
tively as Semicircular, quadrantal, and constant deviation, the latter being the least
important. A clear understanding of the nature of each of these classes is essential
for a comprehension of the methods of compensation.
101. Semicircular Deviation is that due to the combined influence, exerted in a
horizontal plane, of the subpermanent magnetism of a ship and of the magnetism
induced in soft iron by the vertical component of the earth's force. If we regard the
effect of these two forces as concentrated in a single resultant pole exerting an
attracting influence upon the north end of the compass needle, it may be seen that
there will be some heading of the ship whereon that pole will lie due north of the
needle and therefore produce no deviation; now consider that, from this position,
the ship's head swings in azimuth to the right; throughout all of the semicircle first
described an easterly deviation will be produced, and, after completing 180°, the pole
will be in a position diameterically opposite to that from which it started, and will
again exert no influence that tends to produce deviation. Continuing the swing,
throughout the next semicircle the direction of the deviation produced will be always
to the westward, until the circle is completed and the ship returns to her original
neutral position. From the fact that this disturbing cause acts in the two semicircles
with equal and opposite effect it is given the name of semicircular deviation.
In figure 9 a curve is depicted winch shows the deviations of a semicircular nature
separated from those due to other disturbing causes, and from this the reason for
the name will be apparent.
102. Returning to the two distinct sources from which the semicircular deviation
arises, it may be seen that the force due to subpermanent magnetism remains constant
regardless of the geographical position of the vessel; but since the horizontal force
of the earth, which tends to hold the needle in the magnetic meridian, varies with the
magnetic latitude, the deviation due to subpermanent magnetism varies inversely as
the horizontal force, or as Y>; this may be readily understood if it is considered that
the stronger the tendency to cling to the direction of the magnetic meridian the less
will be the deflection due to a given disturbing force. On the other hand, that part
46
THE COMPASS ERROR.
of the semicircular force due to magnetism induced in vertical soft iron varies as the
earth's vertical force, which is proportional to the sine of the dip; its effect in producing
deviation, as in the preceding case, varies inversely as the earth's horizontal force —
that is, inversely as the cosine of the dip ; hence the ratio representing the change of
sin
deviation arising from this cause on change of latitude is - — ^, or tan 6.
C/OS (7
If, then, we consider the change in the semicircular deviation due to a change
of magnetic latitude, it will be necessary to separate the two factors of the deviation
and to remember that the portion produced by subpermanent magnetism varies as
TJ, and that due to vertical induction as tan 6. But for any consideration of the
effect of this class of deviation in one latitude only, the two parts may be joined
together an'd regarded as having a single resultant.
103. Assuming that all the forces tending to produce semicircular deviation
are concentrated in a single pole exerting an influence on the north pole of the
compass, it will be seen that this can be resolved into a horizontal and a vertical
component, just as the earth's magnetic force is illustrated in figure 10. It is now
evident, therefore, that the horizontal component of this
single magnet may be resolved into two components — one
fore-and-aft, and one athwartship; in this case, the semi-
£> circular forces will be represented by two magnets, one fore-
/ and-aft and the other athwartship, and compensation may
/ be made by two separate magnets lying respectively in the
directions stated, but with their north or repelling poles in
the position occupied by the south or attracting poles of the
ship's force.
Figure 11 represents the conditions that have been
described. Let O be the center of the compass, XX7 and
YY', respectively, the fore-and-aft and athwartship lines of
the ship, and OS the direction in which the attracting pole of
the disturbing force is exerted. Now, if OP be laid off on
the line OS, representing the amount of the disturbing force
according to some convenient scale, then O& and Oc, respec
tively, represent, on the same scale, the resolved directions of
that force in the keel line and in the transverse line of the
ship. Each of these resolved forces will exert a maximum
effect when acting at right angles to the needle, the athwart
ship one when the ship heads north or south by compass,
and the longitudinal one when the heading is east or west.
On any other heading than those named the deviation pro
duced by each force will be a fraction of its maximum whose
magnitude will depend upon the azimuth of the ship's head. The maximum devia
tion produced, therefore, forms in each case a basis for reckoning all of the various
effects of the disturbing force, and is called a coefficient.
The coefficient of semicircular deviation produced by the force in the fore-and-aft
line is called B, and is reckoned as positive when it attracts a north pole toward the
bow , negative when toward the stern; that produced by the athwartship force is C,
and is reckoned as positive to starboard and negative to port. These coefficients are
expressed in degrees. a
104. The coefficient B is approximately equal to the deviation on East; or to
the deviation on West with reversed sign; or to the mean of these two. Thus in
the ship having the table of deviations previously given (art. 93), B is equal to
-9° 06', or to -9° 56;, or to £ (-9° 06'-9° 56') = -9° 31'.
^The coefficient C is approximately equal to the deviation on North; or to the
deviation on South with reversed sign; or to the mean of these two. In the example
C is equal to -15° 29', or to -17° 52', or to i (-15° 29' -17° 52')= -16° 40'.
o It should be remarked that in a mathematical analysis of the deviations, it would be necessary to distinguish between the
approximate coefficients, B and C, here described, as alsa A, D, and E, to be mentioned later, and the exact coefficients denoted by
the corresponding capital letters of the German alphabet, which latter are in reality the forces producing those deviations expressed
in terms of the "mean force to north" (An), as unit. In the practical discussion of the subject here given, the question of the dif
ference need not be entered into further.
FIG. 11.
THE COMPASS ERROR.
47
105. The value of the subpermanent magnetism remaining practically constant
under all conditions, it will not alter when the ship changes her latitude; but that
due to induction in vertical soft iron undergoes a change when, by change of geo
graphical position, the vertical component of the earth's force assumes a different
value, and in such case the correction by means of one or a pair of permanent magnets
will not remain effective. If, however, by series of observations in two magnetic
latitudes, the values of the coefficients can be determined under the differing cir
cumstances, it is possible, by solving equations, to determine what effect each force
has in producing the semicircular deviation; having done which, the subpermanent
magnetism can be corrected by permanent magnets after the method previously
described, and the vertical induction in soft iron can be corrected by a piece of
vertical soft iron placed in such a position near the compass as to produce an equal
but opposite force to the ship's vertical soft iron. This last corrector is called a
Flinders par.
Having thus opposed to each of the component forces a corrector of magnetic
character identical with its own, a change of latitude will make no difference in the
effectiveness of the compensation, for in every case the modified conditions will
produce identical results in the disturbing and in the correcting force.
106. Quadrantal Deviation is that which arises from horizontal induction in the
soft iron of the vessel through the action of the horizontal component of the earth's
total force. Let us consider, in figure 12, the effect of any piece of soft iron which
is symmetrical with respect to the compass — that
is, which lies wholly within a plane passing through
the center of the needle in either a fore-and-aft or
an athwartship direction. It may be seen (a) that
such iron produces no deviation on the cardinal
points (for on north and south headings the fore-
and-aft iron, though strongly magnetized, has no
tendency to draw the needle from a north-and-south
line, while the athwartship iron, being at right angles
to the meridian, receives no magnetic induction,
and therefore exerts no force; and on east and
west headings similar conditions prevail, the athwart
ship and the fore-and-aft iron having simply ex
changed positions) ; and (&) the direction of the
deviation produced is opposite in successive quad
rants. The action of unsyinmetrical soft iron is
FIG. 12.
not quite so readily apparent, but investigation shows that part of its effect is to
produce a deviation which becomes zero at the inter-cardinal points and is of oppo
site name in successive quadrants. From the fact that deviations of this class
change sign every 90° throughout the circle, they gain the name of quadrantal devi
ations. One of the curves laid down in the Napier diagram (fig. 9) is that of quad-
rantal deviations, whence the nature of this disturbance of the needle may be
observed.
107. All deviations produced by soft iron may be considered as fractions of
the maximum deviation due to that disturbing influence; and consequently the
maximum is regarded as a coefficient, as in the case of semicircular deviations.'
The coefficient due to symmetrical soft iron is designated as D, and is considered
positive when it produces easterly deviations in the quadrant between North and
East; the coefficient of deviations arising from unsymmetrical soft iron is called E,
and is reckoned as positive when it produces easterly deviations in the quadrant
between ^NW. and NE.; this latter attains importance only when there is some
marked inequality in the distribution of metal to starboard and to port, as in the
case of a compass placed off the amidship line.
108. D is approximately equal to the mean of the deviations on NE. and SW.;
or to the mean of those on SE. and NW., with sign reversed; or to the mean of those
means. In the table of deviations given in article 93, D is equal to ^ ( — 11° 19/ + 25°
35') =+ 7° 08', or to £ ( + 5° 54' + 10° 20') = +8° 07'; or to J (7°08/ + 8°07/) = + 7°37'.
By reason of the nature of the arrangement of iron in a ship, D is almost invariably
positive.
48 THE COMPASS ERBOK.
E is approximately equal to the mean of the deviations on North and South; or
to the mean of those on East and West with sign reversed; or to the mean of those
means. In the example, E is equal to ^ (-15° 29/ + 17° 52')= +1° 11'; or to
i ( + 9006'-9056')=-0°25'; or to J ( + 1° ll'-0° 25') = +0° 23'.
109. Quadrantal deviation does not, like semicircular, undergo a change upon
change of magnetic latitude ; being due to induction in horizontal soft iron, the magnetic
force exerted to produce it is proportional to the horizontal component of the earth's
magnetism; but the directive force of the needle likewise depends upon that same
component ; consequently, as the disturbing force exerted upon the needle increases,
so does the power that holds it in the magnetic ^meridian," with the result that on
any given heading the deflection due to soft iron is always the same.
110. Quadrantal deviation is corrected by placing masses of soft iron (usually
two hollow spheres in the athwartship line, at equal distances on each side of the
compass) , with the center of mass in the horizontal plane of the needle. The distance
is made such that the force exerted exactly counteracts that of the ship's iron. As
the correcting effect of this iron will, like the directive force and the quadrantal
disturbing force, vary directly with the earth's horizontal component, the compen
sation once properly made will be effective in all latitudes; provided that the compass
needles are short and, consequently, exercise little or no induction on the quadrantal
correctors.
With compasses such as the United States Navy standard 7 J-inch liquid compass,
the needles of which are long and powerful, it will usually be found that the position
of the spheres must be changed with change of latitude. This may be accounted for
by the magnetism induced in the spheres by the compass needles at the same time
and in the same manner as the earth's force. In this case the quadrantal correcting
force is the resultant of the constant force due to the induction of the needles in the
spheres and the variable force (the earth's horizontal force, H, varying with change
in magnetic latitude) due to the induction of the earth in the spheres. This resultant
of these two forces is a variable force, and, after a given quadrantal deviation is
corrected in one latitude by this force, the balance will be changed upon going into
another latitude and the correction will fail to hold good.
In practice, the quadrantal deviation due to unsymmetrical iron is seldom
corrected; the correction may be accomplished, however, by placing the soft iron
masses on a line which makes an angle to the athwartship line through the center
of the card.
111. Constant Deviation is due to induction in horizontal soft iron unsym-
metrically placed about the compass. It has already been explained that one effect
of such iron is to produce a quadrantal deviation, represented by one coefficient E ;
another effect is the constant deviation, so called because it is uniform in amount
and direction on every heading of the ship. If plotted on a Napier diagram, it would
appear as a straight line parallel with the initial line of the diagram.
112. Like other classes of deviation, the effect of the disturbing force is repre
sented by a coefficient ; this coefficient is designated as A, and is considered plus for
easterly and minus for westerly errors. It is approximately equal to the mean of
the deviations on any number of equidistant headings. In the case previously given,
it might be found from the four headings, North, East, South, and West, and would
then be equal to J (-15° 29'-9° 06' + 17° 52' + 9° 50')= +0° 48';' or from all of
the 24 headings, when it would equal —0° 01'.
For the same reason as in the case of E, the value of A is usually so small that
it may be neglected; it only attains a material size when the compass is placed off
the midship line, or for some similar cause.
113. Like quadrantal deviation, since its force varies with the earth's horizontal
force, the constant deviation will remain uniform in amount in all latitudes. (See
art. 110.)
No attempt is made to compensate for this class of error.
114. COEFFICIENTS. — The chief value of coefficients is in mathematical analyses
of the deviations and their causes. It may, however, be a convenience to the practical
navigator to find their approximate values by the methods that have been given, in
order that he may gain an idea of the various sources of the error, with a view to
ameliorating the conditions, when necessary, by moving the binnacle or altering the
THE COMPASS ERROR. 49
surrounding iron. The following relation exists between the coefficients and the
deviation:
sin z'+C cos z' + T> sin 2^+E cos 2zr,
where d is the deviation, and z' the ship's heading by compass, measured from
compass North.
115. MEAN DIRECTIVE FORCE. — The effect of the disturbing forces is not confined
to causing deviations ; it is only those components acting at right angles to the needle
which operate to produce deflection; the effect of those acting in the direction of
the needle is exerted either in increasing or diminishing the directive force of the
compass, according as the resolved component is northerly or southerly.
It occurs, with the usual arrangement of iron in a vessel, that the mean effect
of this action throughout a complete swing of the ship upon all headings is to reduce
the directive force — that is, while it varies with the heading, the average value upon
all azimuths is minus or southerly. The result of such a condition is unfavorable
from the fact that the compass is thus made more " sluggish," is easily disturbed
and does not return quickly to rest, and a given deflecting force produces a greater
deviation when the directive force is reduced. The usual methods of compensation
largely correct this fault, but do not entirely do so ; it is therefore the case that the
mean combined horizontal force of earth and ship to north is generally less than the
horizontal force of the earth alone; but it is only in extreme cases that this deficiency
is serious.
116. HEELING ERROR. — This is an additional cause of deviation that arises
when the vessel heels to one side or the other. Heretofore only those forces have
been considered which act when the vessel is on an even keel; but if there is an incli
nation from the vertical certain new forces arise, and others previously inoperative
become effective. These forces are (a) the vertical component of the subpermanent
magnetism acquired in building; (b) the vertical component of the induced magnetism
in vertical soft iron, and (c) the magnetism induced by the vertical component of
the earth's total force in iron which, on an even keel, was horizontal. The first two
of these disturbing causes are always present, but, when the ship is upright, have no
tendency to produce deviation, simply exerting a downward pull on one of the poles
of the needle; the last is a new force that arises when the vessel heels.
The maximum disturbance due to heel occurs when the ship heads North or
South. When heading East or West there will be no deviation produced, although
the directive force of the needle will be increased or diminished. The error will
increase with the amount of inclination from the vertical.
117. For the same reason as was explained in connection with semicircular
deviations, that part of the heeling error due to subpermanent magnetism will vary,
on change of latitude, as YJ> while that due to vertical induction will vary as tan 0.
In south magnetic latitude the effect of vertical induction will be opposite in direction
to what it is in north latitude.
118. The heeling error is corrected by a permanent magnet placed in a vertical
position directly under the center of the compass. Such a magnet has no effect upon
the compass when the ship is upright ; but since its force acts in an opposite direction
to the force of the ship which causes heeling error, is equal to the latter in amount,
and is exerted under the same conditions, it affords an effective compensation. For
similar reasons to those affecting the compensation of B and C, the correction by
means of a permanent magnet is not general and must be rectified upon change of
latitude.
PRACTICAL COMPENSATION.
119. In the course of explanation of the different classes of deviation occasion
has been taken to state generally the various methods of compensating the errors that
are produced. The practical methods of applying the correctors wiu next be given.
120. ORDER OF CORRECTION. — The following is the order of steps to be followed
in each case. It is assumed that the vessel is on an even keel, that the compass is
properly centered in the binnacle, that all surrounding masses of iron or steel are in
their normal positions, all correctors removed, and that the binnacle is one in which
61828°— 16 - 4
50 THE COMPASS EBROB.
the semicircular deviation is corrected by two sets of permanent magnets at right
angles to each other.
In order to ascertain if the compass is properly centered in the binnacle, the
heeling corrector may be temporarily placed in its tube and drawn from its lowest
to its nighest position; if no deflection is shown by the needle the compass is prop
erly centered; if not it should be adjusted by the screws provided for the purpose.
1 . Place quadrantal correctors by estimate.
2. Correct semicircular deviation.
3. Correct quadrantal deviation. _
4. Swin^ ship for residual deviations.
The heeling corrector may be placed at any time after the semicircular and
quadrantal errors are corrected. A Flinders bar can be put in place only after
observations in two latitudes.
121. The ship is first placed on some magnetic cardinal point. If North or
South, the only force (theoretically speaking) which tends to produce deflection of the
needle will be the athwartship component of the semicircular force, whose effect is
represented by the coefficient C. It East or West, the only deflecting force will be
the fore-and-aft component of the semicircular force, whose effect is represented by
the coefficient B. This will be apparent from a consideration of the direction of the
forces producing deviation, and is also shown by the equation connecting the terms
(where A and E are zero) :
•d = B sin zf + C cos z' + D sin 2z'.
If the ship is headed North or South, z' being equal to 0° or 180°, the equation
becomes d = ± C. If on East or West, z' being 9(T or 270°, we have d = ± B.
This statement is exact if we regard only the forces that have been considered
in the problem, but experience has demonstrated that the various correctors when
in place create certain additional forces by their mutual action, and in order to correct
the disturbances thus accidentally produced, as well as those due to regular causes,
it is necessary that the magnetic conditions during correction shall approximate as
closely as possible to those that exist when the compensation is completed; therefore
the quadrantal correctors should first be placed on their arms at the positions which
it is estimated that they will occupy later when exactly located. An error in the
estimate will have but slight effect under ordinary conditions. It should be under
stood that the placing of these correctors has no corrective effect while the ship is on
a cardinal point. Its object is to create at once the magnetic field with which we
shall have to deal when compensation is perfected.
This having been done, proceed to correct the semicircular deviation. If the
ship heads North or South, the force producing deflection is, as has been stated, the
athwartship component of the semicircular force, which is to be corrected by perma
nent magnets placed athwartships ; therefore enter in the binnacle one or more such
magnets, and so adjust their height that the heading of the ship by compass shall
agree with the magnetic heading. When this is done all the deviation on that
azimuth will be corrected.
Similarly, if the ship heads East or West, the force producing deviation is the
fore-and-aft component of the semicircular force, and this is to be corrected by
entering fore-and-aft permanent magnets in the binnacle and adjusting the height
so that the deviation on that heading disappears.
With the deviation on two adjacent cardinal points corrected, the semicircular
force has been completely compensated. Next correct the quadrantal deviation.
Head the ship NE., SE., SW., or NW. The coefficients B and C having been reduced
to zero by compensation, and 2zf ', on the azimuths named, being equal to 90° or 270°,
the equation becomes d = ± D. The soft-iron correctors are moved in or out from
the positions in which they were placed by estimate until the deviation on the heading
(all of which is due to quadrantal force) disappears. The quadrantal disturbing
force is then compensated.
122. DETERMINATION OF MAGNETIC HEADINGS. — To determine when a ship
is heading on any given magnetic course, and thus to know when the deviation has
been corrected and the correctors are in proper position, four methods are available:
THE COMPASS ERROR. 51
(a) Swing the ship and obtain by the best available method the deviations on a
sufficient number of compass courses to construct a curve on the Napier diagram
for one quadrant, and thus find the compass headings corresponding to two adjacent
magnetic cardinal points and the intermediate intercardinal point, as North, NE.,
and East, magnetic.0 Then put the ship successively on these courses, noting the
corresponding headings by some other compass, and when it is desired to head on
the various magnetic azimuths during the process of correction the ship may be
steadied upon them by the auxiliary compass. Variations of this method will suggest
themselves and circumstances may render their adoption convenient. The compass
courses corresponding to the magnetic directions may be obtained from observations
made with the auxiliary compass itself, or while making observations with another
compass the headings by the auxiliary may be noted and a curve for the latter
constructed, as explained in article 95, and the required headings thus deduced.
(6) By the methods to be explained hereafter (Chap. XIV), ascertain in advance
the true bearing of the sun at frequent intervals during the period which is to be
devoted to the compensation of the compasses; apply to these the variation and
obtain the magnetic bearings ; record the times and bearings in a convenient tabular
form, or, better still, plot a curve of magnetic azimuths of the sun on cross section paper,
the coordinates being local apparent time and magnetic bearings of the sun, as described
in article 89. Set the watch accurately for the local apparent time; then when it
is required to steer any given magnetic course, set that point of the pelorus for the
ship's head and set the sight vanes for the magnetic bearing of the sun corresponding
to the time by watch. Maneuver the ship with the helm until the sun comes on the
sight vanes, when the azimuth of the ship's head will be that which is required. The
sight vanes must be altered at intervals to accord with the curve or table of times
and bearings.
(c) Construct a curve or table showing times and corresponding magnetic
bearings of the sun, and also set the watch, as explained for the previous method.
Then place the sight vanes of the azimuth circle of the compass at the proper angular
distance to the right or left of the required azimuth of the ship's head ; leave them so
set and maneuver the ship with the helm until the image of the sun comes on with
the vanes. The course will then be the required one. As an example, suppose that
the curve or table shows that the magnetic azimuth of the sun at the time given by
the watch is N. 87° E., and let it be required to head magnetic North; when placed
upon this heading, therefore, the sun must bear 87° to the right or east of the
direction of the ship's head; when steady on any course, turn the sight vane to the
required bearing relative to the keel. It on N. 11° W., for example, turn the circle
to N. 76° E.; leave the vane undisturbed and alter course until the sun comes on.
The magnetic heading is then North, and adjustment may be made accordingly.
(d) When ranges are available, they may be utilized for determining magnetic
headings.
123. SUMMARY OF ORDINARY CORRECTIONS. — To summarize, the following is
the process of correcting a compass for a single latitude, where magnets at right
angles are employed for compensating the semicircular deviation and where the dis
turbances due to unsymmetrical soft iron are small enough to be neglected.
First. All correctors being clear of the compass, place the quadrantal correctors
in the position which it is estimated that they will occupy when adjustment is com
plete. The navigator's experience will serve in making the estimate, or if there
seems no other means of arriving at the probable position they may be placed at the
middle points of their supports.
Second. Steady the ship on magnetic north, east, south, or west, and hold on
that heading by such method as seems best. By means of permanent magnets alter
the indications of the compass until the heading coincides with the magnetic course.
If heading north, magnets must be entered north ends to starboard to correct easterly
deviation and to port to correct westerly, and the reverse if heading south. If
heading east, enter north ends forward for easterly and aft for westerly deviations,
and the reverse if heading west. (Binnacles differ so widely in the methods of carry
ing magnets that details on this point are omitted. It may be said, however, that
o This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a complete
swing and obtain a full table of deviations, which may give interesting information of the existing magnetic conditions.
52 THE COMPASS ERROR.
the magnetic intensity of the correctors may be varied by altering either their number
or their distance from the compass; generally speaking, several magnets at a dis
tance are to be preferred to a small number close to the compass.)
Third. Steady the ship on an adjacent magnetic cardinal point and correct the
compass heading by permanent magnets to accord therewith in the same manner as
described for the first heading.
Fourth. Steady the ship on an intercardinal point (magnetic) and move the
quadrantal correctors away from or toward the compass, keeping them at equal
distances therefrom, until the compass and magnetic headings coincide.
Fifth. If time permits, it is very important that the ship should next be steadied
on opposite cardinal and semicardinal points and one-half 01 the remaining deviation
corrected by changing the position or number of the correctors.
The compensation being complete, the navigator should proceed immediately
to swing ship and make a table of the residual deviations. Though the remain
ing errors will be small, it is seldom that they will be reduced to zero, and it must
never be assumed that the compass may be relied upon without taking the devi
ation into account. Observations on eight equidistant points will ordinarily
suffice for this purpose.
124. COMPENSATION OF THE COMPASS WHILE CRUISING. — Every effort should
be made to keep at least the standard and steering compasses compensated, as it is
always easier to keep- the compasses compensated than to keep a deviation table
correct, at hand, and in use.
RECTANGULAR METHOD.
By the following method the compasses may be kept practically compensated
and, after the data are once obtained, it requires very little time or trouble.
After the first compensation is completed, or while it is being done, head the
ship north or south and move the athwartship magnets up exactly 1 inch, noting
by the bearing of the sun or of a distant .object, the amount and direction of the
effect on the compass. Then repeat the observation, lowering the magnets 1 inch,
and noting the effect. Then head the ship east or west and take the same obser
vations with the fore-and-aft magnets. Then head on an intercardinal point and
record the effect of moving spheres first in and then out an inch from the correct
position.
The record would then take this form:
Date Latitude Longitude
H e
On North, raising B magnets (6 bundles) 1 inch (from 9.85 to 8.85) causes 12° 30' Easterly deviation,
therefore a movement of ^ inch causes 1° 15' Ely.
Lowering B magnets (6 bundles) 1 inch (from 9.85 to 10.85) causes 10° 15' Westerly deviation,
therefore a movement of -^ inch causes 1° 2/ Wly.
On East, raising G magnet (2 bundles) 1 inch (from 10.45 to 9.45) causes 8° 15' Westerly deviation,
therefore a movement of ^ inch causes 0° 50' Wly.
Lowering C magnet (2 bundles) 1 inch (from 10.45 to 11.45) causes 6° 30' Easterly deviation,
therefore a movement of ^ inch causes 0° 39' Ely.
On Northeast, moving spheres in 1 inch (from 10.6 to 9.6) causes 4° 15' Westerly deviation, therefore a
movement of ^ inch causes 0° 25' Wly.
Moving spheres out 1 inch (from 10.6 to 11.6) causes 3° 207 Easterly deviation, therefore a move
ment of ^j- inch causes 0° 20' Ely.
If now it is^found at any time that there is, say, 1° 45' Easterly on East, it is
evident that raising the C magnets -f$ inch will correct it, and careful observations on
two adjacent cardinal points and an inter-cardinal point are enough to recompensate.
This may ordinarily be done at no expense of time and with little trouble. More
confidence may be felt in the result if observations for deviations are afterwards
obtained on the four cardinal points and the mean of the results on opposite courses
taken for the true value; this must be done if the variation is uncertain. A new
set of data observations should be taken after a large change of magnetic latitude,
but it will usually be found that the changes are slight.
Theoretically the quadrantal deviation, once corrected, should remain at zero.
It will usually be found, however, that the position of the spheres must be changed
THE COMPASS ERROR. 53
with change of latitude. A convenient way of dealing with this is to construct a
curve showing the positions of the spheres for varying values of H. A similar curve
showing the position of the heeling magnet is also convenient.
Whenever the position of any corrector is changed, a note showing new position,
date, latitude, longitude, H and 6 should be made on one of the blank leaves of the
compass record. A complete record of this kind will be found of the utmost value
in keeping track of the compasses.
125. CORRECTING THE HEELING ERROR. — The heeling error may be corrected
by a method involving computation, together with certain observations on shore.
A more practical method, however, is usually followed, though its results may be less
precise. The heeling corrector is placed in its vertical tube, N. end uppermost in
north latitudes, as this is almost invariably the required direction; the ship being on
a course near North or South and rolling, observe the vibrations of the card, which,
if the error is material, will be in excess of those due to the ship's real motion in
azimuth; slowly raise or lower the corrector until the abnormal vibrations disappear,
when the correction will be made for that latitude; but it must be readjusted upon
any considerable change of geographical position.
In making this observation care must be taken to distinguish the vessel's
' 'yawing" in a seaway from the apparent motion due to heeling error; for this
reason it may be well to have an assistant to watch the ship's head and keep the
adjuster informed of the real change in azimuth, by which means the latter may
better judge the effect of the heeling error.
In the case of a sailing vessel, or one which for any reason maintains a nearly
steady heel for a continuous period, the amount of the heeling error may be exactly
ascertained by observing the azimuth of the sun, and corrected with greater accuracy
than is possible with a vessel which is constantly rolling.
126. FLINDERS BAR. — The simplest method that presents itself for the placing
of the Flinders bar is one which is available only for a vessel crossing the magnetic
ec-uator. Magnetic charts of the world show the geographical positions at which the
dip becomes zero — that is, where a freely suspended needle is exactly horizontal and
where there exists no vertical component of the earth's total magnetic force. In such
localities it is evident that the factor of the semicircular deviation due to vertical
induction disappears and that the whole of the existing semicircular deviation arises
from subpermanent magnetism. If, then, w^hen on the magnetic equator the compass
be carefully compensated, the effect of the subpermanent magnetism will be exactly
opposed by that of the semicircular correcting magnets. Later, as the ship departs
from the magnetic equator, the semicircular deviation will gradually acquire a
material value, which will be known to be due entirely to vertical induction, and if
the Flinders bar be so placed as to correct it, the compensation of the compass will
be general for all latitudes.
In following this method it may usually be assumed that the soft iron of the
vessel is symmetrical with respect to the fore-and-aft line and that the Flinders bar
may be placed directly forward of the compass or directly abaft it, disregarding the
effect of components to "starboard or port. It is therefore merely necessary to
observe whether a vertical soft iron rod must be placed forward or abaft the compass
to reduce the deviation, and, having ascertained this fact, to find by experiment the
exact distance at which it completely corrects the deviation.
The Flinders bar frequently consists of a bundle of soft iron rods contained in
a case, which is secured in a vertical position near the compass, its upper end level
with the plane of the needles; in this method, the distance remaining fixed, the
intensity of the force that it exerts is varied by increasing or decreasing the number
of rods ; this arrangement is more convenient and satisfactory than the employment
of a single rod at a variable distance.
The United States Navy Flinders bar, Type II, is made of carefully annealed
pure soft iron, 2 inches in diameter, total length 24 inches, consisting of pieces 12
inches, 6 inches, 3 inches, 1 J inches, and £ inch (2 of these) long. Hardwood blocks
of the same dimensions are used to support the proper length of Flinders bar at the
top of a fixed brass tube, which is secured ordinarily at the forward end of the bin
nacle in the fore-and-aft line.
54 THE COMPASS ERROR.
It should be noted, however, that it is extremely difficult to get soft iron rods
of a satisfactory quality, for, after being placed, they seldom fail to take up more
or less subpermanent magnetism. This magnetism, due to shock of gunfire, vibra
tion while cruising or on speed trials, etc., is subject to greater and more erratic
changes than that of the harder portion of the hull, and its proximity to the compass
intensifies the effect of the variations in its magnetic properties.
127. When it is not possible to correct the compass at the magnetic equator
there is no ready practical method by which the Flinders bar may be placed; the
operation will then depend entirely upon computation, and as a mathematical
analysis of deviations is beyond the scope laid out for this work the details of pro
cedure will not be gone into; the general principles involved are indicated, and
students seeking more must consult the various works that treat the subject fully.
It has been explained that each coefficient of semicircular deviation (B and C)
is made up of a subpermanent factor varying as jj and of a vertical induction factor
varying as tan 0. If we indicate by the subscripts s and v, respectively, the parts due
to each force, we may write the equations of the coefficients:
; and
tr-v tan d.
Now if we distinguish by the subscripts 1 and 2 the values in the first and in the
second position of observation, respectively, of those quantities that vary with the
magnetic latitude, we have :
B. X TT- + BV X tan #!,
**t
and
C2 = C8 X TT- + Cv X t an 02 .
-ti2
The values of the coefficients in both latitudes are found from the observations
made for deviations; the values of the horizontal force and of the dip at each place
are known from magnetic charts; hence we may solve the first pair of equations for
B8 and Bv, and the second pair for C8 and Cv; and having found the values of these
various coefficients, we may correct the effects of Bs and C3 by permanent magnets
in the usual way and correct the remainder — that due to Bv and Cv — by the Flinders
bar.
Strictly, the Flinders bar should be so placed that its repelling pole is at an
angular distance from ahead equal to the "starboard angle" of the attracting pole
of the vertical induced force, this angle depending upon the coefficients Bv and Cv ;
but since, as before stated, horizontal soft iron may usually be regarded as sym
metrical, Cv is assumed as zero and the bar placed in the midship line.
128. To CORRECT ADJUSTMENT ON CHANGE OF LATITUDE. — The compensation
of quadrantal deviation, once properly made, remains effective in all latitudes, except
ing as noted in article 110; but unless a Flinders bar is used a correction of the
semicircular deviation made in one latitude will not remain accurate when the
vessel has materially changed her position on the earth's surface. With this in
mind the navigator must make frequent observations of the compass error during
a passage and must expect that the table of residual deviations obtained in the
magnetic latitude of compensation will undergo considerable change as that latitude
THE COMPASS EKKOB. 55
is departed from. The new deviations may become so large that it will be found
convenient to readjust the semicircular correcting magnets. This process is very
simple.
)he athwartship magnets or alter their number until the deviation disappears; thon
steady on East or West (magnetic) and similarly adjust the fore-and-aft magnets,
Swing ship for a new table of residual deviations.
129. It must be borne in mind that the compensation of the compass is not
an exact science and that the only safeguard is unceasing watchfulness on the navi
gator's part. As the ship's iron is partly "hard" and partly "soft," the subper-
manent magnetism may change appreciably from day to day, especially in a new
ship as the magnetism absorbed in building "shakes out." After a ship has been in
service for one or two years, the magnetic conditions may be said to be "settled."
They undergo changes, however, to a greater or less extent, on account of the follow
ing influences or conditions:
(a) Continuous steaming on one general course for several days, especially in
rough weather, or lying alongside a dock on one heading for a long period.
(b) Shock of gunfire, even on a ship that has been in commission for more than
a year, has been Known to introduce an 8° error, which disappeared in the course of
a few days.
(c) Extensive alterations or repairs in the vicinity of the compass. The use of
scaling hammers on a military top caused a 3° change in one of the U. S. S. 6V/-
necticut's compasses.
(d) Steaming with boilers (especially under forced draft) whose funnel is near
the compass has been known to cause a change of more than 10°, the retained mag
netism being "cooked out."
(e) On the U. S. S. Oregon, a grounded searchlight circuit caused a change of 9°.
(/) Ships have reported changes of as much as 7° when struck by lightning or
after passing through very severe thunderstorms.
The binnacle fittings must be carefully inspected from time to time, to see that
the correctors have not changed position. At least once a year the quadrantal
correctors should be examined for polarity. This can be done by moving them,
one at a time, as close to the compass as practicable and then revolving them slowly
about the vertical axis; if the compass is deflected, the magnetism should be removed
by bringing the sphere to a low red heat and then letting it cool slowly.
Tliere is no excuse for large deviations in a standard or steering compass, and they
should not le allowed to exist. '
CHAPTER IV.
PILOTING,
130. Piloting, in the sense given the word by modern and popular usage, is the
; rt of conducting a vessel in channels and harbors and along coasts, where landmarks
,;nd aids to navigation are available for fixing the position, and where the depth of
v/ater and dangers to navigation are such as to require a constant watch to be kept
upon the vessel's course and frequent changes to be made therein.
Piloting is the most important part of navigation and the part requiring the most
t xperience and nicest j udgment. An error in position on the high seas may be rec tified
by later observation, but an error in position while piloting usually results in disaster.
Therefore the navigator should make every effort to be proficient in this important
branch, bearing in mind that a modern vessel is usually safe on the high seas and in
danger when approaching the land and making the harbor.
131. Requisites. — The navigator should have ready on approaching the land
the charts of the coast and the largest scale detail charts of the locality at which he
xpects to make his landfall, the sailing directions, and the light and buoy list, all
Corrected for the latest information from the Notices to Mariners and other sources.
The usual instruments employed in navigation should be at hand and in good working
rder. The most important instrument — the sounding machine — should be in place
and in order at least a day before the land is to be made. The importance of the
sounding machine can not be exaggerated. The latest deviation table for the standard
compass must be at hand.
132. LAYING THE COURSE. — Mark a point upon the chart at the ship's position;
then mark another point for which it is desired to steer; join the two by a line drawn
v/ith the parallel ruler, and, maintaining the direction of the line, move the ruler
until its edge passes through the center of the compass rose and note the direction.
f the compass rose indicates Redirections, this will be the true course; and must be
orrected for variation and deviation (by applying each in the opposite direction
o its name) to obtain the compass course; ii it is a magnetic rose, the course need
•e corrected for deviation only.
Before putting the ship on any course a careful look should be taken along the
line over which it leads to be assured that it clears all dangers.
133. METHODS OF FIXING POSITION. — A navigator in sight of objects whose
positions are shown upon the chart may locate his vessel by any one of the following
' lethods: ^(a) cross bearings of two known objects; (b) the bearing and distance of a
' nown object; (c) the bearing of a known object and the angle between two known
bjects; (d) two bearings of a known object separated by an interval of time, with
h.e^run during that interval; (e) sextant angles between three known objects.
Besides the foregoing there are two methods by which, without obtaining the precise
^osition, the navigator may assure himself that he is clear of any particular danger.
These are: (f) the danger angle ; (#) the danger bearing.
^ The choice of the method will be governed by circumstances, depending upon
which is best adapted to prevailing conditions.
^ 134. CROSS BEARINGS OF Two KNOWN OBJECTS. — Choose two objects whose
position on the chart can be unmistakably identified and whose respective bearings
i'rom the ship differ, as nearly as possible by 90°; observe the bearing of each, either
by compass or pelorus, taking one as quickly as possible after the other; see that
the ship is on an even keel at the time the observation is made, and, if using the
pelorus, be sure also that she heads exactly on the course for which the pelorus is set.
Correct the bearings so that they will be either true or magnetic, according as they are
to be plotted by the true or magnetic compass rose of the chart— that is, if observed
by compass, apply deviation and variation to obtain the true bearing, or deviation
56
PILOTING. 57
only to obtain the magnetic; if observed by pelorus, that instrument should be set
for the true or magnetic heading, according as one or the other sort of reading is
required, and no further correction will be necessary. Draw on the chart, by means
of the parallel rulers, lines which shall pass through the respective objects in the
direction that each was observed to bear. As the ship's position on the chart is
known to be at some point of each of these lines, it must be at their intersection, the
only point that fulfills both conditions.
In figure 13, if A and B are the objects and OA and OB the lines passing through
them in the observed directions, the ship's position will be at O, their intersection.
The plotting of a position from two bearings is
greatly facilitated by the use of a plotter devised by
Lieut. K. A. Koch, United States Navy, as reference to
the compass rose on the chart, the use of parallel rulers,
and the drawing of lines on the chart are obviated. A
brief description of this plotter and its uses is as follows:
All materials except bolt and washers are transparent.
A square (7 by 7 inches) ruled with two series of lines
at right angles about one-half inch apart, and a disk
(7J inches in 'diameter) marked in degrees are placed
on a central hollow bolt of brass and are capable of
being clamped together with any degree of friction re
quired. Three arms are placed so as to revolve around
the same hollow bolt and can be clamped together in
any position. In order to plot a position from compass
bearings of two objects, and lay off a new course, the FIG. 13.
zero mark of the disk should be revolved to the East
or West of the true North and South line of the square by an amount equal to the
compass error in degrees. Two of the arms are then set by the degrees on the
disk to the two observed compass bearings. The plotter is then manipulated on the
chart until the two arms intersect the objects observed and the vertical lines on the
square are parallel to the meridians of the chart. Mark the point of intersection of
the arms by inserting a pencil in the hollow central bolt. An arm may then be swung
to intersect any object 011 the chart and the compass course to that object read from
the disk. This plotter can also be used to obtain the error of the compass from
bearings of three objects by compass.
135. If it be possible to avoid it, objects should not be selected for cross
bearings which subtend an angle at the ship of less than 30° or more than 150°, as,
when the lines of bearing approach parallelism, a small error in an observed bearing
gives a large error in the result. For a similar reason objects near the ship should be
taken in preference to those at a distance.
136. When a third object is available a bearing of that may be taken and plotted.
If this line intersects at the same point as the other two (as the bearing OC of the
object C in the figure), the navigator may have a reasonable assurance that his "fix"
is correct; if it does not, it indicates an error somewhere, and it may have arisen from
inaccurate observation, incorrect determination or application of the deviation, or a
fault in the chart.
137. What may be considered as a form of this method can be used when only
one known object is in sight by taking, at the same instant as the bearing, an altitude
of the sun or other heavenly body and noting the
tune; work out the sight and obtain the Sumner
line (as explained in Chapter XV), and the inter
section of this with the direction line from the
object will give the observer's position in the same X)
way as from two terrestrial bearings.
138. BEARING AND DISTANCE OF A KNOWN
OBJECT. — When only one object is available, the
ship's position may be found by observing its bear
ing and distance. Follow the preceding method in FlG. 14>
the manner of taking, correcting, and plotting the
bearing; then, on this line, lay off the distance from the object, which will give t
point occupied by the observer. In figure 14, if A represents the object and AO
:ing and distance, the position sought will be at O.
earn
60
PILOTING.
EXAMPLE: A vessel on a course 128° takes the first bearing of an object at
154°, and the second at 182°, running in the interval 0.8 mile. Required the distance
at which she will pass abeam.
Difference between course and first bearing, 26°
Difference between course and second bearing, 54°.
Multiplier from second column, Table 5B, 0.76.
0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.
145. As has been said, there are certain special cases ot this problem where it is
exceptionally easy of application; these arise when the multiplier is equal to unity
and the distance run is therefore equal to the distance from
the object. When the angular distance on the bow at the
second bearing is twice as great as it was at the first bearing,
the distance of the object from the ship at second bearing is
equal to the run, the multiplier being 1.0. For if, in figure 18,
when the ship is in the first position, O, the object A bears a°
on the bow, and at the second position, P, 2a°, we have in the
triangle APO, observing that APO = 180° - 2o?, and POA = a :
PAO = 180°- (POA+APO),
a.
0
FIG. 18.
Or, since the angles at O and A are equal to each other, the sides
OP and AP are equal or the distance at second bearing is equal
to the run. This is known as doubling the angle on the low.
146. A case where this holds good is familiar to every
navigator as the ~bow and 'beam bearing, where the first bearing
is taken when the object is broad on the bow (four points or
45° from ahead) and the second when it is abeam (eight points or 90° from ahead);
in that case the distance at second bearing and the distance abeam are identical
and equal to the run between bearings.
147. When the first bearing is 26J° from ahead, and the second 45°, the distance
at which the object will be passed abeam will equal the run between bearings. This
is true of any two such bearings whose^ natural cotangents ^ differ by unity, and
the following table is a collection of solutions of this relation in which the pairs of
bearings are such that, when observed in succession from ahead upon the same fixed
object, the distance run between the bearings will be equal to the distance of the fixed
object when it bears abeam, provided that a steady course has been steered, unaffected
by current or drift.
The marked pairs will probably be found the most convenient ones to use, as
they involve whole degrees only.
Bearings from ahead.
First.
Second.
First.
Second.
First.
Second.
20
29|
28
48£
37
71f
21
811
*29
51
38
74*
*22
34
30
53f
39
76}
23
36£
31
56-1-
*40
79
24
38|
*32
59
41
811
*25
41
33
61|
42
83£
26
43|
34
64|
43
85}
26J
45
35
66f
*44
88
*27
46
36
69i
*45
90
When the fixed object bears as per any entry of the first column, take the time
and the reading of the patent log. Repeat this procedure on reaching the bearing of
the adjacent entry in the second column. The difference of the patent-log readings
will be the distance at which the fixed object will be passed abeam.
PILOTING.
61
This general solution includes the 26£°-45° rule as well as the seven-tenths rule
to be explained later; furthermore, it has the advantage that the approximate
determination of the distance offshore, at which the fixed object will be passed,
need not wait for the 45° bearing. There are two whole-degree pairs bv which such
a determination can be made before the 45° bearing is reached. It is possible to
get five whole-degree bearings or observations by the time the fixed object bears 30°
forward of the beam, as follows: 22°-34°, 25°-41°, 27°-46°, 29°-51°, 32°-59°. Of
these, the last three should be reasonably accurate; the acuteness of the first angle
in all such observations accounts for the discrepancies noted in practice. The use
of the table given above may be found to be more convenient than the methods of
plotting about to be described, and the use of tables 5A and 5B; but it does not take
the place of those methods. Tables 5A and 5B coyer all combinations of bearings in
which the first bearing is taken when the object is 20° or more on the bow.
The Seven-tenths Rule. — If bearings of the fixed object be taken at two (2)
and four (4) points on the bow (22 J° and 45°), seven-tenths (0.7) of the run between
"bearings will be the distance at which the point will be passed abeam.
From the combination of the seven-tenths rule and the 26^°-45° rule, there
follows an interesting corollary, i. e., if bearings of an object at 22^° and 26^° on the
bow be taken, then seven-thirds (J) of the distance run in the interval will be the
distance when abeam.
If a bearing is taken when an object is two points (22 £°) forward of the beam
and the run until it bears abeam is measured, then its distance when abeam is seven-
thirds (-J) of the run. This rule, particularly, is only approximate.
In case the 45° bearing on the bow is lost, in order to find the distance abeam
that the object is passed, note the time when the object bears 26^° forward of the
beam, and again when it has the same bearing abaft the beam; the distance run in
this interval is the distance of the object when it was abeam.
To steer an arc course in order to round a light, point, or other object without
fixes and be sure the course itself does not decrease the initial distance: Provided
there is no current, stand on course until the light is at the required distance, deter
mined by one or more of the methods described. Immediately bring the light
abeam, and dp not let it get forward of the beam again, then the course wih1 not
decrease the initial distance. When the light is onerhalf point abaft the beam
again bring it abeam; hold course until it is again
one-half point abaft the beam, repeating this pro
cedure until the light is rounded. A polygon is thus
circumscribed about the circle, the nearest approach
to the light being the radius of the inscribed circle.
The number of sides of the polygon may be in
creased indefinitely, so that the light may be rounded,
by changing the course just enough to keep the light
abeam, after it is Jirst brought abeam.
148. There is a graphic method of solving this
problem that is considered by some more convenient
than^the use of multipliers. Draw upon the chart
the lines OA and PA (fig. 19), passing through the
object on the two observed bearings; set the dividers
to the distance run, OP; lay down the parallel rulers
in a direction parallel to the course and move them
toward or away from the observed object until some
point is found where the distance between the lines
of bearing is exactly equal to the distance between
the points of the dividers; in the figure this occurs
when the rulers lie along the line OP, and therefore O represents the position of
the ship at the first bearing and P at the second. For any other positions O'P',
O"P", the condition is not fulfilled.
149. Another graphic solution is given by the Mooring and Maneuvering Board
and the various moclificatlons of it that are in use among navigators.
150. The method of obtaining position by two bearings of the same object is
one of great value, by reason of the fact that it is frequently necessary to locate the
ship when there is but one landmark in sight. Careful navigators seldom, if ever,
FIG. 19.
60
PILOTING.
EXAMPLE: A vessel on a course 128° takes the first bearing of an object at
154°, and the second at 182°, running in the interval 0.8 mile. Required the distance
at which she will pass abeam.
Difference between course and first bearing, 26°
Difference between course and second bearing, 54°.
Multiplier from second column, Table 5B, 0.76.
0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.
145. As has been said, there are certain special cases ot this problem where it is
exceptionally easy of application; these arise when the multiplier is equal to unity
and the distance run is therefore equal to the distance from
the object. When the angular distance on the bow at the
second bearing is twice as great as it was at the first bearing,
the distance of the object from the ship at second bearing is
equal to the run, the multiplier being 1.0. For if, in figure 18,
when the ship is in the first position, O, the object A bears a°
on the bow, and at the second position, P, 2a°, we have in the
triangle APO, observing that APO = 180° - 2a, and POA
a:
PAO = 180°-(POA + APO),
0
FIG. 18.
Or, since the angles at O and A are equal to each other, the sides
OP and AP are equal or the distance at second bearing is equal
to the run. This is known as doubling the angle on the bow.
146. A case where this holds good is familiar to every
navigator as the "bow and beam bearing, where the first bearing
is taKen when the object is broad on the bow (four points or
45° from ahead) and the second when it is abeam (eight points or 90° from ahead) ;
in that case the distance at second bearing and the distance abeam are identical
and equal to the run between bearings.
147. When the first bearing is 26^° from ahead, and the second 45°, the distance
at which the object will be passed abeam will equal the run between bearings. This
is true of any two such bearings whose natural cotangents differ by unity, and
the following table is a collection of solutions of this relation in which the pairs of
bearings are such that, when observed in succession from ahead upon the same fixed
object, the distance run between the bearings will be equal to the distance of the fixed
object when it bears abeam, provided that a steady course has been steered, unaffected
by current or drift.
The marked pairs will probably be found the most convenient ones to use, as
they involve whole degrees only.
Bearings from ahead.
First.
Second.
First.
Second.
First.
Second.
O
20
29f
28
48£
37
n'f
21
31f
*29
51
38
74}
*22
34
30
53f
39
76|
23
36}
31
56}
*40
79
24
38|
*32
59
41
81}
*25
41
33
61^
42
26
43J
34
64}
43
85}
26i
45
35
66f
*44
88
*27
46
36
69}
*45
90
When the fixed object bears as per any entry of the first column, take the time
and the reading of the patent log. Kepeat this procedure on reaching the bearing of
the adjacent entry in the second column. The difference of the patent-log readings
will be the distance at which the fixed object will be passed abeam.
PILOTING.
61
This general solution includes the 26£°-45° rule as well as the seven-tenths rule
to be explained later; furthermore, it has the advantage that the approximate
determination of the distance offshore, at which the fixed object will be passed,
need not wait for the 45° bearing. There are two whole-degree pairs by which such
a determination can be made before the 45° bearing is reached. It is possible to
get five whole-degree bearings or observations by the time the fixed object bears 30°
forward of the beam, as follows: 22°-34°, 25°-41°, 27°-46°, 29°-51°, 32°-59°. Of
these, the last three should be reasonably accurate; the acuteness of the first angle
hi all such observations accounts for the discrepancies noted in practice. The use
of the table given above may be found to be more convenient than the methods of
plotting about to be described, and the use of tables 5A and 5B; but it does not take
the place of those methods. Tables 5A and 5B coyer all combinations of bearings in
which the first bearing is taken when the object is 20° or more on the bow.
The Seven-tenths Rule. — If bearings of the fixed object be taken at two (2)
and four (4) points on the bow (22J° and 45°), seven-tenths (0.7) of the run between
"bearings will be the distance at which the point will be passed abeam.
From the combination of the seven-tenths rule and the 26i°-45° rule, there
follows an interesting corollary, i. e., if bearings of an object at 22^° and 26J0 on the
bow be taken, then seven-thirds (-J) of the distance run in the interval will be the
distance when abeam.
If a bearing is taken when an object is two points (22£°) forward of the beam
and the run until it bears abeam is measured, then its distance when abeam is seven-
thirds (-J) of the run. This rule, particularly, is only approximate.
In case the 45° bearing on the bow is lost, in order to find the distance abeam
that the object is passed, note the tune when the object bears 26J° forward of the
beam, and again when it has the same bearing abaft the beam; the distance run in
this interval is the distance of the object when it was abeam.
To steer an arc course in order to round a light, point, or other object without
fixes and be sure the course itself does not decrease the initial distance: Provided
there is no current, stand on course until the lig;ht is at the required distance, deter
mined by one or more of the methods described. Immediately bring the light
abeam, and dp not let it get forward of the beam again, then the course will not
decrease the initial distance. When the light is onerhalf point abaft the beam
again bring it abeam; hold course until it is again
one-half point abaft the beam, repeating this pro
cedure until the light is rounded. A polygon is thus
circumscribed about the circle, the nearest approach
to the light being the radius of the inscribed circle.
The number of sides of the polygon may be in
creased indefinitely, so that the light may be rounded,
by changing the course just enough to keep the light
abeam, after it is first brought abeam.
148. There is a graphic method of solving this
problem that is considered by some more convenient
than the use of multipliers. Draw upon the chart
the lines OA and PA (fig. 19), passing through the
object on the two observed beanngs; set the dividers
to the distance run, OP; lay down the parallel rulers
in a direction parallel to the course and move them
toward or away from the observed object until some
point is found where the distance between the lines
of bearing is exactly equal to the distance between
the points of the dividers; in the figure this occurs
when the rulers lie along the line OP, and therefore O represents the position of
the ship at the first bearing and P at the second. For any other positions O'P',
O"P", the condition is noMulfilled.
149. Another graphic solution is given by the Mooring and Maneuvering Board
and the various modifications of it that are in use among navigators.
150. The method of obtaining position by two bearings of the same object is
one of great value, by reason of the fact that it is frequently necessary to locate the
ship when there is but one landmark in sight. Careful navigators seldom, if ever,
FIG. 19.
62 PILOTING.
miss the opportunity for a bow and beam bearing in passing a lighthouse or other
well-plotted object; it involves little or no trouble, and always gives a feeling of
addea security, however little the position may be in doubt. If about to pass an
object abreast of which there is a danger — a familiar example of which is when a
lighthouse marks a point off which are rocks or shoals — a good assurance of clearance
should be obtained before bringing it abeam, either by doubling the angle on the
bow, or, if the object be sighted in time, by using any of the pairs of bearings tabulated
under article 147.
151. It must be remembered that, however convenient, the fix obtained by
two bearings of the same object will be in error unless the course and distance are
correctly estimated, the course "made good" and the distance "over the ground"
being required. Difficulty will occur in estimating the exact course when there is
bad steering, a cross current, or when a ship is making leeway; errors in the allowed
run will arise when she is being set ahead or back by a current or when the logging
is inaccurate. A current directly with the course of the ship, if unallowed for, will
give a determination of position too close to the object observed; and a current*
directly against the course of the ship, if unallowed for, will give a determination of
position too far away from the object observed. The existence of such a current
will not le revealed by taking more than two successive bearings. All such observa
tions will place the ship on the same apparent course, which course will be parallel
to the course made good and to the course steered but in error in its distance from
the observed object by an amount dependent upon the ratio of the speed of ship
over ground to the speed of ship by log. A current oblique to the course of the ship
will give a determination of position which will be erroneous. The existence of
such a current but not its amount will "be revealed by taking more than two observa
tions; in this case, following the usual method of plotting, the determination resulting
from any two successive bearings will fail to agree with the determination from any
other two. If, in such a case, the observed bearings be drawn upon the chart and
the distances run by log between them be laid down on the scale of the chart upon a
piece of paper, a course may be found by trial, upon which course the intervals of
run correspond with the intervals between the lines of bearing. The apparent course
thus determined, which must always be oblique to the course steered, will be parallel
to the course actually being made good, but will be in error in its distance from the
observed object by an amount dependent upon the ratio of the speed of ship over
the ground to the" speed of ship by log. If there is an apparant shortening of the
distance run from earlier to later observations, or a shortening of the time if the
speed is invariable, there is a component of set toward the fixed object. Therefore,
if in a current of any sort, due allowance must be made, and it should be remembered
that more dependence can be placed upon a position fixed by simultaneous bearings
or angles, when two or more objects are available, than by two bearings of a single
object.
152. SEXTANT ANGLES BETWEEN THREE KNOWN OBJECTS. — This method,
involving the solution of the three-point problem, will, if the objects be well chosen,
give the most accurate results of any. It is largely employed in surveying, because
of its precision; and it is especially valuable in navigation, because it is not subject
to errors arising from imperfect knowledge of the compass error, improper logging,
or the effects of current, as are the methods previously described.
Three objects represented on the chart are selected and the angles measured
with sextants of known index error between the center one and each of the others.
Preferably there should be two observers and the two angles be taken simultaneously,
but one observer may first take the angle which is changing more slowly, then take
the other, then repeat the first angle, and consider the mean of the first and last
observations as the value of the first angle. The position is usually plotted by
means of the three-armed protractor, or station-pointer (see art. 428, Chap. XVII).
Set the right and left angles on the instrument, and then move it over the chart
until the three beveled edges pass respectively and simultaneously through the
three objects. The center of the instrument will then mark the ship's position, which
may be pricked on the chart or marked with a pencil point through the center hole.
When the three-armed protractor is not at hand, the tracing-paper protractor will
prove an excellent substitute, and may in some cases be preferable to it, as, for
PILOTING. 63
instance, when the objects angled on are so near the observer as to be hidden by
the circle of the instrument. A graduated circle printed upon tracing paper permits
the angles being readily laid off, but a plain piece of tracing paper may be used and
the angles marked by means of a small protractor. The tracing-paper protractor
permits the laying down, for simultaneous trial, of a number of angles, where special
accuracy is sought.
153. The three-point problem, by which results are obtained in this method,
is : To find a point such that three lines drawn from this point to three given points
shall make given angles with each other.
Let A, B, and C, in figure 20, be three fixed objects on shore, and from the
ship, at D, suppose the angles CDB and ADB are found equal, respectively, to 40°
and 60°
With the complement of CDB, 50°, draw the lines BE and CE; the point of
intersection will be the center of a circle, on some point of whose circumference the
ship must be. Then, with the complement of the angle ADB, 30°, draw the lines
AF and BF, meeting at F, which point will be the center of another circle, on some
point of whose circumference the ship must be. Then D, the point of intersection
of the circumference of the two circles, will be the position of the ship.
The correctness of this solution mav be seen as follows: Take the first circle,
DEC; in the triangle EBC, the angle" at E^ the center, equals 180°-2x50° =
2 (90° — 50°), twice the complement of 50°, which is twice the observed angle; now
if the angle at the center subtended by the chord BC equals twice the observed
angle, then the angle at any point on the cir
cumference subtended by that chord, which
equals half the angle, at the center, equals the
observed angle; so the required condition is
fulfilled. Should either 01 the angles exceed
90°, the excess of the angle over 90° must be
laid off on the opposite side of the lines joining
the stations.
It may be seen that the intersection of
the circles becomes less sharp as the centers
E and F approach each other; and finally that
the problem becomes indeterminate when the
centers coincide, that is, when the three
observed points and the observer's position all FlG
fall upon the same circle; the two circles are
then identical and there is no intersection; such a case is called a "revolver," because
the protractor will revolve around the whole circle, everywhere passing through the
observed points. The avoidance of the revolver and the*employment of large angles
and short distances form the keys to the selection of favorable objects.
Generally speaking, the observer, in judging which objects are the best to be
taken, can picture in his eye the circle passing through the three points and note
whether it comes near to his own position. If it does, he must reject one or more
of the objects for another or others. It should be remembered that he must avoid
not only the condition where the circle passes exactly through his position (when
the problem is wholly indeterminate), but also all conditions approximating thereto,
for in such cases the circles will intersect at a very acute angle, and the inevitable
small errors of the observation and plotting will produce large errors in the result
ing fix.
Without giving an analysis of reasons, which may be found in various works
that treat the problem in detail, the following may be eniimerated as the general
conditions which result in a good fix:
(a) When the center object of the three lies between the observer and a line
joining the other two, or lies nearer than either of the other two.
(&) When the sum of the right and left angles is equal to or greater than 180°.
(c) When two of the objects are in range, or nearly so, and the angle to the third
is not less than 30°.
(d) When the three objects are in the same straight line.
64
PILOTING.
FIG. 21.
A condition that limits all of these is that angles should be large — at least as
large as 30° — excepting in the case where two objects are in range or nearly so, and
then the other angle must be of good size. When possible, near objects should be
used rather than distant ones. The navigator should not fall into the error of
assuming that objects which would give good cuts for a cross bearing are necessarily
favorable for the three-point solution.
In a revolver, the angle formed by lines drawn from the center object to the
other two, added to the sum of the two observed angles, equals 180°. A knowledge
of this fact may aid in the choice of objects.
If in doubt as to the accuracy with which the angles will plot, a third angle to
a fourth object may be taken. Another way to make sure of a doubtful fix is to
take one compass bearing, by means of which even
a revolver may be made to give a good position.
154. THE DANGER ANGLE. — When sailing along
a coast, to avoid sunken rocks, or shoals, or danger
ous obstructions at or below the surface of the water,
and which are marked on the chart, the navigator
may pass these at any desired distance by using what
is known as a danger angle, of which tnere are two
kinds, namely, the horizontal and vertical danger
angles; the former requires two well-marked objects
indicated on the^chart, lying in the direction of the
coast, and sufficiently distant from each other to
give a fair-sized horizontal angle; the latter requires
a well-charted object of known height.
155. In figure 21, let AMB be a portion of the
coast along which a vessel is sailing on the course
CD; A and B two prominent objects shown on the
chart; S and S' are two outlying shoals, reefs, or
dangers. In order to pass outside of the danger S'
take the middle point of the danger as a center and the given distance from the
center it is desired to pass as radius, and describe a circle. Pass a circle through
A and B tangent to the seaward side of the first circle. To do this, it is only neces
sary to join A and B and draw a line perpendicular to the middle of AB, and then
ascertain by trial the location of the center of the circle EAB. Measure the angle
AEB, set the sextant to this angle, and remembering that AB subtends the same angle
at all points of the arc AEB, the ship will be outside the arc AEB, and clear the
danger S', as long as AB does not subtend an angle greater than AEB, to which the
sextant is set. At the same time in
order to avoid the danger S, take the
middle point of the danger S and with
the desired distance as a radius de
scribe a circle. Pass a second circle
through A and B tangent to this circle
at G, measure the angle AGB with a
protractor, then, as long as the chord
AB subtends an angle greater than
AGB, the ship will be inside the cir
cle AGB. Therefore, the ship will pass
between the dangers S and S' as long
as the angle subtended by AB is less
than AEB and greater than AGB.
156. The vertical danger angle
involves the same general principle, as
can be readily seen without explana
tion by reference to the figure 22 in which AB represents a vertical object of known
height.
157. THE DANGER BEARING. — This is a method by which the navigator is warned
by a compass bearing when the course is leading into danger. Suppose a vessel to
be steering a course, as indicated in figure 23, along a coast which must not be
FIG. 22.
PILOTING.
65
approached within a certain distance, the landmark A being a guide. Let the navigator
draw through A the line XA, clear of the danger at all points, and note its direction
by the compass rose; then let frequent bearings be taken as the ship proceeds, and
so long as the bearings, YA, ZA, are to the right of XA he may be assured that he is
on the left or safe side of the line.
If, as in the case given, there is but one object in sight and that nearly ahead, it
would be very difficult to get an exact position, but this method would always show
whether or not the ship was on a good course, and would, in consequence, be of
the greatest value. And even if there were other objects visible by which to get
an accurate fix it would be a more simple matter to note, by an occasional glance
over the sightvane of the pelorus or compass, that the
ship was making good a safe course than to be put to the
necessity of plotting the position each time.
158. It will occasionally occur that two natural objects
will so lie that when in range they mark a danger bearing;
advantage should be taken of all such, as they are easier to
observe than a compass bearing; but if in a locality with
which the navigator nas not had previous acquaintance the
compass bearing of all ranges should be observed and com
pared with that indicated on the chart in order to make^sure
of the identity of the objects. The utility of ranges, either
artificial or natural, as guides in navigation, extends also to
established lines of bearing giving the true or magnetic direc
tion of fixed objects, such as lines of bearing limiting the
sectors of navigational lights.
159. SOUNDINGS. — The practice should be followed of
employing one or two leadsmen to take and report soundings
continuously while in shoal water or in the vicinity of dangers.
The soundings must not be regarded as fixing a position, but they afford a check
upon the positions obtained by other methods. An exact agreement with the
soundings on the chart need not be expected, as there may be some little inaccu
racies in reporting the depth on a ship moving with speed through the water, or
the tide may cause a discrepancy, or the chart itself may la'ck perfection; but the
soundings should agree in a general way, and a marked departure from the charac
teristic bottom shown on the chart should lead the navigator to verify his position
and proceed with caution; especially is this true if the water is more shoal than
expected.
160. But if the soundings in shallow water when landmarks are in sight
serve merely as an auxiliary guide, those taken (usually with the patent sounding
machine or deep-sea lead) when there exist no other means of locating the position,
fulfill a much more important purpose. In thick weather, when approaching or
running close to the land, and at all tunes when the vessel is in less than 100 fathoms
of water and her position is in doubt, soundings should be taken continuously and
at regular intervals, and, with the character of the bottom, systematically recorded.
By laying the soundings on tracing paper, along a line which represents the track of
the ship according to the scale of the chart, and then moving the paper over the
chart, keeping the various courses parallel to the corresponding directions on the
chart, until the observed soundings agree with those laid down, the ship's position
will in general be quite well determined. While some localities, by the sharpness
of the characteristics of their soundings, lend themselves better than others to
accurate determinations by this method, there are few places where the mariner
can not at least keep out of danger by the indications, even if they tell him no more
than that the tune has come when he must anchor or lie off till conditions are more
favorable.
161. LIGHTS. — Before coming within range of a light the navigator should
acquaint himself with its characteristics, so that when sighted it will be recognized.
The charts, sailing directions, and light lists give information as to the color, character,
and range of visibility of the various lights. Care should be taken to note all of
these and compare them when the light is seen. If the light is of the flashing,
61828°— If 5
66 PILOTING.
revolving, or intermittent variety the duration of its periods should be noted to
identify it. If a fixed light, a method that may be employed to make sure that it is
not a vessel's light is to descend several feet immediately after sighting it and observe
if it disappears from view; a navigational light will usually do so, excepting in misty
weather, while a vessel's light will not. The reason for this is that navigational lights
are as a rule sufficiently powerful to be seen at the farthest point to which the ray
can reach without being interrupted by the earth's curvature. They are therefore
seen at the first moment that the ray reaches an observer on a ship's deck, and are
cut off if he lowers the eye. A vessel's light, on the other hand, is usually limited
by its intensity and does not carry beyond a distance within which it is visible at
all heights.
Care must be taken to avoid being deceived on first sighting a light, as there are
various errors into which the inexperienced may fall. The glare of a powerful light
is often seen beyond the distance of visibility of its direct rays by the reflection
downward from particles of mist in the air; the same mist may also cause a white
light to have a distinctly reddish tinge, or it may obscure a light except within short
distances. When a light is picked up at the extreme limit at which the height of
the observer will permit, a fixed light may appear flashing, as it is seen when the
ship is on the crest of a wave, and lost when in the hollow.
Many lights are made to show different colors in different sectors within their
range, and by consulting his chart or books, the navigator may be guided by the
color of the sector in which he finds himself; in such lights one color is generally
used on bearings whence the approach is clear, and another covers areas where
dangers are to be encountered.
The visibility of lights is usually stated for an assumed height of the observer's
eye of 15 feet, and must be modified accordingly for any other height. But it should
be remembered that atmospheric and other conditions considerably affect the visibility,
and it must not be positively assumed, on sighting a light, even in perfectly clear
weather, that a vessel's distance is equal to the range of visibility; it may be either
greater or less, as the path of a ray of light near the horizon receives extraordinary
deflection under certain circumstances; the conditions governing this deflection are
discussed in article 296, Chapter X.
162. BUOYS. — While buoys are valuable aids, the mariner should always employ
a certain amount of caution in being guided by them. In the nature of things it is
never possible to be certain of finding buoys in correct position, or, indeed, of finding
them at all. Heavy seas, strong currents, ice, or collisions with passing vessels may
drag them from their places or cause them to disappear entirely, and they are especially
uncertain in unfrequented waters, or those of nations that do not keep a good lookout
upon their aids to navigation. When, therefore, a buoy marks a place where a ship
must be navigated with caution, it is well to have a danger angle or bearing as an
additional guide instead of placing too much dependence upon the buoy being in
place.
Different nations adopt different systems of coloring for their buoys; an
important feature of many such systems, including those adopted by the United
States and various other great maritime nations (though not all), consists in placing
red buoys to be left on the starboard hand of a vessel entering a harbor or fairway,
and black buoys on the port hand. In these various systems the color and character
of the buovs are such as to denote the special purpose for which they aro employed.
163. FOGS AND FOG SIGNALS. — As with fights, the navigator should, in a fog,
acquaint himself with the characteristics of the various sound signals which he is
likely to pick up, and when one is heard, its periods should be timed and compared
with those givon in the light lists to insure its proper identity.
Experiment has demonstrated that sound is conveyed through the atmosphere
in a very uncertain way; that its intensity is not always increased as its origin is
approached, and that areas within its range at one time, will seem silent at another.
Add to these facts the possibility that, for some cause, the signal may not be working
as it should be, and we have reason for observing the rule to proceed with the utmost
caution when running near the land in a fog.
Although the transmission of sound through water from the submarine bells
that have been installed on many light vessels and at points of danger is much more
PILOTING. 67
certain than the transmission of sound through air and can be received in such a
way by vessels equipped with submerged microphones on each side as to enable the
direction of the submarine bell to be approximately determined, yet the lead continues
to prove an ever-serviceable guide, and should accordingly be in constant use.
• The method of plotting soundings described in article 160 will give the most
reliable position that is obtainable. Moreover, the lead will warn the navigator of
the approach to shallow water, when, if his position is at all in doubt, "it is wisest to
to anchor before it becomes too late.
When running slowly in a fog (which caution, as well as the law, requires that
one should do) it must be borne in mind that the relative effect of current is increased;
for instance, the angle of deflection from the course caused by a cross-set is greater at
low than at high speed.
It is worth remembering that when in the vicinity of a bold bluff shore vessels
are sometimes warned of a too close approach by having their own fog signals echoed
back from the cliffs; indeed, from a Knowledge of the velocity of sound (art. 314,
Chap. XI) it is possible to gain some rough idea of the distance in such a case.
When radio-stations, equipped with fog-signaling apparatus, send out simul
taneous radio and sound signals, distances from the sending station can be found
by noting the elapsed interval between the time of arrival of radio signal and sound
signal, and multiplying this interval expressed in seconds by the velocity per second
of sound- in air, or the velocity per second of sound in water, according as the
sound signals are received through air or through water.
By thus determining the distance from a fog-signal station to different positions
between which the course and distance are known, the position of the vessel could
be approximately found in a manner analogous to that wilich would apply in figure 18
if the distances AO and AP were known in addition to the length and direction of OP.
164. TIDES AND CURRENTS. — The information relating to the tides given on
the chart and in other publications should be studied, as it is of importance for the
navigator to know not only the height of the tide above the plane of reference of
the chart, but also the direction and force of ttye tidal current.
The plane of reference adopted for soundings varies with different charts;
on a large number it is that of mean low water, and as no plane of reference above that
of mean low water is ever employed the navigator may with safety refer his sound
ings to that level when in doubt.
When traversing waters in which the depth exceeds the vessel's draft by but a
small margin, account must be taken of the fact that strong winds or a high barom
eter may cause the water to fall below even a very low plane of reference. On coasts
where there is much diurnal inequality in the tides, the amount of rise and fall can
not be depended upon, and additional caution is necessary.
A careful distinction should be made between the vertical rise and fall of the
tide, which is marked at the transition periods by a stationary height, or stand, and
the tidal current, which is the horizontal transfer of water as a result of the difference
of level, producing the flood and ebb: and the intermediate condition, or slack. It
seldom occurs that the turn of the tidal stream is exactly coincident with the high
and low water, and in some channels the current may outlast the vertical movement
which produces it by as much as three hours, the effect being that when the water
is at a stand the tidal stream is at its maximum, and when the current is slack the
rise or fall is going on with its greatest rapidity. Care must be taken to avoid con
founding the two.
The effect of the tidal wave in causing currents may be illustrated by two simple
cases:
(1) Where there is a small tidal basin connected with the sea by a large opening.
(2) Where there is a large tidal basin connected with the sea by a small opening.
In the first case the velocity of the current in the opening will have its maximum
value when the height of the tide within is changing most rapidly, i. e., at a time
about midway between high and low water. The water in the basin keeps at approxi
mately the same level as the water outside. The flood stream corresponds with the
rising and the ebb with the falling of the tide.
In the second case the velocity of the current in the opening will have its maxi
mum value when it is high water or low water without, for then there is the greatest
68 PILOTING.
head of water for producing motion. The flood stream begins about three hours
after low water, and the ebb stream about three hours after high water, slack water
thus occurring about midway between the tides.
Along most shores which lack features like bays and tidal rivers, the current
usually turns soon after high water and low water.
The swiftest current in straight portions of tidal rivers is usually in the middle
of the stream, but in curved portions the most rapid current is toward the outer
edge of the curve, and here the water will be deepest. The pilot rule for best water
is to follow the ebb-tide reaches.
Countercurrents and eddies may occur near the the shores of straits, especially in
bights and near points. A knowledge .of them is useful in order that they may be
taken advantage of or avoided.
A swift current often occurs in the narrow passage connecting two large bodies
of water, owing to their considerable difference of level at the same instant. The
several passages between Vineyard Sound and Buzzards Bay are cases in point. In
the Woods Hole Passage the maximum strength of the tidal streams occurs near
high and low water.
Tide rips are made by a rapid current setting over an irregular bottom, as at
the edges of banks where the change of depth is considerable.
Generally speaking, the rise and fall and strength of current are at their mini
mum along straight stretches of coast upon the open ocean, while bays, bights, inlets,
and large rivers operate to augment the tidal effects, and it is in the vicinity of these
that one finds the highest tides and strongest currents. The navigator need there
fore not be surprised in cruising along a coast to notice that his vessel is set more
strongly toward or from the shore in passing an indentation, and that the evidences
of tide will appear more marked as he nears its mouth. Usually more complete data
are furnished in charts and tide tables regarding the rise and fall, and it frequently
occurs that the information regarding the tidal current is comparatively meager; the
mariner must therefore take every means to ascertain for himself the direction and
force of the tidal and other currents5 either from the set shown between successive
well-located positions of the ship, or by noting the ripple of the water around buoys,
islets, or shoals, the direction in which vessels at anchor are riding, and the various
other visible effects of the current.
Current arrows on the chart must not be regarded as indicating absolutely the
conditions that are to be encountered. They represent the mean of the direction
and force observed, but the observations upon which they are based may not be
complete, or there may be reasons that bring about a departure from the normal
state.
165. CHARTS. — The chart should be carefully studied, and among other things
all of its notes should be read, as valuable information may be given in the margin
which it is not practicable to place upon the chart abreast the locality affected.
The mariner will do well to consider the source of his chart and the authority
upon which it is based. He will naturally feel the greatest confidence in a chart
issued by the Government of one of the more important maritime nations which
maintains a well-equipped office for the especial purpose of acquiring and treating
hydrographic information. He should note the character of the survey from which the
chart has been constructed; and, finally, he should be especially careful that the
chart is of recent issue or bears correction of a recent date — facts that should always
be clearly shown upon its face.
It is well to proceed with caution when the chart of the locality is based upon
an old survey, or one whose source does not carry with it the presumption of accu
racy. Ev^en if the original survey was a good one, a sandy bottom, in a region
where the currents are strong or the seas heavy, is liable to undergo in time marked
changes; and where the depth is affected by the deposit or removal of silt, as in the
vicinity of the estuaries of large river systems, the behavior is sometimes most capri
cious. Large blank spaces on the chart, where no soundings are shown, may be
taken as an indication that no soundings were made, and are to be regarded with
suspicion, especially if the region abounds in reefs or pinnacle rocks, in which case
only the closest sort of a survey can be considered as revealing all the dangers. All
of these facts must be duly weighed.
PILOTING. 69
When navigating by landmarks the chart of the locality which is on the largest
scale should be used. The hydrography and topography in such charts appear in
greater detail, and — a most important consideration — bearings and angles may be
plotted with increased accuracy.
To sum up, the navigator must know the exact draft of the ship when
approaching the land. He must make himself familiar with every detail of the
charts he will be required to use and must read the charts in such a way as to be
able to form a mental picture of how the land and the various aids to navigation
will look when sighted, remembering that the position of the sun at different times
of day, or the position of the moon at night, affects the appearance of the land as
presented to tne navigator approaching from seaward. He must be thoroughly
familiar with the day, night, and fog characteristics of all aids to navigation in the
locality. He must know the state of the tide and the force and direction of the
current at all times when in pilot waters. The navigator, in making his plan for
entering a strange port, should give very careful previous study to the chart, and
should carefully select what appear to be the most suitable marks for use, also pro
viding himself with substitutes for use in case those selected as most suitable should
prove unreliable by not being recognized with absolute certainty. It must be
remembered that buoys seen at a distance, in approaching a channel, are often
difficult to place or identify, because all may appear equally distant, though hi
reality far apart. Ranges should be noted, if possible, and tne lines olrawn, both
for leading through the best water in channels and also for guarding against par
ticular dangers. For the latter purpose, safety bearings should in all cases be laid
down where no suitable ranges offer. The courses to be steered in entering should
also be laid down and distances marked thereon. If intending to use the sextant
and danger angle in passing dangers, and especially in passing between dangers,
the danger circles should be plotted and regular courses planned, rather than to run
haphazard by the indications of the angle alone, with the possible trouble to be
apprehended from wild steering at critical points.
The ship's position should not be allowed to be in doubt at any time, even in
entering ports considered safe and easy of access, and should be constantly checked
by continuing to use for this purpose those marks concerning which there can be
no doubt until others are unmistakably recognized.
The ship should ordinarily steer exact courses and follow exact lines as planned
from the chart, changing course at exact points, and, where the distances are con
siderable, her position on the line should be checked at frequent intervals, recording
the time and the reading of the patent log. This is desirable, even where it may
seem unnecessary for safety; because, if running by the eye alone and the ship's
exact position be suddenly required, as in a sudden squall, fixing at that particular
moment might be impossible.
The habit of running exact courses with precise changes of courses will be found
most useful when it is desired to enter port or pass through inclosed waters during
fog by means of the buoys; here safety demands that the buoys be made successively,
to do which requires, if the fog be dense, very accurate courses and careful attention
to the times, rate of speed, and the set of tne current. Failure to make a buoy as
expected leaves no safe alternative but to anchor at once.
It is a useful point to remember that in passing between dangers where there
are no suitable leading marks, as, for instance, between two islands or an island and
the main shore, with dangers extending from both, a mid-channel course may be
steered by the eye alone with great accuracy, as the eye is able to estimate very closely
the position midway between visible objects.
In piloting among coral reefs or banks, a time should be chosen when the sun
will be astern, conning the vessel from aloft or from an elevated position forward.
The line of demarcation between the deep water and the edges of the shoals, which
generally show as green patches, is indicated with surprising clearness. This method
is of frequent application in the numerous passages of the Florida keys.
Changes of course should in general be made by exact amounts, naming the new
course or the amount of the change desired, rather than by ordering the helm to be
put over and then steadying when on the desired heading, with the possibility of the
attention being diverted and so forgetting in the meantime that the ship is still
70 PILOTING.
swinging. The helmsman, knowing just what is desired and the amount of change
to be made, is thus enabled to act more intelligently and to avoid wild steering,
which in narrow channels is a very positive source of danger.
Coast piloting involves the same principles and requires that the ship's positions
be continuously determined or checked as the landmarks are passed. On well-
surveyed coasts there is a great advantage in keeping near the land, thus holding
on to the marks and the soundings, and thereby knowing at all times the position,
rather than keeping offshore and losing the marks, with the necessity of again making
the land from vague positions, and perhaps the added inconvenience of fog or bad
weather, involving a serious loss of time and fuel.
The route should be planned for normal conditions of weather with suitable
variations where necessary in case of fog or bad weather or making points at night,
the courses and distances, in case of regular runs over the same route, being entered
in a notebook for ready reference, as well as laid down on the chart. The danger
circles for either the horizontal or the vertical danger angles should be plotted,
wherever the method can be usefully employed, and the angles marked thereon;
many a mile may thus be saved in rounding dangerous points, with no sacrifice in
safety. Ranges should also be marked in, where useful for positions or for safety,
and also to use in checking the deviation of the compass by comparing, in crossing,
the compass bearing of the range with its magnetic bearing, as given by the chart.
Changes of course will in general be made with mark or object abeam, the posi
tion (a new "departure") being then, as a rule, best and most easily obtained.
In making the land in a fog the sounding machine must be kept going at intervals
of half an hour some hours before it is expected that soundings can be obtained.
Several soundings taken at random will not locate a ship, but on the contrary may
lead to disaster. In using the sounding machine be careful that the man handling
the tube does not invert the tube when taking it from the tube case, as this would
allow water to run toward the closed end of the tube, causing a discoloration of the
coating and thus bring about an incorrect sounding. It is also essential that the
lead be cleanly and freshly armed for each cast. The bottom having been picked up,
a graphic record of the soundings may be laid down in the manner previously described
in paragraph 160 and an approximation made of the position of the ship. Keep a
sharp lookout for any landmarks that might show up during a momentary lifting
of the fog and have keen ears listening for an aerial or submarine fog signal. Having
picked up any such signal, make sure to ascertain exactly what landmark it is.
From now on proceed with caution and determine whether it is better to anchor or
to proceed through the harbor channel in the fog. If, having approached the land
and failed to hear fog signals at the time they were expected to be heard and the
soundings indicate a dangerous proximity to shore, the only safe course is either to
anchor or to stand off. When running slowly in a fog (which caution, as well as
the law, requires that one should do) it must be borne in mind that the relative effect
of current is increased; for instance, the angle of deflection from the course caused
by a cross set is greater at low than at high speed. It is worth remembering that
when in the vicinity of a bold bluff shore vessels are sometimes warned of a too-close
approach by having their own fog signals echoed back from the cliffs ; indeed, from
a knowledge of the velocity of sound it is possible to gain some rough idea of the
distance in such a case. Great caution must be used in approaching a bold coast
in a fog and, unless soundings can be got that will reasonably assure the navigator
of his distance from the coast, the only safe course is to stand off, if the depth of
the water does not permit of anchoring.
The best aids at the disposal of the navigator when running in a fog are the
sounding machine and the hand lead, and the navigator will do well to make great
use of them. Even in clear weather the sounding machine may be a great aid to the
navigator in verifying his position.
In approaching the land and entering harbors, the navigator must bear in mind
that rules of the road in inland waters sometimes differ from those used on the high
sea, and should inform himself of the boundaries of the waters where different rules
of the road obtain.
166. RECORDS. — It will be found a profitable practice to pay careful attention
to the recording of the various matter relating to the piloting of the ship. A notebook
PILOTING.
71
should be kept at hand on deck or on the bridge, in which are to be entered all bearings
or angles taken to fix the position, all changes of course, important soundings, and
any other facts bearing upon the navigation. (This book should be different from
the one in which astronomical sights and offshore navigation are worked.) The
entries, though in memorandum form, should be complete; it should be clear whether
bearings and courses are true, magnetic, or by compass; and it is especially important
that the time and patent log reading should be given for each item recorded. The
value of this book will make itself apparent in various directions; it will afford
accurate data for the writing of the ship's log; it will furnish interesting information
for the next run over the same ground ; it will provide a means by which, if the ship
be shut in by fog, rain, or darkness, or if there be difficulty in recognizing landmarks
ahead, the last accurate fix can be plotted and brought forward; and, finally, if
there should be a mishap, the notebook would furnish evidence as to where the
trouble has been.
The chart on which the work is done should also be made an intelligible record,
and to this end the pencil marks and lines should not be needlessly numerous, heavy,
or, long. In plotting bearings, draw lines only long enough to cover the probable
position. Mark intersections or positions by drawing a small circle around them,
and writing neatly abreast them the time and patent log reading. Indicate the
courses and danger bearings by full lines and mark them appropriately, preferably
giving both magnetic (or true) and compass directions. A great number of lines
extending in every direction may lead to confusion; however remote the chance
may seem, the responsibilities of piloting are too serious to run even a small risk.
Finally, on anchoring, record and plot the position by bearings or angles taken
after coming to; observe that the berth is a safe one, or, if in doubt, send a boat to
sound in the vicinity of the ship to make sure.
CHAPTER V.
THE SAILINGS.
167. In considering a ship's position at sea with reference to any other place,
either one that has been left or one toward which the vessel is bound, five terms are
involved — the Course, the Distance, the Difference of Latitude, the Difference of
Longitude, and the Departure.* The solutions of the various problems that arise
from the mutual relation of these quantities are called Sailings.
168. KINDS OP SAILINGS. — When the only quantities involved are the course,
distance, difference of latitude, and departure, the process is denominated Plane
Sailing. In this method the earth is regarded as a plane, and the operation proceeds
as if the vessel sailed always on a perfectly level surface. When two or more courses
are thus considered, they are combined by the method of Traverse Sailing. It is
evident that the number of miles of latitude and departure can thus be readily
deduced; but, while one mile always equals one minute in difference of latitude, one
mile of departure corresponds to a difference of longitude that will vary with the
latitude in which the vessel is sailing. Plane sailing therefore furnishes no solution
where difference of longitude is considered, and for such solution resort must be had
to one of several methods, which, by reason of their taking account of the spherical
figure of the earth, are called Spherical Sailings.
When a vessel sails on an east or west course along a parallel of latitude, the
method of converting departure into difference of longitude is called Parallel Sailing.
When the course is not east or west, and thus carries the vessel through various
latitudes, the conversion may be made either by Middle Latitude Sailing, in which
it is assumed that the whole run has been made in the mean latitude, or by Mercator
Sailing, in which the principle involved in the construction
'T1 of the Mercator chart (art. 39, Chap. II) is utilized.
Great Circle Sailing deals with the courses and distances
between any two points when the track followed is a great
circle of the terrestrial sphere. A modification of this method
which is adopted under certain circumstances is called Com-
'Dist. posite Sailing.
PLANE SAILING.
169. In Plane Sailing, the curvature of the earth being
neglected, the relation between the elements of the rhumb
track joining any two points may be considered from the
plane right triangle formed by the meridian of the place left,
FlG- s4- the parallel of the place arrived at, and the rhumb line. In
figure 24, Tis the point of departure; T', the point of destination; Tn, the meridian
of departure; T'n, the parallel of destination; and TT', the rhumb line between the
points. Let C represent the course, TfTn; Dist., the distance, TT'; DL, the dif
ference of latitude, Tn; and Dep., the departure, T'n. Then from the triangle
TT'n, we have the following :
n Dei
sin C =
cos C =
tan C =
« For the definition of these terms, see article 6, Chapter I.
72
Dist.'
Dep.
THE SAILINGS.
73
From these equations are derived the following formulae for working the various
problems that may arise in Plane Sailing:
Given.
Required.
Formulae.
Course and distance.
f Difference of latitude.
D L =Dist. cos C.
Dep. =Dist. sin C.
-*nC-j&.
& -£%•
»-.-£b-
Dep. =D L tan C.
»* -£&•
DL -53%.
i-o-jfr
Dep. =Dist. sin.C.
SinC =§§?:•
D I, =Dist. cos C.
Log D L =log Dist. -flog cos C.
Log Dep. =log Dist. -flog sin C.
Log tan C=log Dep. —log D L.
Log Dist. =log Dep. —log sin C.
Log Dist. =log D L -log cos C.
Log Dep. =log D L +log tan C.
Log Dist. =log Dep. -log sin C.
Log D L =log Dep. -log tan C.
Log cos C=log D L —log Dist.
Log Dep. =log Dist. -flog sin C.
Log sin C =log Dep. —log Dist.
Log D L =log Dist.+log cos C.
Difference of latitude
and departure.
Course and difference of
latitude.
Course and departure. . .
Distance and difference
of latitude.
Distance and departure .
f Course
I Distance
fDistance
' Departure
fDistance
(Difference of latitude,
f Course...
i
1 Departure
f Course
J
I Difference of latitude.
170. The solution of the plane right triangle may be accomplished either by
Plane Trigonometry, by Traverse Tables, or by construction. If the former method
is adopted, the logarithms of numbers may be found in Table 42, and of the functions
of angles in Table 44. A more expeditious method is available, however, in the
Traverse Tables, which give by inspection the various solutions. Table 1 contains
values of the various parts for each unit of Dist. from 1 to 300, and for each quar
ter-point (2° 49'), of C; Table 2 contains values for each unit of Dist. from 1 to
600, and for each degree of C. The method of solving by construction consists in
laying down the various given terms by scale upon a chart or plain paper, and
measuring thereon the terms required.
171. Of the various problems that may arise, the first two given in the foregoing
table are of much the most frequent occurrence. In the first, the given quantities
are course and distance, and those to be found are difference of latitude and departure;
this is the case where a navigator, knowing the distance run on a given course, desires
to ascertain the amount made good to north or south and to east or west. In the
second case the conditions are reversed; this arises where the course and distance
between two points are to be obtained from their known difference of latitude and
departure.
EXAMPLE: A ship sails SW. by W., 244 miles. Required the difference of latitude and the departure
made good.
By Computation.
Dist. 244 log 2.33739
C 56° 15' log cos 9. 74474
DL 135.6 log 2.13213
Dist. 244 log 2.*38739
C 56° 15' log sin 9. 91985
Dep. 202.9 log 2.30724
By Inspection.
In Table 1, find the course SW. by W. (5 points); it
occurs at the bottom of the page, therefore take the names
of the columns from the bottom as well; opposite 244 in
the Dist. column will be seen Lat. 135.6 and Dep. 202.9.
74
THE SAILINGS.
EXAMPLE: A ship sails N. 5° E., 188 miles. Required the difference of latitude and the departure.
By Inspection.
Dist. 188 log 2.27416 In Table 2, find the course 5°; it occurs at the top of the
C 5° loer cos 9. 99834 page, therefore take the names of the columns from the
top; opposite 188 in the Dist. column will be seen Lat.
DL 187. 3 log 2. 27250 187.3 and Dep. 16.4.
Dist.
C
Dep.
EXAMPLE : A vessel is bound to a port which is 136 miles to the north and 203 miles to the west of
her position. Required the course and distance.
By Computation.
188 log 2. 27416
5° log cos 9. 99834
187. 3 log
188 log
5° log
16. 4 log
2. 27250
2. 27416
sin 8. 94030
1. 21446
Dep.
DL
By Computation.
log
log
203
136
G (N.) 56° 11' (W.)
203
Dep.
C
Dist.
56° IV
244.3
By Inspection.
2. 30750 Enter Table 1 and turn the pages until a course
2. 13354 is found whereon the numbers 136 and 203 are
found abreast- each other in the columns marked
log tan 0. 17396 respectively Lat. and Dep. This occurs most nearly
— at the course for 5 points, the angle being taken
log 2. 30750 from the bottom, because the appropriate names
log sin 9. 91951 of the columns are found there. The course is
therefore NW. by W. Interpolating for interme-
2. 38799 diate values, ^ the corresponding number in the
Dist. column is about 244.3.
log
EXAMPLE : As a result of a day's run a vessel changes latitude 244 miles to the south and makes a
departure of 171 miles to the east. What is the course and distance made good?
Dep.
C
Dist.
By Computation.
171 log 2. 23300
244 log 2.38739
(S.) 35° 02' (E.) log tan 9. 84561
171 log 2.23300
35° 02' log sin 9. 75895
By Inspection.
Enter Table 2 and the nearest agreement will be
found on course (S.) 35° (E.), the appropriate names
being found at the top of the page. The nearest
corresponding Dist. is 298 miles.
297.9 log
2. 47405
TRAVERSE SAILING.
172. A Traverse is an irregular track made by a ship in sailing on several different
courses, and the method of Traverse Sailing consists in finding the difference of
latitude and departure corresponding to several courses and distances and reducing
all to a single equivalent course and distance. This is done by determining the
distance to north or south and to east or west made good on each course, taking the
algebraic sum of these various differences of latitude and departure and finding the
course and distance corresponding thereto. The work can be most expeditiously
performed by adopting a tabular form for the computation and using the traverse
tables.
EXAMPLE: A ship sails SSE., 15 miles; SE., 34 miles; W. by S., 16 miles; WNW., 39 miles;
S. by E., 40 miles. Required the course and distance made good.
Courses.
Dist.
N.
S.
E.
W.
SSE.
15
13.9
5.7
SE.
34
24.0
24.0
W. by S.
16
3.1
15.7
WNW.
39
14.9
36.0
S. by E.
40
39.2
7.8
14.9
80.2
37.5
*51.7
14.9
37.5
S. by W.
66.8
65.3
14.2
The result of the various courses is, therefore, to carry the vessel S. by W., 66.8
miles from her original position.
THE SAILINGS.
75
PARALLEL SAILING.
173. Thus far the earth has been regarded as an extended plane, and its spherical
figure has not been taken into account; it has thus been impossible to consider one
of the important terms involved — namely, difference of longitude. Parallel Sailing
is the simplest of the various forms of Spherical Sailing, being
the method of interconverting departure and difference of
longitude when the ship sails upon an east or west course,
and therefore remains always on the same parallel of latitude.
In figure 25, T and T' are two places in the same latitude;
P, the adjacent pole; TT', the arc of the parallel of latitude
through the two places; MM', the corresponding arc of the
equator intercepted between their meridians PM and PM':
and TT', the departure on the parallel whose latitude is
TCM=OTC, and whose radius is OT.
Let D.Lo represent the arc of the equator MM', which is
the measure of MPM', the difference of longitude of the me
ridians PM and PM'; R, the equatorial radius of the earth,
CM = CT; r, the radius OT of the parallel TT'; and L, the latitude of that parallel.
Then, since TT' and MM' are similar arcs of two circles, and are therefore
proportional to the radii of the circles, we have:
TT^ = OT. Dep. r
MM' CM; or' D.Lo R.
From the triangle COT, r =
Dep. _R cos L
~T
cos L; hence
; or, D.Lo = Dep. sec. L; or/Dep.=D.Lo cos L.
Thus the relations are expressed between minutes of longitude and miles of
departure.
174. Two cases arise under Parallel Sailing: First, where the difference of
longitude between two places on the same parallel is given, to find the departure;
and, second, where the departure is given, to find the difference of longitude.
In working these problems, the computation can be made by logarithms; but
the traverse tables may more conveniently be employed. Remembering that those
tables are based upon the formulae,
DL = Dist. cos C, and Dist. = DL sec C,
we may substitute for the column marked Lat. the departure, for that marked Dist.
the difference of longitude, and for the courses at top and bottom of the page the
latitude. The tables then become available for making the required conversions.
EXAMPLE: A ship in the latitude of 49° W sails directly east until making good a difference of
longitude of 3° 307. Required the departure.
By Inspection.
Enter Table 2 with the latitude as C and the difference
of longitude as Dist. As the table is calculated only to
single degrees, we must find the numbers in the pages of
49° and 50° and take the mean. Corresponding to Dist.
210 in the former is Lat. 137.8, and in the latter Lat. 135.0.
The mean, which is the required departure, is 136.4.
EXAMPLES A ship in the latitude of 38° sails due west a distance of 215.5 miles. Required the
difference of longitude.
'By Inspection.
L
D.Lo.
By Computation.
49° 30' log cos 9. 81254
log
210'
2. 32222
Dep. 136.4 log 2.13476
L
Dep.
D.Ix>{4
By Computation.
38° log sec 0. 10347
log 2.33345
215.5
273'. 5
°33/.5
log 2.43692
Entering Table 2 with the latitude, 38°, as a course,
corresponding with the number 215.5 in column of Lat.,
is 273.5 in the column of Dist. This is therefore the
required difference of longitude, being equal to 4° 33X.5.
MIDDLE LATITUDE SAILING.
175, When a ship follows a course obliquely across the meridian the latitude is
constantly changing, and the method of converting departure and difference of
longitude by Parallel Sailing, just described, ceases to be applicable.
76
THE SAILINGS.
In figure 26, T is the point of departure; T', the point of destination; P, the
by the arc of the equator, MM', intercepted between their meridians. This corre
sponds to a departure Tn in the latitude of T, and to the smaller departure TX in the
higher latitude of T'; but since the vessel neither makes all of the departure in the
latitude T, nor all of it in the latitude T', the departure actually made in the passage
must have some intermediate value between these extremes. Dividing the total
difference of longitude into a number of equal parts MPmlf m1Pm2, etc., of such small
extent that, for the purposes of conversion, the change of latitude corresponding to
each may be neglected, we nave the total departure made
p up of the sum of a number of small departures, each equal
to the same difference of longitude, but each different from
the other. These will be d^ in the latitude T, d2r2 in
the latitude rlt etc. Hence we have:
1 sec MT+cZ2r2, sec
s, sec m2r2, -fete.
mtmf
FIG. 26.
Now, if LL' be a parallel of latitude lying midway
between Tn and T'%, since there will be as many of the
small parts lying above as below it, and since for moderate
distances the ratio to be employed in the conversion of
departure and difference of longitude may be regarded as
varying directly with the latitude, it may be assumed for
such distances that the sum of all of the different small
departures equals the single departure between the merid
ians measured in the latitude LI/, and therefore that the
departure obtained by the method of plane sailing on any course may be converted
into difference of longitude by multiplying by the secant of the Middle Latitude.
The method of conversion based upon this assumption is denominated Middle
Latitude Sailing, and by reason of its convenience and simplicity is. usually employed
for short distances, such as those covered by a vessel in a day's run.
176. In Middle Latitude Sailing, having found the mean of the latitudes, the
solution is identical with that of Parallel Sailing (art. 173), substituting the Middle
Latitude for the single latitude therein employed.
EXAMPLE: A ship in Lat. 42° 30' N., Long. 58° 51' W., sails SE. by S., 300 miles. Required the
latitude and longitude arrived at.
From Table 1: Course SE. by S., Dist., 300, we find Lat., 249.4 S. (4° 09'.4), Dep., 166.7 E.
Latitude left,
DL,
42° 3(X. 0 N. Latitude left, 42° 30' N.
4 09 . 4 S. Latitude arrived at, 38 21 N.
Latitude arrived at, 38 20 . 6 N.
Mid. latitude,
2)80 51
40 25 N.
Enter Table 2 with the middle latitude, 40°, as a course; the difference of longitude (Dist.) cor
responding to the departure (Lat.) 166.7 is 217.6; entering with 41°, it is 220.9; the mean is 219.2 (3°
Longitude left,
D.Lo.
58° 51/.0 W.
3 39.2E.
Longitude arrived at, 55 11 .8 W.
EXAMPLE: A ship in Lat. 39° 42' S., Long. 3° 31' E., sails S. 42° W., 236 miles. Required the lati
tude and longitude arrived at.
From Table 2: Course, S. 42° W., Dist., 236 miles; we find Lat., 175.4 S. (2° 55'.4), Dep., 157.9 W.
Latitude left, 39° 42'. 0 S. Latitude left, 39° 42' S
DL, 2- 55 .4 S. Latitude arrived at, 42 37 S.
Latitude arrived at, 42 37 .4 S.
2)82 19
Mid. latitude,
41 09 S.
THE SAILINGS.
77
From Table 2: Mid. Lat. (course), 41°, Dep. (Lat.), 157.9; we find D.Lo (Dist.), 209.3 (3C
Longitude left, 3° 31'.0 E.
D.Lo, 3 29.3W.
29/.3).
Longitude arrived at, 0 01 .7 E.
EXAMPLE: A vessel leaves Lat. 49° 57' N., Long. 15° 16' W., and arrives at Lat. 47° 18' N., Long.
20° 107 W. Required the course and distance made good.
Latitude left 49° 57' N. Longitude left, 15° 16' W.
Latitude arrived at, 47 18 N. Longitude arrived at, 20 10 W.
DT / 2° 39'\o "^T / 4° 54'\w
' \ 159'j u.ix), | 294'J '
2)97° 15X X.
Mid. latitude, 48 38 N.
From Table 2: Mid. Lat. (course), 49°, D.Lo (Dist.), 294; we find Dep. (Lat.), 192.9.
From Table 2: DL 159 S., Dep. 192.9 W., we find course S. 51° W., Dist., 251 miles.
177, It may be remarked that the Middle Latitude should not be used when
the latitudes are of opposite name; if of different names and the distance is small,
the departure may be assumed equal to the difference of longitude, since the meridians
are sensibly parallel near the equator; but if the distance is great the two portions
of the track on opposites of the equator must be treated separately.
178. The assumption upon which Middle Latitude sailing is based — that the
conversion may be made as if the whole distance were sailed upon a parallel midway
between the latitudes of departure and destination — while sufficiently accurate for
moderate distances, may be materially in error where the distances are large. In
such case, either the method of Mercator Sailing (art. 179) must be employed, or else
the correction given in the following table should be applied to the mean latitude to
obtain what may be termed the latitude of conversion, being that latitude in which
the required conditions are accurately fulfilled. The table is computed from the
formula:
cos Lr = — .
ra'
where Lc represents the latitude of conversion, and Z and m are respectively the differ
ences of latitude and of meridional parts (art. 40, Chap. II) between the latitudes of
departure and destination. °
Mid.
Lat.
Difference of latitude.
Mid.
Lat.
1°
2°
3°
4°
5°
6°
7°
8°
9°
10'
12° | 14°
16*
18°
20°
0
15
18
21
-86
-67
-54
-85
-67
-54
-84
-66
-53
-83
-65
-52
-81
-63
-51
-79
-61
-49
/
-76
-59
-47
/
-73
-56
-44
/
-69
-53
40
/
-65
-50
-39
-56
-43
-32
-i
ifj
/
-34
-23
-15
t
-21
-12
- 5
- 6
1
7
0
15
18
21
24
30
35
-44
-31
-23
-44
-30
-22
-44
-29
-21
-42
-29
-21
-41
-28
-19
-40
-26
-18
—38
--24
-17
-36
-23
-15
-33
-20
-12
-31
-18
-10
-24
-12
- 5
-17
- 6
2
- 8
1
10
1
11
18
12
21
28
24
30
35
40
45
50
-17
-12
- 8
-16
-11
- 8
-15
-11
- 7
-14
-10
- 6
-13
- 8
- 5
-12
- 7
- 3
-10
- 5
- 1
Q
- 3
1
- 6
- 1
3
- 4
I
6
2
7
12
8
14
20
16
22
28
25
31
38
34
41
49
40
45
50
55
58
60
- 5
- 4
- 3
- 5
2
- 3
- 4
- 3
- 2
— 3
- 1
_ 2
0
1
0
2
3
2
4
5
5
7
8
7
10
11
10
13
14
17
20
22
25
29
32
35
39
43
46
51
55
58
64
69
55
58
60
62
64
66
- 3
2
- 2
- 2
- 1
- 1
- 1
0
0
0
1
2
2
3
4
4
5
6
7
8
9
9
11
12
13
14
16
17
18
20
25
27
30
35
38
42
46
50
55
60
65
71
75
81
89
62
64
66
68
70
72
- 1
- 1
0
0
0
0
1
1
2
2
3
4
5
5
6
7
8
10
10
12
13
g
18
18
20
23
22
25
28
33
37
41
46
51
57
61
67
76
78
87
97
98
109
123
68
70
72
a The statement often made that the latitude of conversion is always greater than the middle latitude is not correct when the
compression of the earth is taken hi to account, as an inspection of the table will show; that statement is based upon an assumption
that the earth is a perfect sphere, and it was upon that assumption that a table which appeared in early editions of this work was
•computed. The value of the compression adopted for this table is «
78
THE SAILINGS.
EXAMPLE: A vessel sails from Lat. 10° 13' S. to Lat. 20° 21/ S., making a departure of 432 milee.
Required the difference of longitude.
Latitude left, 10° 13' S.
Latitude arrived at, 20 21 S.
Mid. latitude,
Correction,
2)30 34
15 17 S.
- 1 05
For Mid. Lat. 15° and Diff. of Lat. 10°. Correction, -65'.
Lc, 14 12 S.
L0 14° 12' log sec .01348
Dep. 432 log 2.63548
D.Lo 445'.6 log 2.64896
MERCATOR SAILING.
179. Mercator Sailing is the method by which values of the various elements
are determined from considering them in the relation in which they are plotted upon
a chart constructed according to the Mercator projection.
180. Upon the Mercator chart (art. 39, Chap. II), the meridians being parallel,
the arc of a parallel of latitude is shown as equal to the corresponding arc of the
equator; the length of every such arc is, therefore, expanded; and, in order that
the rhumb line may appear as a straight line, the meridians are also expanded by
such amount as is necessary to preserve, in any latitude, the proper proportion
existing between a unit of latitude and a unit of longitude. The length of small
portions of the meridian thus increased are called meridional parts (art. 40, Chap. II),
and these, computed for every minute of latitude from 0° to 80°, form the Table of
Meridional Parts (Table 3), by means of which a Mercator chart may be constructed
and all problems of Mercator Sailing may be solved.
In the triangle ABC (fig. 27), the angle ACB is the course, C; the side AC, the
distance, Dist.; the side BC, the difference of latitude, DL; and the side AB, the
departure, Dep. Then corresponding to the^ difference of lati
tude BC in the latitude under consideration, if CE be laid off to
represent the meridional difference of latitude, m, completing the
right triangle CEF, EF will represent the difference of longitude,
D.Lo. The triangle ABC gives the relations involved in Plane
Sailing as previously described; th# triangle CEF affords the
means for the conversion of departure and difference of longi
tude by Mercator Sailing.
181. To find the arc of the expanded meridian intercepted
between any two parallels, or the meridional difference of latitude,
when both places are on the same side of the equator, subtract
the meridional parts of the lesser latitude, as given by Table 3,
from the meridronal parts of the greater; the remainder will be
the meridional difference of latitude ; but if the places are on dif
ferent sides of the equator, the sum of the meridional parts will
be the meridional difference of latitude.
182. To solve the triangle CEF by the traverse tables it is only necessary to
substitute meridional difference for Lat., and difference of longitude for Dep^. Where
long distances are involved, carrying the computation beyond the limits of the
traverse table, as frequently occurs in this method, either of two means may be
adopted: the problems may be worked by trigonometrical formulae, using logarithms
or the given quantities involved may all be reduced by a common divisor until
they fall within the traverse table, and the results, when obtained, correspondingly
increased. The former method is generally preferable, especially when the distances
are quite large and accurate results are sought. The formulae for the various
conversions are as follows:
DL
Dist.
FIG. 27.
tanC =
D.Lo = mtanC; m = D.LocotC.
THE SAILINGS. 79
EXAMPLE: A ship in Lat. 42° 30' N., Long. 58° 51' W., sails SE. by S., 300 miles. Required the
latitude and longitude arrived at.
From Table 1: Course, SE. by S., Dist., 300; we find Lat. 249.4 S. (4° 09' .4).
Latitude left, 42° 3(X.O N. Merid. parts, +2806.4
DL, 4 09 .4 S.
Latitude arrived at, 38 20 .6 N. Merid. parts, -2480.4
m, 326. 0
By Computation.
By Inspection.
m
C
326.0
33° 45'
log
log tan
2. 51322
9. 82489
Enter Table 1, course 3 points;
involved exceed the limits of the
since the quantities
table, divide by 2;
DT x>
/ 217'.8
log
oViroaat /Tat "\ 1 ftl ft finA •— — — — 1 1
;Dep.), 108.9; hence
2. 33811
aoreasi o l-i^ai.), luo.u, nnu o '
^s Z
. -L. Q
\3° 37'.8
D.Lo=217'.8or3037'.8.
Longitude
left, 58° 51'.0 W.
D.Lo,
3 37 .8 E.
Longitude arrived at, 55 13 .2 W.
EXAMPLE: A ship in Lat. 4° 37' S., Long. 21° 05' W., sails N. 14° W., 450 miles. Required the
latitude and longitude arrived at.
From Table 2: Course, (N.) 14° (W.), Dist., 450; we find Lat. 436.6 N. (7° 16'.6).
Latitude left, 4°37/.OS. Merid. parts, +275.4
DL, 7 16 . 6 N.
Latitude arrived at, 2 39 . 6 N. Merid. parts, +159. 0
m, 434. 4
By Computation. By Inspection,
m 434.4 log 2.63789 From Table 2: Course, 14°, m (Lat.), 434.4, we find
C 14° log tan 9. 39677 D.Lo (Dep.) 108'.3 W., or 1° 48'.3.
L08'. 3
48'. 3
r> T J 108'. 3 log 2.03466
-LMXK^r — ' -
Longitude left, 21° 05'. 0 W.
D.Lo, 1 48 . 3 W.
Longitude arrived at, 22 53 . 3 W.
EXAMPLE: Required the course and distance by rhumb line from a point in Lat. 42° 03' N., Long.
70° 04' W., to another in Lat. 36° 59' N., Long. 25° KK W.
Lat. departure, 42° 03' N. Merid. pts., +2770. 1 Long, departure, 70° 04' W.
Lat. destination, 36 59 N. Merid. pts., —2377. 3 Long, destination, 25 10 W.
DL
{ 5° O4'lg
\ 304'/0'
D.Lo 2694
m 392. 8
C (S.) 81° 42' (E.)
DL 304'
771,
log 3.
log 2.
392.8
43040
59417
D.
log sec. .
log 2.
.Lo
84056
48287
/44° 54'\T?
I 2694'r4'
log tan .
83623
Dist. 2106 log 3.32343
The course is therefore S. 81° 42' E., and the distance is 2,106 miles. Since the
figures involved are so large, it is best to employ only the method by computation.
The formula by which the Dist. is obtained comes from Plane Sailing.
GREAT CIRCLE SAILING.
183. The shortest distance between any two points on the earth's surface is
measured by the arc of the great circle which passes through those points; and the
method of sailing in which the arc of a great circle is employed for the track of the
vessel, taking advantage of the fact that it is the shortest route possible, is denomi
nated Great Circle Sailing.
184. It frequently happens when a great circle route is laid down that it is
found to lead across the land, or to carry the vessel into a region of dangerous naviga-
80 THE SAILINGS.
tion or extreme cold which it is expedient to avoid; in such a case a certain parallel
should be fixed upon as a limit of latitude, and a route laid down such that a great
circle is followed as far as the limiting parallel, then the parallel itself, and finally
another great circle to the port of destination. Such a modification of the great
circle method is called Composite Sailing.
185. The rhumb line (art. 6, Chap. I), also called the loxodromic curve, which
cuts all the meridians at the same angle, has been largely, employed as a track by
navigators on account of the ease with which it may be laid down on a Mercator
chart. But as it is a longer line than the great circle between the same points,
intelligent navigators of the present day use the latter wherever practicable. On
the Mercator chart, however, the arc of a great circle joining two points (unless
both are on the equator or both on the same meridian) will not be projected as a
straight line, but as a curve which seems to be longer than the rhumb line; hence
the shortest route appears as a circuitous one, and this is doubtless the reason that
a wider use of the great circle has not been made.
It should be clearly understood that it is the rhumb line which is in fact the
indirect route, and that in following the great circle the vessel is always heading
for her port, exactly as if it were in sight, while on the course which is shown as a
straight line on the Mercator chart the vessel never heads for her port until at the
very end of the voyage. ^
186. The method of great circle sailing is of especial value to steamers, as such
vessels need not, in the choice of a route, have regard for the winds to the same extent
as must a sailing vessel; but even in navigating vessels under sail a knowledge of the
great circle course may prove of great value. For example, suppose a ship to be
bound from Sydney to Valparaiso; the first great circle course is SE. by S., while the
Mercator course is almost due east. The distance is 748 miles shorter by the former
route (if the great circle is followed throughout, though this would lead to a latitude
of 61° S.). With the wind at E. J S. the ship would he nearer to the Mercator course
on the starboard tack, assuming that she sailed within six points of the wind; but
if she took that tack she would be increasing her distance from the port of destination
by 4J miles in every 10 that she sailed; while on the port tack, neading one point
farther from the rhumb, the gain toward the port would be 9J miles out of every 10.
Any course between East and SSW. would be better than the Mercator course; and
if the wind were anything to the eastward of SE. by S., the ship would gain by taking
the port tack in preference to the starboard.
187. As the great circle makes a different angle with each meridian that is
crossed, it becomes necessary to make frequent changes of the ship's course; in
practice, the course is a series of chords joining the various points on the track line.
If, while endeavoring to follow a great circle, the ship is driven from it, as by
unfavorable weather, it will not serve the purpose to return to the old track at
convenience, but it is required that another great circle be laid down, joining the
actual position in which the ship finds herself with the port of destination.
188. The methods of determining the great circle course may be divided generally
into four classes; namely, by Great Circle Sailing Charts, by Computation, by the
methods of the Time Azimuth, and by Graphic Approximations.
189. GREAT CIRCLE SAILING CHARTS. — Of the available methods, that by means
of charts especially constructed for the purpose is considered greatly superior to
all others.
A series of great circle sailing charts covering the navigable waters of the globe
is published by the United States Hydrographic Office. Being on the gnomonic
projection (art. 44, Chap. II), all great circles are represented as straight lines, and
it is only necessary to join any two points by such a line to represent the great circle
track between them. The courses and distance are readily obtainable by a method
explained on the charts. The track may be transferred to a chart on the Mercator
projection by plotting a number of its points by then* coordinates and joining them
with a curved line.
The navigator who contemplates the use of great circle tracks will find it of the
greatest convenience to be provided with these gnomonic charts for the regions which
his vessel is to traverse.
THE SAILINGS. 81
190. BY COMPUTATION. — This method consists in determining a series of points
on the great circle by their coordinates of latitude and longitude, plotting them upon
a Mercator chart, and tracing the curve that
joins them. The first point determined is the
vertex, or point of highest latitude, even when,
as sometimes occurs, it falls without that por
tion of the great circle which joins the points
of departure and destination.
In figure 28, A represents the point of
departure; B, the point of destination; AVB,
the great circle joining them, with its vertex
at V; and P, the pole of the earth.
Let CA = PAB, the initial course ;
CB = PBA, the final course;
LA, Ly, L^the latitudes of the respective points A, V, B=(90°-PA),
(90° -PV), (90°-PB).
Lo^, LoAV, LoBV = the differences of longitude between A and B, A and V, B and V,
respectively, =APB, APV, BPV.
D = the great circle distance between A and B; and
(p = an auxiliary angle introduced for the computation.
We then have:
tan <p=cos LO^B cot LB;
cot 0A=cot LOAB cos (LA + 9>) cosec <p;
cot D =cps CA tan (LA -f- <p) ;
cos Ly = sin CA cos LA ;
cot LoAV = tan CA sin LA.
By these formulae are determined the initial course and the total distance by
great circle; also the latitude of the vertex and its longitude with respect to A. By
interchanging the subscript letters A and B throughout, we should obtain the final
course, and the longitude of the vertex with respect to B; also the same total distance
and latitude of the vertex as before.
In performing this computation, strict regard must be had to the signs of the
quantities. If the points of departure and destination are in different latitudes, the
latitude of one of these points must be regarded as negative with respect to the other,
and they must be marked with opposite signs. Should LoAV or LoBV assume a
negative value, it indicates that the vertex does not lie between A and B, and is to
be laid off accordingly.
To find other points of the great circle, M, N, etc., let their latitudes be repre
sented by LM, LN, etc., and their longitudes from the vertex by Lo^, LOVK, etc.;
then
tan LH = tan Ly cos Lo^; or, cos LoVM = tan LM cot L^;
tan L^ = tan Ly cos Lo^; or, cos LoVN = tan L^ cot Ly;
and so on. By these formulae intervals of longitude from the vertex of 5°, 10°, -or
any amount, may be assumed, and the corresponding latitudes deduced; or any
latitude may be assumed and its corresponding interval of longitude from the
vertex found. Two positions will result from each solution, and the appropriate
ones may be chosen by keeping in mind the signs involved.
EXAMPLE: Given two places, one in Lat. 40° N., Long. 70° W., the other in Lat. 30° S., Long. 10°
W., find the great circle distance between them; also the initial course, and the longitude of equator
crossing.
LA=+40°; LB=-30°; LoAB=60°.
LoAB 60° cos 9. 69897.. cot 9.76144
LB - 30° cot (-) .23856
LA +40° cos 9. 88425 sin 9.80807
g> - 40° 54' tan ( -) 9. 93753.. cosec (-) .18393
(LA+<P) - 0° 54' cos 9. 99995 tan (-) 8. 19616
CA 131° 24' orS.48°36/E cot (— ) 9. 94532 cos (-) 9. 82041 siii 9.87513 tan (-) .05472
D 89° 24' or 5,364 miles cot 8.01657
LT + 54° 56' cos 9. 75938
LoAT - 53° 54' . ., cot (-) 9.86279
82
THE SAILINGS.
The initial course is therefore S. 48° 36' E., and the distance 5,364 nautical
miles. (It may be found that the course by rhumb line is S. 38° 45' E. and the
distance 5,386 miles.) The vertex of the great circle is in Lat. 54° 56' N., and is
53° 54' in longitude from the point A, in a direction away from B; hence it is in
Long. 123° 54' W. To find the longitude of equator crossing let LM = 0°; then in
the equation,
cos LOVM = tan LM cot Lv,
since tan LM equals zero, cos LoVM also equals zero, or the longitude interval from
the vertex is 90°, which is evident from the properties of the great circle: therefore
the longitude of equator crossing is 123° 54' W.— 90° = 33° 54' W.
191. BY TIME AZIMUTH METHODS. — A convenient method of obtaining the initial
and final couises in great circle sailing is afforded by the tables and graphic methods
which are prepared for the solution of the Time Azimuth problem (art. 352, Chap.
XIV). It will be found by comparison that if the latitude of the point of departure
be substituted for the latitude of the observer in that problem, the latitude of desti
nation for the declination of the celestial body, and the longitude interval for the
hour angle, the solution for the initial course will coincide with that for the azimuth;
by interchanging the latitudes of the points of departure and destination the final
course will be similarly obtained. Advantage may thus be taken of the various
methods provided for facilitating the determination of the azimuth to ascertain
the great circle courses from one point to another.
192. BY GRAPHIC APPROXIMATIONS. — Of the numerous methods that fall
within this class only two need be given.
193. By the use of a Terrestrial Globe the two given points between which the
great circle track is required may be joined by the shortest line between them, either by
means of a piece of thread or by moving the globe until they are brought to the fixed
horizon which is usually provided; the coordinates of the various points of the track
are then transferred to the chart. The number of minutes of arc, as measured on
the scale of the horizon between the points, equals the number of miles of distance;
if there be no Horizon, the measure may be made by a thread along the equator or a
meridian.
194. The Method of Professor Airy consists in drawing on the chart a rhumb
line joining the two points, and erecting at its middle point a perpendicular; the
following table should then be entered with the middle latitude as an argument, and
the " corresponding parallel" of latitude taken out (noting whether it is the same
or opposite in name to the middle latitude) ; where this parallel is intersected by the
perpendicular that was drawn will be the center from which may be swept an arc
approximately representing the great circle between the two points.
Middle lati
tude.
Correspond
ing parallel.
Name.
Middle lati
tude.
Correspond
ing parallel.
Name.
O
e /
0
0 /
20
81 13
Opposite.
52
11 33
Opposite.
22
78 16
Do.
54
6 24
Do.
24
74 59
Do.
56
1 13
Do.
26
71 26
Do.
58
4 00
Same.
28
67 38
Do.
60
9 15
Do.
30
63 37
Do.
62
14 32
Do.
32
59 25
Do.
64
19 50
Do.
34
55 05
Do.
66
25 09
Do.
36
50 36
Do.
68
30 30
Do.
38
46 00
Do.
70
35 52
Do.
40
41 18
Do.
72
41 14
Do.
42
36 31
Do.
74
46 37
Do.
44
31 38
Do.
76
52 01
Do.
46
26 42
Do.
78
57 25
Do.
48
21 42
Do.
. 80
62 51
Do.
50
16 39
Do.
THE SAILINGS. 83
COMPOSITE SAILING.
195. It has already been stated that when, for any reason, it is impracticable
or unadvisable to follow the great circle track to its highest latitude, a limiting parallel
is chosen and the route modified accordingly. This method is denominated Composite
Sailing.
196. The shortest track between points where a fixed latitude is not exceeded
is made up as follows :
1. A great circle through the point of departure tangent to the limiting parallel.
2. A course along the parallel.
3. A great circle through the point of destination tangent to the limitingparallel.
The composite track may be determined by Great Circle Sailing Chart, by
Computation, or by Graphic Approximation.
197. On a Great Circle Sailing Chart, draw lines from the points of departure
and destination, respectively, tangent to the limiting parallel; transfer these great
circles to a Mercator chart in the usual manner, by the coordinates of several points,
including in each case the point of tangency to the parallel. Follow the first great
circle to the parallel; then follow the parallel; then the second great circle.
Determine great circle courses and distances from the gnomonic chart as thereon
described; determine the distance along the parallel by Parallel Sailing.
198. By computation, the problem consists in finding the great circles which
pass, respectively, through the points of departure and destination and have their
vertices in the latitude of the limiting parallel. Resuming the designation of terms
already employed (art. 190), we have:
cos LoVA = tan LA cot Lv;
cos LoVB = tan LB cot Lv;
where LoVA and LoVB represent the distances in longitude from A and from B to the
respective points of tangency; other features of each of the great circles may be
determined in the usual manner.
EXAMPLE: A vessel in Lat. 30° S., Long. 18° W., is bound to a point in Lat. 39° S., Long. 145° E.,
and it is decided not to go south of the parallel of 55° S. Find the longitude of reaching that parallel
and the longitude at which it should be left.
L^=30°S.; LB = 39° S.; LV = 55°S.
LoA=lS°W.; LOB = 145° E.
LA 30° tan 9. 76144 LB 39° tan 9. 90837
Lv 55° cot 9.84523 Lv 55° cot 9.84523
Low 66° 09' E. cos 9. 60667 LoVB 55° 27' W. cos 9. 75360
LoA 18 00 W. LoB 145 00 E.
Lov 48 09 E. Lov 89 33 E.
199. A graphic approximation to the composite track may be obtained by drawing
a straight line between the given points on a Mercator chart and erecting at its middle
point a perpendicular, which should be extended until it intersects the limiting
parallel. Then through this intersection and the two points describe the arc of a
circle, and this will approximate to the shortest distance within the assigned limit
of latitude.
200. A terrestrial globe may be employed for the determination of the composite
track; the method of its use will suggest itself.
201. Another approximation is obtained by joining the two points with a single
great circle, and following this to its intersection with the limiting parallel; thence
sailing along the parallel until the great ^ circle is again intersected; then resuming
the circle and following it to the destination.
CHAPTER VI.
DEAD EECKONINO.
202. Dead Reckoning is the process by which the position of a ship at any instant
is found by applying to the last well-determined position the run that has since been
made, using for the purpose the ship's course and the distance indicated by the log.
203. Positions by dead reckoning, also spoken of as positions by account, differ
from those determined by bearings of terrestrial objects or by observations of celestial
bodies in being less exact, as the correctness of dead reckoning depends upon the
accuracy of the estimate of the run, and this is always liable to be at fault to a greater
or less extent. The course made good by a ship may differ from that which it is
believed that she is making good, by reason of imperfect steering, improper allowance
for compass error and leeway, and the effects of unknown currents; the allowed
distance over the ground may be in error on account of inaccurate logging and
unknown currents.
Notwithstanding its recognized defects as compared with the more exact methods,
the dead reckoning is an invaluable aid to the mariner. It affords him a means of
plotting the position of the ship at any desired time between astronomical deter
minations; it also gives him an approximate position at the moment of taking
astronomical observations which is a great convenience in working up those observa
tions; and finally it affords the only available means of determining the location of
a vessel at sea during those periods (which may continue for several days together)
when the weather is such as to render the observation of celestial bodies an impos
sibility.
204. TAKING DEPARTURE. — Before losing sight of the land, and preferably
while objects remain in good view, it is the duty of the navigator to take a departure;
this consists in fixing the position of the ship by the best means available (Chap. IV),
and using this position as the origin for dead reckoning. ^ There are two methods of
reckoning the departure. The first and simpler consists in taking from the chart the
latitude and longitude of the position found, and applying the future run thereto.
The other requires that the bearing and distance of an object of known latitude and
longitude be found; the position of the object then forms the basis of the reckoning,
and the reversed direction of the bearing, with the distance, forms the first course
and distance ; thus it may be considered that the ship starts from the position of the
object and sails to the position where the bearing was taken; the correction for
deviation in such a case should be that due to the heading of the ship when the bearing
was taken. Each time that a new position is determined it is used as a new departure
for the dead reckoning.
This meaning of the term departure should not be confounded with the other,
which refers to tlie distance run toward east or west.
205. METHODS. — The working of dead reckoning merely involves an application
of the methods of Traverse Sailing (art. 172) and Middle Latitude Sailing (art. 175),
as explained in Chapter V.
The various compass courses are set down in a column, and abreast each are
written the errors by reason of which the course steered by compass differs from the
true course made good over the ground; thence the true course made good is deter
mined and recorded; next, the distance is written in, and afterwards, by means of
Tables 1 or 2 (according as the courses are expressed in quarter points or degrees) , the
difference of latitude and departure are found, separate columns being kept for
distances to the north, south, east, and west.
When the position of the ship at any moment is required, add up all the differ
ences of latitude and departure, and write in the column of the greater the difference
between the northing and southing, and the easting and westing. Apply the differ
ence of latitude to the latitude of the last determined position, which will give the
84
DEAD RECKONING.
85
latitude by D. R., and from which may be found the middle latitude; with the
middle latitude find the difference of longitude corresponding to the departure, apply
this to the longitude of last position, and the result will be the longitude by D. R.
The employment of the tabular form will be found to facilitate the work and
guard against errors. It will be a convenience to include in that form columns
showing the hour, together with the reading of the patent log (if used) each time
that the course is changed or the dead reckoning worked up.
The employment of minutes and tenths in dead reckoning rather than minutes
and seconds is recommended.
EXAMPLE: A vessel under sail heading NE. f E. (on which course deviation is
J pt. Easterly) takes departure from Cape Henry lighthouse (see Appendix IV for
position), bearing SSW. J W. per compass, distant 1.4 miles. She then sails on a
series of courses, with errors and distances as indicated below; wind about SE. by E.
Required the position by dead reckoning; also the course and distance made good by
dead reckoning.
Comp. course.
Var.
Dev.
Leeway.
Error.
True course.
Dist.
N.
S.
E.
W.
D. Lo.
NNE. * E.
tw
iE.
iW.
NNE. iE.
1.4
1.3
0.6
NE. | E.
S. by W.
rWi
rw.
rE.
iW.
iW.
NE. iE.
S. f W.
27.6
31.5
18.5
31.2
20.5
4.6
ENE.
W
i E.
rw.
i\v.
NE.byE.iE.
14.2
7.3
12.2
S.iE.
NE.iN.
W.
W.
0
r|.
0
S.iE.
NE. byN.
11.0
87.0
72.3
11.0
0.5
48.3
99.4
42. 2
82.1
4.6
Made good,
NE. | E.
96.5
57.2
77.5
97.0
Point of departure,
Bun,
By D. R.
Latitude.
36° 55'. 6 N.
57.2 N.
37 52.8 N.
Mid. L., 37<
Longitude.
76° 00'. 5 W.
1 37. OE.
74 23. 5 W.
EXAMPLE: A steamer's position by observation at noon, patent log reading 27.3, is Lat. 49° 15' N.,
Long. 7° 32' W. Thence she steers 262° (per compass), the total compass error on that course being
20° W., until 12.30, at which time, patent log reading 33.9, the course is changed to 260° (p. c.), same
error. At 4.12, patent log 80.5, sights are taken from which it is found that the true longitude is 8° 46' W.,
and the compass error 19° W. At 6.15, patent log reading 6.1, a eight is taken from which it is found
that the true latitude is 48° 34' 30" N. At 8 p. m. the patent log reads 27.5. Required the positions by
D. B. at each sight and at 8 o'clock.
Time.
Comp. course.
Error.
True course.
Pat. Log.
Dist.
S.
W.
D. Lo.
Noon.
g
27.3
12.30
262°
20° W.
242°
33.9
6.6
3.1
5.8
4.12
260°
20° W.
240°
80.5
46.6
23.3
40.3
26.4
46.1
70.3
6.15
260°
19° W.
241°
6.1
25.6
12.4
22.4
34.1
8.00
260°
19° W.
241°
27.5
21.4
10.4
18.7
27.9
Latitude.
Byobs.atnoon, 49° 15'.0 N.
Run to 4.12 sight, 26 .4 S.
Mid. L., 49'
By D. R. at 4.12 sight, 48 48 .6 N.
By obs. at 4.12 sight,
Run to 6.15 sight, 12 .4 S.
By D. R. at 6.15 sight, 48 36 .2 N.
Longitude.
7° 32'.0 W.
1 10 .3 W.
8 42 .3 W.
S 46 .0 W.
Mid. L., 49° 34 .1 W.
By obs. at 6.15 sight,
Run to 8 p. m.,
48 34 .5 N.
10 .4 S.
Mid. L., 4S<
9 20 .1 W.
27 .9 W.
By D. R. at 8 p. m., 48 24 .1 N.
9 48 .0 W.
86
DEAD RECKONING.
206. ALLOWANCE FOR CURRENT. — When a vessel is sailing in a known current
whose strength may be estimated with a fair degree of accuracy, a more correct
position may be arrived at by regarding the set and drift of the current as a course and
distance to be regularly taken account of in the dead reckoning.
EXAMPLE: A vessel in the Gulf Stream at a point where the current is estimated to set 48° at the
rate of 1.8 miles an hour, sails 183° (true), making 9.5 knots an hour through the water for 3h 30m. Middle
latitude 35°. Required the course and distance made good.
True course.
Dist.
N.
S.
E.
w.
D. Lo.
Run
Current
Made good
183°
48°
174°
33.3
6.3
29.3
4.2
33.3
4.7
1.7
3.6
29.1
3.0
207. FINDING THE CURRENT. — It is usual, upon obtaining a good position by
observation (as the navigator usually does at noon), to compare that position with
the one obtained by dead reckoning, and to attribute such discrepancy as may be
found to the effects of current. It has already been pointed out that other
causes than the motion of the water tend to make the dead reckoning inaccurate,
so that it must not be assumed that currents proper are thus determined with com
plete correctness.
Current is said to have set and drift, referring respectively to the direction toward
which it is flowing and the velocity with which it moves.
It is evident that, in calculating current by the method of comparing positions
by observation with those by account, the navigator must limit himself to the periods
during which the dead reckoning has been brought forward independently, without
receiving any corrections due to new points of departure. In case it is desired to
find the current covering a period during which fresh departures have been used,
as from noon to noon, find the algebraical sums of all the differences of latitude and
longitude from the table, and apply these to the latitude and longitude of original
departure — that of the preceding noon; this gives the position from the ship's run
proper, and the difference between this and the position by observation gives the set
and drift for the twenty-four hours ; if an allowance has been made for current, as
explained in the preceding article, that must be omitted in bringing up the position
which is to take account of the run only.
208. DAY'S KUN. — It is usual to calculate, each day at noon, the ship's total run
for the preceding twenty-four hours. Having the positions at noon of each day, the
course and distance between them is found as explained in article 175, Chapter V.
The position by observation is used in each case, ii such has been found; otherwise,
the position by dead reckoning.
t
EXAMPLE: At noon, January 22, the position of a vessel by observation was Lat. 35° 107 N., Long.
134° Olx W. During the next 24 hours, the run by account was 60.1 miles north and 153.2 miles east.
At noon, January 23, the position by observation was Lat. 36° 03' N., Long. 131° 14' W. Required
the position by D. R. at the latter time; also the run and current for the 24 hours.
By obs., noon, 22d,
Run,
Latitude.
35° 10<ON.
1 00 .1 N.
. By D. R., noon, 23d, 36 10 .1 N.
Mid. L., 36°
Dep., 153.2 E.
D.Lo., 189.4 E.
Longitude.
134° Ol'.O W.
3 09 .4 E.
130 51 .6 W.
By obs., noon, 23d? 36 03 .0 N. D.Lo., 22.4 W. 131 14 .0 W.
Current,
p.Lo., 22.4 W.j 131 14 .0 W.
JDep., 18.1 W.J 22.4 W.
6 .9 S. Dep., 18.
Current for 24 hours, 6.9 S., 18.1 W.=249°, 19.4 miles.
Current per hour, 249°, 0.8 mile.
Latitude.
Longitude.
By obs.,
By obs.,
noon,
noon,
23d
22d
36°
35
03'. 0
10 .0
N. 1
N.
Mid.
D.Lo
L., 36°
.,167. OB.
131°
134
14
01
'.0
.0
w.
w.
Run
i
0
53 .0
N. j
Dep., 135.1
2
47
.0
E.
Run for 24 hours, 53.0 N., 135.1
E.=6S°,
146 miles.
CHAPTER VII.
DEFINITIONS KELATING- TO NAUTICAL ASTEONOMY,
209. Nautical Astronomy, or Celo- Navigation, has been defined (art. 3, Chap. I)
as that branch of the science of Navigation in which the position of a ship is deter
mined by the aid of celestial objects — the sun, moon, planets, or stars.
210. THE CELESTIAL SPHERE. — An observer upon the surface of the earth
appears to view the heavenly bodies as if they were situated upon the surface of a
vast hollow sphere, of which his eye is the center. In reality we know that this
apparent vault has no existence, and that we can determine only the relative directions
of the heavenly bodies — not their distances from each other or from the observer.
But by adopting an imaginary spherical surface of an infinite radius, the eye of the
observer being at the center, the places of the heavenly bodies can be projected upon
this Celestial Sphere, or Celestial Concave, at points where the lines joining them with
the center intersect the surface of the sphere. Since, however, the center of the earth
should be the point from which all angular distances are measured, the observer,
by transferring himself there, will find projected on the celestial sphere, not only
the heavenly bodies, but the imaginary points and circles of the earth's surface.
The actual position of the observer on the surface will be projected in a point called
the zenith; the meridians, equator, and all other lines and points may also be projected.
211. An observer on the earth's surface is constantly changing his position with
relation to the celestial bodies projected on the sphere, thus giving to the latter an
apparent motion. This is due to three causes: First, the diurnal motion of the earth,
arising from its rotation upon its axis; second, the annual motion of the earth,
arising from its motion about the sun in its orbit; and third, the actual motion of
certain of the celestial bodies themselves. The changes produced by the diurnal
motion are different for observers at different points upon the earth, and therefore
depend upon the latitude and longitude of the observer. But the changes arising
from the other causes named are independent of the observer's position, and may
therefore be considered at any instant in their relation to the center of the earth.
To this end the elements necessary for any calculation are tabulated in the Nautical
Almanac from data based upon laws which have been found by long series of observa
tions to govern the actual and apparent motion of the various bodies.
212. The Zenith of an observer on the earth's surface is the point of the celestial
sphere vertically overhead. The Nadir is the point vertically beneath.
213. The Celestial Horizon is the great circle of the celestial sphere formed by
passing a plane through the center of the earth at right angles to the line which joins
that point with the zenith of the observer. The celestial horizon differs somewhat
from the Visible Horizon, which is that line appearing to an observer at sea to mark
the intersection of earth and sky. This difference arises from two causes: First, the
eye of the observer is always elevated above the sea level, thus permitting him a
range of vision exceeding 90° from the zenith; and second, the observer's position
is on the surface instead of at the center of the earth. These causes give rise, respec
tively, to dip of the horizon and parallax, which will be explained later (Chap. X).
214. In figure 29 the celestial sphere is considered to be projected upon the
celestial horizon, represented by NESW. ; the zenith of the observer is projected at
Z, and that pole of the earth which is elevated above the horizon, assumed for illus
tration to be the north pole, appears at P, the Elevated Pole of the celestial Sphere.
The other pole is not shown in the figure.
87
88
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
215. The Equinoctial, or Celestial Equator, is the great circle formed by extending
the plane of the earth's equator until it intersects the celestial sphere. It is shown
in the figure in the line EQW. The equinoctial intersects the horizon in E and W,
its east and west points.
216. Hour Circles, Declination Circles, or Celestial Meridians are great circles
of the celestial sphere passing through the poles; they are therefore secondary to
the equinoctial, and may be formed by extending the planes of the respective terres
trial meridians until they intersect the celestial sphere. In the figure, PB, PS, PB',
are hour circles, and that one, PS, which contains the zenith and is therefore formed
by the extension of the terrestrial meridian of the observer, intersects the horizon in
N and S, its north and south points.
217. Vertical Circles, or Circles of Altitude, are great circles of the celestial
sphere which pass through the zenith and nadir; they are therefore secondary to
the horizon. In the figure, ZH, WZE, NZS, are projections of such circles, which
being at right angles to the plane of projection, appear as straight lines. The vertical
circle NZS, which passes through the poles, coincides with the meridian of the
observer. The vertical circle WZE, whose plane is at right angles to that of the
meridian, intersects the horizon in its eastern and western points, and, therefore,
at the points of intersection of the equinoc
tial ; this circle is distinguished as the Prime
Vertical.
218. The Declination of any point in
the celestial sphere is its angular distance
from the equinoctial, measured upon the
hour or declination circle which passes
through that point; it is designated as
North or South according to the direction
of the point from the equinoctial ; it is cus
tomary to regard north decimations as
positive ( + ), and south declinations as nega
tive ( — ). In the figure, DM is the declina
tion of the point M. Declination upon the
celestial sphere corresponds with latitude
upon the earth.
219. The Polar Distance of any point
is its angular distance from the pole (gen
erally, the elevated pole of an observer),
measured upon the hour or declination circle
passing through the point; it must therefore
equal 90° minus the declination, if measured from the pole of the same name as the
declination, or 90° plus the declination, if measured from the pole of opposite name.
The polar distance of the point M from the elevated pole P is rM.
220. The Altitude of any point in the celestial sphere is its angular distance
from the horizon, measured upon the vertical circle passing through the point; it
is regarded as positive when the body is on the same side of the horizon as the zenith.
The altitude of the point M is HM.
221. The Zenith Distance of any point is its angular distance from the zenith,
measured upon the vertical circle passing through the point; the zenith distance
of any point which is above the horizon of an observer must therefore equal 90°
minus tne altitude. The zenith distance of M, in the figure, is ZM.
222. The Hour Angle of any point is the angle at the pole between tl^e meridian
of the observer and the hour circle passing through that point; it may also be regarded
as the arc of the equinoctial intercepted between those circles. It is measured
toward the west as a positive direction through the twenty-four hours, or 360 degrees,
which constitute the interval between the successive returns to the meridian, due
to the diurnal rotation of the earth, of any point in the celestial sphere. The hour
angle of M is the angle QPD, or the arc QD.
223. The Azimuth of a point in the celestial sphere is the angle at the zenith
between the meridian of the observer and the vertical circle passing through the
FIG. 29.
DEFINITIONS RELATING TO NAUTICAL ASTKONOMY. 89
point; it may also be regarded as the arc of the horizon intercepted between those
circles. It is measured from either the north or the south point of the horizon
(usually that one of the same name as the elevated pole) to the east or west through
180°, and is named accordingly; as, N. 60° W., or S. 120° W. The azimuth of M is
the angle NZH, or the arc £sH, from the north point, or the angle SZH, or the arc
SH, from the south point of the horizon.
224. The Amplitude of a point is the angle at the zenith between the prime
vertical and the vertical circle of the point; it is measured from the east or the west
point of the horizon through 90°, as W. 30° N. It is closely allied with the azimuth
and may always be deduced therefrom. In the figure, the amplitude of H is the
angle WZH, or the arc WH. The amplitude is only used with reference to points
in the horizon.
225. The Ecliptic is the great circle representing the path in which, by reason
of the annual revolution of the earth, the sun appears to move in the celestial sphere;
the plane of the ecliptic is inclined to that of the equinoctial at an angle of 23^27^',
and this inclination is called the obliquity of the ecliptic. The ecliptic is represented
by the great circle CVT.
226. The Equinoxes are those points at which the ecliptic and the equinoctial
intersect, and wnen the sun occupies either of these positions the days and nights
are of equal length throughout the earth. The Vernal Equinox is that one at wnich
the sun appears to an observer on the earth when passing from southern to northern
decimation, and the Autumnal Equinox that one at which it appears when passing
from northern to southern declination. The Vernal Equinox is also designated as
the First Point of Aries, and is used as an origin for reckoning right ascension; it is
indicated in the figure at V.
227. The Solstitial Points, or Solstices, are points of the ecliptic at a distance
of 90° from the equinoxes, at which the sun attains its highest declination in each
hemisphere. They are called respectively the Summer and the Winter Solstice,
according to the season in which the sun appears to pass these points in its path.
The Summer Solstice is inolicated in the figure at U.
228. The Eight Ascension of a point is the angle at the pole between the hour
circle of the point and that of the First Point of Aries; it may also be regarded as
the arc of the equinoctial intercepted between those circles. It is measured from
the First Point of Aries to the eastward as a positive direction, through twenty-four
hours or 360 degrees. The right ascension of the point M' is VD'.
229. Celestial Latitude is measured to the north or south of the ecliptic upon
great circles secondary thereto. Celestial Longitude is measured upon the ecliptic
From the First Point of Aries as an origin, being regarded as positive to the eastward
throughout 360°.
230. COORDINATES. — In order to define the position of a point in space, a system
of lines, angles, or planes, or a combination of these, is used to refer it to some fixed
line or plane adopted as the primitive; and the lines,
angles, or planes by which it is thus referred are called H
coordinates.
231. In figure 30 is shown a system of rectilinear
coordinates for a plane. A fixed line FE is chosen, and D
in it a definite point C, as the origin. Then the posi
tion of a point A is defined by CB = x, the distance F C x E
from the origin, C, to the foot of a perpendicular let " B
fall from A on FE; and by AB=7/, the length of the
perpendicular. The distance x is called the abscissa I
ana y the ordinate. Assuming two intersecting right FIG. so.
lines FE and HI as standard lines of reference, the
location of the point A is defined by regarding the distances measured to the right
hand of HI and above FE as positive; those to the left hand of HI and below FE
as negative.
An exemplification of this system is found in the chart, on which FE is represented
by the equator, HI by the prime meridian; the coordinates x and y being the longitude
and latitude of the point A.
232. The great circle is to the sphere what the straight line is to the plane;
hence, in order to define the position of a point on the surface of a sphere, some great
90 DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
circle must be selected as the primary, and some particular point of it as the origin.
Thus, in figure 31, which represents the case of a sphere, some fixed great circle,
CBQ, is selected as the axis and called the primary; and a point C is chosen as the
origin. Then to define the position of any point A, the ab
scissa x equals the distance from C to the point B, where
the secondary great circle through A intersects the primary;
the ordinate y equals the distance of A from the primary
measuied on the secondary — that is, x = CE and y = ABC
233. In the case of the earth, the primary selected is
the equator (its plane being perpendicular to the earth's
axis), and upon this are measured the abscissae, while upon
the secondaries to it are measured the ordinates of all
points on the earth's surface. The initial point for refer
ence on the equator is determined by the prime meridian
FIG. si. chosen, West longitudes and North latitudes being called
positive, East longitudes and South latitudes, negative.
234:. In the case of the celestial sphere, there are four systems of coordinates
in use for defining the position of any point; these vary according to the circle
adopted as the primary and the point used as an origin. They are as follows:
1. Altitude and azimuth.
2. Declination and hour angle.
3. Declination and right ascension.
4. Celestial latitude and longitude.
235. In the system of Altitude and Azimuth, the primary circle is the celestial
horizon, the secondaries to which are the vertical circles, or circles of altitude. The
horizon is intersected by the celestial meridian in its northern and southern points,
of which one — usually that adjacent to the elevated pole — is selected as an origin
for reckoning coordinates. The azimuth indicates in which vertical circle the point
to be defined is found, and the altitude gives the position of the point in that circle.
In figure 29 the point M is located, according to this system, by its azimuth NH
and altitude HM.
236. In the system of Declination and Hour Angle, the primary circle is the
equinoctial, the secondaries to which are the circles of declination, or hour circles.
The point of origin is that point of intersection of the equinoctial and celestial
meridian which is above the horizon. The hour angle indicates in which declina
tion circle the point to be defined is found, and the declination gives the position
of the point in that circle. In figure 29 the point M is located, according to this
system, by its hour angle QD and declination DM.
237. In the system of Declination and Right Ascension, the primary and seconda
ries are the same as in the system just described, but the point of origin differs, being
assumed to be at the First Point of Aries, or vernal equinox. The right ascension
indicates in which declination circle the point to be defined may be found, and the
decimation gives the position in that circle. In figure 29 the point M' is located by
VD', the right ascension, and D'M', the declination. It should^be noted that this
system differs from the preceding in that the position of a point is herein referred to
a fixed point in the celestial sphere and is independent of the zenith of the observer
as well as of the position of the earth in its diurnal motion, while, in the system of
declination and hour angle, both of these are factors in determining the coordinates.
238. In the system of Celestial Latitude and Longitude, the primary circle is the
ecliptic; the point of origin, the First Point of Aries. The method of reckoning by
this system, which is of only slight importance in Nautical Astronomy, will appear
from the definitions of celestial latitude and longitude already given (art. 229).
CHAPTER VIII.
INSTEUMENTS EMPLOYED IN NAUTICAL ASTEONOMY.
THE SEXTANT.
239. The sextant is an instrument for measuring the angle between two objects
by bringing into coincidence at the eye of the observer rays of light received directly
from the one and by reflection from the other, the measure being afforded by the
inclination of the reflecting surf aces. By reason of its small dimensions, its accuracy,
and, above all, the fact that it does not require a, permanent or a stable mounting
but is available for use under the conditions existing on shipboard, it is a most
important instrument for the purposes of the navigator. While the sextant is not
capable of the same degree of accuracy as fixed instruments, its measurements are
sufficiently exact for navigation.
240. DESCRIPTION. — A usual form of the sextant is represented in figure 32.
The frame is of brass or some similar alloy. The graduated arc, AA, generally of
silver, is marked in appro
priate divisions; in the nner ii M
sextants, each division rep
resents 10', and the vernier
affords a means of reading
to 10". A wooden handle,
H, is provided for holding
the instrument. The index
mirror, M, and horizon, mir
ror, m, are of plate glass,
and are silvered, though the
upper half of the horizon
glass is left plain to allow
direct rays to pass through
unobstructed. To give
greater distinctness to the
images, a small telescope, E,
is placed in the line of sight ;
it is supported in a ring, K,
which can be moved by a
screw in a direction at right
angles to the plane of the sex
tant, thus shifting the axis
of the telescope, and therefore the plane of reflection; this plane, however, always
remains parallel to that of the instrument, the motion of the telescope being intended
merely to regulate the relative brightness of the direct and reflected image. In the
ring, K, are small screws for the purpose of adjusting the telescope by making its axis
parallel with the plane of the sextant. The vernier is carried on the end of an index
bar pivoted beneath the index mirror, M, and thus travels along the graduated scale,
affording a measure for any change of inclination of the index mirror; a reading glass,
R, attached to the index bar and turning upon a pivot, S, facilitates the reading of
vernier and scale. The index mirror, M, is attached to the head of the index bar, with
its surf ace perpendicular to the plane of the instrument; an adjusting screw is fitted
at the back to permit of adjustment to the perpendicular plane. The fixed glass m,
half silvered and half plain, is called the Jwrizon glass, as it is through this that the
FIG. 32.
92 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
horizon is observed in measuring altitudes of celestial bodies; it is provided with
screws, by which its perpendicularity to the plane of the instrument may be
adjusted. At P and Q are colored glasses of different shades, which may be used
separately or in combination to protect the eye from the intense light of the sun.
In order to observe with accuracy and make the images come precisely in contact, a
tangent screw, B, is fixed to the index, by means of which the latter may be moved
with greater precision than by hand ; but this screw does not act until the index is
fixed by the screw "C at the back of the sextant; when the index is to be moved any
considerable amount, the screw C is loosened; when it is brought near to its
required position the screw must be tightened, and the index may then be moved
gradually by the tangent screw.
Besides the telescope, E, the instrument is usually provided with an inverting
telescope, I, and a tube without glasses, F; also, with a cap carrying colored glasses,
which may be put on the eye end of the telescope, thus dispensing with the necessity
for the use of the colored shades, P and Q, and eliminating any possible errors which
might arise from nonparallelism of their surfaces.
The latest type of sextant furnished to the United States Navy is fitted with an
endless tangent screw which carries a micrometer drum from which the seconds of
arc are read. By pressure of the thumb the tangent screw is released and the index
bar may be moved to any position on the arc by hand, where the tangent screw is
again thrown into gear by releasing the pressure of the thumb. The endless tangent
screw is accomplished by cutting the edge of the arc with the worm teeth into which
the tangent screw gears. At night the reading of this sextant is facilitated by a
small electric light carried on it and supplied by a battery contained in the handle.
241. The vernier is an attachment for facilitating the exact reading of the scale
of a sextant, by which aliquot parts of the smallest divisions of the graduated scale
are measured. The principle of the sextant vernier is identical with that of the
barometer vernier, a complete description of which will be found in article 52, Chapter
II. The arc of a sextant is usually divided into 120 or more parts, each division
representing 1°; each of these degree divisions is further subdivided to an extent
dependent upon the accuracy of reading of which the sextant is capable. In the
instruments tor finer work, the divisions of the scale correspond to 10' each, and the
vernier covers a length corresponding to 59 such divisions, which is subdivided into
60 parts, thus permitting a reading of 10"; all sextants, however, are not so closely
graduated.
Whatever the limits of subdivision, all sextants are fitted with verniers which
contain one more division than the length of scale covered, and in which, therefore,
scale-readings and vernier-readings increase in the same direction — toward the left
hand. To read any sextant, it is merely
necessary to observe the scale division next
F below, or to the right of, the zero of the
£..••-•'** vernier, and to add thereto the angle cor-
,x responding to that division of the vernier
,,-' scale which is most nearly in exact coin
cidence with a division of the instrument
1 ' scale.
242. OPTICAL PRINCIPLE. — When a
ray of .light is reflected from a plane surface,
the angle of incidence is equal to the angle
^j) of reflection. From this it may be proved
Flo 33 that when a ray of light undergoes two
reflections in the same plane the angle be
tween its first and its last direction is equal to twice the inclination of the reflecting
surfaces. Upon this fact the construction of the sextant is based.
In figure 33, let B and C represent respectively the index mirror and horizon
mirror of a sextant; draw EF perpendicular to B, and CF perpendicular to C; then
the angle CFB represents the inclination of the two mirrors. Suppose a ray to pro
ceed from A and undergo reflection at B and at C, its last direction being CD; then
ADC is the angle between its first and last directions, and we desire to prove that
ADC = 2 CFB.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 93
From the equality of the angles of incidence and reflection:
ABE = EEC, and ABC = 2 EEC;
BCF = FCD, and BCD = 2 BCF.
From Geometry:
ADC = ABC - BCD = 2 (EEC - BCF) = 2 CFB,
which is the relation that was to be proved.
243. In the sextant, since the index mirror is immovably attached to the index
arm, which also carries the vernier, it follows that no change can occur in the inclina
tion between the index mirror and the horizon mirror, excepting such as is registered
by the travel of the vernier upon the scale.
If, when the index mirror is so placed that it is nearly parallel with the horizon
mirror, an observer direct the telescope toward some well-defined object, there will
be seen in the field of view two separate images of the object; and if the inclination
of the index mirror be slightly changed by moving the index bar, it will be seen that
while one of the images remains fixed the^other moves. The fixed image is the direct
one seen through the unsilvered part of the horizon glass, while the movable image
is due to rays reflected by the index and horizon mirrors. When the two images
coincide these mirrors must be parallel (assuming that the object is sufficiently distant
to disregard the space which separates the mirrors; in this position of the index
mirror the vernier indicates the true zero of the scale. If, however, instead of
observing a single object, the instrument is so placed that the direct ray from one
object appears in coincidence with the reflected ray of a second object, then the true
angle between the objects will be twice the angle of inclination between the mirrors,
or twice the angle measured by the vernier from the true zero of the scale. To avoid
the necessity of doubling the angle on the scale, the latter is so marked that each
half degree appears as a whole degree, whence its indications give the whole angle
directly.
244. ADJUSTMENTS OF THE SEXTANT. — The theory of the sextant requires that,
for accurate indications, the following conditions be fulfilled:
(a) The two surfaces of each mirror and shade glass must be parallel planes.
(6) The graduated arc or limb must be a plane, and its graduations, as well as
those of the vernier, must be exact.
(c) The axis must be at the center of the limb, and perpendicular to the plane
thereof.
(d) The index and horizon glasses must be perpendicular, and the line of sight
parallel to the plane of the limb.
Of these, only the last named ordinarily require the attention of the navigator
who is to make use of the sextant ; the others, which may be called the permanent
adjustments, should be made before the instrument leaves the hands of the maker,
and with careful use will never be deranged.
245. The Adjustment of the Index Mirror consists in making the reflecting
surface of this mirror truly perpendicular to the plane of the sextant. In order to
test this, set the index near the middle of the arc, then, placing the eye very nearly
in the plane of the sextant and close to the index mirror, observe whether the direct
image of the arc and its image reflected from the mirror appear to form one continuous
arc ; if so, the glass is perpendicular to the plane of the sextant ; if the reflected image
appears to droop from the arc seen directly, the glass leans backward; if it seems to
rise, the glass leans forward. The adjustment is made by the screws at the back of
the mirror.
246. The Adjustment of the Horizon Mirror consists hi making the reflecting
surface of this mirror perpendicular to the plane of the sextant. The index mirror
having been adjusted, if, in revolving it by means of the index arm, there is found
one position in which it is par ah1 el to the horizon glass, then the latter must also be
perpendicular to the plane of the sextant. In order to test this, put in the telescope
and direct it toward a star; move the index until the reflected image appears to pass
the direct image; if one passes directly over the other the mirrors must be parallel;
94 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
if one passes on either side of the other the horizon glass needs adjustment, which is
accomplished by means of the screws attached.
The sea horizon may also be used for making this adjustment. Hold the sextant
vertically and bring the direct and the reflected images of the horizon line into coin
cidence; then incline the sextant until its plane makes but a small angle with the
horizon; if the images still coincide the glasses are parallel; if not, the horizon glass
needs adjustment.
247. The Adjustment of the Telescope must be so made that, in measuring
angular distances, the line of sight, or axis of the telescope, shall be parallel to the
plane of the instrument, as a deviation in that respect, in measuring large angles,
will occasion a considerable error. To avoid such error, a telescope is employed in
which are placed two wires, parallel to each other and equidistant from the center
of the telescope; by means of these wires the adjustment may be made. Screw on
the telescope, and turn the tube containing the eyeglass till the wires are parallel
to the plane of the instrument; then select two clearly defined objects whose angular
distance must be not less than 90°, because an error is more easily discovered when
the angle is great; bring the reflected image of one object into exact coincidence
with the direct image of the other at the inner wire; then, by altering slightly the
position of the instrument, make the objects appear on the other wire; if the contact
still remains perfect, the axis of the telescope is in its right situation; but if the two
objects appear to separate or lap over at the outer wire the telescope is not parallel,
and it must be rectified by turning one of the two screws of the ring into which the
telescope is screwed, having previously unturned the other screw; by repeating this
operation a few times the contact will be precisely the same at both wires, and the
axis of the telescope will be parallel to the plane of the instrument.
Another method of making this adjustment is to place the sextant upon a table
in a horizontal position, look along the plane of the limb, and make a mark upon a
wall, or other vertical surface, at a distance of about 20 feet; draw another mark
above the first at a distance equal to the height of the axis of the telescope above
the plane of the limb; then so adjust the telescope that the upper mark, as viewed
through the telescope, falls midway between the wires. Some sextants are accom
panied by small sights whose height is exactly equal to the distance between the
telescope and the plane of the limb ; by the use of these, the necessity for employing
the second mark is avoided and the adjustment can be very accurately made.
248. The errors which arise from defects in what have been denominated the
permanent adjustments of the sextant may be divided into three classes, namely:
Errors due to faulty centering of the axis, called eccentricity; errors of graduation;
and errors arising from lack of parallelism of surfaces in index mirror and in shade
glasses.
The errors due to eccentricity and faulty graduation are constant for the same
angle, and should be determined once for all at some place where proper facilities
for doing the work are at hand; these errors can only be ascertained by measuring
known angles with the sextant. If angles of 10°, 20°, 30°, 40°, etc., are first laid
off with a theodolite or similar instrument and then measured by the sextant, a
table of errors of the sextant due to eccentricity and faulty graduation may be made,
and the error at any intermediate angle found by interpolation; this table will
include the error of graduation of the theodolite and also the error due to inaccurate
reading of the sextant, but such errors are small. Another method for determining
the combined errors of eccentricity and graduation is by measuring the angular
distance between stars and comparing the observed and the computed arc between
them, but this process is liable to inaccuracies by reason of the uncertainty of allow
ances for atmospheric refraction.
Errors of graduation, when large, may be detected by "stepping off" distances
on the graduated arc with the vernier ; place the zero of the vernier in exact coinci
dence with a division of the arc, and observe whether the filial division of the vernier
also coincides with a division of the arc; this should be tried at numerous positions
of the graduated limb, and the agreement ought to be perfect in every case.
The error due to a prismatic index mirror may be found by measuring a certain
unchangeable angle, then taking out the glass and turning the upper edge down,
and measuring the angle again; half the difference of these two measures will be
the error at that angle due to the mirror. From a number of measures of angles
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 95
in this manner, a table similar to the one for eccentricity and faulty graduation can
be made ; or the two tables may be combined. When possible to avoid it, however,
no sextant should be used in which there is an index mirror which produces a greater
error than that due to the probable error of reading the scale. Mirrors having a
greater angle than 2" between their faces are rejected for use in the United States
Navy. Index mirrors may be roughly tested by noting if there is an elongated
image of a well-defined point at large angles.
Since the error due to a prismatic horizon mirror is included in the index cor
rection (art. 249), and consequently applied alike to all angles, it may be neglected.
Errors due to prismatic shade glasses can be determined by measuring angles
with and without the shade glasses and noting the difference. They may also be
determined, where the glasses are so arranged that they can be turned through an
angle of 180°, by measuring the angle first with the glass in its usual position and
then reversed, and taking the mean of the two as the true measure.
249. INDEX ERROR. — The Index Error of a sextant is the error of its indications
due to the fact that when the index and horizon mirrors are parallel the zero of the
vernier does not coincide with the zero of the scale. Having made the adjustments
of the index and horizon mirrors and of the telescope, as previously described, it is
necessary to find that point of the arc at which the zero of the vernier falls when the
two mirrors are parallel, for all angles measured by the sextant are reckoned from
that point. If this point is to the left of the zero of the limb, all readings will be
too great; if to the right of the zero, all readings will be too small.
If desirable that the reading should be zero when the mirrors are parallel, place
the zero of the vernier on zero of the arc; then, by means of the adjusting screws of
the horizon glass, move that glass until the direct and reflected images of the same
object coincide, after which the perpendicularity of the horizon glass should again be
verified, as it may have been deranged by the operation. This adjustment is not
essential, since the correction may readily be determined and applied to the reading.
In certain sextant work, however, such as surveying, it will be very convenient to
be relieved of the necessity of correcting each angle observed. The sextant should
never be relied upon for maintaining a constant index correction, and the error
should be ascertained frequently. It is a good practice to verify the correction each
time a sight is taken.
250. The Index Correction may be found (a) by a star, (6) by the sea horizon,
and (c) by the sun.
(a) Bring the direct and reflected images of a star into coincidence, and read off
the arc. The index correction is numerically equal to this reading, and is positive
or negative according as the reading is on the right or left of the zero.
(6) The same method may be employed, substituting for a star the sea horizon,
though this will be found somewhat less accurate.
(c) Measure the apparent diameter of the sun by first bringing the upper limb
of the reflected image to touch the lower limb of the direct image, and then Winging
the lower limb of the reflected image to touch the upper limb of the direct image.
Denote the readings in the two cases by r and rr ; then, if S = apparent diameter
of the sun, and II = the reading of the sextant when the two images are in coincidence,
we have:
r =
r'=R-S,
As R represents the error, the correction will be — R. Hence the rule: Mark the
readings when on the arc with the negative sign; when off, with the positive sign;
then the index correction is one-half the algebraic sum of the two readings.
EXAMPLE : The sun's diameter is measured for index correction as follows : On
the arc, 31' 20"; off the arc, 33' 10". Required the correction.
On the arc, -31' 20"
Off the arc, +33 10
2^+1 50
T C... + 0 RR
96 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
251. From the equations previously given, it is seen that:
S-* (r-rO;
hence, if the observations are correct, it will be found that the sun's semidiameter,
as given in the Nautical Almanac for the day of observation, is equal to one-half the
algebraic difference of the readings. If required to obtain the index correction with
great precision, several observations should be taken and the mean used, the accuracy
being verified by comparing the tabulated with the observed semidiameter. If the
sun is low, the horizontal semidiameter should be observed, to prevent the error that
may arise from unequal refraction.
252. USE OP THE SEXTANT. — To measure the angle between any two visible
objects, point the telescope toward the lower one, if one is above the other, or toward
the left-hand one, if they are in nearly the same horizontal plane. Keep this object
in direct view through the unsilvered part of the horizon glass, and move the index
arm until the image of the other object is seen by a double reflection from the index
mirror and the silvered portion of the horizon glass. Having gotten the direct
image of one object into nearly exact contact with the reflected image of the other,
clamp the index arm and, by means of the tangent screw, complete the adjustment
so that the contact may be perfect; then read the limb.
In measuring the altitude of a celestial body above the sea horizon, it is necessary
that the angle shall be measured to that point of the horizon which lies vertically
beneath the object. To determine this point, the observer should move the instru
ment slightly to the right and left of the vertical, swinging it about the line of sight
as^an axis, taking care to keep the object in the middle of the field of view. The
object will appear to describe the arc of a circle, and the lowest point of this arc
marks the true vertical.
The shade glasses should be employed as may be necessary to protect the eye
when observing objects of dazzling brightness, such as the sun, or the horizon when
the sun is reflected from it at a low altitude. Care must be taken that the images
are not too bright or the eye will be so affected as to interfere with the accuracy of
the observations.
253. CHOICE OF SEXTANTS. — The choice of a sextant should be governed by the
kind of work which is required to be done. In rough work, such as surveying, where
angles need only be measured to the nearest 30" the radius maybe as small as 6 inches,
which will permit easy reading, and the instrument can be correspondingly lightened.
Where readings to 10" are desired, as in nice astronomical work, the radius should be
about 7J inches, and the instrument, to be strongly built, should weigh about 3J
pounds.
The parts of an instrument should move freely, without binding or gritting. The
eyepieces should move easily in the telescope tubes ; the bracket for carrying the tele
scope should be made very strong. It is frequently found that the parallelism of
the line of sight is destroyed in focusing the eyepiece, either on account of the loose
ness of the fit or because of the telescope bracket being weak. The vernier should
lie close to the limbs to prevent parallax in reading. If it is either too loose or too
tight at either extremity of its travel, it may indicate that the pivot is not perpendicu
lar. The balls of the tangent screw should fit snugly in their sockets, so that there
may be no lost motion.
Where possible, the sextant should always be submitted to expert examination
and test as to the accuracy of its permanent adjustments before acceptance by the
navigator.
254. RESILVERING MIRRORS. — Occasion may sometimes arise for resilvering the
mirrors of a sextant, as they are always liable to be damaged by dampness or other
causes. For this purpose some clean tin foil and mercury are required. Upon a
piece of glass about 4 inches square lay a piece of tin foil whose dimensions exceed by
about a quarter of an inch in each direction those of the glass to be silvered; smooth
put the foil carefully by rubbing; put a small drop of mercury on the foil and spread
it with the finger over the entire surface, being careful that none shall find its waj
under the foil; then put on a few more drops of mercury until the whole surface is
fluid. The glass which is to be silvered having been carefully cleaned, it should be
laid upon a piece of tissue paper whose edge just covers the edge of the foil and
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 97
transferred carefully from the paper to the tin foil, a gentle pressure being kept upon
the glass to avoid the formation of bubbles; finally, place the mirror face downward
and leave it in an inclined position to allow the surplus mercury to flow off, the latter
operation being hastened by a strip of tin foil at its lower edge. After five or six
hours the tin foil around the edges may be removed, and the next day a coat of
varnish made from spirits of wine and red sealing wax should be applied. For a
horizon mirror care must be taken to avoid silvering the plain half. The mercury
drawn from the foil should not be placed with clean mercury with a view to use in the
artificial horizon or the whole will be spoiled.
255. OCTANTS AND QUIXTANTS. — Properly speaking, a sextant is an instrument
whose arc covers one-sixth of a complete circle, and which is therefore capable of
measuring an angle of 120°. Other instruments are made which are identical in
principle with the sextant as heretofore described, and which differ from that instru
ment only in the length of the arc. These are the octant, an eighth of a circle, by
which angles may be measured to 90°, and the quintant, a fifth of a circle, whicn
measures angles up to 144°. The distinction between these instruments is not
always carefully made, and in such matters as have been touched upon in the fore
going articles the sextant may be regarded as the type of all kindred reflecting
instruments.
THE ARTIFICIAL HORIZON.
256. The Artificial Horizon is a small, rectangular, shallow basin of mercury,
over which, to protect the mercury from agitation by the wind, is placed a roof
consisting of two plates of glass at right angles to each other. The mercury affords
a perfectly horizontal surface which is at the same time an excellent mirror. The
different parts of an artificial horizon are furnished in
a compact form, a metal bottle being provided for
containing the mercury when not in use, together
with a suitable funnel for pouring.
If MN, in figure 34, is the horizontal surface of
the mercury; S'B a ray of light from a celestial
object, incident to the surface at B ; BA the reflected
ray; then an observer at A will receive the ray BA
as if it proceeded from a point S", whose angular
depression, MBS", below the horizontal plane is
equal to the altitude, MBS', of the object above
that plane. If, then, SA is a direct ray from the
object parallel to S'B, an'observer at A can measure
with the sextant the angle SAS" = S'BS" = 2 S'BM, by
bringing the image of the object reflected by the
index mirror into coincidence with the image S* re
flected by the mercury and seen through the horizon
glass. The instrumental measure, corrected for in
dex error, will be double the apparent altitude of the FIG. 34.
body.
The sun's altitude will be measured by bringing the lower limb of one image to
touch the upper limb of the other. Half the corrected instrumental reading wiU be
the apparent altitude of the sun's lower or upper limb, according as the lower or upper
limb of the reflected image was the one employed in the observation.
In observations of the sun with the artificial horizon, the eye is protected by a
single dark glass over the eyepiece of the telescope through which direct and reflected
rays must pass alike, thereby avoiding the errors that might possibly arise from a
difference in the separate shade glasses attached to the frame of the sextant.
The glasses in the roof over the mercury should be made of plate glass, with
perfectly parallel faces. If they are at all prismatic, the observed altitude will be
erroneous. The error may be removed by observing a second altitude with the roof
reversed, and, in general, by taking one-half of a set of observations with the roof in
one position and the other half with the roof reversed. On the rare occasions when
the atmosphere is so calm that the unsheltered mercury will remain undisturbed,
most satisfactory observations may be made by leaving off the roof.
61828°—
98 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
257. In setting up an artificial horizon, care should be taken that the basin is
free from dust and other foreign matter, as small particles floating upon the surface
of the mercury interfere with a perfect reflection. The basin should be so placed
that its longer edge lies in the direction in which the observed body will bear at the
middle of the observations. The spot selected for taking the sights should be as
free as possible from causes which will produce vibration of the mercury, and pre
cautions should be taken to shelter the horizon from the wind, as the mere placing
of the roof will not ordinarily be sufficient to accomplish this. Embedding the roof
in earth serves to keep out the wind, while setting the whole horizon upon a thick
towel or a piece of such material as heavy felt usually affords ample protection from
wind, tends to reduce the vibrations from mechanical shocks, and also aids in keeping
out the moisture from the ground. In damp climates the roof should be kept dry
by wiping, or the moisture deposited from the inclosed air will form a cloud upon
the glass.
Molasses, oil, or other viscous fluid may, when necessary, be employed as a
substitute for mercury.
258. Owing to the perfection of manufacture that is required to insure accuracy
of results with the artificial horizon, navigators are advised to accept only such
instrument as has satisfactorily stood the necessary tests to prove the correctness of
its adjustment as regards the glasses of the roof.
THE CHRONOMETER.
259. The Chronometer is simply ^ a correct time measurer, differing from an
ordinary watch in having the force of its mainspring rendered uniform by means of
a variable lever. Owing to the fact^that on a sea voyage a chronometer is exposed
to many changes of temperature, it is furnished with an expansion balance, formed
of a combination of metals of different expansive qualities, which produces the
required compensation. In order that its working may not be deranged by the
motion of the ship in a seaway, the instrument is carried in gimbals.
As the regularity of the chronometer is essential for the correct determination
of a ship's position, it is of the greatest importance that every precaution be taken
to insure the accuracy of its indications. There is no more certain way of doing
this than to provide a vessel with several of these instruments — preferably not less
than three — in order that if an irregularity develop in one, the fact may be revealed
by the others.
260. CARE OF CHRONOMETERS ON SHIPBOARD. — The box in which the chro
nometers are kept should have a permanent place as near as practicable to the center
of motion of the ship, and where it will be free from excessive shocks and jars, such
as those that arise from the engines or from the firing of heavy guns; the location
should be one free from sudden and extreme changes of temperature, and as far
removed as possible from masses of vertical iron. The box should contain a separate
compartment for each chronometer, and each compartment should be lined with
baize cloth padded with curled hair, for the double purpose of reducing shocks and
equalizing the temperature within. An outer cover of baize cloth should be pro
vided for the box, and this should be changed or dried out frequently in damp
weather. The chronometers should all be placed with the XII mark in the same
position.
For transportation for short distances by hand, an instrument should be rigidly
clamped in its gimbals, for if left free to swing, its performance may be deranged by
the violent oscillations that are imparted to it.
For transportation for a considerable distance, as by express, the chronometer
should be allowed to run down, and should then be dismounted and the balance
corked.
261. Since it is not possible to make a perfect instrument which will be unin
fluenced by the disturbing causes incident to a sea voyage, it becomes the duty of
the navigator to determine the error and to keep watch upon the variable rate of the
chronometer.
The error of the chronometer is the difference between the time indicated and the
standard time to which it is referred — usually Greenwich mean time.
The amount the chronometer gains or loses daily is the daily rate.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
99
The indications of a chronometer at any given instant require a correction for
the accumulated error to that instant; and this can be found if the error at any
given time, together with the daily rate, are known.
262. WINDING. — Chronometers are ordinarily constructed to run for 56 hours
without rewinding, and an indicator on the face always shows how many hours
have elapsed since the last winding. To insure a uniform rate, they must be wound
regularly every day, and, in order to avoid the serious consequences of their running
down, the navigator should take some means to guard against neglecting this duty
through a fault of memory. To wind, turn the chronometer gently on its side,
enter the key in its hole and push it home, steadying the instrument with the hand,
and wind to^the left, the last half turn being made so as to bring up gently against
the stop. After winding, cover the keyhole and return the instrument to its natural
position. Chronometers should always be wound in the same order to prevent
omissions, and the precaution taken to inspect the indicators, as a further assurance
of the proper performance of the operation.
After winding each day, the comparisons should be made, and, with the readings
of the maximum-and-minimum thermometer and other necessary data, recorded in
a book kept for the purpose.
The maximum-and-mininium thermometer is one so arranged that its highest
and lowest readings are marked by small steel indices that remain in place until
reset. Every chronometer box should be provided with such an instrument, as a
knowledge of the temperature to which chronometers have been subjected is essential
in any analysis of the rate. To draw down the indices for the purpose of resetting,
a magnet is used. This magnet should be kept at all times at a distance from the
chronometers. «
263. COMPARISON OF CHRONOMETERS.— The instrument ^believed to be the best
is regarded as the Standard, and each other is compared with it. It is usual to desig
nate the Standard as A, and the others as B, C, etc. Chronometers are made to
beat half seconds, and any two may be compared by following the beat of one with
the ear and of the other with the eye.
To make a comparison, say of A and B, open the boxes of these two instruments
and close all others. Get the cadence and, commencing when A has just completed
the beat of some even 5-second division of the dial, count " h^lf -one-half- two-half-
three-half -four-half -five/' glancing at B in time to note the position of its second hand
at the last count; the seconds indicated by A will be five greater than the number
at the beginning of the count. The hours and minutes are also recorded for each
chronometer, and the subtraction made. A good check upon the accuracy is afforded
by repeating the operation, taking the tick from B.
Where necessary for exact work, it is possible to estimate the fraction between
beats, and thus make the comparison to tenths of a second; but the nearest half
second is sufficiently exact for the purposes of ordinary navigation at sea.
264. The following form represents a convenient method of recording com
parisons :
STAND. A, No. 777.
CHRO. B, No. 1509.
CHRO. C, No. 1802.
Designation of
Chro. B
with
9f\ riiff
Chro. C
with
2d rliff
rherm
L
T>ftr
PomarVe
comparisons.
Stand. A.
Stand. A.
Max.
Min.
Air.
January
1
Stand. A.
BandC.
h. m. s.
1 13 40
1 12,21.5
s.
h. m. s,
1 14 20
2 04 11
8.
|
63
59
60
30.07
Found errors
by time-
hall
Difference.
1 18.5
-
11 10 09
-
2
Stand. A.
BandC.
1 16 30
1 15 10
1 17 00
2 06 51. 5
64
58
57
30.12
Left New
York for
Difference.
1 20
+ 1.5
11 10 08. 5
-0.5
P. R.
100 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
265. The second difference in the form is the difference between the comparisons
of the same instruments for two successive days. When a vessel is equipped with
only one chronometer there is nothing to indicate any irregularity that it may develop
at sea — and even the best instruments may undergo changes from no apparent cause.
When there are two chronometers, the second difference, which is equal to the algebraic
difference between their daily rates, remains uniform as long as the rates remain
uniform, but changes if one of the rates undergoes a change; in such a case, there is
no mefcns of knowing which chronometer has departed from its expected performance,
and the navigator must proceed with caution, giving due faith to the indications of
each. If, however, there are three chronometers, an irregularity on the part of one
is at once located by a comparison of the second differences. Thus, if the predicted
rates of the chronometers were such as to give for the second difference of A — B, +
1s. 5, and of A — C, — 0s. 5, suppose on a certain day those differences were + 4s. 5 and — 0s. 5,
respectively; it would at once be suspected that the irregularity was in B, and that
that chronometer had lost 3s on its normal rate during the preceding day. Suppose,
however, the second differences were + 48.5 and -f 2S.5; it would then be apparent
that A had gained 3s.
266. TEMPERATURE CURVES. — Notwithstanding the care taken to eliminate the
effect of a change of temperature upon the rate of a chronometer, it is rare that an
absolutely perfect compensation is attained, and it may therefore be assumed that the
rates of all chronometers vary somewhat with the temperature. Where the voyage
of a vessel is a long one and marked changes of climate are encountered, the accu
mulated error from the use of an incorrect rate may be very material, amounting to
several minutes' difference of longitude. Careful navigators will therefore take every
means to guard against such an error. By the employment of a temperature curve in
connection with the chronometer rate the most satisfactory results are arrived at.
267. There should be furnished with each chronometer a statement showing
its daily rate under various conditions of temperature; and this may be supplemented
by the observations of the navigator during the tune that the chronometer remains
on board ship. With all available data a temperature curve should be constructed
which will indicate graphically the performance of the instrument. It is most con
venient to employ for this purpose a piece of " profile paper," on which parallel lines
are ruled at equal intervals at right angles to each other. Let each horizontal line
represent, say, a degree of temperature, numbered at the left edge, from the bottom
up ; draw a vertical line in red ink to represent the zero rate, ana let all rates to the
right be plus, or gaining, and those to the left minus, or losing; let the intervals
between vertical lines represent intervals of rate (as one- tenth of a second) numbered
at the top from the zero rate; then on this scale plot the rate corresponding to each
temperature; when there are several observations covering one height of the ther
mometer, the mean may be used. Through all the plotted points draw a fair curve,
and the intersection of this curve with each temperature line gives the mean rate
at that temperature. The mean temperature given by the maximum and minimum
thermometer shows the rate to be used on any day.
268. HACK OR COMPARING WATCH. — In order to avoid derangement, the chro
nometers should never be removed from the permanent box in which they are kept
on shipboard. When it is desired to mark a certain instant of time, as for an astro
nomical observation or for obtaining the chronometer error by signal, the time is
marked by a "hack" (an inferior chronometer used for this purpose only), or by a
comparing watch. Careful comparisons are taken — preferably both before and
afterwards — and the chronometer time at the required instant is thus deduced. The
correction represented by the chronometer time minus the watch time (twelve hours
being added to the former when necessary to make the subtraction possible) is referred
to asC-W.
Suppose, for example, the chronometer and watch are compared and their
indications are as follows :
Chro. t., 5h 27m 30"
W. T., -2 36 45.5
C-W, 2 50 44.5
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRO>CMY.
101
If then a sight is taken when the watch shows 3h Olra, 27* 5, we
W. T., 3h Olm 278.5
C-W, +2 50 44.5
Chro. t., 5 52 12.0
It may occur that the values of C — W, as obtained from comparisons before and
after marking the desired time, will vary; in that case the value to be used will be
the mean of the two, if the tune marked is about midway between comparisons, but
if much nearer to one comparison than the other, allowance should be made accord
ingly-
Thus suppose, in the case previously given, a second comparison had been taken
after the sight as follows:
Chro. t., 6h 12m 45s
W. T., -3 21 59.5
C-W,
2 50 45. 5
The sight having been taken at about the middle of the interval, the C — W to
be used would be the mean of the two, or 2h 50m 45s.O.
Let us assume, however, that the second comparison showed the following:
Chro. t., 6h 38m 258
W. T., -3 47 39
C-W,
2 50 46
Then, the sight having been taken when only about one-third of the interval
had elapsed between the first and second comparisons, it would be assumed that
only one-third of the total change in the C — W had occurred up to the time of sight,
and the value to be used would be 2h 50m 45s.O.
269. It is considered a good practice always to subtract watch time from
chronometer tune, whatever the relative values, and thus to employ C — W invariably
as an additive correction. It is equally correct to take the other difference, W — C,
and make it sub tractive ; it may sometimes occur that a few figures will thus be saved,
but a chance for error arises from the possibility of inadvertently using the wrong
sign, which is almost impossible by the other method. Thus, the following example
may be taken:
'C, 10h 57m 38s W,
Comparison^' ~U 42 35 C>
-10
42m 35s
57 38
lC-W, 11 15 03 W-C, 0 44 57
Sight
11 50 21
|C-W, +11 15 03
W, 11 50 21
W-C, - 0 44 57
11 05 24
C,
11 05 24
CHAPTER IX.
TIME AND THE NAUTICAL ALMANAC.
270. The subjects of Time and the Nautical Almanac are two of the most
important ones to be mastered in the^ study of Nautical Astronomy, as they enter
into every operation for the astronomical determination of a ship's position. They
will be treated in conjunction, as the two are interdependent.
METHODS OF BECKONING TIME.
271. The instant at which any point of the celestial sphere is on the meriolian
of an observer is termed the transit, culmination, or meridian passage of that point;
when on that half of the meridian which contains the zenith, it is designated as
superior or upper transit; when on the half containing the nadir, as inferior or lower
transit.
272. Three different kinds of time are employed in astronomy — (a) apparent
or solar time, (&) mean time, and (c) sidereal time. These depend upon the hour
angle from the meridian of the points to which they respectively refer. The point
of reference for apparent or solar time is the Center of the Sun; for mean tune, an
imaginary point called the Mean Sun; and for sidereal time, the Vernal Eguinox,
also called the First Point of Aries.
The unit of time is the Day, which is the period between two successive transits
over the same branch of the meridian of the point of reference. The day is divided
into 24 equal parts, called Hours; each hour is divided into 60 equal parts, called
Minutes, and each minute into 60 equal parts, called Seconds.
273. APPARENT OR SOLAR TIME. — The hour angle of the center of the sun affords
a measure of Apparent'or Solar Time. An Apparent or Solar Day is the interval of
tune between two successive transits over the same meridian 01 the center of the
sun. It is Apparent Noon when the sun's hour circle coincides with the celestial
meridian. This is the most natural and direct measure of time, and the unit of
time adopted by the navigator at sea is the apparent solar day. Apparent noon is
the time when the latitude can be most readily determined, and the ordinary method
of determining the longitude by the sun involves a calculation to deduce the apparent
time first.
Since, however, the intervals between the successive returns of the sun to the
same meridian are not equal, apparent time can not be taken as a standard. The
apparent day varies in length from two causes: first, the sun does not move in the
equator, the great circle perpendicular to the axis of rotation of the earth, but in the
ecliptic; and, secondly, the sun's motion in the ecliptic is not uniform. Sometimes
the sun describes an arc of 57' of the ecliptic, and sometimes an arc of 61 ' in a day.
At the points where the ecliptic and equinoctial intersect, the direction of the sun's
apparent motion is inclined at an angle of 23° 27' to the equator, while at the solstices
it moves in a direction parallel to the equator.
274. MEAN TIME. — To avoid the irregularity of time caused bv the want of
uniformity in the sun's motion, a fictitious sun, called the Mean Sun, is supposed to
move in the equinoctial with a uniform velocity that equals the mean velocity of the
true sun in the ecliptic. This mean sun is regarded as being in coincidence with the
true sun at the vernal equinox, or First Point of Aries.
Mean Time is the hour angle of the mean sun. A Mean Day is the interval
between two successive transits of the mean sun over the meridian. Mean Noon is
the instant when the mean sun's hour circle coincides with the meridian.
102
TIME AND THE NAUTICAL ALMANAC. 103
Mean time lapses uniformly; at certain times it agrees with apparent time,
while sometimes it is behind, ana at other times in advance of it. It is tnis time that
is measured by the clocks in ordinary use, and to tnis the chronometers used by
navigators are regulated.
275. The difference between apparent and mean tune is called the Equation of
Time; by this quantity, the conversion from one to the other of these tunes may be
made. Its magnitude and the direction of its application may be found for any
moment from the Nautical Almanac.
276. SIDEREAL TIME. — Sidereal Time is the hour angle of the First Point of
Aries. This point, which is identical with the vernal equinox, is the origin of all
coordinates of right ascension. Since the position of the point is fixed hi the celestial
sphere and does not, like the sun, moon, and planets, have actual or apparent motion
tnerein, it shares in this respect the properties of the fixed stars. It may therefore
be said that intervals of sidereal tune are those which are measured by tne stars.
A Sidereal Day is the interval between two successive transits of me First Point
of Aries across the same meridian. Sidereal Noon is the instant at which the hour
circle of the First Point of Aries coincides with the meridian. In order to interconyert
sidereal and mean times an element is tabulated in the Nautical Almanac. This is
the Sidereal Time of Mean Noon, which is also the Right Ascension of the Mean Sun.
277. CIVIL AND ASTRONOMICAL TIME. — The Civil Day commences at midnight
and comprises the twenty-four hours until the following midnight. The hours are
counted irom 0 to 12, from midnight to noon; then, again, from 0 to 12, from noon
to midnight. Thus the civil day is divided into two periods of twelve hours each,
the first of which is marked a. m. (ante meridian), while the last is marked p. m.
(post meridian).
The Astronomical or Solar Day commences at noon of the civil day of the same
date. It comprises twenty-four hours, reckoned from 0 to 24, from noon of one day
to noon of the next. Astronomical time (apparent or mean) is the hour angle of the
sun (true or mean) measured to the westward throughout its entire circuit from the
time of its upper transit on one day to the same instant of the next.
The civfl day, therefore, begins twelve hours before the astronomical day, and
a clear understanding of this fact is all that is required for interconverting these
times. For example:
January 9, 2 a. m., civil time, is January 8, 14h, astronomical tune.
January 9, 2 p. m., civil time, is January 9, 2h, astronomical time.
278. HOUR ANGLE. — The hour angle of a heavenly body is the angle at the
pole of the celestial concave between the declination circle of the heavenly body
and the celestial meridian. It is measured by the arc of the
celestial equator between the declination circle and the celestial
meridian.
In figure 35 let P be the pole of the celestial sphere, of which
VMQ is the equator, PQ the celestial meridian, and PM, PS,
PV the declination circles of the mean sun, a heavenly body,
and the First Point of Aries, respectively.
Then QPM, or its arc QM, is the hour angle of the mean
sun, or the mean time; QPS, or QS, the hour angle of the
heavenly body; QPV, or QV, the hour angle of the First Point
of Aries, or the sidereal time; VPQ, or VQ, the right ascension of the meridian; VPS,
or VS, the right ascension of the heavenly body; and VPM, or YM, the right ascen
sion of the mean sun.
279. TIME AT DIFFERENT MERIDIANS. — The hour angle of the true sun at any
meridian is called the local apparent time; that of the mean sun, the local mean time;
that of the First Point of Aries, the local sidereal time. The hour angles of the same
body and points from Greenwich are respectively the Greenwich apparent, mean,
and sidereal times^. The difference between the local time at any meridian and the
Greenwich time is equal to the longitude of that place from Greenwich expressed
in time; the conversion from time to arc may be effected by a simple mathematical
calculation or by the use of Table 7.
In comparing corresponding times of different meridians the most easterly
meridian may be distinguished as that at which the time is greatest or latest.
104 TIME AND THE NAUTICAL ALMANAC.
In figure 36 PM and PM' represent the celestial meridians of two places, PS
the declination circle through jhe sun, and PG the Greenwich meridian; let TQ = the
Greenwich tune = GPS ;
TM = the corresponding local time at all places on the meridian PM = MPS;
TM' = the corresponding local time at all places on the meridian PM'=M'PS;
Lo = west longitude of meridian PM = GPM ; and
Lo' = east longitude of meridian PM' = GPM'.
If west longitudes and hour angles be reckoned as positive,
and east longitudes and hour angles as negative, we have:
Lo = TG-TM; and
Lo' = TQ-TM'; therefore
LO-LO'=TM'-TM.
Thus it may be seen that the difference of longitude be
tween two places equals the difference of their local times.
FIG. 3c. This relation may be shown to hold for any two meridians
whatsoever.
Both local and Greenwich times in the above formulae must be reckoned west
ward, always from their respective meridians and from Oh to 24h; in other words, it
is the astronomical tune which should be used in all astronomical computations.
The formula Lo = TG — TM is true for any kind of time, solar or sidereal ; or, in general
terms, TG and TM are the hour angles of any point of the sphere at the two meridians
whose difference of longitude is Lo. S may be the sun (true or mean) or the vernal
equinox.
280. FINDING THE GREENWICH TIME. — Since nearly every computation made
by the navigator requires a knowledge of the Greenwich date and time as a pre
liminary to the use of the Nautical Almanac, the first operation necessary is to
deduce from the local time the corresponding Greenwich date, either exact or approxi
mate, and thence the Greenwich time expressed astronomically.
The formula is:
remembering that west longitudes are positive, east longitudes are negative. Hence
the following rule for converting local to Greenwich time : .
Having expressed the local time astronomically, add the longitude if west,
subtract it u east; the result is the corresponding Greenwich time.
EXAMPLE: In longitude 81° 15' W. the local time is, April, 15d 10h 17m 30s a. m. Required the
Greenwich time.
Local Ast. time, April, 14d 22h 17m 30s
Longitude, + 5 25 00
Greenwich time, 15 3 42 30
EXAMPLE: In longitude 81° 15' E. the local time is, August, 5d 2h 10m 30§ p. m. Required the Green
wich time.
Local Ast. time, August, 5d 2h 10m 30«
Longitude, — 5 25 00
Greenwich time, 4 20 45 30
EXAMPLE: In longitude 17° 28' W. the local time is, May, ld 3h 10m p. m. Required the Greenwich
time.
Local Ast. time, May, ld 3h 10m 00s
Longitude, + 1 09 52
Greenwich time, 1 4 19 52
EXAMPLE: In longitude 125° 30' E. the local time is, May, ld 8h 10m 30« a. m. Required the Green
wich time.
Local Ast. time, April, 30d 2011 10m 30s
Longitude, - 8 22 00
Greenwich time, 30 11 48 30
TIME AND THE NAUTICAL ALMANAC. 105
281. From the preceding article we have:
TG=TM-fLo; hence,
TM=TG-Lo;
thus it will be seen that, to find the local time corresponding to any Greenwich time,
the above process is simply reversed.
Since all observations at sea are referred to chronometers regulated to Greenwich
mean time, and as these instruments are iisually marked on the dial from Oh to 12h, it
becomes necessary to distinguish whether it is a. m. or p. m. at Greenwich. Therefore
an approximate knowledge of the longitude and local time is necessary to determine
the Greenwich date.
EXAMPLE: In longitude 5h 00m 00* W., about 3h 30m p. m. April 15th, the Greenwich chronometer
read 8h 25m, and was fast of Gr. time 3m 15s. Required the local astronomical time.
Approx. local time, 15d 3h 30m Gr. chro., 8h 25m 00s Gr. Ast. time 15d, 8h 21m 45§
Longitude, + 5 00 Corr., — 3 15 Longitude, —5 00 00
Approx. Gr. time, 15 8 30 Gr. Ast. time 15d, 8 21 45 Local Ast. time 15d, 3 21 45
EXAMPLE: In longitude 5h 00m 00s E., about 8 a. m. May 3d, the Gr. chro. read 3h 15m 20s, and was
fast of Gr. time 3m 15s. Required the local astronomical time.
Approx. local time, May, 2d 20h Gr. chro., 3b 15m 20* Gr. Ast. time2d, 15h 12m 05s
Longitude, — 5 Corr., — 3 15 Longitude, + 5 00 00
Approx. Gr. time, 2 15 Gr. Ast. time 2d, 15 1205 Local Ast. time 2d, 20 12 05
THE NAUTICAL ALMANACK
282. The American Ephermeris and Nautical Almanac is divided into three parts
as follows: Part I, Ephemeris for the meridian of Greenwich, gives the ephemerides
of the sun and moon, the geocentric and heliocentric positions of the major planets,
the sun's coordinates, and other fundamental astronomical data for equidistant
intervals of Greenwich mean time ; Part II, Ephemeris for the meridian of Washington
gives the ephemerides of the fixed stars, sun, moon, and major planets for transit
over the meridian of Washington, and Part III, Phenomena, contains predictions of
phenomena to be observed with data for their computation. Tables are also appended
for the interconversion of mean and sidereal time and for finding the latitude and
azimuth by an altitude of Polaris.
Tlie American Nautical Almanac is a smaller book made up of extracts from the
" Ephemeris and Almanac" just described, and is designed especially for the use of
navigators, being adapted to the meridian of Greenwich. It contains the position
of the sun and moon, together with the ephemerides of the planets Venus, Mars,
Jupiter, and Saturn, and the apparent places of 55 stars for the first of each month
and the Greenwich mean tune of transit at Greenwich for each of these stars, also the
mean places of 110 additional stars; solar and lunar eclipses are described, and the
tables for the interconversion of mean and sidereal time and for finding the latitude
by Polaris are included.
The elements dependent upon the sun and moon are placed in the first part of
the book, arranged according to hours, days, and months of the year. The right
ascension of the mean sun for the entire year is given at one opening, also, the mean
time of sidereal noon at Greenwich; the declination of the sun, equation of time, the
right ascension and decimation of the moon and the moon's horizontal parallax and
semidiameter are given for every even hour throughout the year. They must be
taken from the Almanac for some definite instant of Greenwich mean time. In
computations from observations that depend upon the time of the sun's meridian
passage, at which instant the local apparent time is Oh, and the Greenwich apparent
time is equal to the longitude, if west, or to 24h minus the longitude, if east, it
becomes necessary to correct the equation of time for longitude, before it is applied
a See extracts from Ephemeris and Nautical Almanac for 1916, Appendix I.
106 TIME AND THE NAUTICAL ALMANAC.
to the Greenwich apparent time to obtain a Greenwich mean time for use in
out other desired data. This Greenwich mean time is sufficiently correct for all
practical purposes as the equation of time never changes more than 18.3 hi an hour.
283. KEDUCTION OF ELEMENTS. — The reduction of elements in the Nautical
Almanac is usually accomplished by Interpolation, but in certain cases where extreme
precision is necessary the method of Second Differences must be used.
The Ephemeris, being computed for the Greenwich meridian, contains the right
ascensions, declinations, equations of time, and other elements for given equidistant
intervals of Greenwich time. Hence, before the value of any of these quantities can
be found for a given local time it is necessary to determine the corresponding Green
wich time. Should that time be one for which the Nautical Almanac gives the
value of the required element, nothing more is necessary than to employ that value.
But if the time falls between the Almanac times, the required quantity must be
found by interpolation.
The Almanac contains the rate of change or difference of each of the principal
quantities for some unit of time, and, unless great precision is required, the first
differences only need be regarded. In order to use the difference columns to advan
tage, the Greenwich date should be expressed in the unit of time for which the
difference is given. Thus, for using the hourly differences, the Greenwich time
should be expressed in hours and decimal parts of an hour; when using the differences
for one minute, the time should be in minutes and decimal parts of a minute. Instead
of using decimal parts, some may prefer the use of aliquot parts.
Since the quantities in the Almanac are approximate numbers, ^iven to a cer
tain decimal, any interpolation of a lower order than that decimal is unnecessary
work. Moreover, since, hi computations at sea, the Greenwich time is more or less
inexact, too great refinement need not be sought in reducing the Almanac elements.
Simple interpolation assumes that the differences of the quantities are
proportional to the differences of the times; in other words, that the differences
given in the Almanac are constant ; this is seldom the case, but the error arising from
the assumption will be smaller the less the interval between the times in the Almanac.
Hence those quantities which vary most irregularly are given for the smallest units
of time; as the variations are more regular, the units for which the differences are
given increase.
In taking from the Almanac the elements relating to the fixed stars the data
may be found either hi the table which gives the "mean place" of each star for the
year or in that which gives the " apparent place " occupied by each one on the first
day of each month. As the annual variation of position of the fixed stars is small,
the results will not vary greatly whichever table may be used. Yet, as it is proper
to seek always the greatest attainable accuracy, the use of the table showing the
exact positions is recommended.
284. To find from the Nautical Almanac a required element for any given time
and place, it is first necessary to express the time astronomically and to convert it
to Greenwich time and date. Then take from the Almanac, for the nearest given
preceding instant, the required quantity, together with its corresponding " hourly5' or
" two-hourly difference," noting the name or sign in each case. Multiply the " hourly
difference" by the number of hours and fraction of an hour, or use Table IV, N. A.
(proportional parts), corresponding to the interval between the time for which the
quantity is given in the Almanac and the time for which required ; apply the correc
tion thus obtained, having regard to its sign.
A modification of this rule n
may be adopted if the time for which the quantity is
desired falls considerably nearer a subsequent time given in the Almanac than it does
to one preceding; in this case the interpolation may be made backward, the sign of
application of the correction being reversed.
TIME AND THE NAUTICAL ALMANAC.
107
EXAMPLE: At a place in longitude 81° 15' W., April 17, 1916, find the sun's declination and the
equation of time at apparent noon.
G. A. T., 17d,
Eq. t.,
G. M. T., 17d,
Long. =81° 15' W
5h 25m 00-
27
G. A. T.=17d 5h 25m=17d+5h.42.
Eq. t.,17d4h.
Corr.,
0™ 26M
+ .8
H. D.,+0-,6
Int., 1M2
5 2433 Eq. t., 17d 5h 25m, 0 26.9
= 5h.4 (Add to mean time.)
Dec., 17d4h, 10° Sl'.ON. H. D., +0'.9
Corr., + 1 .3 G. M. T., lh.4
Corr., +1^2
Corr., +0».852
Dec., 17d 5h 25m, 10 32 .3 N.
EXAMPLE: At a place in longitude 81° 15' E., April 17, 1916, find the sun's declination and the
equation of time at apparent noon.
Long. =81° 15' E.
G. A. T.=16d 18h 35m=17d-5h.42.
G.
Eq
G.
A.
. t,
M.
T.,
• »
T.,
16d,
16d,
Dec.,
Corr.,
18h 35m
0
00s
20
.5
Eq. t., 16d 18h, Om 20».2
Corr., + 0 .3
H. D.,
Int.,
Corr.
MX.9
0^.58
0s
Oh
.6
.58
18 34
18 .58
16d 18h,
39
.5
10°
+
Eq. t., 16d18h35m, 0 20.5
(Add to mean time.)
22'.2 N. H. D., -
.5 G. M. T.,
+0*
.348
Dec., 16d18h35m, 10° 22'.7 N. Corr., +(X.522
EXAMPLE: April 15, 1916, at llh 55m 30s a. m., local mean time, in Long. 81° 15' W., required the
declination and semidiameter of the sun, the equation of time, and the right ascension, declination,
horizontal parallax, and semidiameter of the moon and Jupiter.
Local mean time, 14d 23h 55m 30s
Longitude, + 5 25 00
f!5 5 20 30
Greenwich mean time, U5d 5h 20m.5
[l5d 5h.34
For the Sun.
S. D., 15' 58"
(Same as at G. A. Noon.)
Dec., 15d4h,
Corr., +
Dec.,
9° 48'.5
1.2
9 49 .7
H. D., +
G. M. T.,
Corr., -f
0'.9
lh.34
1'.20
N.
Eq. t., 15d 4h,
Corr.,
02'.8
0.8
0 02
R. A. 15d 4h,
Corr.,
R. A.,
H. D.,
G. M. T.,
llh 28m 14s
+ 2 38
11 30 52
+ 118s
lh.34
For the Moon.
Hor.Par.,15d5h.34, 57'.1
S. D., 15d5h.34, 15'.6
Eq. t..
H. D.,
G. M. T.,
Corr., - 0-.804
(Subtract from fnean time.)
Os.6
lh.34
Corr.,
158s
2m 38s
(By proportional parts Table IV, N. A.'
R. A., 15d6h, llh 32m 109
Corr.,39m.5, - 1 18
Dec.,15h4h,
Corr.,
Dec..
H. D.,
G. M. T.,
Corr.,
0° 397.8S.
19 .8
0 59 .68.
14X.7
lh.34
- 1978
(By proportional parts Table IV, N. A.)
R. A.,
11 30 52
R. A., 15dOh.
Corr.,
R. A.,
H. D.,
G. M. T.,
, Oh 56m 28-
+ 12
0 56 40
-f 2'.25
5h.34
For Jupiter.
Hor. Par., 15d,
S. D., 15d,
Dec.,15d 6h,
Corr., 39m.o.
Dec.,
+
09X.3S.
19 .7
0/.02
(K.26
0 59 .68.
X.
Corr., + 12s
(Prop, parts Table IV, N. A. (See p. 2536.))
R. A.,15dO*, Oh 56m 28-
Corr., 5h 20m, + 12
R. A., 0 56 40
Dec., 15dOh, + 4° 5V. 5
Corr., + 1.2
Dec., 4 52 .7 X.
H. D., + 0/.23
G. M. T., 5h.34
Corr., + 1^22
(Prop, parts Table IV, N. A.)
Dec., 15dOb, + 4° 5K5 N.
Corr., 5h 20m, + 1.2
Dec., 4 52 .7 N.
108 TIME AND THE NAUTICAL ALMANAC.
285. Should greater precision be required than that attainable by simple inter
polation, resort must be had to the reduction for second differences, for which use
the Ephemeris and Nautical Almanac.
The differences between successive values of the quantities given in the Ephem
eris and Nautical Almanac are called the first differences; the differences between
successive first differences are called the second differences. Simple interpolation,
which satisfies the necessities of sea computations, assumes the first differences to be
constant ; but if the variation of the first differences be regarded, a further interpo
lation is required for the second difference.
The difference for a unit of time in the American Ephemeris and Nautical
Almanac abreast any element expresses the rate at which the element is changing at
that precise instant of Greenwich time. Now, regarding the second difference as
constant, the first difference varies uniformly with the Greenwich time; therefore
its value may be found for any intermediate time by simple interpolation.
Hence the following rule for second differences : Employ the interpolated value
of the first difference which corresponds to the middle of the interval for which the
correction is to be computed.
EXAMPLE: For the Greenwich date 1916, April, 10d 18h 25m 30s, find the moon's declination.
Dec., 18h, (+)21° 09' 41". 8 N. First diff., - 8".522 Second diff., -0".096
Corr., 3 37 .8 Corr., — 0 .020 Interval, +0h .213
Dec., 21 06 04 N. M. D., - 8 .542 Corr., -0".020
No. min., + 25m.5
Corr., -{
3'37".8
The difference for one minute being -8".522 at 18h, and -8".618 at 19h, the
difference for one minute undergoes a change of — 0".096 during one hour. The
time for which it is desired to obtain the difference is at the middle instant between
18h Om and 18h 25m.5— that is, at 18h 12m.75, or its equivalent, 18h.213. With a
change of — 0".096 in one hour, the change in Oh.213 is readily obtainable; correcting
the minute's difference at 18h.O accordingly, the process of correcting the declination
becomes the same as in simple interpolation.
CONVERSION OP TIMES.
286. Conversion of Time is the process by which any instant of time that is
defined according to one system of reckoning may be defined according to some other
system; and also by which any interval of time expressed in units of one system may
be converted into units of another.
287. SIDEREAL AND MEAN TIME. — Mean time is the hour angle of the Mean
Sun; sidereal time is the hour angle of the First Point of Aries. Since the Right
Ascension of the Mean Sun is the angular distance between
the hour circles of the First Point of Aries and of the Mean
Sun, mean time may be converted into sidereal time by adding
to it the Right Ascension of the Mean Sun; and similarly,
p^ sidereal time may be converted into mean time by subtracting
from it the Right Ascension of the Mean Sun.
This is explained in figure 37, which represents a projec
tion of the celestial sphere upon the equator. If P be the
P°k?> QPQ'? the meridian; V, the First Point of Aries; M, the
position of the mean sun (west of the meridian) ; then QPV, or
Q the arc QV, is the sidereal time; QPM, or the arc QM, is the
FIG. 37. mean time; and VPM, or the arc VM, is the Right Ascension
of the Mean Sun. From this it will appear that :
or
Sidereal time = Mean time + Right Ascension of Mean Sun.
TIME AND THE NAUTICAL ALMANAC. 109
If the mean sun be on the opposite side of the meridian, at M', then the mean
time equals 24h — M'Q. In this case:
= VM'-M'Q, or
Sidereal time = Right Ascension of Mean Sun— (24h — Mean time),
= Right Ascension of Mean Sun -f Mean time — 24h.
Right ascension being measured to the east and hour angle to the wes% the
sidereal time will therefore always equal the sum of these two; but 24h must be sub
tracted when the sum exceeds that amount.
From the preceding equations, we also have:
M = QV-VM; and
' = VM'-
M'Q = VM'-QV, or
(24h-M'Q) = (24h + QV)-VM'.
From this it may be seen that the mean time equals the sidereal time minus
the Right Ascension of the Mean Sun, but the former must be increased by 24h
when necessary to make the subtraction possible.
288. APPARENT AND MEAN TIMES. — Apparent tune is the angle between the
meridian and the hour circle which contains the center of the sun; mean time is the
angle between the meridian and the hour circle which contains the mean sun. Since
the equation of time represents the angle between the hour circles of the mean and
apparent suns, it is clear that the conversion of mean time to apparent time may be
accomplished by the application of the equation of time, with its proper sign, to
the mean time ; and the reverse operation by the application of the same quantity,
in an opposite direction, to the apparent time.
The resemblance of these operations to the interconversion of mean and sidereal
times may be observed if, in figure 37, we assume that PV is the hour circle of the
true sun, PM remaining that of the mean sun; then the arc QM will be the mean
time; QV, the apparent time; and VM, the equation of time; whence we have as
before :
QV = QM + VM, or
Apparent tune = Mean time + Equation of time;
the equation of time will be positive or negative according to the relative position of
the two suns.
289. SIDEREAL AND MEAN TIME INTERVALS. — The sidereal year consists of
366.25636 sidereal days or of 365.25636 mean solar days. If, therefore, M be any
interval of mean time, and S the corresponding interval of sidereal time, the relations
between the two may be expressed as follows:
S_366. 25636
M ~365. 25636"
M 365. 25636 _
S ~ 366. 25636 -°'"726'
Therefore, 8=1.0027379 M = M + . 0027379 M;
M = 0.9972696 S =S -. 0027304 S.
If M = 24h, S = 24h + 3m 56S.6; or, in a mean solar day, sidereal time gains on
mean time 3m 568.6, the gain each hour being 9S.S565.
If S = 24h, M = 24h — 3m 55s. 9; or, in a sidereal day, mean tune loses on sidereal
time 3m 558.9, the loss each hour being 9S.8296.
If M and S be expressed in hours and fractional parts thereof,
.8565M;
M= S-9S.8296S.
Tables for the conversion of the intervals of mean into those of sidereal time
and the reverse are based upon these relations. Tables 8 and 9 of this work give
the values for making these conversions, and similar tables are to be found in the
Nautical Almanac.
110 TIME AND THE NAUTICAL ALMANAC.
290. To CONVERT MEAN SOLAR INTO SIDEREAL TIME. — Apply to the local mean
time the longitude, adding if west and subtracting if east, and thus obtain the Green
wich mean time. Take from the Nautical Almanac the Right Ascension of the
Mean Sun at Greenwich mean noon, and correct it for the Greenwich mean time by
Table III, N. A., or Table 9 (Bowditch), or by the hourly difference of 9S.857. Add
to the local mean time this corrected right ascension, rejecting 24h if the sum is
greater than that amount. The result will be the local sidereal time.
EXAMPLE: April 22, 1916, in Long. 81° 15' W., the local mean time is 2b 00" 00* p. m. Required
the corresponding local sidereal time.
L. M. T., 22d 2h 00m 00« R. A. M. S., 22d Oh, 2h 00m 50-.4 L. M. T., 2* 00m 00-
Long., + 5 25 00 Red.for 7h25"(Tab. 9),-f I 13.1 R.A.M.S.,+ 2 02 03.5
G.M.T., 22 7 25 00 R. A. M. S., 7h 25", 2 02 03.5 L. S. T., 4 02 03.5
EXAMPLE: April 22, 1916, in Long. 75° E., the local mean time is 4h 00» 00« a. m. Required the
local sidereal time.
L.M.T., 21d 16h 00m 00- R. A. M. S., 21d 0*, lh 56» 53V8 L. M. T., 21d 16h 00" 00"
Long., 5 00 00 Red. for llh (Tab. 9), -f 1 48 .4 R.A.M.S.,+ 1 58 42.2
G.M.T., 21 11 00 00 R.A.M.S., llb, 1 58 42.2 L. S. T., 21 17 58 42.2
In these examples the reduction of the R-. A. M. S. has formed a separate opera
tion in order to make clear the process. It would be as accurate to add together
directly L. M. T., R. A. M. S., and Red., and the work would thus be rendered more
brief. r< i
291. To CONVERT SIDEREAL INTO MEAN SOLAR TIME. — Take from the Nautical
Almanac the Right Ascension of the Mean Sun for Greenwich mean noon of the'
given astronomical day, and apply to it the reduction for longitude, either by Table 9J
or by the hourly difference of 9S.857, and the result will be the Right Ascension of;
the Mean Sun at local mean noon, which is equivalent to the local sidereal time at
that instant. Subtract this from the given local sidereal time (adding 24h to the
latter if necessary), and the result will be the interval from local mean noon, expressed,
in units of sidereal time. Convert this sidereal time interval into a mean tune interval !
by subtracting the reduction as given by Table II, N. A., or Table 8, or by the hourlyj
difference of 98.830; the result will be the local mean time.
EXAMPLE: April 22, 1916, a. m., in Long. 75° E., the local sidereal time is 17h 58m 42«.2. _ What is;
the local mean time?
Astronomical day, April 21.
L. S. T., 17h 58m 428.2 R. A. M. S., Gr. 21d 0* lh 56m 53«.8
R. A. M. S., - 1 56 04 .5 Red. for -5h long. (Tab. 9), r - 49 .3
Sid. interval from L. M. noon, 16 02 37.7 R. A. M. S., local Oh, " 1 56 04.5
Red. for sid. interval (Tab. 8), 2 37 .7
L. M. T., 21d, ' 16 00 00.0
EXAMPLE: April 22, 1916, p. m., at a place in Long. 81° 15' W., the sidereal time is 4h 02m 038.5.
What is the corresponding mean time?
Astronomical day, April 22.
L. S. T., 4h 02m 03-.5 R. A. M. S., Gr. 22d 0", 2h 00m 50-.4
R. A. M. S., - 2 01 43.8 Red. for +5h 25mlong. (Tab. 9),-f 0 53.4
Sid. interval from L. M. Noon, 2 00 19.7 R. A. M. S., local 0*, 2 01 43.8
Red. for sid. interval (Tab. 8),- 0 19 .7
L. M. T., 22d, 2 00 00.0
292. To CONVERT MEAN INTO APPARENT TIME AND THE REVERSE. — Find the
Greenwich time corresponding to the given local time. If apparent time is given,
find the Greenwich apparent time and take the equation of time from the Almanac.
If mean time, find the Greenwich mean time, correct the equation of time for the
required instant and apply it with its proper sign to the given time.
TIME AND THE NAUTICAL ALMANAC. Ill
EXAMPLE: April 21, 1916, in Long. 81° 15' W., find the local apparent time corresponding to a local
mean time of 3h 05m 00" p. m.
L. M. T., 21d 3h 05m 00* L. M. T., 21d 3h 05m 00' Eq. t., 8h, lm 218.3
Long., + 5 25 00 Eq. t., + 1 21 .5 Corr., + 0.2
G. M. T., 21 8 30 00 L. A. T., 21 3 06 21 .5 Eq. t., 1 21. 5
H. D., + 0«.5
G. M. T.,+ Oh.5
Corr., + 08.25
(Add to mean time.)
EXAMPLE: April 3, 1916, in Long. 81° 15' E., the local apparent time is 8h 45m 00* a. m. Required
the mean time.
L A. T., 2d 20h 45m CO- L. A. T., 2d 2011 45m 00« Eq. t., 14h, 3m 30V6
Long., - 5 25 CO Eq. t., + 3 29 .7 Corr., - 0 .9
G. A. T., 2 15 20 00 L. M. T., 2 20 48 29 .7 Eq. t., 3 29 .7
H. D., - 0-.7
Int., + lh.33
Corr., - Os.93
(Add to apparent time.)
293. To FIND THE HOUR ANGLE OF A BODY FROM THE TIME, AND THE
REVERSE. — In figure 37, if M and M' represent the positions of celestial bodies
instead of those of the mean sun as before assumed, then the hour angles of the
bodies will be Q M and 24h — M' Q, respectively, and their right ascensions will be
T M and V M'.
t As before, we have:
QV = QM + VM,
=VM'-M'Q;
QM =QV-VM;
M'Q =VM'-VQ, or
(24h - M' Q) = (24h + Q V) - V M'.
Substituting, therefore, hour angle of the body for mean time, and right ascension
of the body for Eight Ascension of the Mean Sun, the rules previously given for the
conversion of mean and sidereal times will be applicable for the conversion of hour
angle and sidereal time. Thus, the sidereal time is equal to the sum of the right
ascension of the body and its hour angle, subtracting 24h when the sum exceeds
that amount ; and the hour angle equals the sidereal tune minus the right ascension
of the body, 24h being added to the former when necessary to render the subtraction
possible.
EXAMPLE: In Long. 81° 15' W., on April 25, 1916, at 12h 10* 30- (astronomical) mean time, find the
hour angle of Sinus.
L. M. T., 12h 10m 30' L. M. T., 12h 10* 30-.0
Long., + 5 25 00 R. A. M. S., 0*,+ 2 12 40 .0
Red. (Tab. 9), + 2 53 .4
G. M. T., 17 35 30
L. S. T., 14 26 03 .4
R. A. Sinus, - 6 41 27 .6
H. A. Sirius, 7 44 35 .8
EXAMPLE: May 9, 1916, Arcturus being 2b 27m 42V52 east of the meridian, find the local sidereal time.
24h 00" 00- H. A., 21h 32m 17V48
H. A., 2 27 42.52 E. R. A., +14 11 52 .9
H. A., 21 32 17.48 W. L. S. T., 11 44 10 .38
Or thus:
H. A., - 2h27m42«.52
R. A., +14 11 52 .9
L. S. T., 11 44 10 .38
112
TIME AND THE NAUTICAL ALMANAC.
294. M*ny navigators find the conversion of time much simplified and more
easily grasped by roughly plotting the elements as they are presented in any given
case, in a figure drawn on the plane of the celestial equator. Noting the known ele
ments and the elements required to be found, a study of the figure shows very
quickly how to combine the known elements to get the unknown elements.
Following this method, the examples of articles 290, 291, and 293 are here
solved as an alternative to the preceding treatment, since it is found that, for many
who have learned this method of procedure in the beginning, every difficulty in
reckoning or converting time has been obviated. Although the explanation may
appear somewhat long, the actual plotting and solution
of any given case take only a few seconds when the
method is understood. In the figures, P represents the
elevated pole; Q, the intersection of the local meridian
with the equator; G, the intersection of the meridian
of Greenwich with the equator; V, the First Point of
Aries (Vernal Equinox); Sm, the mean sun; Sa, the
apparent sun; and >K, a star or planet.
FIKST EXAMPLE OF ARTICLE 290. (SEE FIGURE 38.)
Draw a circle to represent the plane of the celestial
equator, P being the projection of the pole, and PQ the
projection of the local meridian. From P draw the
projection of the hour circle of the Greenwich meridian
which (since the longitude is west) is laid off to the right
or eastward of the local meridian so that the arc QG
Xals the longitude. The arrow indicates westerly direction and shows the direction in
ch the hour circles of the heavenly bodies move around the circle on the earth's axis.
The L. M. T. being p. m., we lay oft the hour circle of the mean sun to the westward
of the local meridian so that the arc QSm equals the L. M. T. We see at once from
the figure that the G. M. T. (the position of the hour circle of the mean sun, Sm, with
reference to the Greenwich meridian) is the arc GQSm, which equals Long. + L. M. T.
Having thus found the G. M. T., we can find the right ascension of the mean sun at
that instant f rom the Nautical Almanac (picked out for the day and corrected for the
G. M. T.) which, in this case, is 2h 02m 03S.5. The correction is ( + ) or additive to the
angle which represents the R. A. M. S. for Greenwich Mean Noon because this angle
has been increased by this amount owing to the
gain of the Vernal Equinox over the mean sun for
the angle through which the mean sun has traveled
from the Greenwich meridian. ^The mean sun is to
the eastward of the Vernal Equinox by the amount
of its right ascension. We therefore lay off PV,
the hour circle of the Vernal Equinox, so that the
arc VSm equals the R. A. M. S. Since the L. S. T.
equals the H. A. of the Vernal Equinox, we see at
once from the figure that the L. S. T. equals R. A. M.
S. + L.M.T.
SECOND EXAMPLE OF ARTICLE 290. (SEE FIGURE 39.)
FIG. 38.
FIG. 39.
Draw a circle to represent the plane of the celes
tial equator. Project the pole P and the local me
ridian JPQ. Draw the arrow pointed west to show the
direction in which the hour circles move. Since the longitude is east, we know that
the Greenwich meridian is to the westward of the local meridian, and we draw PG, the
Greenwich meridian, so that the arc QG equals the longitude, equals 5 hours. Since
the L. M. T. is 4h 00m 00s a. m., we know that it will be 12h-4h equals 8h before the
sun crosses the local meridian; hence we lay off the arc QSm to equal the sun's
H. A., which equals 8h, and draw PSm, the hour circle of the mean sun. We see
from the figure that the hour angle of the mean sun from Greenwich (G. M. T.) is
equal to 24h — (Long. + H. A. SjJ , and that, since the mean sun must travel around
the arc to the west from Sm to G to make the time 0 hours on April 22 at
TIME AND THE NAUTICAL ALMANAC.
113
FIG. 40.
Greenwich, the date must be April 21, and the G. M. T. is 11 hours. For this
Greenwich date, we get, from the Nautical Almanac (corrected for G. M. T.) the
R. A. M. S. equal to lh 58m 428.2, which is the amount the hour circle of the mean
sun is to the eastward of the hour circle of the Vernal Equinox. The correction is +
or additive for the reason given in the preceding example. Lay off the arc SmV
equal to the R. A. M. S. and draw the hour circle of the Vernal Equinox PV.
An inspection of the figure shows us that the L. S. T. is the arc QGV which is equal
to the Long. + G. M. T. + R. A. M. S., or to the L. M. T. + the R. A. M. S. We
also see that L. M. T. equals the Long, -f G. M. T.
FIRST EXAMPLE OF ARTICLE 291. (SEE FIGURE 40.)
Draw the figure as shown, laying off the longitude
equal to 5 hours east, to the westward from Q, thus
finding the Greenwich meridian G. The given L. S. T.
is 18 hours, so lay off QV (equal to 18 hours) to the
westward from Q, given the position of V, the Vernal
Equinox or First roint of Aries, for the instant de
sired. The problem is to plot the position of the
mean sun at this hist ant, and thence find its local
hour angle, or the L. M. T. We plot this position of
the mean sun by laying off its right ascension to
the eastward from V. The R. A. M. S. is found from
the Almanac for a particular instant which is at
Greenwich mean noon of the astronomical date,
April 21, and which we find is lh 56m 53s. 8. Plot in Smi, over the Greenwich merid
ian and lay off this angle GV17 to the westward from G, giving us the position of V
at Greenwich mean noon. As we are reckoning hour angles from the local meridian,
we must move the sun back to Q and find the position \ 3 at the instant of local mean
noon. To find V2 we must find the angle Q V3 which will be less than GVt, as the
First Point of Aries always advances faster toward the west than the mean sun.
The amount of this gain of the Vernal Equinox over the mean sun depends on the
angular distance through which the mean sun travels, i. e., hi this case from Q to G
equals the longitude, equals 5 hours. From Table 9 we find the gain, which is
represented by the sector Q in the figure, to be 49s. 3 for the 5 hours, so that QV2
equals GVl - 49S.3^ equals lh 56m 538.8 - 498.3, eauals lh 56m 043.5. Now we
have the position V2 for the instant of tune when tne mean sun was at Q, that is
for the position Sm2 or local mean noon. For the instant of time desired the Vernal
Equinox is not at V2 but at V and at this instant we must find Sm2. The Vernal
Equinox has moved from V2 to the westward to V or through the arc V2 V which
equals QVrQV2, equals 17h 58m 428.2-lh 56m 048.5, equals 16h 02m 378.7, which
is called a sidereal interval. During this travel of the
Vernal Equinox the mean sun will lose a certain an
gular amount on the Vernal Equinox, depending on
the travel of the latter, which travel is 16h 02m 378.7.
From Table 8, we find for this travel that the loss
will be 2m 378.7, which is represented by the sector
C2 in the figure, so that the angle QSm is V2 V-2m
37S.7, equals 16h 02m 378.7-2m 378.7, equals 16h
00m 00s, which, from the figure, equals the aesired L.
M. T.
SECOND EXAMPLE OF ARTICLE 291 . (SEE FIGURE 41 .)
Draw the figure as shown, laying off the longitude
equal to 5h west, to the eastward from Q, thus finding
the Greenwich meridian G. The problem is similar
to the above problem except that in moving the mean FIQ. 41.
sun from G to Q we see that the angle Smi Vl is in
creased to find Sm2 V2, as the Vernal Equinox has gained a certain amount on the
mean sun during the travel of the sun to the westward from G to Q. For the travel
of V2 to V, the mean sun will travel from Sm2 to Sm, losing a certain amount on the
Vernal Equinox for the travel of V3 V of the latter, and we find QSm equals the L. M. T.
114
TIME AND THE NAUTICAL ALMANAC.
FIRST EXAMPLE OF ARTICLE 293. (SEE FIGURE 42.)
Draw the figure as explained above, using longitude given equals 5 hours west,
and L. M. T. given, 12 hours ( + ). Then G. M. T. equals 12 + 5 or 17 hours (+ ) of
April 25. For this instant of time the mean sun is plotted at Sm.
Now the problem is, knowing the positions of G, Q,
and Sm, to find the position of the given star on the di
agram, and thence its local hour angle. If we can find
the relative angles from the mean sun and from the
star to some third object, we can plot this third object
and find the required hour angle of the star. The third
object is the First Point of Aries (the Vernal Equinox)
and the angles from the mean sun and from the star
are the right ascensions of the mean sun and the star.
The right ascension of the mean sun is found from the
Almanac, not for the instant we want, but for the
Greenwich mean noon of the date. This R. A. must
be increased by a correction for the angle through
which the mean sun has traveled since noon, — the
G. M. T. In the problem the R. A. M. S. so increased
is 2 hours, so we lay^ off SmV from Sm to the westward
2 hours, plotting the position of the Vernal Equinox at the desired instant. From
the Almanac we find the R. A. of the star to be 6 hours, and we lay; off V * equal
to 6 hours to the eastward. The required local hour
angle of the star is then Q ^c which equals QSm +
VSm-V * equals L. M. T. + R. A. M. S.-R. A. equals
12h+2h-6h equals 8 hours.
SECOND EXAMPLE OF ARTICLE 293. (SEE FIGURE 43.)
Draw the figure as before. The problem is, know
ing the position of the star at a certain instant, to find
the L. S. T., so we must plot the position of the star,
then that of the Vernal Equinox. The local hour angle
of the latter is the required L. S. T.
The hour angle 01 the star is given as 2 hours, bear
ing east from the meridian, so lay off Q ^c =2 hours to
the east from Q. Now find from the Almanac the R. A.
of the ^ which is 14 hours, and lay off >fc V equal to 14h to
the westward from % . The L. S. T. is then QV, equals
V * — Q *, equals the R. A. * —II. A. *, equals 14h — 2h equals 12 hours.
When doubt exists as to the Greenwich date the navigator, by plotting the data
in exactly the same way as explained above, can at once remove all doubt on the
subject and can get the correct G. M. T.
CHAPTER X.
COKRECTION OF OBSERVED ALTITUDES,
294. The true altitude of a heavenly body at any place on the earth's surface
is the altitude of its center, as it would be measured by an observer at the center of
the earth, above the plane passed through the center of the earth at right angles
to the direction of the zenith.
The observed altitude of a heavenly body, as measured at sea, may be converted
to the true altitude by the application of the following-named corrections: Index
Correction, Dip, Refraction, Parallax, and Semidiameter. The corrections for parallax
and semidiameter are of inappreciable magnitude in observations of the fixed stars,
and with planets are so small that they need only be regarded in refined calculations.
In observations with the artificial horizon there is no correction for dip.
For theoretical accuracy, the corrections should be applied in the order in which
they are named, but in ordinary nautical practice the order of application makes
no material difference, except in the case of the parallax of the moon as explained
in article 306 ; and hence, instead of turning to the separate tables referred to in the
following articles as containing these corrections, their combined amount, given in
Table 46, may be applied to observed altitudes of the sun, the planets, and the stars,
after the manner shown in article 308.
INDEX CORRECTION.
295. This correction is fully explained in articles 249 and 250, Chapter VIIL
REFRACTION.
296. It is known by various experiments that the rays of light deviate from
their rectilinear course in passing obliquely from one medium into another bf a
different density; if the latter be more
dense, the ray will be bent toward the per
pendicular to the line of junction of the
media; if less dense, it will be bent away
from that perpendicular.
The ray of light before entering the
second medium is called the incident ray;
after it enters the second medium it is
called the refracted ray, and the difference of
direction of the two is called the refraction.
The rays of light from a heavenly body
must pass through the atmosphere before
reaching the eye of an observer upon the
surface of the earth. The earth's atmos
phere is not of a uniform density, but is
most dense near the earth's surface, gradu
ally decreasing in density toward its upper
limit; hence the path of a ray of light, by
passing from a rarer medium into one con
tinually increasing density becomes a curve,
which is concave toward the earth. The
last direction of the ray is that of a tangent to the curved path at the eye of the
observer, and the difference of the direction of the ray before entering the atmosphere
and this last direction constitutes the refraction.
297. To illustrate this, consider the earth's atmosphere as shown in figure 44;
let SB be a ray from a star S, entering the atmosphere at B, and bent into the curve
BA; then the apparent direction of the star is AS', the tangent to the curve at the
point A, the refraction being the angle between the lines BS and AS'. If CAZ is
115
FIG. 44.
116
CORRECTION OF OBSERVED ALTITUDES.
the vertical line of the observer, by a law of optics the vertical plane of the observer
which contains the tangent AS' must also contain the whole curve BA and the incident
ray BS. Hence refraction increases the apparent altitude of a star without affecting
its azimuth.
At the zenith the refraction is nothing. The less the altitude the more obliquely
the rays enter the atmosphere and the greater will be the refraction. At the horizon
the refraction is the greatest.
298. The refraction for a mean state of the atmosphere (barometer 30in, Fahr.
thermometer 50°) is given in Table 20 A; the combined refraction and sun's parallax
in Table 20 B; and the combined refraction and moon's parallax in Table 24.
Since the amount of the refraction depends upon the density of the atmosphere,
and the density varies with the pressure and the temperature, which are indicated
by the barometer and thermometer, the true refraction is found by applying to the
mean refraction the corrections to be found in Tables 21 and 22; these are deduced
from BesseFs formulae, and are regarded as the most reliable tables constructed. It
should be remembered, however, that under certain conditions of the atmosphere a
very extraordinary deflection occurs in rays of light which reach the observer's eye
from low altitudes (that is, from points near the visible horizon), the amount of
which is not covered by the ordinary corrections for pressure and temperature ; the
error thus created is discussed under Dip (art. 301) ; on account of it, altitudes less
than 10° should be avoided.
EXAMPLE: Required the refraction for the apparent altitude 5°, when the thermometer is at 20°
and the barometer at 30in.67.
The mean refraction by Table 20 A is, 9' 52"
The correction for height of barometer is, -f- 13
The correction for the temperature, -f 42
True refraction, 10 47
299. The correction for refraction should always be subtracted, as also that
for combined refraction and parallax of the sun; the correction for combined refrac
tion and parallax of the moon is invariably additive.
DIP.
300. Dip of the Horizon is the angle of depression of the visible sea horizon below
the true horizon, due to the elevation of the eye of the observer above the level of
the sea.
In figure 45 suppose A to be the position of an observer whose height above the
level of the sea is AB. CAZ is the true vertical at the position of the observer, and
AH is the direction of the true horizon, S
being an observed heavenly body. Draw
ATH' tangent to the earth's surface at T.
Disregarding refraction, T will be the most
distant point visible from A. Owing to
refraction, however, the most distant visi
ble point of the earth's surface is more re
mote from the observer than the point T,
and is to be found at a point T', in figure
46. But to an observer at A the point T'
will appear to lie in the direction of AH",
the tangent at A to the curve AT'. If the
verticalplane were revolved about CZ as
an axis, the line AH would generate the
plane of the true horizon, while the point
T' would generate a small circle or the
terrestrial sphere called the Visible or Sea
Horizon. The Dip of the Horizon is
HAH", being the angle between the true
FIG. 43. horizon and the apparent direction of the
sea horizon. Values of the dip are given
in Table 14 for various heights of the observer's eye, and in the calculation of the
table allowance has been made for the effect of atmospheric refraction as it exists
under normal conditions.
CORRECTION OF OBSERVED ALTITUDES.
117
FIG. 46.
301. The fact must be emphasized, however, that under certain conditions the
deflection of the rav in its path from the horizon to the eye is so irregular as to give a
value of the dip widely different from that which is tabulated for the mean state of
atmosphere. These irregularities usually occur when there exists a material differ
ence between the temperature of the sea water and that of the air, and they attain a
maximum value in calm or nearly calm weather, when the lack of circulation permits
the air to arrange itself in a series of horizontal strata of different densities, the denser
strata being below when the air is warmer, and the reverse condition obtaining when
the air is cooler. The effect of such an arrangement is that a ray of light from the
horizon in passing through media of different densities, undergoes a refraction quite
unlike that whicn occurs in the atmosphere of much more nearly homogeneous
density that exists under normal conditions.
Various methods have been suggested for computing the amount of dip for
different relative values of temperature of air and water, but none of these afford a
satisfactory solution, there being so many ele
ments involved which are not susceptible of
determination by an observer on shipboard
that it will always be difficult to arrive at
results that may be depended upon.
As the amount of difference between the
actual and tabulated values of the dip due to
this cause may sometimes be very consider
able — reliable observations having frequently
placed it above 10', and values as high as 32'
having been recorded — it is necessary for the
navigator to be on his guard against the
errors thus produced, and to recognize the
possible inaccuracy of all results derived from
observations taken under unfavorable condi
tions. Without attempting to give any method
for the determination of the amount of the ex
traordinary variation in dip, the following rules may indicate to the navigator the con
ditions under which caution must be observed, and the direction of probable error:
(a) A displacement of the horizon should always be suspected when there is a
marked difference between the temperatures of air and sea water; this fact should
be especially kept in mind in regions such as those of the Red Sea and the Gulf
Stream, where the difference frequently exists.
(6) The error In the tabulated value of the dip will increase with an increase in the
difference of temperature, and will diminish with an increase in the force of the wind.
(c) The error will decrease with the height of the observers eye; hence it is
expedient, especially when error is suspected, to make the observation from the most
elevated position available.
(d) When the sea water is colder than the air the visible horizon is raised and the
dip is decreased; therefore the true altitude is greater than that given by the use of
the ordinary dip table. When the water is warmer than the air, the horizon is
depressed and the dip is increased. At such times the altitude is really less than that
found from the use of the table.
The same cause, it may be mentioned here, affects the kindred matter of the
visibility of objects. When the air is warmer, terrestrial objects are sighted from a
greater distance and appear higher above the horizon than under ordinary conditions.
When the water is warmer than the air, the distance of visibility is reduced, and
terrestrial objects appear at a less altitude.
302. What has peen said heretofore about the dip supposes the horizon to be
free from all intervening land or other objects; but it often nappens that an obser
vation is required to be taken from a ship sailing along shore or at anchor in harbor,
when the sun is over the land and the snore is nearer the ship than the visible sea
horizon would be if it were unconfined; in this case the dip will be different from
that of Table 14, and will be greater the nearer the ship is to that point of the shore
to which the sun's image is brought down. In such case Table 15 gives the dip at
different heights of the eye and at different distances of the ship from the land.
303. The dip is always to be subtracted from the observed altitude.
118
CORRECTION OF OBSERVED ALTITUDES.
PARALLAX.
304. The parallax of a heavenly body is, in general terms, the angle between
two straight lines drawn to the body from different points. But in Nautical Astron
omy geocentric parallax is alone considered, this
being the difference between the positions of a
heavenly body as seen at the same instant from
the center of the earth and from a point on
its surface.
The zenith distance of a body, S (fig. 47),
seen from A, on the surface of the earth, is ZAS;
seen from C it is ZCS; the parallax is the dif
ference of these angles, ZAS-ZCS=ASC.
Parallax in altitude is, then, the angle at
the heavenly body subtended by the radius
of the earth.
If the heavenly body is hi the horizon as
at II', the radius, being at right angles to AH',
subtends the greatest possible angle at the
star for the same distance, and this angle is
called the horizontal parallax. The parallax
is less as the bodies are farther from the earth,
as will be evident from the figure.
FIG. 47.
Let par. = parallax in altitude, ASC;
Z=SAZ, the apparent zenith distance (corrected for refraction);
R=AC, the radius of the earth; and
D = CS, the distance of the object from the center of the earth.
Then, since SAC = 180°-SAZ, the triangle ASC gives:
R sin Z
sin par. = — ^ — .
If the object is in the horizon at H', the angle AH'C is the horizontal parallax,
and denoting it by H. P. the right triangle AH'C gives:
sin H. P.
R
R.
Substituting this value of ^ in the above,
sin par. = sin H. P. sin Z.
If A- = SAH', the apparent altitude of the heavenly body, then Z = 90° — 7i; hence,
sin par. = sin H. P. cos 7i.
Since par. and H. P. are always small, the shies are nearly proportional to the
angles; hence,
par. = H. P. cos 7i.
305. The Nautical Almanac gives the horizontal parallax of the moon, as well
as .of the planets Venus, Mars, Jupiter, and Saturn.
In Table 16 will be found the values of the sun's parallax for altitude intervals
of 5° or 10°, while Table 20 B contains the combinea values of the sun's parallax
and the refraction. In Table 24 is given the parallax of the moon, combined with
the refraction, at various altitudes and for various values of the horizontal parallax.
CORRECTION OF OBSERVED ALTITUDES. 119
306. Parallax is always additive; combined parallax and refraction additive in
the case of the moon, but subtractive for the sun.
As the correction for parallax of the moon is so large, it is essential that it be
taken from the table with considerable accuracy; the corrections for index correc
tion, semidiameter, and dip should therefore be applied first, and the l ' approximate
altitude" thus obtained should be used as an argument in entering Table 24 for
parallax and refraction.
SEMIDIAMETEB.
307. The semidiameter of a heavenly body is half the angle subtended by the
diameter of the visible disk at the eye of the observer. For the same body the
semidiameter varies with the distance; thus; the difference of the sun's semidiameter
at different times of the year is due to the change of the earth's distance from the
sun; and similarly for the moon and the planets.
In the case 01 the moon, the earth's radius bears an appreciable and considerable
ratio to the moon's distance from the center of the earth; hence the moon is materially
nearer to an observer when in or near his zenith than when in or near his horizon,
and therefore the semidiameter, besides having a menstrual change, has a semi
diurnal one also.
The increase of the moon's semidiameter due to increase of altitude is called its
augmentation. This reduction may be taken from Table 18.
The scmidiameters of the sun, moon, and planets are given in their appropriate
places in the Nautical Almanac.
The semidiameter is to be added to the observed altitude in case the lower limb
of the body is brought into contact with the horizon, and to be subtracted in the
case of ^ the upper limb. When the artificial horizon is used, the limb of the reflected
image is that which determines the sign of this correction, it being additive for the
lower and subtractive for the upper.
EXAMPLE: May 6, 1916, the observed altitude of the sun's upper limb was 62° 1(X 40"; I. C., -f 3' 10";
height of the eye, 25 feet. Required the true altitude.
Obs. alt. & 62° 1(X 40" I. C., + 3' 10"
Corr., - 18 04
S. D. (Naut. Aim.), - 15' 53"
True alt., 61 52 36 dip (Tab. 14), - 4 54
p. &r. (Tab. 20 B), - 27
- 21 14
Corr., - 18' 04X/
EXAMPLE : The altitude of Sirius aa observed with an artificial horizon was 50° 59' 30"; I. C. , — V 30".
Required the true altitude.
Obs. 2 alt. *, 50° 59' 30*
I. C., - 1 30
2)50 58 00
Obs. alt., 25 29 00
ref. (Tab. 20 A), - 2 02
True alt., 25 26 58
EXAMPLE: April 16, 1916, observed altitude of Venus 53° 26' 10"; I. C., + V 30"; height of eye,
20 feet. Required the true altitude.
Obs. alt. *, 53° 26' 10" par. (Tab. 17), + (/ 06" Hor. Par. (Naut. Aim.), 11".4
Corr., — 2 30 I. C., + 2 30
53 23 40 + 2 36
dip (Tab. 14), - 4' 23"
ref. (Tab. 20 A), - 43
- 5 06
Corr., - 2' 30"
120 CORRECTION OF OBSERVED ALTITUDES.
EXAMPLE: May 6, 1916, at 13h 24m G. M. T., the observed altitude of the moon's lower limb was
25° 3(X 30"; I. 0.,-1' 30"; height of eye, 20 feet. Required the true altitude.
Obs. alt. j[_, 25° 3(K 30" S. D. (Naut. Aim.), +14' 48" Hor. Par. (Naut. Aim ) 54' 06"
1st corr., + 9 01 Aug. (Tab. 18), + 06
Approx. alt., 25 39 31 +14 54
p. & r. (Tab. 24),
True alt.,
*±U 1<J
dip. (Tab. 14),
i.e.,
- 4' 23"
- 1 30
26 26 16
- 5 53
1st corr.,
+ 9' 01"
Or, the following modification may be adopted:
Obs. alt.£, 25° 30' 30" S. D., +14' 48" H. P., 3246" log. 3.51135
1st corr., -f 6 59 Aug., + 06 App. alt., 25° 38' cos 9.95504
Approx. alt., 25 37 29 +14 54 f 2927" log. 3.46639
par., + 48 47 „ _T1F ^ W 47"
True alt., 26 26 16 ref, - 2 02
I. C., - 1 30
- 7 55
1st corr., + 6' 59"
308. The corrections for dip, parallax, refraction, and semidiameter, which
must be applied to the observed altitude of a star or of the sun's lower limb in order
to obtain the true altitude, have been combined in Table 46, and for the moon's
upper and lower limb in Table 49, and will henceforth be used in all subsequent
problems. This is done in order to save the time and labor involved in referring
to separate tables of these corrections.
The tabulated correction for an observed altitude of a star combines the mean
refraction and the dip; and that for the observed altitude of the sun's lower limb,
the mean refraction, the dip, the parallax, and the mean semidiameter, which is
taken as 16'. A supplementary table, taking account of the variation of the sun's
semidiameter in the different months of the year, is given in connection with the
main table.
Thus, in the first example under article 324, we may, when variations from the
mean state of the atmosphere (barometer 30 inches, Fahr. thermometer 50°) are
left out of consideration, proceed as follows:
Measured altitude _ £} = 40° 04' 00"
I.C. = + 3 00
Correction from Table 46, height of eye 20 feet. +10' 35" 40 07 00
Supplementary table for June 21 _ — 0 14 10 21
True altitude 40 17 21
CHAPTER XI.
THE CHKONOMETER EEKOR
309. It has already been explained (art. 261, Chap. VIII) that the error of a
chronometer is the difference between the time indicated by it and the correct standard
time to which it is referred; and that the daily rate is the amount that it gams or
loses each day. In practice, chronometer errors are usually stated with reference to
Greenwich mean time. It is not required that either the error or the rate shall be
zero, but in order to be enabled to determine the correct time it is essential that both
rate and error be known and that the rate shall have been uniform since its last
determination.
310. DETERMINING THE RATE. — Since all chronometers are subject to some
variation in rate under the changeable conditions existing on shipboard, it is desirable
to ascertain a new rate as often as possible. The process of obtaining a rate involves
the determination of the error on two different occasions separated by an interval
of time of such length as may be convenient ; the change of error during this interval,
divided by the number of days, gives the daily rate.
EXAMPLE: On March 10, at noon, found chronometer No. 576 to be Om 32V5 fast of G. M. T. ; on March
20, at noon, the same chronometer was Om 48s.O fast of G. M. T. What was the rate?
Error, March 10d Oh, - -f Om 32'. 5
Error, March 20d 0*, +0 48 . 0
Change in 10 days, -}- 15 . 5
Daily rate, + 1-.55
The chronometer is therefore gaining 18.55 per day.
311. DETERMINING ERROR FROM RATE. — The error on any given day being
known, together with the daily rate, to find the error on any other day it is only
necessary to multiply the rate by the number ^of days that may have elapsed and
to apply the product with proper sign to the given error.
EXAMPLE: On December 17 a chronometer is 3m 27s. 5 slow of G. M. T. and losing 08.47 daily. What
is the error on December 26?
Error Dec. 17, -3m 27'.5 Daily rate, -OV47
Correction, — 4 .2 No. days, 9
Error Dec. 26, -3 31.7 Corr., -4.23
The chronometer is therefore slow of G. M. T. on December 26, 3m 318.7.
312. It is necessary to distinguish between the signs of the chronometer correc
tion and of the chronometer error. A chronometer fast of the standard time is
considered as having a positive error, since its readings are positive to (greater than)
those of an instrument showing correct tune; but the same chronometer has a
negative correction, as the amount must be subtracted to reduce chronometer readings
to correct readings.
313. Numerous methods are available for determining the error of a chronometer
in port. The principal of these will be given.
BY TIME SIGNALS.
314. In nearly all of the important ports of the world a time signal is made each
dav at some defined instant. In many cases this consists in the dropping of a time
ball — the correct instant being given telegraphically from an observatory. In a
number of places where there is no tune ball a signal may be received on the instru
ments at the telegraph offices, whereby mariners may ascertain the errors of their
chronometers. Such signals are to be had in almost every port of the United States,
and similar signals are being sent out from Government radio stations, so that
it is now possible to find the error of the chronometer on board ships fitted with
121
122 THE CHRONOMETER ERROR.
receiving instruments when lying in port and also when underway within radio
distance of these stations.
The time signal may be given by a gunfire or other sound, in which case allowance
must be made by the observer for the length of time necessary for the sound to travel
from the point of origin to his position. Sound travels 1,090 feet per second at 32° F.,
and its velocity increases at the rate of 1.15 feet per second with each degree increase
of temperature. If V be the velocity of sound in feet per second at the existing
temperature, and D the distance in feet to be traversed, » is the number of seconds
to be subtracted from the chronometer reading at the instant of hearing the signal
to ascertain the reading at the instant the signal was made.
This method of obtaining the chronometer error consists in taking the difference
between the standard time and chronometer time at the time of observation and
marking the result with appropriate sign.
EXAMPLE: A time ball drops at 5h Om 0s, G. M. T., and the reading of a chronometer at the same
moment is 4h 57m 523.5. What is the chronometer error?
G. M. T., 5h OOmOOI
Chro. t., 4 57 52.5
Chro. error, - 2 07 . 5
That is, chronometer is slow 2m 07". 5; chronometer correction additive.
BY TRANSITS.
315. The most accurate method of finding the chronometer correction is by
means of a transit instrument well adjusted in the meridian, noting the times of
transit of a star or the limbs of the sun across the threads of the instrument.
At the instant of the body's passage over the meridian wire, mark the time by
the chronometer. The hour angle at the instant is Oh; therefore the local sidereal
time is equal to the right ascension of the body in the case of a star, or the local
apparent time is Oh in the case of the sun's center. By converting this sidereal or
apparent time into the corresponding mean time and applying the longitude, the
Greenwich mean time of transit is given. By comparing with this the time shown
by chronometer the error is found.
EXAMPLE: 1916, May 9 (Ast. day), in Long. 44° 39' E., observed the transit of Arcturus over the
middle wire of the telescope, the time noted by a chronometer regulated to Greenwich mean time being
8h 05m 33s. 5. Required the error.
L. S. T. (R. A. #), 14h llm 528.9
Long., — 2 58 36
G. S. T., 11 13 16.9
R. A. M. S., 9dOh, - 3 07 51.8
Sid. int. from Oh, 8 05 25.1
Reduction (Tab. 8), - 1 19.5
G. M. T., 8 04 05.6
Chro. t., 8 05 33.5
Chro. fast, 1 27 . 9
EXAMPLE: June 25, 1916, in Long. 60° E., observed the transit of both limbs of the sun over the
meridian wire of the telescope, noting the times by a chronometer. Find the error of the chronometer
onG.M. T.
Transit of western limb, 8h 04m 02s. 5 Eq. t., 24d 20*., 2m 19s. 1
Transit of eastern limb, 8 06 20 . 0 Add to apparent time.
Chro. time, loc. app. noon, 8 05 11 . 25
L. A. T., loc. app. noon, Ob 00m 00s
Eq. t., + 2 19.1
L. M. T., loc. app. noon, 0 02 19 . 1
Long., - 4 00 00
G. M. T., loc. app. noon, 8 02 19.1
Chro. time, loc. app. noon, 8 05 11 . 25
Chro. fast, 2 52 . 15
THE CHRONOMETER ERROR.
123
BY A SINGLE ALTITUDE (TIME SIGHT).
I. The problem involved in this solution, by reason of its frequent application
mining the longitude at sea, is one of the most important ones in Nautical
316,
in determining
Astronomy. It consists in finding the hour angle from given values of the altitude,
latitude, and polar distance. The hour angle thus obtained is converted by means
of the longitude and equation of time in the case of the sun, or longitude and right
ascension in the case of other celestial bodies, into Greenwich mean time; and this,
compared with the chronometer time, gives the error.
317. It should be borne in mind that the most favorable position of the heavenly
body for time observations is when near to the prime vertical. When exactly in
the prime vertical a small error in the latitude produces no appreciable effect.
Therefore, if the latitude is uncertain, good results may be obtained by observing the
sun or other body when bearing east or west. If observations are made at the same
or nearly the same altitude on each side of the meridian and the mean of the results
is taken, various errors are eliminated of which it is otherwise impossible to take
account, and a very accurate determination is thus afforded.
318. With a sextant and artificial horizon or good sea horizon, several altitudes
of a body should be observed in quick succession, noting in each case the time as shown
by a hack chronometer or comparing watch whose error upon the standard chronom
eter is known. Condensing the observation into a brief interval justifies the assump
tion that the altitude varies uniformly with the time. A very satisfactory method
is to set the sextant in advance at definite intervals of altitude and note the time as
contact is observed.
319. Correct the observed altitude for instrumental and other errors, reducing
the apparent to the true altitude.
If the sun, the moon, or a planet is observed, the declination is to be taken from
the Nautical Almanac for the time of the observation. If the chronometer correction
is not approximately known and it is therefore impossible to determine the Greenwich
mean time of observation with a fair degree of accuracy, the first hour angle found
will be an approximate one ; the declination corrected by this new value of the tune
will produce a more exact value of the hour angle, and the operation may be repeated
until a sufficiently precise value is determined.
320. In figures 48 and 49 are given:
• AM =7i, the altitude of the body M;
DM = d, the declination ; and
Q'Z = L, the latitude of the place.
In the astronomical triangle PMZ there may be found from the foregoing:
= z, the zenith distance of the body, = 90° — Ji;
124
THE CHKONOMETER ERROR.
PM = p, the polar distance, = 90° ± d; and
PZ =co.L, the co-latitude of the place, = 90° — L.
From these data it is required to find the angle MPZ the hour angle of the
body, =t. This is given by the formula:
snr5 * t =
cos L sin p
If we let s = J
this becomes:
sin J t = ^/sec L cosec p cos s sin (s — 7i).
The polar distance is obtained by adding the declination to 90° when of different
name from the latitude and subtracting it from 90° when of the same name. Like
latitude and altitude, it is always positive.
If the sun is the body observed, the resulting hour angle is the local apparent
time and is to be taken from the a. m. or p. m. column of Table 44 according as the
altitude is observed in the forenoon or afternoon. If the moon, a star, or a planet
be taken, the hour angle is always found in the p. m. column.
Local apparent time as deduced from an observation of the sun is converted to
local mean time by the application of the equation of time; then, by adding the
longitude if west and subtracting it if east, the Greenwich mean time is obtained.
The hour angle of any other body, added to its right ascension when it is west of
the meridian at observation or subtracted therefrom when east, gives the local sidereal
time, which may be reduced to Greenwich sidereal time by the application of the
longitude, and thence to Greenwich mean time by methods previously explained.
A comparison of the Greenwich mean time with the chronometer time of sight
gives the error of the chronometer.
EXAMPLE: January 20, 1916, p. m., in Lat. 48° 4V 00" S., Long. 69° 03' 00" E., observed a series
of altitudes of the sun with a sextant and artificial horizon; mean double altitude, 59° 03' 10", images
approaching; mean of times by comparing watch, 4h 40m 56s; C — W, 7h 23m 25s; index correction, - V 30";
approximate chronometer correction,— Om 10s. What was the exact chronometer error?
W. T.. 4h
C— W, 7
40°> 56s Obs. 2 alt. Q 59° 03' 10"
23 25 I.C., 1 30
Dec. Oh.,
20° 20'.8 S.
Eq. t. Oh, 10"» 5K7
H. D., + Qs.7
G. M. T., Qh.07
Chro. t., 0
04 21
0 10
2)59 01 40
G.' M.''T.,
Corr
Oh.07
App. . .,
29 30 50
+ 14 43
ft' 03 <?
Corr., + 0".049
Eq. t., Oh 4* 11", 10m sie.8
(Add to apparent time.)
4h 30m408. 4
+ 10 51.8
App. G. M. T., 0
1
L
P
s
s—h
L. A
04 11 g)rr.,
ft,
S.D.,
p. & r.,
Corr.,
29° 45' 33"
48 41 00
69 39 14
Dec.,
18031
02798
43906
84403
20° 20' 46" S.
69° 39' 14"
L. A. T.,
Eq. t.,
L. M. T.,
Long.,
G. M. T.,
Chro. t.,
Chro. slow,
29 45 33
+ 16' 17"
- 1' 34"
+ 14' 43"
sec
cosec
cos 9.
sin 9.
4 41 32.2
-4 36 12 . 0
2)148 05 47
74 02 54
44 17 21
. T., 4h 30m408.4
0 05 20.2
0 04 21.0
2)19.
49138
0 00 59.2
sin | t 9.
74569
THE CHRONOMETER ERROR.
125
EXAMPLE: May 18, 1916, p. m., in Lat. 8° 03' 22" S., Long. 34° 51' 57" W., observed a series of
altitudes of the star Arcturus. east of the meridian, using artificial horizon; mean double altitude,
60° KK; mean watch time, 6h 50» 32s; C— W, 2h 20™ 59V5; I. C., +2' 00". Find the true error of the
chronometer.
N.
W. T.,
r1 w
6»
2
50m
20
32s
59.5
Obs. 2 alt. #, 60°
I. C., +
1(X 00"
2 00
R. A. :
*:, 14h llm 52».9
Dec. #, 19° 36
/ 54//
Chro. t., 9
h 30°
L 8
p 109
11
04'
03
36
31.5
20"
22
54
2)60
12 00
P,
109° 36
14h llnl
- 3 36
/ 54//
52s. 9
01.3
30
ref.,
06 00
1 40
h, 30
sec . 00431
cosec . 02596
cos 9. 44372
sin 9. 84019
04 20
R. A. #,
H. A.,
L. S. T.,
Long.,
G. S. T.,
R. A. M. S., 0",
Sid. int. from O11,
Red. (Tab. 8),
G. M. T.,
Chro. t.,
10
+ 2
35
19
51.
27.
6
8
I
s-h
H.A.,
2)147
44
36
73 52
43 47
3h36m01«
18
58
.3E.
12
- 3
55
43
19 .
20.
4
8
2)19. 31418
9
11
1
58.
30.
6
4
sin * t 9. 65709
9
9
10
11
28.
31.
2
5
Chro. fast,
1 03.3
BY DOUBLE ALTITUDES OB ALTITUDES ON OPPOSITE SIDES OF THE MEBEDIAN.
320. Instead of relying on a single determination of the chronometer error from
altitudes on one side of the meridian, it is better to observe the same body on both
sides of the meridian, and, if possible, at about the same altitude. The error of the
chronometer having been found from each set of sights, the mean is taken as the
correct error, and this mean will probably be nearer the true error than the result
from either set,' the effect of the constant errors of latitude, instrument, and observer,
being opposite in the two cases, will be eliminated by taking the mean.
CHAPTER XII.
LATITUDE,
BY MERIDIAN ALTITUDE.
321. The latitude of a place on the surface of the earth, being its angular
distance from the equator, is measured by an arc of the meridian between the zenith
and the equator, and hence is equal to the declination of the zenith; therefore, if the
zenith distance of any heavenly body when on the meridian be known, together with
the declination of the body, the latitude can be found.
Let figure 50 represent a projection of the celestial sphere on the plane of the
meridian NZS; O, the center of the sphere; NS, the horizon; P and P', the poles of
the sphere; QOQ', the equator; Z, the zenith of the
observer. Then, by the above definition, ZQ will
be the latitude of the observer; and NP, the altitude
of the elevated pole, will also equal the latitude.
Let M be the position of a heavenly body north
of the equator, but south of the zenith; QM = d, its
declination^ MS = /i, its altitude; and ZM = z = 90°
— Jij its zenith distance.
From the figure we have:
QZ = QM+MZ, or
FIG. 50.
By attending to the names of z and d, marking
the zenith distance north or south according as the
zenith is north or south of the body, the above
equation may be considered general for any position of the body at upper transit,
asM, M', M".
In case the body is below the pole, as at M"' — that is, at its lower culmination —
the same formula may be used by substituting 180° — d for d. Another solution is
given in this case by observing that:
NP=PM'"
or
322. A^common practice at sea is to commence observing the altitude of the
sun's lower limb above the sea horizon about 10 minutes before noon, and then, by
moving the tangent-screw, to follow the sun as long as it rises; as soon as the highest
altitude is reached, the sun begins to fall and the lower limb will appear to dip.
When the sun dips the reading of the limb is taken, and this is regarded as the
meridian observation.
It will, however, be found more convenient, and frequently more accurate, for
the observer to have his watch set for the local apparent time of the prospective noon
longitude, or to know the error of the watch thereon, and to regard as the meridian
altitude that one which is observed when the watch indicates noon. This will save
time and try the patience less, for when the sun transits at a low altitude it may
remain "on a stand," without appreciable decrease of altitude for several minutes
after noon; moreover, this method contributes to accuracy, for when the conditions
are such that the motion in altitude due to change of hour angle is a slow one, the
motion therein due to change of the observer's latitude may be very material, and
thus have considerable influence on the time of the sun's dipping. This error is large
enough to take account of in a fast-moving vessel making a course in which there is a
good deal of northing or southing.
LATITUDE. 127
In observing the altitude of any other heavenly body than the sun, the watch
time of transit should previously be computed and the meridian altitude taken by
time rather than by the dip. This is especially important with the moon, whose
rapid motion in decimation may introduce still another element of inaccuracy.
323. The watch time of transit for the sun, or other heavenly body, may be
found by the forms given below, knowing the prospective longitude, the chronometer
error, and the amount that the watch is slow of the chronometer. In this connection,
article 404 describing the method of setting the watch to L. A. T. may be
profitably read.
For the Sun. For other Bodies.
h m •
L. A. T. noon, Oh 00m 00* L. S. T. transit, (Right ascension.)
Long. (+ if west), ± Long, (-{-if west), dt
G. A. T., G. S. T.,
Eq. t., ± R. A. M. S.,011, -
G. M. T., Sid int. from O11,
C. C. (sign reversed), T Red. (Tab. 8), -
Chro. time, G. M. T.,
O— W, - C. C. (sign reversed), T
Watch time noon, Chro. time,
C— W, -
Watch time transit,
324. From the observed altitude deduce the true altitude, and thence the true
zenith distance. Mark the zenith distance North if the zenith is north of the body
when on the meridian, South if the zenith is south of the body.
Take out the declination of the body from the Nautical Almanac for the time
of meridian passage, having regard for its proper sign or name.
The algebraic sum of the decimation and zenith distance will be the latitude.
Therefore, add together the zenith distance and the declination if they are of the
j same name, but take their difference if of opposite names; this sum or difference
i will be the latitude, which will be of the same name as the greater.
EXAMPLE: At sea, June 21, 1916, in Long. 60° W., the observed meridian altitude of the sun's lower
limb was 40° 4'; sun bearing south; I. C.,+3' 0"; height of the eye, 20 feet; required the latitude.
Obs. alt., 40° 04' 00" (Tab. 46), +10' 21" Dec., 23° 27M N. G. A. T., 4* 00*» 00-
Corr., + 13 21 I. C., + 3 00 Eq. t., 1 31 .7
H. D., 0 .0
ft, 40 17 21 Corr., +13' 21" G. M. T., 4 01 31 .7
z, 49° 42' 39" N. Eq. t., 4* 1m 31-.7
*, (Add to app. time.)
L, 73 09 45 N.
EXAMPLE: At sea, April 14, 1916, in Long. 140° E., the observed meridian altitude of the sun's lower
limb was 81° 15' 30"; sun bearing north; I. C.,-2' 30"; height of the eye, 20 feet.
Obs. alt.. 81° 15' 30" (Tab. 46), +11' 30" Dec., 13* 14*, 9° 14'.4 N. G. A. T.. 13<* 14^ 40°> 00" Eq. t., 13<i 14>>, 0" 26«.6
Corr., + 9 00 I. C., - 2 30 Eq. t., + 26 .2 Corr., .4
H. D., + O'.J
ft, 81 2430 Corr., + 9' 00" G. M. T., 0*>.67 G.M.T., 13 14 40 26.2 Eq.t.,13<i 14h40c°,0 26.2
«-» O OO OtF O . WU. i . j T <J . \JW H . 1 ' . , •" ' U8 . D
d, 9 15 00 N. Int., 0^7
L, 0 39 30 N. Corr., - (K42
EXAMPLE: At sea, May 15, 1916, in Long. 0°, the observed meridian altitude of the sun's lower
limb was 30° 13' 10"; sun bearing north; I. C.,+1' 30"; height of the eye, 15 feet.
Obs. alt., 30° 13' 10" (Tab. 46), +10' 32" Dec., 14<i 22*, 18° 50'.2 N. G. A. T., Oh 00"> 00"
Corr., + 12 02 I. C., +1 30 — — Eq. t., — 3 47 .5
H. D., + 0'.6
30 25 12 Corr., +12 02 G. M. T., 1^.94 G. M. T., 14d 23* 56* 12«.5
Corr.,
Dec.,
59° 34' 48" S. Corr.,
18 51 24 N.
40 43 24 S.
128 LATITUDE.
EXAMPLE: January 1, 1916, the observed meridian altitude of Siriua was 53° 23' 40", bearing south-
I. C.,+5' 0"; height of the eye, 17 feet.
Obs. alt., 53° 23' 40" (Tab. 46)-4/ 45" Dec. *, 16° 36' 00" S.
Corr., + _ 15 I. C. +5 00
h, 53 23 55 Corr. +0' 15"
2, 36° 36' 05" N.
d 16 36 00 S.
L, 20 00 05 N.
EXAMPLE: June 13, 1916, in Long. 65° W., and in a high northern latitude, the meridian altitude of
the sun's lower limb was 8° 16' 10" below the pole; height of the eye, 20 feet; I. C., CK 00".
Greenwich apparent time of lower culmination, June 13, 16h 20m (=Long.+12h).
Obs. alt., 8° 16' 10" (Tab. 46), + 5' 11" G. A. T.,-16h 20m 00»
Corr., 5 11 Eq. t., — 04. 3
A, 8 21 21 Dec-16h' 23°15/1N" G.M.T.,16>19-55-.7
— — H D 4. 0// 1
n Q1 ° QQ' QQ" Q ') \ v •*
z, 01 oo oy o. rj. M T nb ^
180°-d, 156 44 52 N. "«MrTM _ ° "^
L, 75 06 13 N. Oorr" + Q//-03
Alternative method. Dec., 23° 15' 08" N.
r oo 91 / 9 1 // ————_-»
;'( 66 44 52 P, 66° ^ 52"
L, 75 06 13 N. 180°-rf' 156° 44' 52" N.
EXAMPLE: July 10, 1916, in Long. 80° W., the observed meridian altitude of the moon's upper limb
was 59° 6X 40", bearing north; I. C., +2X 0"; height of the eye, 19 feet.
Obs. alt., 59° 06X 40" (Tab. 49), + 97 30" G. M. T., of Gr. transit 7h 40m
Corr., + 11 30 I. C., + 2 00 Corr. for Long. (Tab. 11),+ 13
h, 59 18 10 Corr., + IV 30" L. M. T. local transit, 7 53
30 41 50 S. Hor Par 59, 12/, L°ng" +_5_20_
d, 22 40 42 S. G. M. T., local transit, 13h 13m
L, 53 22 32 S. Dec 12h 22o 30/ 4 g H. D., ~ 8/5
Corr., 10.3 G. M. T., lh.22
Dec., 22° 40X.7 S. Corr., - lO^S
was 51
EXAMPLE: At sea, September 16, 1916, in Long. 75° E., the observed meridian altitude of Jupiter
51° 257 24", bearing north; I. C.,+3< 0"; height of the eye, 16 feet.
Obs. alt., 51° 25' 24" (Tab. 46),- 4/ 42" G. M. T., Gr. transit, 14h
Corr., 1 42 I. C., + 300 Corr. for Long.,
ft, 51 23 42 Corr., - 1' 42" L.M.T., of local transit, 14
2,
d,
38 36 18 S.
~ 5 °°
11 38 54 N. G.M.T. of local transit, 9 29
26 57 24 S- Dec. Oh, 11° 39r.5 N. H. D.,
Coir., - _ .6^ G. M. T.,
Dec., 11° 387.9 N. Corr., -37"=.6X
325. CONSTANT. — In working a meridian altitude, especially the daily nooni
observation of the sun, it is frequently a convenience to arrange the terms so that
aD computation, excepting the application of the observed altitude, is completed1
beforehand; then the ship's latitude will be known immediately after the sight has
been taken, it being necessary only to add or subtract the altitude. (See art. 323.) '
It is assumed that the noon longitude will be sufficiently accurately known in
advance to enable the navigator to correct the declination; also the approximate
meridian altitude to correct the parallax and refraction ; if the latter is not known,
it may readily be found from the declination and approximate latitude.
(Generally speaking,
Lat. = Zenith distance + Dec . ,
= 90° -True alt. + Dec.,
= 90° - (Obs. alt. + Corr.) + Dec.,
= (90° + Dec. - Corr.) - Obs. alt.,
LATITUDE. 129
in which the quantity (90° -f Dec. — Coir.) may be termed a Constant for the meridian
altitude of the day, as it remains the same regardless of what the observed altitude
may prove to be. The constant having been worked up before the observation is
made, the latitude will be known as soon as the observed altitude is applied.
To avoid the confusion that might arise from the necessity of combining the
terms algebraically according to their different names, it may be convenient to divide
the problem into four cases and lay down rules for the arithmetical combination of
the terms, disregarding their respective names as follows :
Case I. Lat. and Dec. same name, Lat. greater, -f 90° + Dec. — Coir. — Obs. alt.
Case II. Lat. and Dec. same name, Dec. greater, — 90° + Dec. -fCorr. + Obs. alt.
Case III. Lat. and Dec. opposite names, + 90° — Dec. —Corr. — Obs. alt.
Case IV. Lat. and Dec. same name, lower transit, +90° — Dec. + Corr. + Obs. alt.
The correctness of such an arrangement will become readily apparent from an
inspection of figure 50. The assumption has been made that tne correction to the
observed altitude is positive ; when this is not true the sign of the correction must
be reversed.
As examples of this method, the first, second, third, and fifth of the examples
previously given illustrating the meridian altitude will be worked, using the constant;
the details by which Corr. and Dec. are obtained are omitted, being the same as in
the originals.
IST EXAMPLE. 2D EXAMPLE. 3o EXAMPLE. STH EXAMPLE.
Case I. Case II. Case III. Case IV.
+ 90° 00' 00" -90° 00' 00" +90° 00' 00" +90° 00' 00"
Dec., + 23 27 06 Dec., + 9 15 00 Dec., -18 51 24 Dec., -23 15 08
Corr., - 13 21 Corr., + 9 00 Corr., - 12 02 Corr., + 5 11
Constant, + 113 13 45 Constant, -80 36 00 Constant, +70 56 34 Constant, +66 50 03
Obs. alt., - 40 04 00 Obs. alt., +81 15 30 Obs. alt., -30 13 10 Obs. alt., + 8 16 10
Lat., 73 09 45 (N.) Lat., 0 39 30 (N.) Lat., 40 43 24 (S.) Lat., 75 06 13 (N.)
BY BEDUCTION TO THE MERIDIAN.
326. Should the meridian observation be lost, owing to clouds or for other
reason, altitudes may be taken near the meridian and the times noted by a watch
compared with the chronometer, from which, knowing the longitude, the hour angle
may be deduced.
If the observations are within 26 m from the meridian, before or after, the correc
tion to be applied to the observed altitude to reduce it to the meridian altitude may
be found by inspection of Tables 26 and 27. Table 26 contains the variation of the
altitude for one minute from the meridian, expressed in seconds and tenths of a
second. Table 27 contains the product obtained by multiplying the square of the
minutes and seconds by the change of altitude in one minute.
Let a = change of altitude (in seconds of arc) in one minute from the meridian:
H = meridian altitude;
Ji = corrected altitude at observation; and
t = interval from meridian passage.
The value of the reduction to the meridian altitude of each altitude is found by
the formula:
a being found in Table 26, and at2 in Table 27; hence the following rule:
Find the hour angle of the body in minutes and seconds of time. Take from
Table 26 the value of a corresponding to the declination and the latitude. Take
from Table 27 the value of at2 corresponding to the a thus found and to the interval,
in minutes and seconds, from meridian passage. This quantity will represent the
amount necessary to reduce the corrected altitude at the time of observation to the
corrected altitude at the meridian passage; it is always additive when the body is
near upper transit, and always to be subtracted when near lower transit.
If the mean of a number of sights is to be taken, determine each reduction sepa
rately, take the mean of all the reductions, and apply it to the mean of the altitudes;
61828°— 16 - 9
130 LATITUDE.
it is incorrect, in such a case, to take the mean of the times and work the sight with
this single value of t. The differences of altitude being small, the parallax and
refraction will .be sensibly the same for all, and one computation of the correction to
the observed altitude will suffice.
Knowing the meridian altitude, the latitude is to be found as previously explained.
327. When several sights are taken, the most expeditious method of calculating
will be to find first the watch time of transit, and thence obtain the hour angle of each
observation by comparing the watch time of observation. The watch time of transit
may be found as already explained (art. 323) for computing that quantity as a guide
in taking the meridian altitude, but the hour angle thus obtained is subject to a
correction. The difference between watch time of transit and watch time of observa
tion gives the watch time — that is, the mean time — elapsing between transit and
observation. A fixed star covers in that time an angle corresponding to the sidereal
and not to the mean time interval, and a reduction should be made accordingly to
give its true hour angle at the instant of observation. A planet's hour angle should
be corrected in the same way (for we may disregard its very small change in right
ascension) . The correction may be entirely neglected in the case of the sun, as the
diiference between mean and apparent time intervals is immaterial. The reduction
of the hour angle in the case of the moon becomes rather cumbersome, so much so
that it is better to find the hour angle of this body by the more usual method of
converting watch time to G. M. T., and thence to L. S. T., and finding the difference
between the latter and the R. A. ; an additional reason for this is that the G. M. T.
of observation must be known exactly, with the moon, for the correction of the
declination (art. 330).
328. Table 26 includes values of the latitude up to 60°, and those of the declina
tion up to 63°, thus taking in all frequented waters of the globe and all heavenly
bodies that the navigator is likely to employ. No values 01 a are given when the
altitudes are above 86° or below 6°, as the method of reduction to the meridian is
not accurate when the body transits very near the zenith, and the altitudes themselves
are questionable when very low. In case it is desired to find the change of altitude
in one minute from noon for conditions not given in the tables, it may be computed
by the formula:
_ l"-9635 cos L cos d
sin (L— d)
In working sights by this method where great accuracy is required, as in deter
mining latitudes on shore for surveying purposes, it is well to compute the a rather '
than to take it from the table, as one is thus enabled to employ the value as found to |
the second decimal place.
Due regard must be paid to the names of the declination and latitude in working
this formula; if they are of opposite names, the declination is negative, and L and a
should be added together to obtain L — d.
329. Table 27 contains values of at2 up to the limits within which the method ,
is considered to apply with a fair degree of accuracy. It must not be understood
that the plan of reduction to the meridian is not available for wider limits, but it '
would seem preferable to employ the <j>' <$>" formula, described hereafter, when the
hour angle falls beyond that for which the table is computed. On the other hand,
the reduction is not exact in all cases covered by the table; while sufficiently so for
sea navigation, the limits given are far too wide for the precise determinations
required in surveying, where the aim should be to observe bodies under such conditions
that the total reduction at2 shall not exceed 1'.
330. It should be kept clearly in mind when employing the method of reduction
to the meridian that the resulting latitude is that of the ship at the instant of observa
tion, and to bring it up to noon the run must be applied. The declination should
properly be corrected for the instant of observation; with the sun or a planet, it is
sufficiently accurate to use the declination at meridian passage, unless the^ interval
from the meridian be quite large; but the moon's declination changes so rapidly that
the exact time of observation must be used in its correction when working with
this body.
LATITUDE. 131
EXAMPLE: In latitude 47° S., having previously worked up the constant for meridian altitude,
78° 42' 10", observed altitude of sun near meridian, 31° ll/ 50"; Dec. 11° N.; watch time, llh 40™ 21",
watch fast of L. A. T., 7s. Find the latitude.
Watch time, llh 40™ 21- Obs. alt., 31° IV 50" a (Tab. 26), 1".6
Watch fast, 07 at*, + 10 24
Her. alt,, 31 22 14 (1".0=6/30/
Constant, 78 42 10 ^ (Tab 2?) I . 6= 3 54
Lat., 47 19 56 S. [l .6=10 24
EXAMPLE: At sea, July 12, 1916, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude of
the sun's lower limb, 61° 48' 30", the time by a chronometer regulated to Greenwich mean time being
2n 4im 395. ckro. corr>j _2m 30» I. C.,— 3' 0"; height of the eye, 15 feet. Find the latitude.
Chro t 2h 41m39" Q 61° 48' 30" Dec. 2h, 21° 58'. 9 N. Eq.t.2h., 5m 24M
C. C., - 2 30 Corr., + 8 31
H. D., - V.4 H. D., + 0".3
G. M. T., 2 39 09 Ji, 61 57 01 G. M. T., 0*. 65 G. M. T., 0*. 65
Eq. t., -^ ^ (Tab. 46),+ IV 31" Corr., - O7. 26 Corr., + OM95
G. A. T., 2 33 44.7 I.C., - 3 00
Long -2 40 00.0 Dec., 21° 58' 38"N. Eq. t., 5m 24«. 3
Corr., + 8' 31" (Subtract from mean
L. A. T., 11 53 44.7 time.)
t, 6 15.3
ft, 61° 57' 01" a (Tab. 26), 2". 5
a«2,+ 1 38
* • ro// t) -t/ no//
H, 61 58 39 0 '?~ 0 90
gp(Tab.27),j° '5=='
2, 28 01 21 N. o *_i QG
J, 21 58 38 N.
L, 49 59 59 N.
EXAMPLE: May 31, 1916, in Lat, 30° 15' N., Long. 5h 25m 42" W., about 9 p. m., observed with a
sextant and artificial horizon a series of altitudes of Spica; mean observed double altitude 98° 06' 34";
noted times as enumerated below by a watch compared with a chronometer which was 2m 33s fast of
G. M. T.; C-W, 5h 29m 40s; I. C.,-3' 00". Find the latitude.
•p » .t- /T o rr\
transit) ' 13h 20m 48s. 9 Mean 2 alt, *, 98° 06X 34" R. A. *, 13h 20™ 48". 9
Long + 5 25 42 I. C., - 3 00 _,
T Dec., 10° 43X 42" S.
GST 18 46 30.9 2)98 03 34 ___
R \ M S. Gr. 0", 4 34 36 . 1 a (Tab. 26), 2". 5
49 01 47
Sid. int. from O11, 14 11*54.8 ref., - 50
Red. (Tab. 8), - 2 19 . 7
h, 49 00 57
G. M. T., 14 09 35.1
C. C. (sign reversed), + 2 33
Chro. time transit, 14 12 08 . 1
C-W, - 5 29 40
Watch time transit, 8 42 28
Intervals from transit, at2 (Tab. 27).
Watch times. Meantime. Sid. time. 2.0 0.5 2.5 h, 49° OO7 57" ;
8ti 33m05s.O - 9m23s. 0 - 9m 24« 2' 56" (X 44" 37 40" at 2, + 1 40
35 06.5 7 21.5 7 23 1 49 0 27 2 16
37 54.0 4 34.0 4 35 0 42 0 10 0 52 H, 49 02 37
40 37.0 1 51.0 1 51 0 07 0 02 0 09
42 54 . 5 -f 0 26 . 5 + 0 27 0 00 0 00 0 00 z, 40 57 23 N.
45 32.5 3 04.5 3 05 0 19 0 04 0 23 d, 10 43 42 S.
47 33.0 5 05.0 5 06 0 52 0 13 1 05
49 20.0 6 52.0 6 53 1 35 0 23 1 58 L, 30 13 41 N.
52 59.5 10 31.5 10 33 3 42 0 55 4 37
9)15 00
1 40
132
LATITUDE.
EXAMPLE: August 6, 1916, Lat. 59° S., Long. 175° 27' E., during evening twilight, observed an
altitude of Achernar, near lower transit, 26° 52'; watch time, 4h 31m 12s; C-W, Oh 18m 07§- chro fast of
G. M. T., 12m 42s; I. C., +1' 20"; height of eye, 24 ft. Find hour angle by both methods; thence the
latitude.
R. A. # + 12h \
L. S. T. lower trans./
Long.,
G. S. T.,
R. A. M. S. Gr. 5d Oh, -
Sid. int.,
Red. (Tab. 8),
G. M. T.,
C. C. (sign reversed), +
Chro. time,
C-W,
Watch time transit,
Watch time oba.,
. /Meantime,
1 \Sid. time,
Obs. alt. #, 26° 52' 00"
Corr., 5 23
h,
13h
11
34m
41
38».4
48
1
8
52
54
50.4
48.9
16
58
2
01.5
46.8
16
55
12
14.7
42
5
0
07
18
56.7
07
4
4
49
31
49.7
12
18
18
37.7
40.8
Watch time,
C-W,
Chro. t.,
C. C.,
G. M. T. 5d
R. A. M. S. Gr. 5d Oh, +
Red. (Tab. 9),
G. S. T.,
Long.,
L. S. T.,
R. A. # -f 12h
4h
31*
1 12s
+ o
18
07
4
49
19
—
12
42
16
36
37
+ 8
54
48.9
+
2
43.7
1
34
09.6
+ 11
41
48
13
15
57.6
13
34
38.4
(Tab. 46), -6' 43"
I.C., +1 20
H,
P,
26° 46' 37"
3 29
26 43 08
32 20 48
59 03 56 S.
Corr.,
5' 23'
R. A. #,
Dec.,
P,
a (Tab. 26),
at2 (Tab. 27),
18 40.8
lh 34m 38. 84
57° 39' 12" S.
32° 20' 48 ''
0".6
3' 29"
331 . Advantages are gained in working out meridian altitudes and reductions to
ike meridian, in finding the constant for a meridian altitude or a reduction to the
meridian, and in predicting the approximate altitude of a body to be observed on
or near the meridian, by projecting, in a quickly and roughly drawn diagram on the
plane of the meridian of the observer, the known data entering into the problem.
The diagram or figure will show at once how to combine the data to find the required
result, and its use tends greatly to accuracy. It is
only necessary to know the meaning of the terms
already defined and to remember the single principle
that the latitude of a place is equal to the declination
of its zenith.
In every case draw a circle (a rough approxima
tion will do) to represent the plane of the meridianj as
in figure 51. The center O is the position of the ob
server. Draw a horizontal line through O, marking
its intersection with the circumference on the right-
hand side S, and on the left-hand side N. Erect a
perpendicular to this line at O, and mark its inter
section with the circumference Z. The line NS is
the horizon; Z is the zenith. The arc ZS is that por
tion of the meridian between the zenith and the south
point of the horizon; the arc ZN is that portion of the
meridian between the zenith and the north point of the horizon. If the meridian
altitude of a body is known (i. e., its altitude above the horizon on the meridian),
and if it is known whether it bears to the southward or to the northward, its posi-
FlO. 51.
LATITUDE. 133
tion can be projected at once on the figure. Having the position of the heavenly
body on the meridian and knowing the declination of the body, it is evident where
to draw in the projection of the equator. Having the projection of the equator,
the angular distance between the equator and the
zenith (i. e., the declination of the zenith) is the
latitude.
Thus in figure 52, supposing the meridian alti
tude of any heavenly body, M, nas been observed,
and that at the time of observation it was bearing
south; also that the declination, d, of the body was
south. It is known that the true altitude, h, =
observed altitude ± altitude coir. Since the body
bears south, if the true altitude is h, the position
of the body, M, can be located by laying off the
arc SM=ft, or bv drawing OM so that tne angle
BOM = ft. This gives the position of the heavenly
body on the meridian. Since this body is south of _
the equator by the amount of the declination, the FIG. 52.
position of the equator may be drawn by laying off
the angle MOQ = a. OQ is the projection of the equator, and the arc ZQ (or the
angle ZOQ), being the declination of the zenith, is equal to the latitude. The for
mula for finding the latitude may be written by inspection of the figure:
L = 90°-(ft + <Z) = 90°-A-(Z. (1)
Since ^=obs. alt.±corr.,
L=90°-obs. alt.±corr.-d. (2)
By a similar process formulae may be written for determining the approximate
altitude of the heavenly body when on the meridian and for getting a noon constant.
The former is necessary to get the altitude correction before taking the sight ; the
latter, so that the latitude may be obtained as soon as the altitude is read from the
sextant. In these cases the D. R. latitude and longitude, which have to be worked
out in advance for noon, are used. The longitude is used to get the correction to be
applied to the equation of time to get the G. M. T. of local apparent noon in order to
get the correct declination at Local Apparent Noon at the noon position. Knowing
the approximate latitude and the declination, they are projected on the figure in this
way. If the latitude is north, the zenith is to the northward of the equator by
the amount of the latitude, and to get the position of the equator lay off the angle'
ZOQ = Lat. If the latitude were south, the equator would of course be on the north
side of the zenith by the amount of the latitude, and OQ would be on the north side of
the circle. Having the position of the equator, draw in the position of the heavenly
body by laying it off to the north side or to the south side of the equator according
to the amount and direction of its declination. The angle between the horizon and
the heavenly body will be the altitude of the body. This is the usual method of
plotting, and all that has to be done is to lay the angles off on the proper sides,
marking them appropriately, and then write down the formulae. Suppose it is
required to find the approximate noon altitude. An inspection of the figure shows
that
approx. 7i = 90° - (L + d) where L is the D. R. Lat. (3)
Suppose it is required to find the constant (K) for a meridian altitude. It is
seen from the figure that
= K-obs. alt.
or
K = 90°±corr.-d. (4)
In the same way any combination may be plotted, and the correct formulae may
be written out at once. Suppose on a certain day it is found that at noon the
position will be approximately Lat. 10° S., Long. 30° 15' W., and that the declination
of the sun at noon, corrected for G. M. T. of local apparent noon at the noon position,
134
LATITUDE.
is 20° 30' S., and it is desired to find the approximate noon altitude and obtain the
constant, K. Draw the circle representing the plane of the meridian (see fig. 53),
draw NS representing the horizon, and OZ representing the line to the zenith. Since
the approximate latitude is 10° S, the equator must be 10° north of the zenith, and
OQ is drawn to the north of Z so that the angle ZOQ = 10°. OQ is then the pro
jection of the equator^ JThe body being 20° 30' south
M °f
the equator, lay off OM so that the angle QOM =
20° 30'. SOM will be the approximate altitude, and
the formula for it is
approx. 7i = 90° + L - d
it is also seen that
SL
(5)
alt.
or
If, instead of the formulae for a meridian altitude,
the formulsB for a reduction to the meridian are re-
no. 53. quired, ^there is no change in the figure or the method.
The altitude observed before or after noon is corrected
to make it the noon altitude by the formula Ji = 1\>' + at2, where h is the noon alti
tude, h' the altitude observed t minutes before or after noon, and a the rate of
change of altitude near noon. So that in the case shown in figure 53
or
The formula for the approximate value of h, as shown in (5), is used for getting
the altitude correction in this case, as the slight difference in altitude makes no
change in the correction.
The formula for latitude, given in equation (6), is the formula for the latitude at
noon at the point where the observation was taken. But a ship steaming on a
course does not remain at that point, and what is desired is the correct latitude of
the ship's position at noon. If L' represents the latitude of the place where the
observation was taken, and L the latitude of the place where the ship is at noon,
then L = L'± JL, where JLis the change in latitude from the time of observation
until noon. This is taken from the Traverse Tables. But from equation (6) it is
seen that L' = obs. alt. ± corr. + at2 + d - 90°
or
.'.L=L'±JL=obs. alt
= K + obs. alt.
K=
BY A SINGLE ALTITUDE AT A GIVEN TIME.
332. This observation should be limited to conditions where the body is within
three hours of meridian passage and where it is not more than 45° from the meridian
in azimuth; also where the declination is at least 3°. On ^the prime vertical the
solution by this method is inexact, and when the hour angle is 6h, or the declination
0°, it is impracticable.
The problem is: Given the hour angle, declination, and altitude; to find the
latitude. The solution is accomplished by letting fall, in the usual astronomical
triangle, a perpendicular from the body to the meridian, and considering separately
the distances on the meridian, from the pole and zenith, respectively, to the j)oint
of intersection of the perpendicular; the sum or difference of these distances is the
co-latitude.
LATITUDE. 135
Following the usual designation of terms and introducing the auxiliaries <j>'
and <£", the formulae are as follows:
tan (f>" = tan d sec t;
cos </>' =sin h sin <j>" cosec d;
lj == <z> -j- o .
The terms </>' and (f)" will have different directions of application according to
the position of the body relative to the observer. From a knowledge of the
approximate latitude, the method of combining them will usually be apparent; it is
better, however, to have a definite plan for so doing, and this may be based upon the
following rule :
Mark <j>" north or south, according to the name of the declination; mark <£'
north or south, according to the name of the zenith distance, it being north if the
body bears south and east or south and west, and south if the body bears north and
east or north and west. Then combine cf>" and <£' according to their names; the
result will be the latitude, except in the case of bodies near lower transit, when
180°— <f>" must be substituted for $" to obtain the latitude.^
It may readily be noted that if we substitute $" for declination and <j>' for zenith
distance, the problem takes the form of a meridian altitude; indeed, the method
resolves itself into the finding of the zenith distance and declination of that point on
the meridian at which the latter is intersected by a perpendicular let fall from the
observed body.
The time should be noted at the instant of observation, frotn which is found the
local time, and thence the hour angle of the celestial object.
If the sun is observed, the hour angle is the L. A. T. in the case of a p. m. sight,
or 12h — L. A. T. for an a. m. sight. If any other body, the hour angle may be found
as hitherto explained.
EXAMPLE: June 7, 1916, in Lat. 30° 25' N., Long. 81° 25' 30" W., by account; chro. time, 6h 22m 52';
obs. Q 75° 13', bearing south and west; I. C., — 3' 00"', height of the eye, 25 feet; chro. corr. -2m 36s.
Find the latitude.
Chro. t, 6h 22m 52» Obs.alt.Q, 75° 13' 00" Eq. t., 6^, 1» 20-.4 Dec., &>, 22° 46'.6 N.
C. C., — 2 36 Corr., -f 7 39 Coir., .2 Corr., + .07
G.M.T., 6 20 16 A, 75 20 39 Eq.t., 1 20.2 Dec., 22° 46' 40" N.
(Tab. 46). + 10' 39" H. D., - 0*.5 H. D., + 0'.2
G.A.T., 6 21 36 I. C., - 3 00 G. M. T., Qh.3 G. M. T., Qh.33
Long., - 5 25 42
Corr., + 7' 39" Corr., - O».15 Corr., 0'.066
TAT/ / Oh 55"* 54» "VY". (Add to mean time.)
L.A.T.=f, \ir & 30"
t, 13° 58' 30" sec . 01305
d, 22 46 40 tan 9.62315 cosec .41211
75 20 39 sin 9.98563
23 23 55 N. tan 9.63620 sin 9.59893
7 05 00 X. cos 9.99667
Lat., 30 28 55 X.
EXAMPLE: October 10, 1916, p. m., in Lat. 6° 20' S. by account, Long. 30° 21' 30" W.; chro. time,
12h45m10«; observed altitude of moon's upper limb, 70° 15' 30", bearing north and east; I. C., —3' 00"]
height of eye, 26 feet; chro. fast of G. M. T., lm 378.5. Required the latitude.
Chro.t., 12h 45m iQe Obs.alt. d, 70° 15' 30" R. A. C (12h), Oh 42m 16- Dec.(12h), 9° 52'.9 N.
C. C., - 1 37.5 Corr., - 4 27 Corr., -f 1 32 Corr., + 10.1
G.M.T., 12 43 32.5 h, 70 11 03 R. A., Oh 43" 48» Dec., 10° 03' N.
Red.(Tab.9),+ 2 05.4 (Tab. 49), - 1' 27" H. D., + 128-.5 H. D., + 14'.05
I.C., - 3' 00" G. M. T., Oh.?2 G.M.T., Qh.72
G.S.T., 2 00 39.3
R.A.£, - 0 43 48.0 COTT., - 4' 27" Corr., + 92".5 Corr., + lO'.ll
H.A.fromGr., 1 16 51.3W.
Long., 2 01 26 .0 W.
i?«?#iR Hor-Par" 58MS"
136
LATITUDE.
t. 11° 08' 40//
d, 10 03 00
h, 70 11 03
<£", 10 14 21 N.
<£', 16 36 00 S.
Lat. 6 21 39 S.
sec
tan
. 00827
9.24853
cosec .75819
tan 9.25680
sn
sin
cos
9.97349
9.24983
9. 98151
EXAMPLE: August 6, 1916, p. m., in Lat. 52° W S. by D. R., Long. 146° 32' E., observed altitude of
Achernar, near lower transit, 24° OK 20" bearing south and east; watch time, 6h 48m 22s; C-W, 2h 13m
33'; chro. corr. on G. M. T., + lm 57s; height of eye, 18 feet; I. C. +1/ 00". Find the latitude.
Watch time,
C-W,
Chro. t.,
C.C.,
6h 48m 22-
+ 2 13 33
9 01 55
+ 1 57
Obs. alt.*,24° OF 20"
Corr., - 5 19
G. M. T. 5d, 21 03 52
R.A. M. S., + 8 54 48.9
Red. (Tab. 9), + 3 27.6
(Tab. 46),
I. C.,
Corr.,
23 56 01
-
- 6' 19"
+ 1 00
R. A.
Dec.,
:, lh 34m 38S.4
57° 39' 12" S.
- 5' 19"
G.
S.
T.,
6
02
08.
5
R.
A.
*,
1
34
38.
4
H.
A.
from Gr.,
4
27
30.
1W.
Long.
»
9
46
08
E.
H.
A.
p
14
13
38
W.
9
46
22
E.
i
2h
33°
13"
24'
>388
30/
/
i
33
57
24
39
30
12
h,
23
56
01
180° -V', 117
51
52 S.
•,
64
52
49 N.
Lat.
t
52
59
03 S.
sec. . 07843
tan. . 19838
tan. .27681
cosec.
sin.
sin.
cos.
.07323
9.60818
9. 94648
9. 62789
If the sidereal time is
BY THE POLE STAB.
333. This method, confined to northern latitudes, is available when the star
Polaris and the horizon are distinctly visible, the time of the observation being noted
at the moment the altitude is measured.
Reduce the observed altitude of Polaris to the true altitude.
.Reduce the recorded time of observation to the local sidereal time.
less than lh 29.2m, subtract it from lh 29.2m;
between lh 29.2m and 13h 29.2m, subtract lh 29.2m
from it ;
greater than 13h 29.2m, subtract it from 25h 29.2m;
and the remainder is the hour-angle of Polaris.
With this hour-angle take out the correction from Table I of the Nautical
Almanac, and add it to or subtract it from the true altitude, according to its sign.
The result is the approximate latitude of the place.
EXAMPLE: 1916, August 5, at 1011 40m 30s p. m. local mean solar time, in longitude 59° west of Green
wich, suppose the true altitude of Polaris to be 33° 20X 0", required the latitude of the place.
Local astronomical mean time 10h 40m 30'
Reduction from Table 9 for 10h 40m 30s + 01 45
Greenwich sidereal time of mean noon, August 5 8 54 49
Reduction from Table 9 for longitude (=3b 56m west, or plus) + 00 39
Sum (having regard to signs) is equal to local sidereal time 19 37 43
Subtract sidereal time..
25h 29m 12s
19 37 43
Remainder is equal to hour angle of Polaris
5 51 29
LATITUDE.
137
True altitude +33° 20' 00"
Correction from Table I of the Nautical Almanac — 1 51
Approximate latitude of the place +33 18 09
Observations of Polaris for latitude should be made when practicable near the
times of upper or of lower culminations (hour angle Oh or 12h). However, at sea,
if made near elongation (hour angle 6h or 18h), the hour angle, and hence the local
time, should be known within one minute.
334. The latitude may be approximately found from an altitude of Polaris by
computation from the formula:
L = h ± p cos t ,
in which,
h = true altitude, deduced from the observed altitude ;
p = polar distance = 90 ° — d, the apparent decimation being taken from the
Nautical Almanac for the time of observation.
t = star's hour angle.
Reduce the recorded time of observation to the local sidereal time.
Take out, from the Nautical Almanac, the apparent right ascension of Polaris
for the time of observation.
Subtract the apparent right ascension from the local sidereal time, and the
remainder will be tne hour angle.
To the log cosine of the hour angle add the logarithm of the polar distance in
minutes; the number corresponding to the resulting logarithm will be a correction
in minutes to be subtracted from the star's true altitude to find the latitude when the
hour angle is less than 6h or more than 18h, and to be added to the star's true altitude
to find the latitude when the hour angle is more than 6h and less than 18h.
EXAMPLE: June 11, 1916, from an observed altitude of Polaris, the true altitude was found to be
29° 5' 55". The time noted by a Greenwich chronometer was 13h 41m 26s; chro. corr.-2m 22§; Long.
5h 25m 42s W.
Chro. time,
C.C.,
G. M. T., lld,
R. A. M. S.,
Red. (Tab. 9),
—
13h
41"
2
126§
22
+
+
13
5
39
17
2
04
58.2
14.5
p cos
Lat.,
29° 05'
t,+ 1 08
55"
36
30 14 31 N.
R. A.
Dec.,
lh 29m19«
88° 51
G. S. T., 18 59 17
R. A. #, - 1 29 19
H. A. fromGr.,
Long.,
H. A.,
17 29 58 W.
5 25 42 W.
12 04 16 W.
/ llh 55m44s E.
\178° 56' 00"
P,
p, 68'. 6
t, 178° 56'
.
pcos f,-
68'.
08/
log 1. 83632
cos(-) 9.99992
-) 1.83624
If the computation is extended according to the following formula, inserting the
value of p in seconds of arc :
p* sin 1" sin2 1 tan h,
cos
the resulting latitude is subject to no greater error than 1" ; but if p cos t is the only
correction applied to the altitude of Polaris, as in the above example, the resulting
latitude, while subject to little error when Polaris is observed near the meridian, wifl
have an error, when t = 6 hours, increasing with the altitude and amounting to 1'
when ft = 54° and to 3' when ft = 68° 30'.
DETERMINATION ON SHORE.
335. In finding the latitude on shore all the methods are available that have
been heretofore explained for employment in finding the latitude at sea, provided
only that an artificial horizon (art. 256) be supplied to take the place of the natural
horizon of the sea in obtaining a measurement, by the sextant, or the altitude of the
celestial body. In addition, other methods may be conveniently employed, involving
138 LATITUDE.
the use of a theodolite or an altazimuth instrument, which the observer at sea is
precluded from using because the employment of such instruments requires a steady
platform.
If the observation is to be made with a theodolite or altazimuth> the instrument
must first be placed level so that the line of collimation of the telescope revolves in
the plane of the true meridian. This may be accomplished by means of laying off a
true meridian from the true bearing of a terrestrial object from the instrument, as
determined by the observation described in articles 360 and 361.
The altitude of the celestial body is then measured by bringing the horizontal
cross wire of the telescope on the body at the instant the body transits the meridian
or crosses the vertical cross wire of the telescope, and then reading the vertical
circle.
The latitude is then deduced from the formula, ~L = d + z, after applying the proper
corrections for index error, parallax, and refraction. The correction for index error
is obtained by bringing the telescope to a horizontal position, as indicated by the
level tube attached to the telescope, and taking the corresponding reading of the
vertical circle immediately before and after each observation.
By observing the altitude of each of two stars with approximately the same
zenith distance, one north of the zenith and one south of the zenith, a mean value
for latitude resulting from the two observations may be obtained which is not
affected by the error in estimating the absolute value of the astronomical refraction,
but simply by the error in estimating a very small difference of refraction of two
stars at nearly the same altitude.
This method of determining the latitude of a station is known as the Horrebow-
Talcott method, and consists of the measurement of the small differences of zenith
distance of two stars which transit at about the same time on opposite sides of the
zenith. The effect of this procedure is the attainment of greater precision due to
the increased accuracy of a differential measurement over the corresponding absolute
measurement, the elimination of the use of a graduated circle in the measurement,
and the fact that the computed result is not affected by the error in estimating the
absolute value of the astronomical refraction, but simply by the error in estimating
a very small difference of refraction of two stars at nearly the same altitude.
After measuring the difference of meridional zenith distances of two stars which
transit at about the same time on opposite sides of the zenith and with nearly the
same zenith distances, the latitude may be deduced from the following formula:
Let d = decimation of star south of zenith.
d' = declination of star north of zenith.
2 = zenith distance of star south of zenith.
z' = zenith distance of star north of zenith.
Then L = d + z
that is, the latitude is equal to one-half the sum of the declinations plus one-half the
difference of zenith distances. The form of instrument used in measuring the differ
ences of zenith distances is known as a zenith telescope, and consists of a telescope
mounted on a horizontal axis supported by an upright or uprights in such a manner
that it can be revolved about a vertical axis. A vertical circle is attached to the
telescope for use in setting the telescope at the proper inclination with the horizontal i
to bring a particular star into the field of the telescope. A level tube is also attached
to the telescope for use in bringing the telescope to the same inclination when observ
ing on each of a pair of stars. The eyepiece of the telescope is fitted with a micro
meter screw which operates a movable horizontal cross wire with which the bisections
of the image of the observed body are made.
The process of observing for difference of zenith distances is as follows: If the
first star of the pair of stars to be observed has a]sollth zenith distance the telescope
is revolved about its vertical axis until it pointsj soutn in the plane of the meridian.
LATITUDE. 139
The approximate mean zenith distance of the two stars is then set off on the vertical
circle, and the level bubble brought to the center of the tube. When the star appears
in the field of the telescope the horizontal cross wire is brought to bisect the star
and such bisection retained until the star crosses the vertical cross wire of the tele
scope. The micrometer head is then read. The telescope is then revolved through
180° about its vertical axis and brought to the same inclination with the horizontal
by moving the telescope itself about its horizontal axis^ until the level bubble is at
the center of the tube. In like manner the second star is bisected by the horizontal
cross wire and the micrometer head again read. The difference between the two
micrometer readings gives the difference of zenith distances of the two stars in terms
of divisions of the micrometer, which when multiplied by the known angular value
of one division of the micrometer gives the angular difference of the zenith distances
of the two stars.
CHAPTER XIII.
LONGITUDE.
336. The longitude of a position on the earth's surface is measured by the arc
of the equator intercepted between the prime meridian and the meridian passing
through the place, or by the angle at the pole between those two meridians.
Meridians are great circles of the terrestrial sphere passing through the poles.
The prime meridian is that one assumed as the origin, passing through the
location of some principal observatory, such as Greenwich, Paris, or Washington. That
of Greenwich is the prime meridian not only for English and American navigators, but
for those of many other nations.
Secondary meridians are those connected with the primary meridian, directly
or indirectly, by exchange of telegraphic time signals.
Tertiary meridians are those connected with secondaries by carrying time in the
most careful manner with all possible corrections.
Longitude is found by taking the difference between the hour angle of a celestial
body from the prime meridian and its hour angle, at the same instant, from the local
meridian. In determinations ashore the hour angle from the prime meridian may
be found either from chronometers or from telegraphic signals; the local hour angle
may be found by transit instrument or by sextant. In determinations at sea the
chronometer and sextant give the only means available.
DETERMINATION ON SHORE.
337. TELEGRAPHIC DETERMINATION OF SECONDARY MERIDIANS. — In order to
locate with accuracy the positions of prominent points on the coasts, it is necessary
to refer them, by chronometric measurements, to secondary meridians of longitude
which have been determined with the utmost degree of care.
Before the establishment of telegraphic cables, this was attempted principally
through the observation of moon culminations, which seemed always to carry with
them unavoidable errors, or by transporting to and fro a large number of chronometers
between the principal observatory and the position to be located; and in this method
it can be conceived that errors would be involved, no matter how thorough the
theoretical compensation for error of the instruments.
By the aid of telegraph and radio, differences of longitude are determined with
great accuracy, and an ever-increasing number of secondary meridional positions are
thus established over the world; these afford the necessary bases in carrying on the
surveys to map correctly the various coast lines, and render possible the publication
of reliable and accurate navigators' charts.
338. To determine telegraphically the difference of longitude between two points,
a small observatory containing a transit instrument, ^chronograph, break-circuit
sidereal chronometer, and a set of telegraph instruments is established at each of the
two points, and, being connected by a temporary wire with the cable or land line at
each place, the two observatories are placed in telegraphic communication with each
other.
By means of transit observations of stars, the error of the chronometer at each
place on its own local sidereal time is well determined, and the chronometers are
then accurately compared by signals sent first one way and then the other, the times
of sending and receiving being very exactly noted at the respective stations. The
error of each chronometer on local sidereal time being applied to its reading, the
difference between the local times of the two places may be found, and consequently
the difference of longitude. The time of transmission over the telegraph line is
eliminated by sending signals both ways. By the employment of chronometers
14O
LONGITUDE. 141
keeping sidereal time, the computation is simplified, though mean-time chronometers
may be used.
339. ESTABLISHMENT OF TERTIARY MERIDIANS. — Let it be supposed that the
meridional distance between A and B is to be measured, of which A is a secondary
meridional position accurately determined, and B a tertiary meridional position to
be determined.
If possible, two sets of observations should be taken at A to ascertain the errors
and rates of the chronometers. The run is then made to B, and observations made
to determine local time, and hence the difference of longitude; and on the same spot
altitudes of the sun, or of a number of pairs of stars, or both, should be taken to
determine the latitude.
Now, if chronometer rates could be relied on to be uniform, this measurement
would suffice, but since variations may always arise, the run back to A should be
made, or to another secondary meridional position, C, and new rates there obtained.
Finally, the errors of the chronometers on the day when the observations were made
at the tertiary position should be corrected for the loss or gain in rate, and for the
difference of the errors as thus determined.
When opportunity does not permit obtaining a rate at the secondary meridional
station or stations, both before and after the observations at B, the navigator may
obtain the .errors only, and assume that the rate has been uniform between those
errors.
A modification of the foregoing method which may sometimes prove convenient
is to make the first and third sets of observations at the position of the tertiary
meridian, and the intermediate one at the secondary meridian; in this case the error
will be obtained at the secondary station and the rate at the tertiary.
EXAMPLE: A vessel at a station A, of known longitude, obtained chronometer errors as follows:
May 27, noon, chro. slow, 7m 18'. 9,
June 3, noon, chro. slow, 7 12 . 7;
then proceeding to a station B a series of observations for longitude was taken on June 17; after which,
returning to A, the following errors were obtained:
July 3, noon, chro. slow, 7m 00*. 7,
July 10, noon, chro. slow, 6 59 . 8.
Required the correct error on June 17.
May 27, -7m 18*. 9 July 3, -7m OO4. 7
JuneS, -7 12.7 July 10, -6 59.8
Change, -f- 6.2 Change, +
Daily rate, + 0s. 89 Daily rate, +
Therefore, assuming that these rates were correct at the middle of the periods for which they were
determined, we have,
May 30, Midnight, Rate, +0'. 89
July 6, Midnight, Rate, +0 . 13
Change of rate, 37 days, —0 . 76
Daily change of rate, —0s. 021
Change of rate for 3£ days, -Of.07; rate June 3, noon, +0«.89-0a.07=+0i. 82
Change of rate for \1\ days, -0 .37; rate June 17, noon, +0 .89-0 .37= +0 . 52
Mean daily rate, June 3 to 17, +0 . 67
Total change of error, June 3 to 17, +0m 09*. 38
Error, June 3, -7 12 . 7
Error, June 17, -7 03 . 3
34:0. SINGLE ALTITUDES. — The determination of longitudes on shore by single
altitudes of a celestial body is identical in principle with the determination at sea
by that method, which will be explained hereafter (art. 341). It may be remarked,
however, that by taking observations on opposite sides of the meridian, at altitudes
as nearly equal as posssible, a means is afforded, which is not available at sea, of elimi
nating certain constant errors of observation.
142
LONGITUDE.
DETERMINATION AT SEA.
341. THE TIME SIGHT. — A method of determining longitude at sea is that of
the time sight, sometimes called the chronometer method. The altitude of the body
above the sea horizon is measured with a sextant and the chronometer time noted;
the hour angle of the body is then found by the process described in article 316,
Chapter XI.
If the sun is observed, the hour angle is equal to the local apparent time; the
Greenwich apparent tune may be determined by applying the equation of time to the
Greenwich mean time as shown by the chronometer; the longitude is then equal to
the difference between the local and the Greenwich apparent times, being east when
the local time is the later and west when it is the earlier of the two.
If any other celestial body is employed, the hour angle from the local meridian,
found from the sight, is compared with the hour angle from the Greenwich meridian to
obtain the longitude; the Greenwich hour angle is found by converting the Greenwich
mean time into Greenwich sidereal time in the usual manner, and then taking the
difference between the latter and the right ascension of the body, the remainder being
marked east or west, according as the Greenwich sidereal time is the lesser or greater
of the two quantities; and as the local hour angle may be marked east or west accord
ing to the side of the meridian upon which it was observed, the name of the longitude
wul be indicated in combining the quantities.
342. As has been stated, the most favorable position of the celestial body for
finding the hour angle from its altitude is when nearest the prime vertical, provided
the altitude is not so small as to be seriously affected by refraction.
343. In determining the longitude at sea by this method, it is necessary to
employ the latitude by account. This is seldom exactly correct, and a chance of
error is therefore introduced in the resulting hour angle; the magnitude of such an
error depends upon the position of the body relative to the observer. The employ
ment of the Sumner line, which is to be explained in a later chapter, insures the navi
gator against being misled by this cause, and its importance is to be estimated
accordingly.
EXAMPLE: At sea, May 18, 1916, a. m.; Lat. 41° 33' N.; Long. 33° 37' W., by D. R., the following
altitudes of the sun's lower limb were observed, and times noted by a watch compared with the Green
wich chronometer. Chro. corr., + 4m 59V2; I. C., -30"; height of the eye, 23 feet; C-W, 2h 17m 06s.
Required the true longitude.
W. T.
Mean,
c-w,
Chro. t.,
Eq. t.,
G. A.T.,
7h 20°» 15»
20 47
21 14
7 20 45.3
+ 2 17 06
9 37 51 .3
3 44.1
-
21 46 34.6
Obs. alt. 0,29° 35' 30"
46 10
Dec., 17d 20^,19° 30'.3 * N.
Eq.t.,17d 20^, 3"> 44».3
Corr.,
ft,
h,
L,
py
s,
s-h,
Corr., + 9' 04"
29° 50' 04"
41 33 00
70 28 42
2)141 51 46
70 55 53
41 05 49
H. D., +
G. M. T.,
0'.6
H.D.,
G. M. T.,
Corr.,
l'> '.7
Corr., +
i'-Q?
- 0«.17
Dec., 19°
31' 18" N.
Eq. t.,
3°> 44«.l
sec., .12588
cosec., .02571
cos.,
Bin.,
G. A. T., 21h 46m 34«.6
L. A. T., 19 32 05 .5
9.51415
9.81779
2)19. 48353
sin. \ t, 9. 74176
Long.,
2h 14m 29M
33o 37, 16//
W
W.
LONGITUDE.
143
EXAMPLE: At sea, April 16, 1916, p. m., in Lat. 11° 47' S., Long. 0° 20' E., by D. R., observed an
Ititude of the star Aldebaran, west of the meridian, 23° 13' 20"; chronometer time, 6h 58m 29s, chro-
ometer fast of G. M. T., 2m 27s; I. C.,-2' 00"; height of eye, 26 feet. What was the longitude?
Chro. t.,
6h 58m 29s
9 27
Obs. al
Corr.,
h,
(Tab. <
Corr..
23° 04'
11 47
106 20
:t. >|c, 23°
13' 20" R. A. >|c, 4h 31m06s. 8
G. M. T.,
RA M tS
Drr ifi° °ry °RX/ "M
6 56 02
r-1 37 11
1- 1 09
23
01 05 — ••-. - .— .
Red. (Tab. 9), -
G. S. T.,
R. A. *,
H. A. from Gr.,
16), -
7' 15"
2 00
8 34 22
4 31 07
05"
00
36
9 15
sec . 00925
cosec . 01791
cos 9. 52141
sin 9. 86783
4 03 15 W.
L,
P,
Jli,
Gr. H. A.
H.A.,
Long.,
2)141
11
41
70
47
35
31
50
45
, 4*
4
03"
05
L15S W.
42 W.
2)19. 41640
sin £ t 9. 70820
/ Oh
1 0°
02m
36'
27s \r
45"/ •
EXAMPLE: At sea, July 26, 1916, a. m., in Lat. 25° 12' S., Long. 75° 3(K W., by D. R., observed an
Ititude of the planet Jupiter, east of the meridian, 32° 46' 10"; watch time, 2h 48m 02s; C- W, 5h 05m 42s;
. C.,+2m 18s; I. C.,+17 30"; height of eye, 18 feet, Required the longitude.
\7. T.,
C-W,
Chro. t.,
C.C.,
G. M. T., 25^,
R. A. M.S., Oh,
Red. (Tab. 9),
G. S. T.,
R. A. *,
H. A. from Gr.,
5
48« 02«
05 42
Obs. alt. #
Corr.,
(Tab. 46).
id,
Corr.,
32°
25
101
32°
46' 10"
4 09
R. A.,25dOh, 2h OS°>20»
Corr. 4- 18
H. D., + 0».9
G.M.T., 19^.9
7
+
53
2
44
18
32
— •
42 01
5' 39"
1 30
4 09
01"
00
18
R. A., 2 08 38
Dec. 25dOh, 11° 35'. 9 N.
Corr., + 1.4
Corr., +17-.9
H. D., + 0'.07
G.M.T., 19^.9
Corr., + 1'.39
19
+ 8
+
56
11
3
02
26.8
16.5
42'
12
37
Dec., 11° 37' 18" N.
p, 101° 37' 18"
sec . 04343
cosec . 00900
cos 9. 24983
sin 9. 86456
4
2
10
08
45.3
38
2
02
07.3 W.
fc
P,
s—h,
Gr. H.
H. A.,
2)159
31
19
79
47
45
03
40
39
A., 2*
3
00
L 07" W.
15 E.
2)19. 16682
sin}* 9.58341 -.
Long.,
{ 75° 35
35X 30"
CHAPTER XIV.
AZIMUTH,
344. The azimuth of a body has been defined (art. 223, Chap. VII) as the arc
of the horizon intercepted between the meridian and the vertical circle passing through
the body; and the amplitude (art. 224) as the arc measured between the position of
the body when its true altitude is zero and the east or west point of the horizon.
The amplitude is measured from the east point at rising and from the west point at
setting, and, if added to or subtracted from 90°, will agree with the azimuth of the
body when in the true horizon. The azimuth is usually measured from the north point
of the horizon in north latitude, and from the south point in south latitude, through
180° to the east or west; thus, if a body bore N. by E., its azimuth would be named
N. lli° E. in north, or S. 168J° E. in south latitude.
The determination of the azimuth of a celestial body is an operation of frequent
necessity. At sea, the comparison of the true bearing with a bearing by compass
affords the only means of ascertaining the error of the compass due to variation and
deviation; on shore, the azimuth is required in order to furnish a knowledge of the
variation, and is further essential in all surveying operations, the true direction of
the base line being thus obtained.
345. There are various methods of ob taming the true azimuth of a celestial
body, which will be described as follows: (a) Amplitudes, (b) Time Azimuths, (c)
Altitude Azimuths, (d) Time and Altitude Azimuths. A further method, by means
of the Summer line, will be explained later (Chap. XV). Still another operation
pertains to this subject, namely: (e) The determination of the True Bearing of a
Terrestrial Object.
AMPLITUDES.
346. The method of obtaining the compass error by amplitudes consists in
observing the compass bearing of the sun or other celestial body when its center is
in the true horizon, the true bearing, under such conditions, being obtained by a
short calculation. Since the true horizon is not marked by any visible line (differing
as it does from the visible horizon by reason of the effects of refraction, parallax, and
dip), allowance may be made for the difference by an estimate of the eye, or else the
observation may be made in the visible horizon and a correction applied.
347. When the center of the sun is at a distance above the horizon equal to its
own diameter it is almost exactly in the true horizon; at such a time, note its bearing
by compass, and also note (as in all observations for determining compass error)
the ship's head by compass, and the angle and direction of the ship's heel.
Or, note the bearing at the instant at which the center of the body is in the visible
horizon; in the case of the sun and moon, the correct bearing at that time may be
most accurately ascertained by taking the mean of the bearings when the upper and
the lower limbs of the disk are just appearing or disappearing.
348. To find the true amplitude by computation, there are given the latitude, L, ,
and declination, d. The quantities are connected by the formula,
sin Amp. = sec L sin d,
from a solution of which the amplitude is obtained..
To find the true amplitude by inspection enter Table 39 with the declination at
the top and the latitude in the side column; under the former and opposite the latter
will be given the true amplitude. To obtain accurate results, interpolate for minutes
of latitude and declination.
144
AZIMUTH.
145
To reduce the observed amplitude when taken in the visible horizon to what it
would have been if taken in the true horizon, enter Table 40 with the latitude and
declination to the nearest degree and apply the correction there found to the
observed amplitude; the result will be the corrected amplitude by compass, which,
by comparison with the true amplitude, gives the compass error. When the body
observed is the sun, a star, or a planet, apply the correction, at rising in north lati
tude or at setting in south latitude, to the right, and at setting in north latitude or
at rising in south latitude, to the left. For the moon, apply half the correction in
a contrary direction.
EXAMPLE: At sea, in Lat. 11° 29/ N., the observed bearing of the sun, at the time of rising, when
its center was estimated to be one diameter above the visible horizon, was E. 31° N.; corrected
declination 22° 32' N. Required the compass error.
By computation.
By inspection (Table 39).
L 11° 29'
d 22 32
sec
sin
True amp.
Obs. amp.
Error,
E. 23° 01' N. sin
E. 31 00 N.
7° 59' E.
. 00878
9. 58345
9. 59223
L, 11°. 5 N.
d, 22 . 5 N.
Obs. amp.
Error,
E. 23°. ON.
E. 31 .ON.
8°.OE.
EXAMPLE: At sea, in Lat. 25° 03' S., the observed bearing of Venus, when in the visible horizon at
rising, was E. 18° 307 N., its declination being 21° 44' N. Required the compass error.
By computation.
By inspection (Table 39).
L 25° 03'
d 21 44
sec .04290
sin 9.56854
True amp. E.24° 08' N.sin 9.61144
Comp. amp. E. 18 48 N.
Error,
5° 207 W.
L,
d,
Obs. amp.
Corr. (Tab. 40)
Error,
21°' 7 N*
True
- 24°-
- 18 '
5°. 3 W.
EXAMPLE: At sea, in Lat. 40° 27' N., the mean of the observed bearings of the upper and lower
limbs of the moon, when in contact with the visible horizon at setting, was W. 17° S. ; declination, 21° 12' S.
What was the error of the compass?
By computation.
40° 27'
21 12
sec . 11863
sin 9. 55826
By inspection (Table 39).
U°' 9 ^' } True amp. W. 28°. 4 S.
True amp. W. 28° 22' S. sin 9. 67689
Comp. amp. W. 16 42 S.
Error,
11° 40'
Error,
11°. 7 W.
TIME AZIMUTHS.
349. In this method are given the hour angle, t} at tune of observation, the
polar distance, p, and the latitude, L; to find the azimuth, Z.
Any celestial body bright enough to be observed with the azimuth circle may
be employed for observation ; the conditions are, however, most favorable for solu
tion when the altitude is low.
350. Take a bearing of the object, bisecting it if it has an appreciable disk,
and note the time with a watch of known error. Record, as usual, the ship's head
by compass and the amount of heel. If preferred, a series of bearings may be taken
with their corresponding tunes, and the means taken.
351. First prepare the data as follows:
(a) Find the Greenwich time corresponding to the local time of observation.
(b) Take out the declination of the body from the Nautical Almanac; if the
method of computation is employed, the polar distance and the co-latitude should
be noted.
(c) Find the hour angle of the body by rules heretofore given.
61828°— 16 10
146
AZIMUTH.
This having been done, the true azimuth may be determined either by Time
Azimuth Tables, by the graphic method of an Azimuth Diagram, or by Solution of
the Astronomical Triangle. Owing to the possibility of more expeditious working,
either of the first-named two is to be considered preferable to the last, and the
navigator is recommended to supply himself with a copy of a book of Azimuth
Tables, such as published by the Hydrographic Office, or with an Azimuth Diagram
such as Weir's or Sigsbee's; an explanation of the method of use accompanies each
of these.
352. To solve the triangle:
Let S = J sum of polar distance and co-Lat.
D = J difference of polar distance and co-Lat.
\t — \ hour angle.
Z = true azimuth.
Then, tan X = sin D cosec S cot £ t;
tan Y = cos D sec S cot \ t;
Z=X+Y, orX~Y.
First Case. — If the half -sum of the polar distance and co-Lat. is less than 90°:
take the sum of the angles X and Y, if the polar distance is greater than the co-Lat. ;
take the difference, if the polar distance is less than the co-Lat.
Second Case. — If the half -sum of the polar distance and co-Lat. is greater than
90°: always take the difference of X and Y, which subtract from 180°, and the result
will be the true azimuth.
In either case, mark the true azimuth N. or S. according to the latitude, and
E. or W. according to the hour angle. It may sometimes be convenient to use the
supplement of the true azimuth, by subtracting it from 180° and reversing the
prefix N. or S., in order to make it correspond to the compass azimuth when the
latter is less than 90°.
The cotangent of half the hour angla may be found from Table 44 abreast the
whole hour angle in the column headed "Hour P. M."
EXAMPLE: At sea, in Lat. 30° 25' N., Long. 5h 25m 42« W., the observed bearing of sun's center was
N. 135° 30' E., and the Greenwich mean time, December 3, 2h 36m 11". The corrected declination of the
sun was 22° 07' S.; the equation of time (additive to mean time), 10m 03s. Required the error of the
compass.
G.M.T.(Dec.3), 2h 36m 11- co-Lat., 59° 35'
Long.,
- 5 25 42 p,
112 07
L.M.T.(Dec.2), 21 10 29
Eq. t., + 10 03
L.A.T.,
21 20 32
2h 39m 28'
p+co-L, 171
S,
42
85 51
2h39m 28'
85° 51'
26 16
50 44
88 19
cot** .44051
cosec . 00114
sin 9. 64596
tan
. 08761
cot it .44051
sec 1. 14045
cos 9. 95267
tan 1. 53363
p-co-L, 52° 32' X+Y139 03
D, t 26 16
True azimuth,
Comp. azimuth,
Compass error,
N. 139° 03' E.
N. 135 30 E.
3 33 E.
EXAMPLE: At sea, in Lat. 2° 16' N., the observed bearing of the sun's center was N. 85° 15' E: sun's
hour angle, 3h 44m 16% and its declination, 7° 38' N. Required the compass error.
co-Lat.,
87°
44/
t
Pi
82
22
S
p+co-L,
170
06
s,
85
03
Y
co-L— p,
5°
22'
Y
3h 44m 16s
85° 03'
2 41
5 03
87 22
cot \
cosec
sin
tan
. 27372
. 00162
8. 67039
8. 94573
sec
cos
tan
. 27372
1. 06406
9. 99952
1. 33730
82 19
2 41
True azimuth,
Comp. azimuth,
Compass error,
N. 82° 19' E.
N. 85 15 E.
2 56 W
AZIMUTH. 147
EXAMPLE: At sea, in Lat. 16° 32' S., observed bearing of Venus N. 56° 00' W., its hour angle being
4b 27m 31s, and its declination 23° 12' N. What was the error of the compass?
co-Lat.,
73°
28'
I
4n 27m31s
cot^t
: . 18022
cot \ i
! . 18022
113
12
S
93° 20'
cpsec
.00074
sec
1. 23549
~r\
10 50
sin
9 53126
COS
9 97335
p-fco-L,
186
40
-L«7 ' O£
X
27 16
tan
9. 71222
s,
93
20
Y
87 40
tan
1. 38906
p— co-L,
39°
44/
Y-X
60 24
P,
19
52
Z
119° 36'
True azimuth,
S. 119°
36' W.
Comp.
azimuth,
S. 124
00 W.
Compass error, 4 24 W.
ALTITUDE AZIMUTHS.
353. This method is employed when the altitude of the body is observed at the
same time as the azimuth; in such a case the hour angle need not be known, though
the time of observation should be recorded with sufficient accuracy for the correction
of the declination of the sun, moon, or a planet.
There are given the altitude, h, the polar distance, p, and the latitude, L; to
find the azimuth, Z.
354. Take a bearing of the body by compass, bisecting it if the disk is of
appreciable diameter, and simultaneously measure the altitude; note the time
approximately. . Observe also the ship's heading (by compass) and the heel.
Or a series of azimuths, with corresponding altitudes, may be observed, and the
means employed.
355. Calculate the true altitude and declination from the observed altitude
and the time. Then compute the true azimuth from the following formula:
cos J Z = VGOS s cos (s — p) sec L sec Ji,
in which s = % (h+Ij + p). The resulting azimuth is to be reckoned from the north
in north latitude and from the south in south latitude.
It may occur that the term, (s — p) , will have a negative value, but since the cosine
of a negative angle less than 90° is positive, the result will not be affected thereby.
EXAMPLE: At sea, in Lat. 30° 25' N., the observed bearing of the sun's center was N. 135° 3(K E.,
and its corrected altitude 24° 59'; the approximate G. M. T. was 2h.6, the declination at that time being
22° 07' S. Required the compass error.
h 24° 59' sec .04267
L 30 25 sec .06431
p 112 07
2 ) 167 31 True azimuth, N. 139° 00' E.
Comp. azimuth, N. 135 30 E.
s 83 45 cos 9.03690
s—p -28 22 cos 9.94445 Compass error, 3 30 E.
2 ) 19. 08833
*Z 69 30 cos 9.54416
Z 139 00
TIME AND ALTITUDE AZIMUTHS.
356. When, at the time of observing the compass bearing of a celestial body,
the altitude is measured and the exact time noted, the true azimuth may be very
expeditiously determined, a knowledge of the latitude being unnecessary.
In view of the simplicity of the computation, this method strongly commends
itself to observers not provided with azimuth tables or diagram.
357. The observation is identical with that of the altitude azimuth (art. 354),
with the exception that the times of observation must be exactly instead of approx
imately noted.
148 AZIMUTH.
358. Ascertain the declination of the body at time of sight, and correct the
observed altitude; compute the hour angle. We then have:
sin Z = sin t cos d sec li,
from which the azimuth may be found.
This method has a defect in that there is nothing to indicate whether the resulting
azimuth is measured from the north or the south point of the horizon; but as the
approximate azimuth is always known, cases are rare when the solution will be in
question.
EXAMPLE: At sea, in Lat. 30° 25' N., Long. 5h 25m 42f W., the observed bearing of the sun's center
was N. 135° 30' E.; its altitude at the time was 24° 59'; hour angle, 2h 39m 28f (39° 52'), and declination,
22° 07' S. Find the compass error. (See example under Altitude Azimuths and first example under
Time Azimuths.)
t 39° 52' sin 9.80686 True azimuth, N. 139°04/E.
d 22 07 cos 9. 96681 Comp. azimuth, N. 135 30 E.
h 24 59 sec .04267
Compass error, 3 34 E.
Z S. 40° 56' E. sin 9. 81634
TRUE BEARING OF A TERRESTRIAL OBJECT.
359. Thus far, sea observations for combined variation and deviation have been
discussed, but if it becomes necessary, as in surveying, to ascertain the True Bearing
of a Terrestrial Object, or to find the variation at a shore station, more accurate
methods than the foregoing must be resorted to.
The most reliable method is that by an Astronomical Bearing. This consists in
finding the true bearing of some well-defined object by taking the angle between it
and the sun or other celestial body with a sextant or a theodolite, and simultaneously
noting the time by chronometer, or measuring the altitude, or observing both time
and altitude. It should always be noted whether the object is right or left of the sun.
360. By Sextant. — Measure the angular distance between the object and the
sun's limb; and if there is a second observer, measure the altitude of the sun at the
same moment and note the time. In the absence of an assistant, first measure the
altitude of the sun; next, the angular distance between the sun and the object; then,
a second altitude of the sun, noting the time of each observation. Also measure the
altitude of the defined point above the sea or shore horizon.
By Theodolite. — This instrument is far more convenient than the sextant, for,
being leveled, the horizontal angle between the sun and the object is at once given,
no matter what may be the altitudes of the objects. In case the altitude of the sun
is needed, it may be read accurately enough from the vertical circle, although not as
finely graduated as the limb of the sextant. The error in altitude must, however,
be found by the level attached to the telescope, since it will usually be found to differ
from the levels of the horizontal circle. If, in directing the telescope to the sun, there
is no colored eyepiece, an image of the sun may be cast on a piece of white paper
held at a little distance from the eyepiece, and by adjusting the focus the shadow
of the cross wires will be seen.
It should be understood that any celestial body may be used as well as the sun,
and there are, in fact, certain advantages in the use of the stars; the sun is chosen
for illustration, because it will usually be found most convenient to employ that body.
361. Find the true azimuth of the celestial bod}7 by one of the methods pre
viously explained in this chapter, and apply to it the azimuth difference, or horizontal
angle between the celestial and the terrestrial body, having regard to the direction
of one from the other.
To find the azimuth difference from sextant observations, change^ the observed
altitudes of the bodies into apparent altitudes by correcting them for index error of
the sextant, dip, and semidiameter; change the observed angular distance into
apparent angular distance, by correcting for index error and semidiameter. Then if
S = J (App. Dist. + App. Alt.O +App. Alt. Object), we have:
cos i Az. Diff. = A/sec App. Alt.O sec App. Alt. Object cos S cos (S— App. Dist.)
whence the azimuth difference is deduced.
AZIMUTH.
149
When the theodolite is used, the horizontal angle is given directly. If only one
limb of the sun is observed, it will be necessary to apply a correction for semidiameter
(S. D. Xsec h), but it is usual to eliminate this correction by taking the mean of
observations of both limbs.
EXAMPLE: From a. m. observations, in Lat. 30° 25' 24" N., Long. 81° 25' 24" W., obtained the follow
ing data for finding the true bearing of a station:
Watch time, llh 22m 36'
C-W, 5 21 18
Chro. corr., -f 2 16
Obs. Ang. Dist. £>, 117° 07' Left.
Obs. 2
Obs. alt. Station,
i. c.,
71° 37' 20/x
2(K
zero.
Dec. S., 22° 56' 27"
Eq.t., + 7mOO"
S. D., W 17"
Required the true bearing of the object.
W. T.,
C-W,
Chro. t.,
C.C.,
G. M. T.,
Eq. t.,
5
22m 36"
21 18
2Q,
£>,
S. D.,
App. Alt.,
p. & r.,
7>
71°
=— •«-
35
-f
37'
MMM^
48
16
20 "
•«*»
40
17
f
<*
ft
•f*
8° 08'
22 56
36 03
9° 17'
170 43
00"
27
37
E.
E.
sin
cos
sec
9. 15069
9. 96422
. 09239
4
+
43 54
2 16
sin
9. 20730
36
04
1
57
13
4
46 10
7 00
36
OS
44
G. A. T., 4 53 10
Long., — 5 25 42
L. A. T., 23 27 28
JO* 32m329
*• \8° 08' 00"
Obs. Anj. Dist.,
G'sS. D., +
App. Ang. Dist.,
117° 07' 00"
16 17
App. Dist.
App Alt. 0
App. Alt. Obje<
S
S-App. Dist.
i Az. Diff.
Az. Diff.
117° 23'
36 05
sec 0.09250
sec 0.00001
cos 9.35536
cos 9. 88115
True bearing Q> i'O0
Az. Diff., 125
43' E.
00 Left.
117 23 17
True bearing object, N. 45°
43' E.
2)153 48
76 54
-40 29
62° 30'
125 00
2)19. 32902 t
cos 9.66451
EXAMPLE: Same date and place and same objects as in the preceding example; measurement made
with a theodolite, angular distance (£>, 123° 17X; object left of sun. Watch time, llh 16m 34s. 5 ; watch slow
of L. A. T., 4m 53s .5. Dec. Q, 22° 567 S. Required the true bearing. (See article 352.)
W. T., llh
16m
34S.5
co-Lat., 59° 35' t
Oh 38m 32s
cot \ t
1. 07435
coti< 1.07435
W.810W,+
4
53 .5
p, 112 56 S
86° 15'
cosec
.00093
sec 1. 18440
~r\
oft 41
GI n
Q f^^^^A
r»r\a Q Q^llO
L. A. T., 23
21
28 .0
p+co-L, 172 31
^Q T-L
bill
•tor
79° 24' '
j
797CO
t, 0
38
32
S, 86 15 Y
89 39
. fZ/OO
\
tan 2. 20985
p-co-L, 53 21 X+Y169 03
D, 26 41
True bearing 0,
X. 169° 03' E.
Az. Diff.,
123 17 Left
•
True bearing object, N. 45 46 E.
CHAPTER XV.
THE SUMNEE LINE,
DESCRIPTION OF THE LINE.
362. The method of navigation involving the use of the Sumner line takes its
name from Capt. Thomas H. Sumner, an American shipmaster, who discovered it
and published it to the world. As a proof of its value, tne incident which led to its
discovery may be related:
"Having sailed from Charleston, S. C., 25th November, 1837, bound for Greenock,
a series of heavy gales from the westward promised a quick passage; after passing
the Azores the wind prevailed from the southward, with thick weather; after passing
longitude 21° W. no observation was had until near the land, but soundings were
had not far, as was supposed, from the bank. The weather was now more boisterous,
and very thick, and the wind still southerly; arriving about midnight, 17th December,
within 40 miles, by dead reckoning, of Tuskar light, the wind hauled SE. true, making
the Irish coast a lee shore; the ship was then kept close to the wind and several
tacks made to preserve her position as nearly as possible until daylight, when,
nothing being in sight, she was kept on ENE. under short sail with heavy gales. At
about 10 a. m. an altitude of the sun was observed, and the chronometer time noted;
but, having run so far without observation, it was plain the latitude by dead reckoning
was liable to error and could not be entirely relied upon.
The longitude by chronometer was determined, using this uncertain latitude,
and it was found to be 15' E. of the position by dead reckoning; a second latitude
was then assumed 10' north of that by dead reckoning, and toward the danger,
giving a position 27 miles ENE. of the former position; a third latitude was assumed
10' farther north, and still toward the danger, giving a third position ENE. of the
second 27 miles. Upon plotting these three positions on the chart, they were seen
to be in a straight line, and this line passed through Smalls light.
"It then at once appeared that the observed altitude must have happened at
all the three points and at Smalls light and at the ship at the same instant."
Then followed the conclusion that, although the absolute position of the ship
was uncertain, she must be somewhere on that line. The ship was kept on the course
ENE., and in less than an hour Smalls light was made, bearing ENE. \ E. and close
aboard.
The latitude by dead reckoning was found to be 8' in error, and if the position
given by that latitude had been assumed correct, the error would have been 8 miles
too far S., and 31' 30" of longitude top far W., and the result to the ship might have
been disastrous had this wrong position been adopted. This represents one of the
practical applications of the Sumner line.
The properties of the line thus found will now be explained.
363. CIRCLES OF EQUAL ALTITUDE. — In figure 54, if EE'E" represent the earth
projected upon the horizon of a point A, and if it be assumed that, at some particular
instant of time, a celestial body is in the zenith of that point, then the true altitude
of the body as observed at A will be 90°. In such a case the great circle EE'E",
which forms the horizon of A, will divide the earth into two hemispheres, and from
any point on the surface of one of these hemispheres the body will be visible, while
over the whole of the other hemisphere it will be invisible. The great circle EE'E",
from the fact of its marking the limit of illumination of the body, is termed the circle
of illumination, and from any point on its circumference the true altitude of the
center of the body will be zero. If, now, we consider any small circle of the sphere,
150
THE SUMNER LINE.
151
BB'B", CC'C", DD'D", whose plane is parallel to the plane of the circle of illumina
tion and which lies within the hemisphere throughout which the body is visible, it will
be apparent that the true altitude of the body at any point of the circumference of
one or these circles is equal to its true altitude at any other point of the same circum
ference; thus the altitude of the body at B is equal to its altitude at B' or B", and
its altitude at D is the same as at D' or D".
It therefore follows that at any instant of time there is a series of positions on
the earth* at which a celestial body appears at the same given altitude, and these
positions lie in the circumference of a circle described upon the earth's surface whose
center is at that position which has the body in the zenith, and whose radius depends
upon the zenith distance, or — what is the same thing — upon the altitude. Such
circles are termed circles of equal altitude. It is important to note that an observer
making an instantaneous transit through the latitudes and longitudes passed over
by any rhumb line or loxodromic curve drawn within the hemisphere of illumination,
through the point A, will
experience no astronomical
difference, with reference to
the observed body in the
zenith of A, save an altitude
difference.
364. The data for an
astronomical sight comprise
merely the time, declination,
and altitude. The first two
fix the position of the body
and may be regarded as
giving the latitude and lon
gitude of that point on the
earth in whose zenith the
body is found; the zenith
distance (the complement of
the altitude) indicates the
distance of the observer
from that point ; but there is
nothing to show at which of
the numerous positions ful
filling the required condi
tions the observation may
have been taken. A num
ber of navigators may meas
ure the same altitude of a
body at the same instant
of time, at places thousands of miles apart; and each proceeds to work out his
position with identical data, so far as this sight is concerned. It is therefore
clear that a single observation is not enough, in itself, to locate the point occu
pied by the observer, and it becomes necessary, in order to fix the position, to
employ a second circle, which may be either that of another celestial body or that of
the same body given by an observation when it is in the zenith of some other point
than when first taken; knowing that the point of observation lies upon each 01 two
circles, it is only possible that it can be at one of their two points of intersection;
and since the position of the ship is always known within fairly close limits, it is easy
to choose the proper one of the two. Figure 55 shows the plotting of observations
of two bodies vertically over the points A and A' upon the earth, the zenith distances
corresponding respectively to the radii AO and A'O.
365. THE SUMXER LIXE. — In practice, under the conditions existing at sea, it
is never necessary to determine the whole of a circle of equal altitude, as a very small
portion of it will suffice for the purposes of navigation; the position is always known
within a distance which will seldom exceed 30 miles under the most unfavorable
conditions, and which is usually very much less; hi the narrow limits thus required,
the arc of the circle will practically coincide with the tangent at its middle point,
FIG. 54.
152
THE SUMNER LINE.
and may be regarded as a straight line. Such a line, comprising so much of the circle
of equal altitude as covers the probable limits of position of the observer, is called a
Sumner line or Line of position.
The latter designation has also a more extended meaning, embracing any line,
straight or curved, which forms a locus of the ship's position, whether it be obtained
from observations of celestial bodies or from bearings or distances of terrestrial
objects.
366. Since the direction of a circle at any point — that is, the direction of the
tangent — must be perpendicular to the radius at that point, it follows that the
Sumner line always lies in a direction at right angles to that in which the body bears
from the observer. Thus, in figure 55,
it may be seen that m m' and n n', the
extended Sumner lines corresponding to
the bodies at A and A', are respectively
perpendicular to the bearings of the bodies
OA and OA'. This fact has a most im-
FlG. 55.
portant application in the employment of
the Sumner line.
367. USES OF THE SUMNER LINE. —
The Sumner line is valuable because it
gives to the navigator a knowledge of all
of the probable positions of his vessel,
while a sight worked with a single assumed
latitude or longitude gives but one of the
probable positions; it must be recognized
that, in the nature of things, an error in
the assumed coordinate will almost invariably exist, and its possible effect should
be taken into consideration; the line of position reveals the difference of longitude
due to an error in the latitude, or the reverse.
Since the Sumner line is at right angles to the bearing, it may be seen that when
the body bears east or west — that is, when it is on the prime vertical — the resulting
line runs north and south, coinciding with a meridian; if, in this case, two latitudes
are assumed, the deduced longitudes will be the same. When the body bears north
or south, or is on the meridian, the line runs east and west, and becomes identical with
a parallel of latitude; in such a case, two assumed longitudes will give the same
latitude. Any intermediate bearing gives a Sumner line inclined to both meridians
and parallels; if the line agrees in direction more nearly with the meridian, latitude
should generally be assumed and the longitude worked; if it is nearer a parallel, the
reverse course is Usually preferable. The values of the assumed coordinates may
vary from 10' to 1°, according to circumstances.
368. The greatest benefit to be derived from the Sumner method is when two
lines are worked and their intersection found. The two lines may be given by
different bodies, which is generally preferable, or two different lines may be obtained
from the same body from observations taken at different times. The position
given by the intersection of two lines is more accurate the more nearly the lines are
at right angles to each other, as an error in one line thus produces less effect upon the
result. When two observations of the same body are taken, the position of the ship
at the time of first sight must be brought forward to thafc at the second in considering
the intersection; if, for ^example, a certain line is determined, and the ship then runs
NW. 27 miles, it is evident that her new position is on a line parallel with the first and
27 miles to the NW. of it ; a second line being obtained, the intersection of this with
the first line, as corrected for the run, gives the ship's position.
Besides the employment of two lines for intersection with each other, a single
line may be made to serve various useful purposes for the navigator. These are
described in article 389, Chapter XVI.
METHODS OF DETERMINATION.
369. ^There are three methods in common use for determining the Sumner line:
(a) THE CHORD METHOD: To assume two values of one coordinate and find the
corresponding values of the other. Two values of the latitude may be assumed and
i
THE SUMNER LINE. 153
the longitudes determined, as was done by Capt. Simmer on the occasion that led to
the discovery of his method; or else two values of the longitude may be assumed
and the latitudes determined. Two points are fixed in this way, and the line joining
them is the Sumner line.
(b) THE TANGENT METHOD: To assume either one latitude or one longitude and
determine the corresponding coordinate. This gives one point of the Sumner line.
The azimuth of the observed celestial body is then ascertained, and a line is drawn
through the determined point at right angles to the direction in which the body bore
at the time of the sight. This will be the Sumner line.
(c) In accordance with the method of Saint Hilaire, to be described in article
371, to lay off from an assumed geographical position, along the line of direction
in which the body bore at the time of the sight, the determined distance to the
Sumner line.
370. It follows that if the Sumner line be located by the first method and its
direction thus defined, the azimuth of the observed body may be determined by
the angle made by the line with the meridian and adding or subtracting 90°.
EXAMPLE: At sea, July 26, 1916, a. m., in Lat. 25° 12' S., Long. 75° 3(X W., by D. R., observed an
altitude of the planet Jupiter, east of the meridian, 32° W 10"; watch time, 2h 48m 02s; C-W, 5h 05m 42§;
C. C., -f 2m 18s; I. C., 4- I' 30"; height of eye, 18 feet. Required the Sumner line.
From a solution of this same problem for a single longitude (art. 343, Chap. XIII), the following
were found: H. A. from Gr., 2h 02m 07s W.; h, 32° 42' 01'?; p, 101° 37' 18". Assume values of Lat.
25° 02' and 25° 22' S.
h 32° 42' 01"
Lj 25 02 00 sec . 04284 L2 25° 22' 00" sec . 04403
p 101 37 18 cosec .00900 cosec .00900
2)159 21 19
t 79 40 40 cos 9.25330 So 79 50 40 cos 9.24630
i-h 46 58 39 sin 9.86397 sl-h 47 08 39 sin 9.86514
Gr. H. A. 2h 02m 07s W. 2)19. 16911 Gr. H. A. 2h 02m 07s 2)19. 16447
H. A.x 3 00 45 E. sin $ ^ 9.58455 H. A.2 2 59 44 sin £ ^ 9.58224
5h 02m 52s 1 w T / 5h Olm 51s
75o 43/ <,<)„ JW. Long.2{ ^0 2?/ 4&/
A comparison of these results with those obtained by the solution with a single
latitude shows that the hour angle, and consequently the longitude, corresponding
to the latitude 25° 12' S. are the means of those corresponding to the latitudes here
used; and therefore that the assumption that the Sumner line is a straight line is
accurate.
The line of the same sight might also have been found as follows :
Working with the single latitude 25° 12' S., it was found that the corresponding
longitude was 75° 35 ' 30" W. Now, by referring to an azimuth table or azimuth
diagram, the azimuth corresponding to Lat. 25°.2 S., Dec., 11°.6 N., H. A., 3h 00m.2
E. is S. 124° 30' E.; therefore the Sumner line extends S. 34° 30' E.
The line may therefore be defined in either of two ways, thus:
A J25° 02' 00" S. A /25° 22' 00" S.
AH75 43 00 W. A2\75 27 45 W.
n . J25° 12' 00" S. Line runs S. 34° 30' E.
'Jr> A175 35 30 W.
By inspection of the coordinates of A^ and A2 it may be seen that —
+ 20' diff. lat. makes -15'.25 diff. long.; or
+ 20 miles diff. lat. makes - 13.8 miles departure.
Therefore by reference to Table 2 it appears that the line runs about S. 34° 30'
E., and the azimuth of the body is S. 124° 30' E.; thus the results obtained by the
two methods agree.
154 THE SUMNER LINE.
; sea, May 18, 1916, a. m., Lat. 41° 33' N., Long. 33° 37' W., by D. R., the mean of a
altitudes of the sun's lower limb was 29° 41' 00"; the mean watch time, 7h 20m 45S.3;
EXAMPLE: At
series of observed
C. C.,+4m 59S.2; I. C., -30"; height of the eye, 23 feet; C-W, 2h 17m 06s. Required the Sunrner line.'
From a solution of this same problem for a single longitude (art. 343, Chap. XIII) the following
were found: G. A. T., 21h 46m 35s- h 29° 50' 04": », 70° 28' 42". Assume values of the latitude 41° 03'
and 42° 03' N.
h 29° 50' 04"
Lj 41 03 00 sec . 12255 L2 42° 03' 00" sec . 12927
p 70 28 42 cosec .02571 cosec .02571
2)141 21 46
s1 70 40 53 cos 9.51959 S2 71 10 53 cos 9.50863
Sl-h 40 50 49 sin 9.81560 s2—h 41 20 49 sin 9.81995
G. A. T., 21h 46m 35s 2)19.48345 G. A. T. 21h 46m 35s 2)19.48356
L. A. T.j 19 32 07 sin £ ^ 9. 74172 L. A. T.2 19 32 05 sin $ t2 9. 74178
/ 2h 14m 283 \w / 2h 14m 30s \w
Long.! | 33o 37, 00//fW. -Long.2 <^0 37/ 30"}^-
. / 41° 03' 00" N. A /42° 03' 00" N. +60' diff. lat, makes+0'.25 long.
AI \ 33 37 00 W. A2\33 37 30 W. +60 miles diff. lat. makes+0.2 mile departure.
Line runs, N. i° W. Azimuth, N. 89f° E.
The same site worked with a single latitude, 41° 33' N., as was done in the
original example, with azimuth taken irom tables or diagram, gives:
41° 33' 00" N. Azimuth, N. 89° 45' E.
33° 37' 16" W. Line runs, N. 0° 15' W.
This example illustrates the case in which an observation is taken practically
on the prime vertical; the azimuth shows the bearing to be within 0° 15' of true East,
and the Sumner line is therefore within 0° 15' of the meridian; a variation of 30'
in either direction from the dead reckoning latitude makes a difference of only 7". 5
in the longitude.
EXAMPLE: October 10, 1916, in Lat. 6° 20' S. by account, Long. 30° 21' 30" W.; chro. time, 12M5m10s;
observed altitude of moon's upper limb, 70° 15' 30", bearing north and east; I. C., —3' 00"; height of
eye, 26 feet; chro. fast of G. M. T., lm 37s. 5. ^ Required the Sumner line.
From a solution of the same problem with a single longitude (art. 332, Chap. XII), the following
values are obtained: H. A. from Greenwich, lh 16m 51s W.; h, 70° 11' 03"; d, 10° 03' 00" N. Assume
the longitudes 30° 10' and 30° 30' W.
Gr. H. A.
Long.:
t
lh 16m 51s W. Gr. H. A. lh 16m 51s
2 00 40 W. Long.2 2 02 00
f Ob 43in 498
l\10° 57' 15"
f Qh 45m 093
Hll° 17' 15"
h
Lat.i
10°
10
70
10
16
57'
03
11
13
43
15"
00
03
57 N.
30 S.
sec . 00799
tan 9. 24853 cosec
. 75819
9 97349 A i 6° 29/ 33" S"
AH30 10 00 W.
9. 24955
sin
tan 9. 25652 sin
cos
9. 98123
6
29
33 S.
t2
d
h
11°
10
70
17'
03
11
15"
00
03
sec . 00848
tan 9. 24853 cosec
. 75819
9.97349 A2{«; ™ gj"£
sin
V*
10
16
14
31
38 N.
00 S.
tan 9. 25701 sin
cos
9. 25002
9. 98170
Lat.2 6 16 22 S.
THE SUMNER LIXE. 155
Working by the other method, and finding the azimuth, we have:
° ' "' Line mns K 55° 50' W'
It might be shown that the results check with each other, as in previous cases.
EXAMPLE: At sea, July 12, 1916, in Lat. 50° N., Long., 40° W., observed circum-meridian altitude
of the sun's lower limb, the time by a chronometer regulated to Greenwich mean time bein<* 2h 41m 39s-
chro. corr., -2- 30s; I. C., -3' 0"; height of the eye, 15 feet. Find the Sumner line.
From the solution of the same problem for a single latitude (art. 330, Chap. XII) the following values
were obtained: G. A. T., 2h 33m 45s; h, 61° 57' 01"; d, 21° 58' 38" N.; a (Tab. 26), 2".5. Assume longi
tudes 39° 45' and 40° 15' W.
Gr. H. A. 2h 33m 45s Gr. H. A. 2h 33m 45«
Long.! — 2 39 00 Long.2 — 2 41 00
^ 5 15 t2 7 15
h 61° 57' 01" h 61° 57' 01"
atf + 1 09 at,2 + 2 11
H, 61 58 10 H2 61 59 12
zl 28 01 50 N. z2 28 00 48 N.
d 21 58 38 N. d 21 58 38 N.
L! 50 00 28 N. L2 49 59 26 N.
The line given by these coordinates is then:
A
J50° 0<y 28" N. * /49° 59' 26" X.
H39 45 00 W. A2\40 15 00 W.
This shows that the Sumner line lies so nearly in a due east-and-west direction
that a difference of longitude of 30' makes a difference of latitude of only 1'.
From the azimuth tables or diagram, it is found that the azimuth of the sun
corresponding to Lat. 50° N. Dec. 22° N. and H. A. 6m 15s E., is N. 176° 55' E.
Therefore, using the values given by the earlier solution, the line is defined as follows:
A)49° 59' 59" N. T. XT Rfi0 „/ F
A\40 00 00 W. Lme runs N' 8 55 -k'
The direction of the line thus given and of the one found from the double co
ordinates may be shown to agree as in examples before given.
THE METHOD OF SAINT HILAIBE OB OF THE CALCULATED ALTITUDES.
371. The forego ing parts of this work have set forth that, when the purpose
of the navigator is to find the latitude, the observed celestial body should be situated
on or near the meridian or at least not remote from it, and that he must apply different
rules according as the body is on or near or more remote from the meridian; and
again when his purpose is to find the longitude, the observed celestial body should
be situated on or near or at least not remote from the prime vertical, and that he
must then apply another set of rules. It is also explained in article 363 that a navi
gator, who has measured the altitude of a celestial body at a known instant of time,
has really located his geographical position on the circumference of a circle whose
radius is equal to the zenith distance (90° — Alt.) and whose center is the geographical
position of the celestial body or that point on the earth's surface which falls vertically
under the observed body at the instant of observation.
It has been pointed"out that practical needs are concerned only with that portion
of the circumference of the circle of position which lies in the vicinity of the estimated
position of the ship, and, having seen how this portion may be determined and laid
down by methods depending upon the computation of latitudes and longitudes, we
proceed to extend our view to the accomplishment of this purpose by a method which
is now rapidly growing in favor among practical navigators, because it brings the
whole of astronomical navigation under a single rule by rendering the course of
Erocedure the same, whatever the situation in the heavens of the observed body may
e, provided only that the conditions admit of accurate measurement of its altitude.
156 THE SUMNER LINE.
In figure 54, the circumference of a circle of position is represented as having
been laid down from A, the geographical position of the observed body, as a center,
with a radius AC' equal to the zenith distance of the observed celestial body; but it
is evident that a small arc of the circumference, not differing sensibly from a straight
line within the extent of a Sumner line, may be determined in the following manner
from a neighboring geographical position, as at P, inside or outside of the circum
ference and at or near the position of the ship as given by dead reckoning :
1. Find the great-circle distance (zenith distance) and bearing (azimuth) of the
geographical position of the observed body A from the observer's assumed position P.
2. Take the difference, in minutes of arc (nautical miles), between this zenith
distance AP due to the observer's assumed position, and the zenith distance AC'
found from the true altitude resulting from observation.
3. Lay off this difference, which is called the altitude-difference, or intercept,
from the assumed position P either away from or toward the observed celestial body
according as the true altitude by observation is less or greater than the altitude at
the assumed position, and through the point thus reached draw a line at right angles
to the bearing.
The line so drawn^will evidently be a tangent to the circumference of the circle
of position, and will be 'so nearly coincident with this circumference throughout such
length as the Sumner line' need have, in all those cases in which the zenith distance
is as great as 10°, that the tangent itself may be taken as the true line of position.
Obviously the only trigonometrical computation that occurs under this method is
in calculating the length and bearing of the great-circle arc joining the position P,
which is assumed or known from the dead reckoning, with the geographical position
A, which is always in a latitude equal to the declination of the observed celestial
body at the instant of observation and in a longitude equal to the hour angle of the
body from the prime meridian (Greenwich). In the case of the sun the Greenwich
hour angle is expressed, by Greenwich apparent time, and in the case of any other
celestial body the Greenwich hour angle is found as explained in article 293, using
G. M. T. instead of L. M. T.
372. Being strictly in the nature of calculating the great-circle distance and
course between two points whose latitudes and longitudes are given, these compu
tations may be made according to articles 190 and 191, Chapter V; but in practice
it is unnecessary to do so, since various altitude and azimuth tables give the distance
and azimuth or true bearing, on the globe or on the celestial sphere, of any place from
every other place, and consequently the altitude and azimuth, or zenith distance and
bearing, that any celestial body would have at any given time to an observer situated
in any given geographical position. So that an observer in a geographical position
as yet unknown, about to measure the altitude of a celestial body for the purpose
of deducing geographical position, may assume beforehand a geographical position
in the region of his station and find from the tables the altitude and azimuth which
the celestial body would have if observed from the assumed position; and then,
comparing the altitude so taken from the tables with the true altitude obtained by
measurement, may at once find the Sumner line by laying off from the assumed geo
graphical position along the direction of the bearing an intercept, called the altitude-
difference, and drawing through its extremity a line at right angles to the bearing.
After finding the altitude-difference or intercept, the simplest procedure consists
in laying it off on the chart from the assumed position and drawing the Sumner line
through its extremity, but if, for any reason, this process is not desirable, the latitude
and longitude of the extremity of the intercept, which is a point on the Sumner line,
called the " computed point," may be found by the use of the Traverse Tables, or
may be computed directly.
The exact position of the observer on the Sumner line is, of course, indeterminate
from one observation, unless either the latitude or longitude of the observer's position
be known beforehand, but the computed point will always be nearer to the actual
position of ^the observer than the dead reckoning or assumed position is. To obtain
a fix, that is, to find the actual position, it is necessary to determine the intersection
of the first Sumner line with another line of position, which may be another Sumner
line or a line of bearing or any other line containing the ship's position at the same
time.
THE SUMNER LINE. 157
When the specially prepared altitude and azimuth tables are not preferred, the
required azimuth or true bearing of the observed celestial body may be taken from
the time azimuth tables, and the zenith distance, and hence the altitude, that the
observed body would have at the instant of observation to an observer in the
assumed geographical position may be conveniently computed by the following
formula :
hav z = hav (L ~ d) + cos L cos d hav t
or by the formula of haversines, which is rid of all doubt as to the algebraical signs
of the quantities and requires reference to only one trigonometrical table:
hav z = hav (Co. L-P. D.) + {hav (Co. L + P. D.)-hav (Co. L-P. D.)}hav t
These are modifications of the fundamental formula:
sin 7i = sin L sin d + cos L cos d cos t,
which is itself often preferred for the computation of the altitude from the latitude,
declination, and hour angle.
In the computations which follow, the parts of the several formulae have been
designated as follows:
IN THE COSINE-HAVERSINE FORMULA :
hav 6=coB L cos d hav t; /
hence,
hav z=hav (L~cT)+hav 6
IN THE HAVERSINE FORMULA:
hav A=hav (Co. L+P. D.)-hav (Co. L-P. D.)
hav B = {hav (Co. L+P. D.)— hav (Co. L-P. D.)} hav t;
hence,
hav 2=hav (Co. L-P. D.)+hav B.
IN THE SINE-COSINE FORMULA:
A=sin L sin d< B=cos L cos d cos t;
hence,
sin ft=A+B.
EXAMPLE: At sea, May 18, 1916, a. m., Lat. 41° 33' N.; Long. 33° 37' W., by D. R., the mean of a
series of observed altitudes of the sun's lower limb was 29° 41' 00"; the mean watch time, 7h 20m 45. 3f;
C. C., +4m 59.2»; I. C., -30"; height of eye, 23 feet; C.-W., 2h 17m 06s. Required the Sumner line.
From a solution of the same problem under article 343. Chapter XIII, and article 370, Chapter XV, the
following are taken from among the prepared data: G. A. T., 21h 46m 35s; P. D. . 70° 28' 42"; h, 29° 50' 04",
and, therefore, the measured zenith distance (90° -ft), 60° 09' 56".
Assume a position in latitude 41° 30' N. and longitude 33° 38' 45" or 2h 14m 35s W.. then the solution
will be as follows:
L. 41° 30' 00" G. A. T. 21* 46ra 35s
Long. 2 14 35 W.
Co. L. 48 30 00
P. D. 70 28 42 L. A. T. 19 32 00 =t.
NOTE.— After obtaining the G. A. T., it will be seen that the longitude of the assumed position may
be so chosen as to avoid seconds in the L. A. T. or H. A.
The azimuth found from the azimuth tables is N. 89° 45' E. ^r~
BY THE COSIXE-HAVERSINE FORMULA:
t 19h 321" 00' log hav 9. 48378
L 41° 30' 00" N. log cos 9.87446
d 19° 31' 18" N. log cos 9. 97429
log hav 6 9. 33253 «
nat hav 6 0. 21505
21° 58' 42" nat hav 0. 03634
Calculated z 60° 11' 00" nat hav 0. 25139
90° OCK 00"
Calculated h 29 49 00
Observed ft 29 50 04
Altitude-difference 1' 04'
a The arrangement of Table 45 is such as to obviate the necessity of taking out the value of the angle in finding the natural
haversine from the log. haversine, or vice versa.
158
THE SUMNEK LINE.
BY THE HAVERSINE FORMULA:
Co. L+P. D. 118° 58' 42" nat hav 0. 74225
Co. L-P. D. 21 58 42 nat hav 0.03634
nat hav A
log hav A
log hav t
log hav B
nat hav B
nat hav (Co. L— P. D.)
nat hav z
Calculated z
Calculated h
Observed h
Altitude-difference
BY THE SINE-COSINE FORMULA:
t 19h 32mOOs
293° 00' 00"
L 41 30 00 N.
d 19 31 18 N.
0. 70591"
9. 84876
9. 48378
9. 33254
0. 21505
0. 03634
0. 25139
60° 11' 00"
90 00 00
29 49 00
29 50 04
1 04
log sin 9. 82126
log sin 9. 52396
log cos 9. 87446
log cos 9. 97429
log A 9. 34522
A 0. 22142
log B 9. 44063
B 0. 27581
A 0. 22142
Calculated A=29° 49' 00" nat sin=A+B
0. 49723
Since the observed altitude is higher than the calculated altitude, the observer's
position is nearer to the observed body than the assumed position. Consequently
the altitude-difference should be laid off in a direction to the east and north, 89° 45',
1.0 nautical mile from the assumed position.
Or, by the Traverse Tables :
Course.
Distance.
Difl. Lat.
Dep.
Diflf. Long.
89° 45'
1.0
0/.ON.
1'. 0 E.
1'. 3 E.
Assumed position, Lat.
Diff. Lat.
41° 30' 00" N.
00 N.
Computed point on Sumner line, 41° 30' 00" N.
Long. 33° 38' 45" W.
Diff. Long. 1 18 E.
33° 37' 27" W.
The direction of the Sumner line, being at right angles to the azimuth or true
bearing of the observed celestial body, runs N. 0° 15' W. and S. 0° 15' E. or 359° 45'
and 179° 45'.
EXAMPLE: At sea, October 10, 1916, in Lat. 6° 20' S. by account, Long. 30° 21' 30" W.; chro. time,
12h 45m 10s; observed altitude of moon's upper limb, 70° 15' 30", bearing north and east; I. C., -3' 00";
height of eye, 26 feet; chro. fast of G. M. T., lm 37s. 5. Required the Sumner line.
From a solution of the same problem under article 332, Chapter XII, and again under article 370,
Chapter XV, the following quantities are taken from among the prepared data: H. A. from Greenwich,
lh 16m 51s W.; corrected altitude, ft, 70° 11' 03"; d, 10° 03' 00" N. and, hence, P. D., 79° 57' 00".
Assume a position in Lat. 6° 00' S. and Long. 30° 27' 45" W.; then the solution will be as follows:
L 6° 00' 00" S. Gr. H. A. lh 16m 51s W.
Long. 2 01 51 W.
Co. L 96 00 00
P. D. 79 57 00 t- 0 45 00
o The arrangement of Table 45 is such as to obviate the necessity of taking out the value of the angle in finding the natural
haversine from the log. haversine, or vice versa.
THE SUMNER LINE.
159
BY THE COSINE-HAVERSINE FORMULA :
Calculated h
Observed h
Altitude-difference
BY THE HAVERSINE FORMULA
0* 45mOOs
6° 00' 00" S.
10 03 00 N.
16° 03' 00//
19 34 30
90 00 00
70 25 30
70 11 03
14 27
log hav 7. 98260
log cos 9. 99761
log cos 9. 99328
log have 7.97349
nat hav 6 0. 00941
nat hav 0. 01949
nat hav 0. 02890
Co. L-f P. D. 175° 57' 00" nat
Co. L-P. D. 16 03 00 nat
nat hav A
log hav A
log hav t
log hav B
nat hav B
nat hav (Co. L-P. D.)
nat hav z
Calculated z
Calculated h
Observed h
hav 0.99875
hav 0. 01949
0. 97926
9. 99090
7. 98260
Altitude-difference
BY THE SINE-COSINE FORMULA I
t Oh 45mOOs
11° 15' 00"
L 6 00 00 S.
d 10 03 00 N.
7.97350
0.00941
0. 01949
0. 02890
19° 34' 30"
90 00 00
70 25 30
70 11 03
14 27
log sin 9. 01923-
log sin 9. 24181
log A 8.26104-
A =-0.01824
.log cos 9.99157
log cos 9. 99761
log cos 9. 99328
log B 9. 98246
B =0. 96044
A =-0.01824
Calculated h=70° 25' 30" nat. sin=A+B 0. 94220
The azimuth from the Azimuth Tables S. 145° 5^ E. or N. 34° W E.
Since the observed altitude is lower than the calculated altitude, the observer's
position is further removed from the observed body than the assumed position.
Consequently the altitude-difference should be laid off to the south and west, 214°
14.4 nautical miles from the assumed position.
Or, by the Traverse Tables:
Course.
Distance. .
Diff. Lat.
Dep.
j Diff. Long.
214°
14.4
11'.9 S.
8'.0 W.
8'.0 W.
i
Assumed position, Lat.
Diff. Lat
6° W 00" S.
11 54 S.
Computed point on Sunnier line, 6 11 54 S.
Long. 30° 27' 45" W.
Diff. Long. 8 00 W.
30 35 45 W.
160
THE SUMNER LINE.
The direction of the Sumner line, being at right angles to the azimuth or true
bearing of the observed body, is N. 55° 50' W. and S. 55° 50' E., or 304° 10'
and 124° 10'.
EXAMPLE: At sea, July 12, 1916, in Lat. 50° N., Long. 40° W., observed an ex-meridian altitude of
the sun's lower limb, 61° 48' 30", the time by chronometer regulated to Greenwich mean time being
2h 41m 398; chro. corr.,— 2m 30s; I. C.,— 3' 00"; height of eye, 15 feet. Find the Sumner line.
From a solution of the same problem under article 330, Chapter XII, and again under article 370,
Chapter XV, the following quantities are taken from among the prepared data: G. A. T., 2h 33m 45s; h,
61° 57' 01"; d, 21° 58' 38" N.
Assume a position in Lat. 49° 507 N., Long. 40° 11' 15" or 2h 40m 45s W., then the solution will be
as follows:
L.
49° 50' 00" N.
Co. L 40 10 00
P. D. 68 01 22
G. A. T.
Long.
2b 33m45s
2 40 45 W.
L. A. T=t 0 07 00 E.
BY COSINE-HAVERSINE FORMULA:
d 21° 58' 38" N.
P. D. 68 01 22
Calculated h
Observed h
Altitude-difference
Oh 7m 00s
49° 50' 00" N.
21° 58' 38" N.
27° 51' 22"
27° 53' 15"
90° 00' 00"
62 06 45
61 57 01
9 44
log hav 6. 36774
log cos 9. 80957
log cos 9. 96724
log hav 6 6. 14455
nat hav d 0. 00014
nat hav 0. 05793
nat hav 0. 05807
BY HAVERSINE FORMULA:
Co. L+P. D. 108° 11' 22"
Co. L-P. D. 28 11 22
nat hav A
log hav A
log hav t
log hav B
nat hav B
nat hav (Co. L— P. D.)
nat hav z
Calculated z
Calculated h
Observed h
Altitude-difference
nat hav 0. 65607
nat hav 0. 05793
0. 59814
9. 77681
6. 36774
6. 14455
0. 00014
0. 05793
0. 05807
27° 53' 15"
90 00 00
62 06 45
61 57 01
9 44
BY THE SINE-COSINE FORMULA:
t Oh 07mOOs
1° 45' 00"
log cos
9. 99980
L 49 50 00 N.
d 21 58 38 N.
log sin
log sin
9. 88319
9. 57315
log cos
log cos
9. 80957
9. 96724
log A
A
9. 45634
0. 28598
,ogB
A
9. 77661
0. 59787
0. 28598
Calculated fc=62° 06' 37"
nat sin =
The azimuth from the Azimuth Tables: N. 177° E. or S. 3° E.
A+B 0. 88385
THE SUMNER LINE.
161
Since the observed altitude is lower than the calculated altitude, the observer's position is farther
removed from the observed body than the assumed position. Consequently the altitude-difference
should be laid oft to the north and west, 857°, 9.7 nautical miles from the assumed position
Or, by the Traverse Tables:
Course.
Distance.
Diff. Lat.
Dep.
Diff. Long.
357°
9.7
9.7 N.
(X.5 W.
(X.78 \V.
Assumed position, Lat.
Diff. Lat.
49° 50' 00" N.
9 42 N.
Long.
Diff. Long.
40C
11'
0
15" W.
46 W.
Computed point of Sunnier line 49 59 42 N.
40 12 01 W.
The direction of the Sumner line, being at right angles to the azimuth or true bearing of the observed
body, is N. 87° E. and S. 87° W., or 87° and 267°.
373. In the first of the three foregoing examples, the observed celestial body is
represented as being near the prime vertical; in the second, remote from both the
prime vertical and the meridian; and in the third, near the meridian. These examples
have been solved in the preceding chapters by three different methods known,
respectively, as the time sight, the <£' d>", and the ex-meridian; but we have here
treated all of them by one method, and have determined Sumner lines which are in
agreement with those determined by the various preceding methods. And it would
be likewise if we should take examples in which meridian altitudes have been observed.
Inasmuch as the local hour angle of a celestial body is 0° at the time of its passage
across the meridian of an observer, the second member of the right-hand side of the
equation of haversines becomes zero in cases in which the meridian altitude has
been observed, since the haversine of 0Q is equal to zero. The equation therefore
reduces to
havz = hav (Co. L-P. D.)
or
z= (Co. L-P. D.)
which leads at once to the usual formulae given in article 321, Chapter XII, for
finding the latitude from a meridian altitude. By this we are taught the full inter
pretation of a meridian altitude, which is that it gives the latitude of the intersection
with the local meridian of a Sumner line coinciding with a parallel of latitude.
374. In addition to the simplicity which arises from always working by the
same rule, the navigator has, by this method, the further practical advantage of being
able to do the most of the work of obtaining the Sumner line before taking the
observation, since, in clear weather, he may, in selecting the assumed geographical
position, assume an hour angle and calculate what time the chronometer or watch
ought to show at the instant when the celestial body has this hour angle, and then
observe the altitude at this instant; or, if anything sfiould happen to make him a few
seconds late in getting the altitude, he may alter the assumed longitude by a corre
sponding amount so as to make the hour angle right, and then the rest of the work
will hold good.
After correcting the observed altitude and obtaining from it the true altitude,
no more time need subsequently elapse in determining the Sumner line than is
necessary to take the difference between the altitudes found by calculation and by
observation and to rule a line at right angles to the bearing of the observed body
through the point found by laying off this altitude-difference as an intercept from the
assumed position.
375. It has already been remarked that the labor of performing such computa
tions as the foregoing may be saved when a book of altitude and azimuth tables is
at hand. These tables are arranged to be entered with the hour angle, the declina
tion, and the latitude; and they contain the corresponding values of the altitude
and azimuth. In the various books containing such tables, the special rules to be
observed in their use are set forth.
61828°— 16 11
162 THE SUMNER LINE.
It has been implied that when the altitude of the observed body is greater than
80° and, therefore, the zenith distance or radius of the circle of position is less than
10°, the tangent drawn to the circumference to represent the Sumner line could no
longer be regarded as coinciding throughout its proper length with the arc of the
circumference. When the zenith distance is 10°, the departure of the tangent from
the circumference is one-tenth of a mile at a distance of 10 miles from the theoretical
point of tangency and seven-tenths of a mile at a distance of 30 miles from the
theoretical point of tangency. These departures are doubled when the zenith distance
is reduced to 5Q, and they are nearly ten times the amounts stated for 10° when the
zenith distance is shortened to 1 Q.
There is not, however, any occasion for resorting to the proceeding of laying
down a straight line as a substitute for an arc of the actual circle of position when
the zenith distance is only a few degrees in length. In such cases the greatest con
venience and the best results are found by drawing circles of position directly on the
navigator's chart. For this purpose the polyconic chart, being issued to navigators
throughout all latitudes from 20° to 60° north of the Equator in connection with the
works of the United States Coast and Geodetic Survey, and therefore being available
throughout a like extent of south latitude by mere inversion, is generally serviceable,
because a chart embracing any certain parallels of latitude is available between these
parallels of latitude throughout all longitudes; and the Mercator projection may also
be used for this purpose within the Tropics, since the length of a minute of latitude
as represented on this projection varies but little within tropical limits. For instance,
it happens in crossing the tropical zone that, for a day or so, the sun is very near the
zenith — perhaps not more than 1Q away on one day and 2Q or 3° on another. In
such circumstances, having a chart of suitable scale embracing the parallels of latitude
of the region in which the ship is situated, plot the sun's geographical position with
Greenwich hour angle as longitude and declination as latitude, take on the dividers the
zenith distance, or complement of the corrected altitude, and draw in a portion of
the circumference of the actual circle of position lying near the position of the ship
as given by dead reckoning. Then wait until the azimuth has changed 30° or so —
which it does very rapidly near noon — and draw a second similar arc. The inter
section of these arcs gives the ship's position with accuracy. Of course if the ship
has moved in geographical place in the interval between the two sights, it will be
necessary, in order to find the geographical position at the instant of the second sight,
to move the first circle of position in direction and amount equal to the course and
distance made good in the interval.
FINDING THE INTERSECTION OF STJMNEB LINES.
376. The intersection of Sumner lines may be found either graphically or by
computation.
(a) GRAPHIC METHODS. — Each line may be plotted upon the chart of the locality
in which the ship is being navigated, in accordance with the data for its determination
(see art. 367), and the intersection thus found. This plan will commend itself
especially when the vessel is near shore, as the chart in use will then probably be
one of large enough scale, and it will be an advantage to see where the Sumner lines
fall with reference to the soundings and landmarks. To aid the extension of this
convenient practice on the ocean, where the navigator is usually furnished only with
a general chart, position-line plotting sheets have been provided for the use of navi
gators upon an ample scale.
(b) METHODS BY COMPUTATION. — The finding of the intersection of two Sumner
lines by computation may be divided into two cases:
Case I. When one line lies in a NE.-SW. direction, and the other in a NW.-SE.
direction, as shown in figure 56.
Case IL When both lie in a NE.-SW., or both in a NW.-SE. direction, as shown
in figure 57.
377. If each Sumner line is defined by the latitude and longitude of one of its
points and the azimuth of the celestial body at right angles to whose true bearing the
line runs, we may then, by means of Table 47, find the longitude of any other point
on such a line when its difference of latitude from the known point has been ascer-
THE SUMXER LINE.
163
tained. The numbers in Table 47 are values of the longitude factor, usually denoted
by the letter F. They vary with the latitude of the observer and the celestial body's
azimuth at right angles to the direction of the line, and express the change in longitude
due to a change of 1 ' in latitude along any given Sumner line. So that the difference
of latitude between any two points of a line, being multiplied by the longitude factor,
will give the difference of longitude between those points.
Turning to figures 56 and 57 and considering the Sumner lines A1 A2 and Bt B2
there represented to be defined by the azimuth at right angles to each and the lati
tudes and longitudes of the points At and Bt, respectively, we proceed to show the
relations which exist for determining the latitude and longitude of the fix at their
intersection by means of the tabulated longitude factors. The line PO being drawn
perpendicular to the parallel of latitude through the points Al and B1? the latitude
of the intersection will be a distance OP from the common latitude of A± and B1? and
its longitude will be a distance A1 O from At and Bt O from Bt. Let Y1 and F2 repre
sent the longitude factors from Table 47 for the Sumner lines Aj A2 and Bt B2,
respectively. Then, since Fj is the difference of longitude corresponding to a change
of 1' of latitude along the line Ax A2, the difference of longitude At O must be equal
to Fx multiplied into the number of minutes of latitude in the length OP. Therefore,
and likewise
A1O = OPxF1,
B10 = OPxF3;
and, since the known difference of longitude between the points At and Bx is com
posed of the sum of At O and Bt O in Case I, and the difference of Aj O and E1 O in
Case II, we have
A,
= AX B^
+ OPxF^OP (F^F,), in Case I, and
^OP (^-F,), in Case II.
thus:
From which, placing the known quantities on the right-hand side of the equations,
OP = T-, in Case I, and
"~
in Case II.
and Bj
etween
Hence, we obtain the difference of latitude from the common parallel of Al
to the point of intersection by dividing the known difference of longitude b
the points At and Bt by the sum of the longitude factors of the respective Sumner
lines in Case I, and by their difference in Case II.
Having determined OP and hence the latitude of the point of intersection of
the Sumner line, we proceed to multiply OP by Fj to get the difference of longitude
AjO, and apply that difference to the known longitude of Al to find the longitude
of the point of intersection P; and also, as a check, to multiply OP by F2 to get the
difference of longitude BA which, being applied to the longitude of Bx, gives again
the longitude of the point of intersection, P.
164 THE SUMNER LINE.
The following is a summary of the successive steps to be taken in following this
method :
1. Make a rough sketch of the Sumner lines whose intersection is to be fixed in
latitude and longitude, classifying them under Case I or Case II.
2. Take from Table 47 the longitude factors Fj and F2, respectively, for the
Sumner lines.
3. If the given coordinates of the points on the two lines have not a common
latitude, reduce them to a common latitude by multiplying the difference between
the latitudes of the points on the two lines by the longitude factor of one of the
lines and applying the product to the longitude of the point on that line. The
sketch will show whether the difference of longitude is to be added or subtracted, and
the result will be the longitude of a point of this line on the common parallel of
latitude.
4. The difference between the longitudes of the points of the two Sumner lines,
on the common parallel, divided by the sum of the longitude factors (Fj-fF.,), will
give the difference of latitude between the point of intersection and the common
parallel, when the lines are classified under Case I; and the difference between the
longitudes of the points of the two Sumner lines, on the common parallel, divided by the
difference of the longitude factors (Fx — F2), will give the difference of latitude between
the point of intersection and the common parallel, when the lines are classified under
Case II.
The sketch will show whether the intersection of the Sumner lines lies to the
northward or southward of the common parallel, and hence whether the difference
of latitude is to be added to or subtracted from the latitude of the common parallel.
5. Having found the difference of latitude between the point of intersection of
the Sumner lines and the common parallel, multiply this difference by the longitude
factor of each line and apply the products each to the longitude of its corresponding
line on the common parallel. The products are applied in opposite directions in
Case I, and both of them must lead to the same longitude for the point of intersection ;
and the products are applied in the same direction in Case II, and in this case also
both of them must lead to the same longitude for the point of intersection.
EXAMPLE: Find the intersection of the Sumner lines defined below by the latitude and longitude of
a single point on each and by the respective azimuths of the celestial bodies upon which the lines depend.
FIG. 58.
f 25° 40' S 1
A j -Q^O 3^ ^ > Azimuth, at right angles to line, N. 51° E.
f O£O on:/ Q ^
B 1 -n£o QQ/ c w ^Azimuth, at right angles to line, N. 72° W.
^ J-J-O oo »O W» J
From Table 47:
Longitude factor for line A=0.90=F!.
Longitude factor for line B=0.36=F2.
Reduce the given points to a common parallel of latitude by transferring
the point on line B to the latitude of the point on line A,
(25° 40' S.-250 25' S.)XF2=15'X0.36= 5'.4 W.
115° 33'.5 W.
115° 38'.9 W.
Hence we have for the point on the line B at which the latitude is the same as the latitude of the point
on the line A,
{OCO Af)/ Q 1
115° 38' 9 W [Azimuth, at right angles to line, N. 72° W.
We now have two Sumner lines, under Case I, whose common latitude is 25° 40' S. and whose longitudes
on the common parallel are:
115° 38'.9 W.
115° 31'.0 W.
7/.9=Diff. Long, on common parallel.
79 79 79
•p _|_-p = QQ\ 36=ifi>6==^7 ^iff- kat. between intersection and common parallel.
THE SUMNER LINE.
165
Corrections in longitude:
6. 27XF1=6. 27X0. 90=5'. 64
6. 27XF2=6. 27X0. 36=2 . 26
Long. A
Diff. Long.
115° 31'.OOW.
5.64W.
Intersection 115 36 .
Long. B 115° 38'.90W.
Diff. Long. -2.26E.
115 36 .64 W.
Lat. common parallel 25° 40/.00 S.
Diff. Lat. 6 .27 N.
25 33 .738.
EXAMPLE: Find the intersection of the Sumner lines defined below:
f4Q° <*(V N 1
A{ 5 24 8 W j Azimutn> at ri8nt angles to line, N. 81° W.
T49° 307 N 1
Bs c o~ Q w f Azimuth, at right angles to line, X. 31° W.
[ O /O .5 \V .J
A sketch of the lines shows their classification to be under Case II.
From Table 47:
Longitude factor for line A=0.24=F!.
Longitude factor for line B=2.57=F2.
Diff. Long, on common parallel=5° 25' .8—5° 24' .8=1' .0.
-F2- 57-0.
==Diff- Lat' between
B
tion and common parallel.
Corrections in longitude:
FIG. 59.
0. 429XFa=0. 429X0. 24=0. 10.
0. 429XF2=0. 429X2. 57=1. 10.
Long. A
Diff. Long.
5° 24' .8 W.
0 .IE.
Long. B
Diff. Long.
5° 25' .8 W.
1 .1 E.
Lat. common parallel
Diff. Lat.
49° SO7 .0 N.
0 .4 N.
Intersection 5 24 .7 W.
5 24 .7 W.
49 30 .4 N.
B
FIG. 60.
378. If the two geographical positions defining two Simmer lines have a
common longitude instead of a common latitude, as represented in figures 60 and 61,
their intersection may be found by means of the latitude factors
tabulated in Table 48, in a manner similar to the use of the lon
gitude factors in connection with the Sumner lines whose known
points have a common latitude. The latitude factors vary with
the latitude of the observer and the celestial body's azimuth at
right angles to the direction of the line, and express the change in
latitude due to a change of 1' in longitude along any given Sumner
line. So that the difference of longitude between any two points
of a line being multiplied by the latitude
factor will give the difference of latitude be
tween those points.
The latitude factors of two Sumner lines
whose intersection is to be found are usually
denoted by the letters i1 and f2, and the
successive steps to be taken in finding the in
tersection are here summarized:
1. Make a rough sketch of the Sumner
lines whose intersection is to be fixed in latitude and longitude,
classifying them under Case I or Case II.
2. Take from Table 48 the latitude factors fx and f2,
respectively, for the Sumner lines.
3. The difference between the latitudes of the points of
the two Sumner lines, in the common longitude, divided by
the sum of the latitude factors (fj + f2), will give the difference
of longitude between the point of intersection and the common meridian when the
lines are classified under Case I; and the difference between the latitudes of the
FIG. 61.
166 THE SUMNER LINE.
points of the two Sumner lines, in the common longitude, divided by the difference
of the latitude factors (fx — f2), will give the difference of longitude between the point
of intersection and the common meridian when the lines are classified under Case II.
The sketch will show whether the intersection of the Sumner lines lies to the
eastward or westward of the common meridian, and hence whether the difference of
longitude is to be added to or subtracted from the common longitude.
4. Having found the difference of longitude between the point of intersection
of the Sumner lines and the common longitude, multiply this difference by the
latitude factor of each line and apply the products each to the latitude of its corre
sponding line on the common meridian. The products are applied in opposite
directions in Case I, and both of them must lead to the same latitude for the point of
intersection; and the products are applied in the same direction in Case II, and in
this case also both of them must lead to the same latitude for the point of intersection.
EXAMPLE: Find the intersection of the Sumner lines denned below:
A{yJ0 if 'go \v'} Azimuth, at right angles to line, N. 57°. 6 W.
B{^° J||' '^ ^ 1 Azimuth, at right angles to line, N. 77° W.
A sketch of the lines shows their classification to be under Case II.
From Table 48:
Latitude factor for line A=l. 23=ft.
Latitude factor for line B=3. 32=ft.
Diff. Lat. on common meridian =7'. 15.
7. 15 7. 15 7. 15
• • •= — — — — - — -= — — =3'. 42 Diff. Long, between intersection and common meridian.
f2-ft 3.32-1.23 2.09
Corrections in latitude:
3. 42X^=3. 42X1. 23= 4'. 20
3. 42Xf2=3. 42X3. 32=11 . 35
Lat. A 40° 13'. 55 N. Lat. B 40° 06'. 40 N. Long, on common me-
Diff. Lat. 4 . 20 N. Diff. Lat. 11 . 35 N. ridian 71° 14'. 86 W.
— — Diff, Long. 3. 42 E.
Intersection 40° 17'. 75 N. 40° 17'. 75 N. — •
71° 11'. 44 W.
379. When a Sumner line is defined by the latitudes and longitudes of two of
its points, the longitude factor for the line may be found by dividing the difference
between the longitudes of the two given points by the difference between their
latitudes; and the latitude factor, being the reciprocal of the longitude factor, may
be found by dividing the difference between the latitudes of the two given points by
their difference of longitude.
The method of finding the intersection of Sumner lines by longitude and lati
tude factors, described in articles 377 and 378, may, therefore, be applied as well
when the lines are defined by pairs of geographical positions as when they are defined
by the azimuth and one geographical position.
380. The modification of the methods for finding the intersection of two Sumner
lines, where there is a run between the observations from which they are deduced,
will be readily apparent. It is known that at the time of taking a sight the vessel
is at one of the points of the Sumner line, but which of the various points represents
her precise position must remain in doubt until further data are acquired. Suppose,
now, that after an observation, the vessel sails a given distance in a given direction;
it is clear that while her exact position is still undetermined it must be at one of the
series of points comprised in a line parallel to the Sumner line and at a distance and
direction therefrom corresponding to the course and distance made good; hence, if
THE SUMNEK LINE. 167
a second sight is then taken, the position of the vessel may be found from the inter
section of two lines — one, the Sumner line given by the second observation, and the
other a line parallel to the first Sumner line but removed from it by the amount of
the intervening run.
Positions may be brought forward graphically on a chart by taking the course
from the compass rose with parallel rulers, and the distance by scale with dividers.
If one of the methods by computation be adopted, the point or points of the first
line are brought forward by the traverse tables, using middle latitude sailing. The
direction of a Sumner line as determined from the azimuth of the body always
remains the same, whatever shift may be made in the position of the point *by which
the line is further defined.
EXAMPLE: Taking the Sumner lines, which are denned in the first example under article 377. by the
latitude and longitude of a point of each and by the respective azimuths of the celestial bodies upon
which the lines depend, as follows:
A{ll5° 31 W }Azimutn> at right angles to line, N. 51° E.
5 W }Azimutn> at right angles to line, N. 72° W.
33'
and supposing the vessel from which the observations were taken that gave these lines to have
N. 54° E. (true) 35 miles in the interval between the sights, find the position of the vessel at the tim
run
time of
the second sight.
The point A; in 25° 4(X S. and 115° 31' W., is first transferred to the point A', 35 miles N. 54° E.(true)
from A, by the method of Middle Latitude Sailing (article 177) by means of the Traverse Tables, thus:
From'Table 2, course N. 54° E.; Dist., 35 miles; we find Diff. Lat. 20.6 N., Dep. 28.3 E. Therefore,
Lat. A 25° 4(K S. Lat. A 25° 4<X S.
Diff. Lat. 20 .6 N. Lat. A' 25 19 .4 S.
Lat. A' 25 19 .4 S. 2)50 59 .4
Middle Lat. 25 29 .7
From Table 2, Middle Lat, (course), 25£°, Dep. (Lat.), 28.3 E., we find Diff. Long. (Dist,), 31.3 E.
Therefore,
Longitude A. 115° 31' W.
Diff. Long. 31 .3 E.
Longitude A', 114 59 .7 W.
The Sumner lines whose intersection is to be found are therefore defined as follows:
A/{ll4° 5<T *7 W }Azimutn» at rignt an£les to the line> N- 51° E-
B L^° I!' 5 |; JAzimuth, at right angles to the line, N. 72° W.
From Table 47:
Longitude factor for line A/=0.90=F1
Longitude factor for line B =0.36=F2
Reduce the given points to a common parallel of latitude by transferring the point on line B to the
latitude of the point on line A',
(25° 19M S.-250 25' S.)XF2=-5.6X0.36= 2'.0 E.
115° 33 .5 W.
115 31 .5 W.
Hence we have for the point on the line B at which the latitude is the same as the latitude of the point
on the line A7,
^A 25° 19'.4 S.
B\115 31.5W.
168 THE SUMNEK LINE.
We now have two Sumner lines, A' and B', under Case I, whose common latitude is 25° 19'. 4 S. , and whose
longitudes on the common parallel are 114° 59'. 7 and 115° 31'. 5. Hence, the difference of longitude on
the common parallel is
115° 31'.5 W.
114° W.I W.
31 .8=Diff. Long, on common parallel.
O1 Q O1 Q ^18
-=—^==25. 2=Diff. Lat. between intersection and common parallel.
25.2XF1=25.2X0.90=22.7
25.2XF2=25.2X0.36= 9.1
Corrections in longitude:
Long. Ax 114°59/.7W. Long. W 115° 31r.5W. Lat. common par. 25° 19X.4 S.
Diff. Long. 22 .7 W. DifE. Long. 9.1 E. Diff. Lat. 25 .2 N.
Intersection 115 22.4W. 115 22.4 24 54 .2 S.
CHAPTER XVI.
THE PEAOTICE OF NAVIGATION AT SEA,
381. Having set forth in previous chapters the methods of working dead
reckoning and of solving problems to find the latitude, longitude, chronometer
correction, and azimuth from astronomical observations, it will be the aim of the
present chapter to describe the conditions which govern the choice and employment
of the various problems, together with certain considerations by which the navigator
may be guided hi his practical work at sea.
382. DEPARTURE AND DEAD RECKONING. — On beginning a voyage, a good
departure must be taken while landmarks are still in view and favorably located for
the purpose; this becomes the origin of the dead reckoning, which, with frequent
new departures from positions by observation, is kept up to the completion of the
voyage, thus enabling the mariner to know, with a fair degree of accuracy, the posi
tion of his vessel at any instant.
At the moment of taking the departure, the reading of the patent log (which
should have been put over at least long enough previously to be regularly running)
must be recorded, and thereafter at the time of taking each sight and at every other
time when a position is required for any purpose, the Tog reading must also be noted.
It is likewise well to read the log each hour, for general information as to the speed
of the vessel as well as to observe that it is in proper running order and that the
rotator has not been fouled by seaweed or by refuse thrown overboard from the ship.
It is a good plan to record the tune by ship's clock on each occasion that the log is
read, as a supplementary means of arriving at the distance will thus be available in
case of doubt. If a vessel does not use the patent log but estimates her speed by
the number of revolutions of the engines or the indications of the chip log, the
noting of the time becomes essential. A good sight is of no value unless one knows
the point in the ship's run at which it was taken, so that the position it gave may be
brought forward with accuracy to any later time.
383. GENERAL DESCRIPTION OF THE DAY'S WORK. — The routine of a day's
work at sea consists in working the dead reckoning, an a. m. time sight and azimuth
taken when the sun is in its most favorable position for the purpose, a meridian alti
tude of the sun (or, when clouds interfere at noon, a sight for latitude as near the
meridian as possible), and a p. m. time sight and azimuth. This represents the
minimum of work, and it may be amplified as circumstances render expedient; but
no part of it should ever be omitted unless cloudy weather renders its performance
impossible.
384. MORNING SIGHTS. — The morning time sight and azimuth should be
observed, if possible, when the sun is on the prime vertical. As the body bears
east at that tune, the resulting Sumner line is due north and south, and the longitude
will thus be obtained without an accurate knowledge of the latitude. Another
reason for^ so choosing the time is that near this point of the sun's apparent path
the body is changing most slowly in azimuth, and an error in noting the time will
have the minimum effect in its computed bearing. The time when the sun will be
on the prime vertical — that is, when its azimuth is 90° — may be found from the
azimuth tables or the azimuth diagram. Speaking generally, during half the year
the sun$ does not rise until after having crossed the prime vertical, and is therefore
never visible on a bearing of east. In this case it is best to take the observation as
soon as it has risen above the altitude of uncertain atmospheric effects — between 10°
and 15°.
A series of several altitudes should be taken, partly^ because the mean is more
accurate than a single sight, and partly because an error in the reading of the watch
or sextant may easily occur when there is no repetition. If the sextant is set in
advance of the altitude on even five or ten minute divisions of the arc, and the time
169
170 THE PEACTICE OF NAVIGATION AT SEA.
marked at contacts, the method will be found to possess various advantages. As
the sight is being taken the patent log should be read and ship's time recorded. It
is well, too, to make a practice of noting the index correction of the sextant each time
that the sextant is used. The bearing of the sun by compass should immediately
afterward be observed, and the heading by compass noted, as also the time (by the
same watch as was used for the sight) .
Before working out the sight, the dead reckoning is brought up to the time of
observation, and the latitude thus found used as the approximate latitude at sight.
It is strongly recommended that every sight be worked for a Sumner line, either by
assuming two latitudes, or by using one latitude and the azimuth, or yet more
advantageously by the method of Saint Hilaire.
The compass error is next obtained. From the time sight the navigator learns
that his watch is a certain amount fast or slow of L. A. T., and he need only apply
this correction to the watch time of azimuth to obtain the L. A. T. at which it was
observed; then he ascertains the sun's true bearing from the azimuth tables or
azimuth diagram, compares it with the compass bearing, and obtains the compass
error; he should subtract the variation by chart and note if the remainder, the devia
tion, agrees with that given in his deviation table; but in working the next dead
reckoning, if the ship's course does not change, the total compass error thus found
may be used without separating it into its component parts. It should be increased
or decreased, however, as the ship proceeds, by the amount of any change of the
variation that the chart may show.
385. If there is any fear of the weather being cloudy at noon, the navigator
should take the precaution, when the sun has changed about 30° in azimuth, to observe
a second altitude and to record the appropriate data for another sight, though this
need not actually be worked unless the meridian observation is lost. If it is required
it may be worked for either a time sight or $' $" sight, or by the Saint Hilaire
method, according to circumstances, and a second Sumner line thus obtained, whose
intersection with earlier Sumner line, brought forward for the run in the interval
between the sights, will give the ship's position.
386. NOON SIGHTS. — Between 11 and 11.30 o'clock (allowing for gain or loss
of time due to the day's run) the ship's clocks should be set for the L. A. T. of the
prospective noon position. The noon longitude may be closely estimated from the
morning sight and the probable run. The navigator should also set his own watch for
that time, to the nearest minute, and note exactly the number of seconds that it is
in error. He may now compute the constant (art. 325, Chap. XII) for the meridian
altitude. The daily winding of the chronometer is a most important feature of the
day's routine, and may well be performed at this hour. At a convenient time before
noon, the observations for meridian altitude are commenced and continued until the
watch shows L. A. noon, at which time the meridian altitude is measured and the
latitude deduced.
If the weather is cloudy and there is doubt of the sun being visible on the meridian
an altitude may be taken at any time within a few minutes of noon, the time noted,
and the interval from L. A. noon found from the known error of the watch. It is
then the work of less than a minute to take out the a from Table 26, the at2 from
Table 27, and apply the reduction to the observed altitude to obtain the meridian
altitude. Indeed, the method is so simple that it may be practiced every day and
several values of the meridian altitude thus obtained, instead of only one.
387. It now becomes necessary to find the longitude at noon. This may be
done graphically by a chart or bv computation. The former plan needs no explana
tion. There are a number of variations in the methods of computation, one of which
will be given as a type.
By the ship's run, work back the noon latitude to the latitude at a. m. time sight.
If the Sumner line was found from two assumed latitudes which differed + m minutes,
while the corresponding longitudes differed ±ri minutes, then 1' difference of latitude
A1)
causes ±— minutes difference of longitude. If the true latitude at sight is±#min-
ffb
utes from one of the assumed latitudes, then±a: X— is the corresponding difference of
longitude. If the Sumner line was found from one assumed latitude and an azimuth,
Z, the longitude factor of the line may be found from Table 47 ; and this multiplied
THE PRACTICE OF NAVIGATION AT SEA. 171
by the difference between the true and assumed latitude will give the correction to
be applied to the computed longitude corresponding to the assumed latitude.
Having thus the longitude at sight, the longitude at noon is worked forward for the
run. If the sights show a considerable current it should be allowed for, both in
working back the latitude and in bringing up the longitude for the run between the
sight and noon.
EXAMPLE: Suppose that an a. m. time sight, taken when the sun's azimuth was S. 39° 48' E., has
given a longitude of 30° 31' W. when solved with a dead-reckoning latitude of 50° 54' N. Suppose that
when the noon latitude is worked back to the time of the a. m. sight, by means of the vessel's run, the
true latitude at that time was found to be 50° 58' N. The longitude was thus computed with a latitude
that was 4' too much to the southward. Find the corresponding error in longitude, and the longitude
at the time of sight.
down in connection with the Explanation of Table 47, the correction in longitude must, in this case,
be applied to the eastward.
Hence we have-
Longitude computed with D. R. Lat., 50° 54' N 30° 31' W.
Correction in long, due to change of 4'' in latitude to the northward 7. 6 E.
True longitude at the time of sight 30° 23. 4 W.
388. CURRENT AND RUN. — The current may be found by comparing the noon
positions as obtained by observation and by dead reckoning,' and the day's run is
calculated from the difference between the day's noon position bv observation and
that of the preceding day. To "current" is usually attributed all discrepancies
between the dead reckoning and observations; but it is evident that this is not
entirely due to motion of the waters, as it includes errors due to faulty steering,
improper allowance for the compass error, and inaccurate estimate of tie vessel's
speed through the water.
The noon position by observation becomes the departure for the dead reckoning
that follows.
389. AFTERNOON SIGHTS. — The p. m. time sight and azimuth is similar to the
morning observation.
390. SUMNER LINES. — By performing the work that has just been described a
good position is obtained at noon each day, which, in a slow-moving vessel with
plenty of sea room, may be considered sufficient; but conditions are such at times as
to render it almost imperatively necessary that a more frequent determination of the
latitude and longitude be made. If the vessel is near the land or in the vicinity of
off-lying dangers, if she is running a great circle course requiring frequent changes,
if she is making deep-sea soundings, S she has just come through a period of fo^gy
or cloudy weather, or if the indications are that she is about to enter upon such a
period, or if she is running at high speed, it is obviously inexpedient to await the
coming of the next noon for a fix. The responsibilities resting upon the navigator
require that he shall earlier find his ship's position; and, generally speaking, the
greater the speed made by the vessel the more absolute is this requirement.
The key to all such determinations will lie in the Sumner line, and a clear under
standing of the properties of such a line will greatlv facilitate the solutions. The
mariner must keep in mind two facts: First, that a single observation of a heavenly
body can never, by itself, give the paint occupied by an observer on the earth's
surface; and second, that whenever any celestial body is visible, together with
enough of the horizon to permit the measuring of its altitude, an observer may
thereby determine a line which passes through his own position on the earth's surface
in a direction at right angles to the bearing of the body.
It may readily be seen that if two Sumner lines are determined the observer's
position must be at their intersection, and that that intersection will be most clearly
marked when the angle between the lines equals 90°; hence, if two heavenly bodies
are in sight at the same time the position may be found from the intersection of their
Sumner lines, the angle of intersection being equal to the horizontal angle between
the bodies. If only one body is in sight, as is generally the case when the sun is
shining, one line of position may be gotten from an altitude taken at one time, and a
second line from another altitude taken when it has changed some 30° in^ azimuth—
usually, a couple of hours later. Bringing forward the first line for the intervening
run, the intersection may be found.
172 THE PEACTICE OF NAVIGATION AT SEA.
With the general principles of the Sumner line clearly before him, the navigator
will find no difficulty in making the choice of available bodies. If about to take a
star sight, and sky and horizon are equally good in all quarters, two bodies should
be taken whose azimuths differ as nearly as possible by 90°. If one body can be taken
on or near the meridian, its bearing being practically^ north or south, the resulting
Sumner line will be east and west — that is, it may be said that whatever the longitude
(within its known limits) the latitude will be the same; the other sight may then
be worked as a time sight with this single latitude, and time will thus be saved. The
same is true if Polaris is observed, and it is a very convenient practice to take an
altitude of that star at dawn and obtain a latitude for working the a. in. time sight
of the sun. A similar case arises when a body is^ observed on the prime vertical,
its Sumner line then runs north and south and coincides with a meridian; if the other
body is favorably located for a q>' <p" sight, it may be worked with a single longitude
and the latitude thus found directly.
If it is not possible to obtain two lines and thus exactly locate the ship, the
indications of a single line may be of great value to the navigator. A Sumner line
and a terrestrial bearing will give the ship's position by their intersection in the same
manner as two lines of position or two bearings; or the position of the ship on a line
may be shown with more or less accuracy by a sounding or a series of soundings.
If the body be observed when it bears in a direction at right angles to the trend of a
neighboring shore line, the resulting line will be parallel with the coast and thus
show the mariner his distance from the land, which may be of great importance even
if his exact position on the line remains in doubt. If the bearing be parallel to the
coast line, then the Sumner line will point toward shore; the value -of a line that leads
to the point that the vessel is trying to pick up is amply demonstrated by the
experience of Captain Sumner that led to the discovery of the method. (Art. 362,
Chap. XV.)
For especially accurate work three Sumner lines may be taken, varying in
azimuth about 120°; if they do not intersect in a point, the most probable position
of the ship is at the center of the triangle that they form.
If two pairs of lines be determined, each pair based upon observation of two
bodies bearing in nearly opposite directions and at about the same altitude, the
mean position that results from the intersection of the four lines will be as nearly
as possible free from those errors of the instrument, of refraction, and of the observer,
which can not otherwise be eliminated. This is fully explained in article 449,
Chapter XVII.
391. USE OF STARS, PLANETS, AND MOON. — It may be judged that the
employment in navigation of other heavenly bodies than the sun is considered of
the utmost importance, and mariners are urged to familiarize themselves with the
methods by which observations of stars, planets, and the moon may be utilized to
reveal to them the position of their vessels at frequent intervals throughout the
twenty-four hours.
It should be remembered, however, that in order to be of value these observations
must be accurate; and to measure an accurate altitude of the body above the horizon
it is required not only that the body be visible but also that the horizon be distinctly
in view. Care should therefore be taken to make the observations, if possible, at
the time when the horizon is plainest — that is, during morning and evening twilight.
It may be urgently required to get a position during hours of darkness, and a dim
horizon line may sometimes be seen and an observation taken, using the star telescope
of the sextant; if the moon is shining, its light will be a material aid; but results
obtained from such sights should be regarded as questionable and used with caution.
Altitudes measured, however, just before sunrise and just after sunset are open to
no such criticism; a fairly well-practiced observer who takes a series of sights at
such a time, setting the sextant for equal intervals of altitude, will find the regularity
of the corresponding time intervals such as to assure him of accuracy.
392. IDENTIFICATION OF UNKNOWN BODIES. — On account of the very great
value to be derived from the use of stars and planets in navigation, it is strongly
recommended that all navigators familiarize themselves with the names and positions
of those fixed stars whose magnitude renders possible their employment for obser
vations, and also with the general characteristics — magnitude and color — of the
three planets (Venus, Jupiter, and Mars) which are most frequently used. A study
THE PRACTICE OF NAVIGATION AT SEA. 173
of the different portions of the heavens, with the aid of any of the numerous charts
and books which bear upon the subject, will enable the navigator to recognize the
more important constellations and single stars by their situation with relation to
each other and to the pole and the equator.
It may occur, however, that occasion will arise for observing a body whose name
is not known, either because it has not been learned, or because the surrounding
stars by which it is usually identified are obscured by clouds or rendered invisible
by moonlight or daylight. In such a case the observer may estimate the hour angle
and decimation (the hour angle applied to local sidereal time giving the right
ascension), and the star or planet may thus be recognized from a chart or from an
inspection of the Nautical Almanac. This rough method will generally suffice when
the body is the only one of its magnitude within an extensive region of the heavens;
but cases often arise where a much closer approximation is necessary, and more
exact data are required for identification.
393. If in doubt as to the name of the body at the time of taking the sight, it
should be made an invariable rule to observe its bearing by compass, whence the
true azimuth may be approximately deduced by applying the compass error.
Star Identification Tables giving simultaneous values of the declination and
hour angle, corresponding to the values of the latitude, altitude, and azimuth ranging
from 0° to 88° in latitude and altitude and from 0° to 180° in azimuth, are published
by the Hydrographic ^ Office for the convenience of navigators. In the absence of
these Star Identification Tables, the following method affords a means of identi
fication:
sin d = sin L sin 7i + cos L cos Ti cos Z (1 )
sin t = sin Z cos Ji sec d (2)
Having computed the value of d, the declination, from (1), noting carefully the
sign of cosine Z, the value of t, the hour angle, is computed from (2) . In the catalogues
and lists giving the names and magnitudes of the stars, they are tabulated by their
declinations and right ascensions because these coordinates are independent of
diurnal rotation, and, this being so, it becomes necessary, on finding the hour angle
from (2), to convert it into right ascension; and then, with the values of the declina
tion and right ascension thus found, to scan the list of stars and find the name of
that one whose catalogued coordinates best agree with these values. The stars that
are bright enough to be observed with nautical instruments are so far apart in the
firmament that the identification will be complete if the computation be but roughly
made. The possibility that the observed body may be a planet must always be kept
in mind in scanning the star table or chart.
EXAMPLE : At sea, February 26, 1916, L. M. T. 6h 20m p. m. Weather overcast and cloudy. Observed
the altitude of an unknown star through a break in the clouds to be 31° 3(X (true), bearing 285° (true).
What is the name of the star? Ship's position, by D. R., latitude 35° 2(K N., longitude 60° W.
L 35° 2(X log sin 9. 762 log cos 9. 912
h 31° 3(X log sin 9. 718 log cos 9. 931 log cos 9. 931
Z 285° 00' log cos 9. 413 log sin 9. 985
A 0.302 log... 9.480
B 0.180 log... 9.256
A-f B = 0.302 + 0.180 = 0'482 = nat sin d .'. d = 28° 49/.. . log sec 10. 057
t=K. A.=70°=4h 40m log sin 9.973
Then converting the hour angle into right ascension, as follows:
L. M. T. 6h 20m
R. A. M. S. 22 20
corr. for G. M. T. +2
L. S. T. 4 42
H. A. 4 40
R. A. 0 02
174 THE PRACTICE OF NAVIGATION AT SEA.
394. VALUE OF THE MOON IN OBSERVATIONS . — Next to the sun, the most con
spicuous body in the heavens is the moon, and it may therefore frequently be
employed by the mariner with advantage. Owing to its nearness to the earth and
the rapidity with which it changes right ascension and declination, the various cor
rections entailed render observations of this body somewhat longer to work out,
with consequent increased chances of error; and errors in certain parts of the work
will have more serious results than with other bodies^ the navigator will therefore
usually pass the moon by if a choice of celestial bodies is offered for a determination
of position; but so many occasions present themselves when there is no available
substitute for the moon that the extra time and care necessary to devote to it are
well repaid. During hours of daylight it is often clearly visible, and its line of
position may cut with that of the sun at a favorable angle, giving a good fix from
two observations taken at the same time, when the only other method of finding
the position would be to take two sights of the sun separated by a time interval in
which an imperfect allowance for the true run intervening would affect the accuracy
of the result, or a clouding-over of the heavens would prevent any definite result
whatever being reached; and during the night, the gleam upon the water directly
below the moon may define the horizon and give opportunity for an altitude of that
body when it is impossible to take an observation of any other. It has been the
purpose of this work to point out the features of the various sights wherein the
practice with the moon differs from that of the sun, stars, or planets; care and
intelligent consideration will render these quite clear.
Besides its availability for determining Sumner lines of position, which it shares
with other bodies, the moon affords a means for ascertaining the Greenwich mean
tune independently of the chronometer, thus rendering it possible to deduce the
longitude and chronometer error. This is accomplished by the method of lunar
distances.1 If the Greenwich time given by an observation of lunar distance could
be relied upon for accuracy, the method would be a great boon to the navigator;
but this is not the case. The most practiced observer can not be sure of obtaining
results as close as modern navigation demands, and the errors to which the method
is subject are larger than the errors that may be expected in the chronometer, even
when the instrument is only a moderately good one and its rate is carried forward
from a long voyage. The method is not, therefore, recommended for use except
where the chronometer is disabled or where it is known to have acquired some
extraordinary error; and when lunar distances are resorted to care must be taken
to navigate with due allowance for possible inaccuracy of the results. In this con
nection it is appropriate to say that the best safeguard against the dire consequences
that may result from a disabled or unreliable chronometer is for every vessel to carry
two — or, far better, three — of those instruments, the advantages of which plan are
stated in article 265, Chapter VIII.
395. EMPLOYMENT OF BODIES DEPENDENT UPON THEIR POSITION. — The prac
tical navigator will soon observe that there are certain conditions in which bodies
are especially well adapted for the finding of latitude, and others where the longitude
is obtained most readily.
Taking the sun for an example, when a vessel is on the equator and the declina
tion is zero, that body will rise due east of the observer and continue on the same
bearing until noon, when for an instant it will be directly overhead, with a true
altitude of 90°, and will then change to a bearing of west, which it will maintain
until its setting. In such a case any observation taken throughout the day will
give a true north-and-south Sumner line, defining longitude perfectly, but giving no
determination of the latitude, excepting for a moment only when the body is on the
meridian. With the exception noted, all efforts to determine the latitude will fail.
The reduction to the meridian takes the form ^, becoming indeterminate, and in the
<f>' $" sight the cosine of <£ ' will assume a value that corresponds alike to any angle
within certain wide limits — the limits within which the circle of equal altitude has
practically a north-and-south direction. In conditions approximating to this we
may obtain a longitude position more easily than one for latitude, even within a few
minutes of noon.
1 The tables of lunar distances have been omitted from the American Ephemeris and Nautical Almanac after the volume for
THE PRACTICE OF NAVIGATION AT SEA. 175
As the latitude and declination separate, conditions become more favorable for
finding latitude and less so for longitude; the intermediate cases cover a wide range,
wherein longitude may be well determined by observations three to five hours from
the meridian, and latitude by those within two hours of meridian passage. As
extreme conditions are approached the accuracy of longitude determinations con
tinues to decrease; at a point in 60° north latitude, when the sun is near the southern
solstice, its bearing differs only 39° from the meridian at rising; or, in other words,
even if observed at the most favorable position, the resulting Sumner line is such
that '!' in latitude makes a difference of 1.3 miles of departure, or 2'. 6 of longitude,
and is far better for a latitude determination than for longitude. And in higher
latitudes still this condition is even more marked.
Having grasped these general facts, the navigator must adapt his time for
taking sights to the circumstances that prevail, and when the sun does not serve
for an accurate determination of either latitude or longitude the ability to utilize
the stars, planets, and moon as a substitute will be of the greatest advantage.
396. USE OF VARIOUS SIGHTS. — Except when employing the method of Saint
Hilaire (Chapter XV), the navigator may sometimes be in doubt as to the best
method of working a sight. Xo rigorous rules can be laid down, and experience
alone must be his guide. In a general way it may be well, when the body is nearer
to the prime vertical than to the meridian, to work it for longitude, assuming lati
tude, and using the time sight; and when nearer the meridian to work it for latitude,
assuming longitude, by the <£' <f>* method. The time sight is more generally used
than the other, it has wider limits of accurate application and is probably a little
quicker; but as the meridian is approached and the hour angle decreases small
errors in the terms make large ones in the results. The <f>' </>" or latitude method
should not ordinarily be employed beyond three hours from the meridian, and then
only when the body is within 45° of azimuth from the meridian and has a declina
tion of at least 3Q; with an hour angle of 6h (90°) or a declination of 0° the trigono
metric functions assume such form that the method is not available; nor does it
give definite results when the azimuth is 90° or thereabouts.
When the body is close enough to the meridian for the method of reduction to
the mericlian to be applicable, that method is to be preferred because of its quickness
and facility. It should be noted, however, that, though close enough to employ
the reduction, it may not be sufficiently correct to assume that the body bears due
north or south, and the sight should be worked with two longitudes, or the Sumner
line determined by the azimuth, unless the bearing nearly coincides with the direc
tion of the meridian.
397. WORKING TO SECONDS AND ACCURACY OF DETERMINATIONS. — The beginner
who seeks counsel from the more experienced in matters pertaining to navigation will
find that he receives conflicting advice as to whether it is more expedient to carry
out the terms to seconds of arc, or to disregard seconds and work with the nearest
whole minute.
It is a well-recognized fact that exact results are not attainable in navigation at
sea; the chronometer error, sextant error, error of refraction, and error of observa
tion are all uncertain; it is impossible to make absolutely correct allowance for them,
and the uncertainty increases if the position is obtained by two observations taken
at different times, in which case an exactly correct allowance for the intervening
run of the ship is an essential to the correctness of the determination. Xo navigator
should ever assume that his position is not liable to be in error to some extent, the
precise amount depending upon various factors, such as the age of the chronometer
rate^the quality of the various instruments, the reliability of the observer, and the
conditions at the time the sight was taken; perhaps a fair allowance for this possible
error, under favorable circumstances, will be 2 miles; therefore, instead of plotting
a position upon the chart, and proceeding with absolute confidence in the belief that
the ship's position is on the exact point, one may describe, around the point as a
center, a circle whose radius is 2 miles — if we accept that as the value of the possible
error — and shape the future courses with the knowledge that the ship's position may
be anywhere within the circle.
It is on account of this recognized inexactness of the determination of position
that some navigators assume that the odd seconds may be neglected in dealing with
176 THE PEACTICE OF NAVIGATION AT SEA.
the different terms of a sight ; the average possible error due to this course is probably
about one minute, though under certain conditions it may be considerably more. It
is possible that, in a particular case, the error thus introduced through one term
would be offset by that from others, and the result would be the same as if the
seconds had been taken into account; but that does not affect the general fact that
the neglect of seconds as a regular thing renders any determination liable to be in
error about one minute. Those that omit the seconds argue, however, that since, in
the nature of things, any sight may be in error two minutes, it is immaterial if we
introduce an additional possibility of error of one minute, because the new error is
as liable to decrease the old one as to increase it; but the fallacy of the argument
will be apparent when we return to the circle drawn around our plotted point... The
eccentricity of the sextant may exactly offset the improper allowance for refraction,
and the mistake in the chronometer error may offset the observer's personal error,
but unless we know that such is the case — which we never can — we nave no justi
fication for doing otherwise than assume that the ship may be any place within the
2-mile circle. If, now, we increase the possible error by 1 mile, our radius of uncer
tainty must be increased to 3 miles, and the diameter of the circle, representing the
range of uncertainty in any given direction, is thereby increased from 4 to 6 miles.
It is deemed to be the duty of the navigator to put forth every effort to obtain
the most probable position of the ship, which requires that he shall eliminate possible
errors as completely as it lies within his power to do. By- neglecting seconds he
introduces a source of error that might with small trouble be avoided. This becomes
of still more importance since modern instruments and modern methods constantly
tend to decrease the probability of error in the observation, and to place it within
the power of the navigator to determine his ship's position with greater accuracy.
398. There is a more exact way of denning the area of the ship's possible position
than that of describing a circle around the most probable point, as mentioned in the
preceding article, and that is to draw a line on each side of each of the Sumner lines
by which the position is defined, and at a uniform distance therefrom equal to the
possible error that the navigator believes it most reasonable to assume under existing
conditions; the parallelogram formed by these four auxiliary lines marks the limit
to be assigned for the ship's position; this method takes account of the errors due
to poor intersections, and warns the navigator of the direction in which his position
is least clearly fixed and in which he must therefore make extra allowance for the
uncertainty of his determination.
It must be remembered in this connection that no position can ever be obtained,
when out of sight of the land, except from the intersection of two Sumner lines,
whether or not the lines are actually plotted; thus, a meridian altitude gives a Sumner
line that extends due east and west, and a sight on the prime vertical a line that
extends north and south, though it may not have been considered necessary to work
the former with two longitudes or the latter with two latitudes.
399. THE WORK BOOK AND FORMS FOR SIGHTS. — The navigation work book,
or sight book, being the official record of all that pertains to the navigation of the
ship when not running by bearings of the land, should be neatly and legibly kept,
so that it will be intelligible not only to the person who performed the work, but
also to any other who may have reason to refer to it.
Each day's work should be begun on a new page, the date set forth clearly at
the top, and preferably, also, a brief statement of the voyage upon which the ship is
engaged. It is a good plan to have the -dead reckoning begin the space allotted for
the day, and then have the sights follow in the order in which taken. The page
should be large enough to permit the whole of any one sight to be contained thereon
without the necessity of carrying it forward to a second page. No work should be
commenced at the bottom of a page if there is not room to complete it. Every
operation pertaining to the working of the sights should appear in the book, and all
irrelevant matter should be excluded.
It is' well to observe a systematic form of work for each sight, always writing
the different terms in the same position on the page; this practice will conduce to
rapidity and lessen the chances of error. In order to facilitate the adoption of such
a method, there are appended to this work (Appendix II) a series of forms that are
recommended for dead reckoning, and for the various sights of the sun, stars,
THE PRACTICE OF NAVIGATION AT SEA. 177
planets, and moon, respectively. For beginners, these are deemed of especial
importance, and it is recommended that, until perfect familiarity with the dif
ferent sights is acquired, the first step in working out an observation be to
write down a copy of the appropriate blank form, indicating the proper sign of appli
cation of each quantity (for which the notes will be a guide), and not to put in any
figures until the scheme has been completely outlined; then the remainder of the
work will consist in writing down the various quantities in their proper places and
performing the operations indicated.
The navigator may make up his work book by having printed forms of the
various sights which can be placed in a loose-leaf binder when they have been filled
in with his computations. Instead of printed forms on separate sheets, he may
employ rubber stamps of the various forms of sights which he may stamp in his
work book or on loose leaves.
THE SPECIFIC STEPS FOB CARRYING OUT THE DAY'S WORK.
400. The day's work as described herein is so laid out that the true position
at noon is known some few minutes before noon, as, when cruising in company,
naval vessels have to make their noon position report by signal at exactly 12 o'clock.
When cruising singly the noon position need not be known until after 12 o'clock,
but it is advisable to do a day's work always in one way, and, therefore, the plan of
getting the correct noon position before noon will be followed.
401 • THE TIME TO TAKE AN A. M. OBSEKVATION. — The navigator of a vessel
cruising may, by dead reckoning or by plotting on a chart, predict the approximate
position of me snip the following morning, and from that position may easily determine
the best time to observe the sun (or other body) for longitude. Having determined
his approximate 8 a. m. position, he takes from the Nautical Almanac the declination
of the sun for Greenwich noon of that day. With the latitude of the 8 a. m. position
and declination for the day, he enters tne Azimuth Tables and takes out tne local
apparent time when the sun will bear 90°. By getting the error of his watch on local
apparent time for the approximate 8 a.1 m. longitude, he may easily find the watch
tune when the sun will bear 90°, which is the tune he should take his sight. Suppose
on the evening of July 18, 1916, a navigator finds that at 8 a. m. the next day he will
be in approximate Lat. 35° 12' N., Long. 65° 15' W., and wishes to find at what
time ly Ms watch the sun will be on the prune vertical. He compares his watch
with the chronometer, of which he knows the correction, and which is, we will say,
slow lm 10s on G. M. T., and finds that when the chronometer reads, say llh 59m 30s,
the watch reads 7h 15m 12s. He then does the following work:
He takes from the Nautical Almanac the declination and the equation of time
for Greenwich mean noon on July 19 and finds Dec. = 20° 52' N.;. Eq. t. 6m 048,
subtractive from mean time.
With Lat. 35°.2 N., Dec. 21°.0 N., enter the Azimuth Tables, and find, for a
bearing of 90°, the L. A. T. is about 8h 10m.
Write down the reading of the chronometer face at comparison llh 59m 30s
Apply the chronometer correction + 1 10
G. M. T. of the time of comparison 12 00 40
Apply equation of time — 6 04
Greenwich apparent time of comparison 11 54 36
For Long. 65° 15' W., X=4h 21m 00s. Apply X 4 21 00
At time of comparison the L. A. T. at the 8 a. m. position was 7 33 36
At time of comparison the watch time was ' 7 15 12
Error of watch on L. A. T. of 8 a. m. position 18 24 slow.
L. A. T. when sun is on prime vertical 8 10
Watch time to take a. m. observation 7 51 36
The observation should therefore be taken when the watch face reads about 7-52,
which will bring the sun very close to the prime vertical.
When the latitude and decimation are of different names the sun crosses the
prune vertical before rising. In that case, the observation is taken as soon as the
61828°— 16 12
178 THE PRACTICE OF NAVIGATION AT SEA.
sun is sufficiently high to be unaffected by any peculiar condition of the atmosphere,
usually about an hour after sunrise. The L. A. T. of sunrise and sunset is given at
the bottom of the page in the Azimuth Tables. Suppose in the above example the
approximate 8 a. m. latitude was 35°.2 S. instead of 35°.2 N. Entering the tables
with Lat. and Dec. of different names, we find the time of sunrise is about 7 a. m.
The observation should therefore be taken at about 8 a. m. L. A. T., the watch time
of which can be found in the same way as explained above.
In a similar manner Azimuth Tables may be used to find the best time to take
p. m. observations for longitude.
402. THE MORNING WORK OF THE NAVIGATOR. — The navigator, having deter
mined the time at which he will take his morning observation, is called sufficiently
early to be ready for work about 15 minutes before the time chosen.
The first thing the navigator does is to check up his time. To save the trouble
of going below to compare the watch with the standard chronometer each time that
an observation is taken, most navigators keep the hack chronometer in the chart
house and use it for comparisons during the day. It is necessary to check the hack
with the standard chronometer each day to make sure of its error on G. M. T. and
rate. This comparison is made the first thing in the morning, the date, the error
on G. M. T., and the rate of the hack being written on a slip of paper that is placed
in the hack case. The hack is then taken to the chart house and is used for the
day's work. As hack chronometers frequently have hi<jh daily rates, an additional
correction sometimes has to be made for the rate when observations have been taken
some hours after the comparison. The hack is sometimes used for marking the time
of observation, and. when so used, the G. M. T. is at once obtained by applying the
hack error.
Having checked up the hacu chronometer, the navigator then prepares his
sextant and takes it, with his watch and notebook, to the place from which he takes
his observations. At about the time he has selected for his purpose, he observes
altitudes of the sun, which, with the corresponding watch times are noted in his note
book. The patent log is read while the observations are being taken and the reading
is entered in the notebook. The navigator then goes to the standard compass and
gets a bearing of the sun, which with the watch time of the bearing and the compass
eading of the ship is entered in the notebook. Either just before or just after
observing the altitude of the sun with the sextant, the index correction should be
found and entered in the notebook. The navigator next compares his watch with
the hack chronometer and gets the C-W, which is also entered in the notebook.
From the log book he gets tne courses and distances run from the last "fix" and
enters them in his notebook. This completes the data for his morning's work.
The computations are then made in the navigator's work book. The first step
is to work up the dead reckoning from the last "fix" to the time of sight. It may
be well here to call the attention of the student to the fact that for "distance run"
the propellers frequently are a more accurate gauge than the patent log which some-
tunes gets foul. In a smooth sea the distance by revolutions is usually very accurate,
especially if the effect of the condition of the bottom as to fouling is loiown. In
heavy weather the patent log is a better gauge as the effects of the wind and sea on
the speed of the ship are hard to determine. But for distance run both the patent
log and revolutions should be considered, and, if there is a discrepancy between
them, it should be investigated and the more accurate distance should be used.
Having brought the dead reckoning up to the time of sight, the latitude so found
is taken as the base of the computation of the longitude by observation. It is
assumed that the student is familiar with the various methods of getting a line of
position from an observation. Any one of the various methods gives the same line
and the choice of method is naturally the choice of the individual.
Having obtained the line of position, the longitude factor is next found, as
explained in article 387. The longitude factor is used twice, first to find the longitude
by observation corresponding to the D. R. latitude, and again after the noon latitude is
determined, to find the true noon longitude. As soon as the longitude factor has been
obtained, the longitude by observation corresponding to the D. R. latitude is found,
and it is this point on* the line of position that is used for the rest of the work to noon.
£This point, corrected for run, is also the point adopted as the 8 a. m. position, and
THE PRACTICE OF NAVIGATION AT SEA. 179
as by using it future steps are simplified, it is advisable always to work from this
point. Of course, any other point on the line can be moved up, and the final result
will be the same, but the computation will be a little more complicated.
Having obtained the position at time of sight (D. R. Lat., Long, by obs.) and
the longitude factor, the navigator next proceeds to get the compass error. The
work he has already performed in getting the line of position gives nun certain data
that will shorten his work in finding the compass error. If the sight has been worked
out as a Simmer line the navigator, by taking the L. A. T. found by his computation
and correcting it for the difference between the watch times of his observation for
altitude and observation for azimuth, may obtain at once the L. A. T. of the time
at which he took the sun's azimuth. With this L. A. T., and the Lat. and Dec. used
in working out his sight, he may at once find from the Azimuth Tables the true
bearing of -the sun and get the compass error. If the line of position has been
obtained by one of the tangent methods, the navigator has, in his computation, deter
mined the true bearing of the sun at the tune of sight. All he has to do to get the
true azimuth for compass error is to correct this bearing for the change in azimuth
due to the difference in time between his observation for altitude and his observation
for azimuth. This correction is easily found from the Azimuth Tables by inspection.
This completes the morning work when the amount of work each day is a
minimum. When very accurate positions are required at other times than at
noon, as for instance, when a vessel is scouting, when in dangerous waters,
moving at high speed, or when making a landfall, other lines of position are
worked out, and the ship's position found on each line by moving the next preceding
line up to it for run. For instance, lines obtained from morning twilight sights of
the moon, stars, or planets, may be run up to the 8 a. m. line, the 8 a. m. line may
be run up to one taken at 9.30 or 10, or later, and so on. When getting the position
by the intersection of lines moved up for run, it is usual to perform the work on the
plotting charts supplied for this particular purpose. These charts are Mercator
projections covering each 5° of latitude from 0° to 60°. The parallels are numbered
for every degree of latitude, and the navigator selects the chart covering the latitude
in which he is working. The meridians on these charts, not being numbered, the
navigator is left free to mark them with the longitudes through which he is working.
The charts are of large scale, and, being on heavy paper, may be used over and over,
lines on these being drawn in lightly and erased when no longer required.
Intersections of lines of position may be computed, as explained in Chap. XV,
when there are no charts at hand suitable for plotting the lines graphically. Special
plotting sheets prepared by the United States Hydrographic Office are supplied to
vessels of the Navy.
403. THE WORK BETWEEN 11 A. M. AND NOON. — Two important steps, not
usually fully explained in the text books, must be studied. These are: First, to
determine me exact run from the time of the a. m. sight to local apparent noon;
second, to set the watches and clocks to the local apparent tune of the place the ship
will be at local apparent noon.
If the ship has been making westing, the watches and clocks will be ahead
of the0 local apparent time of the noon position and will have to be set back by the
amount of the change in longitude. As the change of time is made between 11 a. m.
and noon, it will be seen that the elapsed time between the tune of the a. m. sight
and the new watch time of noon wiQ be more than the watch face shows by the
amount the watch has been set back, and this difference must be allowed for in
computing the run to noon. In the same way, if the ship has been making east
ing, the clocks and watches will have to be set ahead and the elapsed time between
the time of the a. m. sight and the new watch time of noon will be less than the watch
face shows by the amount the watch has been set ahead, and must be allowed for in
computing me run to noon. It must be remembered that this time can not be
computed exactly, but it can be approximated very closely in this way. Suppose a
ship has been steaming on course 66° true, and the navigator finds from his a. m.
observation taken at watch time, 8h 00m 038.5, that the L. A. T. for the position,
Lat. by D. R. 38° 03'.2 N., Long, by obs. 72° 50' 26" W., is 8h 17m 23S.9. He sees
at once that at 8 a. m. his watch is already slow 17m 20S.4 on L. A. T. Now, if he
180 THE PEACTICE OF NAVIGATION AT SEA.
continues on this course 66° true, at a speed of 11.7 knots per hour, the watch will
be still slower at noon. He therefore turns to the Traverse Tables and finds that
on that course and at a speed of 11.7 knots the ship will each hour go 10.69 miles to
the eastward, which, in Lat. 38°, makes a change of longitude of 13'. 6 each hour.
Now, from time of sight to 11 a. m. the change of longitude will be 3X13'.6 = 40'.8
of longitude, which is equal to a further loss 01 2m 43s. 2 of time; but the watch was
already slow 17m 20S.4, so that at 11 a. m. the watch will be slow 20m 038.6, and
the time to noon will be lh— (20m 04s), the difference due to change in longitude in
39m 56s (lh - 20m 04s) . Now39m 56s = 0.66h and the change of longitude = 0.66 X 13'.6 =
9'.0 of long. = 36s. 0 of time. Hence the total amount the time will be changed will be :
Change to time of a. m. sight 17m 20s. 4
Change between a. m. sight and 11 a. m 2 43 . 2
Change between 11 a. m. and L. A. noon 0 36 . 0
Total change 20 39.6
and the run to noon will be four hrs. minus this change = 3h 39m 20S.4 = 3.66 hrs. The
distance run to noon will be 3.66hX llkts.7 = 42kts.8.
The navigator can now run the a. m. point, determined by dead reckoning lati
tude and longitude by observation, up to noon, and, after that he is ready to set
his watch and clocks to the time of the coming local apparent noon position.
404. If the body observed for the a. m. sight was on or near the prime vertical,
the longitude found from it would be correct for the time of observation, since an error
in latitude makes no change in the longitude. This longitude when compared with
the longitude by dead reckoning at the time of sight will show if there has been an
easterly or westerly set of the current, and the amount of it. If a current is found
and allowed for, for the time of the run from time of sight to noon, the noon longitude
can be found very accurately. If the heavenly body used for the a. m. observation
was not near the prime vertical, the exact easterly- or westerly set can not be deter
mined; but a close approximation to it can generally be made by comparing the.
longitude found by observation with the D. R. longitude, and the current so found
should be allowed for in running the a. m. point up to noon. The error will be
small and will give results sufficiently accurate for ordinary work. Having allowed
for easterly or westerly current and having run the a. m. position point by observa
tion up to noon, the navigator can then set his watch to local apparent time of the
noon position, and his watch can be used to set the deck clocks. A convenient way
to set the watch is as follows : Having looked at the hack face and found what it
reads, say 4h 09m 50s, let it be determined to set the watch to the correct local
apparent time of the noon position when the hack face reads 4h 15m 00s.
Write down reading of hack face at time watch is to be set 4h 15m 00s
Apply the hack correction (in this case hack is 5m 38s fast on G. M. T. ) ( - ) 5 38
This gives G. M. T. at which watch is to be set to L. A. T 4 09 22
Apply equation of time corrected for longitude of noon position (+)H 33.8
This gives G. A. T. of time watch is to be set 4 20 55.8
Now apply longitude for noon position (in this case) 4 48 23
Watch face should read 11 32 32.8
The watch is now to be set so that, at 4h 15m 00s by hack, the watch face will show
as near llh 32m 33s as possible. It will be found, since the second hand of a watch
can not be set, that the watch can not be set to the exact reading. By care, however,
the watch can be set so that it will be 30 seconds or less fast or slow on the desired
time. The number of seconds the watch is fast or slow on L. A. T. should be noted
in the work book, as it will be a help in taking near-noon sights to get the correct
L. A. T. at once from the reading of the watch face instead of comparing the watch
again with the chronometer. The watch being set as nearly as possible to the
correct L. A. T. and the error being recorded, the deck clocks are set ; and the navi
gator then proceeds to work up his constants for his near-noon observations for
latitude, and completes all his forms and fills them out as far as possible before
taking the observations.
THE PRACTICE OF NAVIGATION AT SEA. 181*
405. Now suppose the navigator wishes to take his observations at 15, 10, and
5 minutes before local apparent noon and desires to get constants for these times to
which he can apply his sextant altitudes and at once get his correct noon latitude.
To find the watch times at which he should take these observations, he must know
the error of his watch on local apparent time of the place of observation. He knows
the error of his watch on the L. A. T. of the noon position (in this case we will sup-
Eose the watch is IS8 fast). He knows that on course 66° true, speed 11.7 knots, in
at. 38°, that in 1 hour he changes longitude 13'.6. Therefore 15 minutes before
noon the ship will be 3'.4 of longitude west of where it will be at noon = 138.6 of time.
Hence the observation 15 minutes before noon should be taken at watch time
llh 45m 008 + 188 ( = amount watch is fast on L. A. T. of noon position) + 138.6
(= amount watch is fast on L. A. T. of place of first near-noon observation) = llh
45m 31S.6. Similarly the observation taken 10m before noon should be taken at
watch time llh 50m 008-f 188 + 9M ( = amount watch is fast on L. A. T. of place of
second observation) = llh 50m 27M. The observation taken 5 minutes before noon
should be taken at watch time llh 55m OOs-H8s + 48.5 ( = amount watch is fast on
L. A. T. of place of third observation) = llh 55m 22*.5. A meridian altitude would
of course be taken at watch time 12h 00m 18s.
Having obtained the watch times of the observations, the navigator next works
out the constants. These constants are obtained in the same way as meridian
altitude constants but to each are applied two corrections to the meridian altitude
constant. These are:
(1) at2 or the correction to be applied to an observed altitude near noon to make
it a meridian altitude.
(2) JL or the difference in latitude for the run from the time of observation
to noon.
In working out the constant, the method of obtaining a meridian altitude con
stant is followed and the two corrections mentioned above are applied to it. In
getting a meridian altitude constant, one has first to ascertain the approximate
altitude. If the student will in every case plot his elements roughly on the plane
of the meridian, putting O, the observer, at the center, a horizontal line through the
O with the right end marked S for south, and the left end N for north, to represent
the horizon, and draw a vertical line upward from O (marking its intersection with
the circle Z) to represent the zenith, he can by inspection write out his formulae and
see exactly how to apply all corrections. A few minutes7 study will make this method
clear and will fully repay the very slight mental effort required to master it.
Now suppose L is the latitude of the noon position and L' the latitude of the
point from which the near-noon observation was taken. Then L = L'±JL where
JL is the change in latitude from the tune of observation to noon.
Suppose, by inspection of the figure we have drawn, we see that for a meridian
altitude,
L' = 90°-cZ-obs. alt. ± corr. to alt.
Now when the observed altitude is taken before noon the correction at2 has to
be applied to it to bring it to what the meridian altitude would be. Therefore, for
an altitude taken before noon,
L' =90°-<Z-(obs. alt. + aZ2)± corr. to alt.
= 90° - d - obs. alt. - at2 ± corr.
L =90°-d-obs. alt,-a^±con\±JL.
= K-obs. alt,
or K = 90° - d - at2 ± corr. ± ^/L.
Having the watch time at which the near-noon observation is taken and K corre
sponding to it, it is only necessary to apply the observed altitude to its proper K
to get the correct noon latitude. Having the correct noon latitude, find by how
many minutes it differs from the D. K. noon latitude and multiply this difference
by the longitude factor to get the correction to be applied to the 8.00 a. m. longitude
by observation run up to noon, in order to get the correct noon longitude. This
182 THE PRACTICE OF NAVIGATION AT SEA.
part of the work is done roughly on deck in the navigator's note book as soon as the
altitude is taken. To facilitate this work the navigator writes his data in his note
book in the following form, filling the blank spaces alter getting his altitude :
For watch time llh 45m 30' llh 50m 26s llh 55m 22- 12h 00m 18-
K 84 54 44 84 59 03 85 01 29 85 02 02
Obs. Alt.
Noon Lat. by Obs.
Mean
Noon Lat. by D. R. 38° 20' 35"
DL
Long, factor (Tab. 47) . 65
Corr. in Long.
Noon Long, by a. m. Obs. 72° 05' 44"
True longitude at noon
406. Having obtained the correct noon position in the above manner, the
navigator completes his work in his work book and plots the ship's position on the
chart. Having the correct noon position, he compares it with his previous noon
position (or point of departure) and gets the true course and distance made good.
Having the position by dead reckoning and by observation, he gets the set and
drift of the current. He then computes the total distance gone since leaving port
and the distance yet to go to his destination. Blank forms xor the noon report are
arranged for the following data:
(1) Lat. by observation.
(2) Long, by observation.
(3) Lat. by D. R.
(4) Long, by D. R.
(5) Current: Set and Drift.
(6) Course made good.
(7) Distance made good since noon.
(8) Distance made good since departure.
(9) Distance to destination.
If the course sailed is a rhumb line, and the ship is practically on the line laid
out as the track, no change of course is necessary. If the ship is decidedly off the
rhumb line course as laid out, or is sailing on a great circle track that requires a
change in compass course, the new course is laid out as soon as the true noon position
is obtained. This completes the navigator's work to noon.
407. THE AFTERNOON WORK OF THE NAVIGATOR. — In the afternoon the navi
gator must take an observation for longitude. He selects a time when the sun is
as near as possible to the prime vertical, which time is determined in the same way
as explained for the a. m. observation. He runs his true noon position up to the
time of his p. m. observation, making an allowance for any evident current that was
found at noon. He then gets a position point on a line of position determined from
his observation. This point is run up to 8 p.' m. by dead reckoning, which position
is plotted on the chart and completes the minimum navigation work for any day.
When particularly accurate positions are required, especially at 8 p. m., the
navigator takes an additional observation of the sun, or of some other heavenly body
at twilight, and gets the intersection of two lines of position. Or he may get a line
for longitude and a line for latitude by an altitude of Polaris or another star. In
this way the navigator may, at either morning or evening twilight, get a very accurate
fix; and this is done frequently. In fact, fixes obtained from observations of two
heavenly bodies taken at about the same time are the most accurate fixes that can be
obtained at sea, as the intersection of the two lines of 'position give a position point
that is correct at the time, no matter what the current is. Careful navigators will
therefore take such observations and the student should prepare himself to do so.
The methods of using position points obtained in this way are exactly the same as
the methods of using the points already explained.
THE PRACTICE OF NAVIGATION AT SEA. 183
The following example will give a good idea of the minimum day's work for the
navigator at sea. The form laid out is one that can always be followed. The cosine-
haversine formula is used for getting the lines of position, but any other method may
be substituted for it.
EXAMPLE: On October 4, 1916, the U. S. S. Delaware left Hampton Roads for
Lisbon. From the Chesapeake Capes the great circle course was followed. The
distance to Lisbon by great circle course is 3,120 miles. It is 25 miles from Hampton
Roads to the point from which the departure was taken. At 5 p. m., with Cape Henry
Light bearing 301° (mag.), dist. 8.3 miles, took departure, set course 74° (p. s. c.)
(Var. 5° W., Dev. 3° W.), and put over patent log, reading 0. (The point of de
parture is Lat. 36° 51' 59" N., Long. 75° 51' 03" W.)
The next morning by comparison with the standard, the hack chronometer was
found to be 5m 388 fast on G. M. T. and gaining la.5 daily. At about 8 a. m., patent log,
reading 175.0, the navigator took an a. m. observation for longitude: W. T. 8h 00m
038.5; obs. alt. 22° 55' 10"; I. C. + l' 50"; ht. of eye 40 ft. The navigator then
observed an azimuth of the sun as follows: W. T. 8h 02 m 29s; bearing of sun p. s. c.
125° 30'; ship's head 74°. He then compared his watch with the hack as follows:
hack face lh 13m 00s; watch face 8h 10m 11s.
Perform the a. m. part of the day's work.
The ship continues on same course at same speed (11.7 knots). When the hack
face reads 4* 15m 00s, at what time should the watch be set to be on local apparent
time at the noon position ?
If the watch was set 18 seconds fast on local apparent time at the noon position,
work out constants for observations for latitude to be taken 15, 10, and 5 minutes
before noon and at noon. Prepare all forms for the noon work.
The observed altitudes near noon were as follows: 15 minutes before, 46° 12' 30*;
10 min. before, 46° 16' 50"; 5 min. before, 46° 19' 20". The noon alt. was 46° 19' 40".
The patent log read 217.5 at noon.
Complete the day's work for noon.
At noon the course was changed to 86° (p. s. c.), Var. 10° W., Dev. 4° W.
Steamed until 4p. m. on this course, when at W. T. 4h 00m 12", obs. alt. of sun
18° 32' 40"; C-W, 4h 40m 568; I. C., +1' 50"; ht, of eye, 40 ft.; patent log reading,
264.3.
Find position of ship at 4 p. m. by observation.
The course and speed remaining unchanged, find the 8 p. m. position.
184
THE PKACTICE Otf NAVIGATION AT SEA
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CHAPTER XVII.
MAEINE SURVEYING.
4:08. DEFINITIONS. — Surveying is the art of making such field observations and
measurements as are necessary to determine positions, areas, elevations, and move
ments on the surface of the earth, giving its characteristic features, such as, on land,
the position of prominent objects, heights, and depressions, and on water, the depth,
nature of bottom, position of shoals, and velocity of currents.
Topographic Surveying relates to the land, and Hydrograpjiic Surveying to the
water; and both are underlaid by Trigonometrical Surveying which, when it is carried
on with high precision over such large areas as to contribute to form a basis for
determining the size and shape of the earth, becomes a department of Geodetic
Surveying.
It is not deemed appropriate to include in this work a complete treatise on
marine surveying. The scope of this chapter will be to set forth such general infor
mation regarcling the principles of surveying and the instruments therein employed
as will give the navigator an intelligent understanding of the subject sufficient to
enable him to comprehend the methods by which marine charts are made, and, if
occasion should arise, to conduct a survey with such accuracy as the instruments
ordinarily at hand on shipboard permit. For a more detailed discussion of marine
surveying, the student is referred to the various publications which treat the subject
exhaustively.
INSTRUMENTS EMPLOYED IN MARINE SURVEYING.
409. THE THEODOLITE AND TRANSIT. — The Theodolite (fig. 62) is an instrument
for the accurate measurement of horizontal and vertical angles. While these instru
ments vary in detail as to methods of construction, the essential principles are always
identical.
A telescope carrying crosshairs in the common focus of the object glass and
eyepiece is 'so mounted as to have motion about two axes at right angles to one
another; graduated circles and verniers are provided by which angular motion in
azimuth and (usually) in altitude may be measured; and the instrument is capable
of such adjustment by levels that the planes of motion about the respective axes
will correspond exactly with the horizontal and the vertical.
The telescope is carried in appropriate supports upon a horizontal plate which
has, immovably attached to it, one or more verniers, and which revolves just over a
graduated circle that is marked upon the periphery of a second horizontal plate, a
means of measuring the motion of the upper plate relative to the lower one being
thus provided. Thumb screws are fittecf by which the upper plate may be clamped
to the lower, and (excepting in some simpler forms of me instrument) others by
which the lower plate may be made immovable in azimuth, or allowed free motion,
at will; all clamping arrangements include slow-motion tangent screws for finer
control.
A vertical graduated circle, or arc, with a vernier, clamps, and tangent screws,
is fitted to most theodolites, for the measurement of the angular motion of the tele
scope in altitude.
The theodolite usually carries a magnetic needle, with a graduated circle and
vernier for compass bearings. The instrument is mounted upon a tripod, and levels
and leveling screws afford a means of bringing the instrument to a truly horizontal
position.
189
190
MARINE SURVEYING.
The Transit used in surveying is a modified form of the theodolite, and is
generally employed where less accuracy is required; it takes its name from the f act-
that the telescope may be turned completely about its horizontal axis, or transited,
without removal from its supports.
410. The line of collimation of a telescope is an imaginary line passing through
the optical center of the object glass in a direction at right angles to that of its axis of
rotation. This is also called the axis of collimation. The line of sight is an imaginary
line passing through the
optical center of tne ob
ject glass and the point
of intersection of the
cross hairs.
A theodolite or
transit, before it can be
used for the accurate
measurement of angles,
must be in adjustment
in the following re
spects: (a) The vertical
axes of revolution of
the upper and lower
horizontal plates must
be coincident; (&) the
axis must be vertical
and the plates horizon
tal when the bubbles of
the levels are in their
central positions; (c)
the vertical cross hair
must be perpendicular
to the horizontal axis of
the telescope; (d) the
line of collimation must
coincide with the line of
sight; (e) the horizon
tal axis of the telescope
must be perpendicular
to the vertical axis of
the instrument; (f) the
bubble of the telescope
level must stand at the
middle of its scale, and
the vertical circle must
read zero, when the line
of collimation is hori
zontal.
The last-named
condition may be disre-
FIG. 62. garded if vertical angles
are not to be measured.
The instrument being in adjustment, to observe angles it should be set
up, leveled, and focused. This involves placing the tripod so that a plumb bob
from the center of the instrument shall hang directly over the spot at which the
measurement is to be made. The legs of the tripod should be firmly placed in such
manner that the height shall be convenient for the observer and the instrument
shall be nearly level. Then the horizontal plates are brought to a true level by
means of the leveling screws and bubbles. The telescope should next be focused
by moving the object glass and eyepiece in such manner that the object sighted
MARINE SURVEYING. 191
and the cross hairs may be plainly seen and that the object will not appear to have
motion relatively to the cross hairs as the eye is moved to the right or left of the
eyepiece. This last condition insures the cross hairs being at the common focus of
the eyepiece and objective.
To observe a horizontal angle with a theodolite or transit, clamp the upper
plate to the lower at zero, leaving the lower plate undamped; swing the telescope
so that its vertical cross hair bisects one of the objects, and clamp the lower plate;
unclamp the upper plate and bring the telescope to bisect the other object, and the
reading of the vernier on the scale will give the required angle. (Tne final nice
motion by which the cross hair is brought exactly upon a point is always given by
the tangent screw.)
In taking a round of angles, this operation is repeated successively upon each
object to be observed about the horizon, the upper piate always being swung, while
the lower is kept svhere set upon the first object, or origin. The result will give the
angular distance of each object from the origin, and, If the observations have been
accurately made, upon finally sighting back to the origin, the reading should be zero.
To repeat an angle, having made the first measurement of it in the usual way,
unclamp the lower circle and swing back the telescope until it again points to the
first object, and clamp it; then unclamp the upper circle, swing to the second object,
and clamp. The scale reading should now be double that of the first angle. Repeat
as often as the importance of the angle requires, and the accepted value will be the
final reading divided by the number of measurements. An angles of the main
triangulation, and others of importance in the survey, are repeated.
Defects in adjustment of the instrument may be eliminated by taking one
series of angles with the telescope direct and another with the telescope reversed. To
reverse the telescope, revolve it about its horizontal axis through 180°, then swing
it about its vertical axis through 180° — in other words, invert it.
Vertical angles are measured on the same principle as that described for hori
zontal ones.
The process of setting up the instrument at a station and observing the angles
between the various objects that are visible is called occupying the station.
412. THE PLANE TABLE. — This is an instrument by which positions are plotted
in the field directly upon a working sheet. It consists (fig. 63) of a drawing board
mounted upon a tripod in such manner as to be capable of motion in azimuth, and
with facilities for being brought to a perfect level; in connection with it is employed
an alidade, consisting of a straightedge ruler, upon which is mounted a telescope
with cross hairs whose line of si<mt is exactly parallel to the vertical plane through
the edge of the rule. It is evident that if a sheet representing a chart be placed
upon such a board and turned so that the true meridians, as portrayed thereon, He
in the direction of the earth's meridian at that place, then all lines of bearings on
the chart will coincide with the corresponding lines on the earth's surface; from
which it follows that if the alidade be so placed that its rule passes through the spot
on the chart representing the position of the observer, while the telescope is directed
to some visible object, the position of that object on the chart lies somewhere upon
the line drawn along the edge of the rule. Upon this general principle depend the
various applications of the plane table.
The drawing board is usually made of several pieces of well-seasoned wood,
tongued and grooved together, with the gram running in different directions to
prevent warping; about its edge are several metal clips for securing the paper in
place. It is supported upon three strong brass arms, to which it is attached by
screws, thus permitting its removal at will. The arms are attached to a horizontal
plate which revolves upon a second horizontal plate lying immediately below it; a
clamp and tangent screw are fitted, by which the upper plate, and with it the draw
ing board, may oe secured to the lower plate, or may be given a fine motion in azimuth.
Three equidistant lugs of brass, grooved on the under side, project down from the
lower plate, resting on screws in the top of the tripod, by which the instrument is
leveled; when adjusted in this respect it is firmly clamped in position, and, as the
tripod is made unusually large, the adjustment is not easily deranged.
192
MARINE SURVEYING.
The alidade is a metal straightedge with a vertical column at its center, at the
top of which are the supports which carry the telescope; a vertical arc and vernier
are provided for measuring the motion of ^ the telescope ir\ altitude. The telescope
is usually so fitted that it may be revolved in azimuth through an arc of exactly 180°,
for the purpose of adjusting the line of collimation. On top of the rule near its center
is the level — sometimes replaced by two levels at right angles — by means of which it
may be seen when the table is in a true horizontal position.
A magnetic needle mounted in a rectangular metal box, whose outer straight
edge is parallel to the zero line of a graduated scale over which the needle swings, is
provided for drawing the north-and-south line on the chart; this is called a declinatoire.
FIG. 63.
4:13. To be hi correct adjustment, a plane table must comply with the following
conditions:
(a) The fiducial edge of the rule must be perfectly straight. (6) The level must
have the bubble in its central position when the table is truly horizontal, (c) The
vertical cross hair must be perpendicular to the horizontal axis of the telescope.
(d\ The line of collimation must coincide with the line of sight, (e) The horizontal
axis of the telescope must be parallel to the plane of the table. (/) The vertical
circle should read zero when the line of collimation is horizontal.
&14:. The results derived from the use of the plane table, like all others dependent
upon graphic methods, must be regarded as less accurate than those deduced by
computation, and even less accurate than those derived from the careful plotting of
theodolite angles. Hence it is that, in a careful marine survey, this instrument
would be employed only for the topography and shore line.
For whatever purpose used, the plane table would not ordinarily be called into
requisition until the survey had so far progressed that a chart could be furnished the
observer showing certain stations whose positions were already established; with
this chart, the first step would be to occupy one of the determined points. The table
MARINE SURVEYING. 193
must be set up with the point on the chart directly over the center of the station ; it
must then be leveled and the telescope focused as described for the theodolite or
transit; and finally it must be oriented — that is, so turned in azimuth that all lines of
the chart are parallel to similar lines of the earth's surface. To orient, unclamp the
table and swing it until the north-and-south line of the chart is approximately
parallel to that of the earth, one means of doing which is afforded by the declinatoire;
place the alidade so that the edge of the rule passes through the points on the chart
representing the station occupied and some second station which is clearly in view;
then, sighting through the telescope, perfect the adjustment of the table by swinging
it until the second station is exactly bisected by the vertical cross hair, the final slow
motion being obtained by clamping the table and working the tangent screw. If the
adjustment has been correctly made, the rule may be laid along the line joining the
station occupied and any other on the chart, and the telescope will point exactly to
that other station.
Being properly oriented, if the alidade be so placed that the edge of the rule pass
through the station occupied and the telescope point directly to some unknown
object whose position is to be determined, then a line drawn along the rule will
contain the point which represents the position of that object. If, now, the plane
table be set up at a second station, oriented for its new position, and a Hue be similarly
drawn from that station toward the one to be established, it will intersect the first
line in the required point. This is the method of determining positions by prosection.
Actually, the surveyor does not regard the point as well established until the inter
section is checked by a line from a third station.
In practical work, of course, each station is not occupied separately for the
determination of each point; the instrument is set up at a station, lines are drawn
to all required points in view, and each line is appropriately marked; then a second
station is occupied, and the operation is repeated, and so on, the various intersections
being marked as the work proceeds.
A second method of establishing positions is that of resection; in this the first
line is drawn from some known station, as in the preceding method, and the observer
next proceeds to the place whose position is required and occupies it ; the plane table
is there oriented by means of the line already drawn, placing the edge of the rule
along the line, sighting back toward the first station, and swinging the table until
that station is in the line of sight of the telescope; then choose some other established
station as nearly as possible at right angles to the direction of the first; place the
edge of the rule upon the plotted position of this station and swing the alidade (the
rule always being kept on the plotted point) until the object is bisected by the
telescope cross hairs; draw this fine, and its intersection with the first will give 'the
required point, the accuracy of which can be checked from some other plotted station.
A third method of locating a point is by means of a single bearing from a known
station, with the distance from the occupied station to the required one, the process
of plotting being self-evident.
A fourth method is given by occupying an undetermined position from which
three established stations are in view; the point occupied by the observer is then
plotted by an application of the "three-point problem."
415. It may be seen that where the greatest accuracy is not essential the plane
table may be employed for plotting all the points of a survey. In such a case it would
only be necessary to begin with the two base stations, plotted on the sheet on any
relative bearing whatsoever and at a distance apart equal to the length of the base
line (reduced to scale), as measured by the most accurate means available. The
work of plotting might even proceed before the base line had been measured, the
two stations being laid off at any convenient distance apart; when later the base
line was measured, the scale of the chart would be determined, being equal to the
distance on the chart between base stations divided by the length of the base line.
416. A plane table could be improvised on shipboard which would greatlv
facilitate the operation of any surveying work that a vessel not equipped with
instruments might be called upon to perform. A drawing board could be mounted
upon a tripod (as, for example, the tripod supplied for compass work on shore) in
such manner as to be capable of motion in azimuth ; it could be brought nearly to the
horizontal, if no better means offered, by moving the tripod legs, and this adjust-
61828°- 16 13
194 MARINE SURVEYING.
ment could be proved by any small spirit level; sight vanes could be erected upon
an ordinary ruler to take the place of the alidade; in case there was difficulty in
observing any object with such an alidade, because of its altitude or for other reasons,
a horizontal angle might be observed with a sextant and plotted with a protractor.
By this means work could be done which, even if it should lack complete accuracy,
might be of great value.
417. THE TELEMETER AND STADIA. — Any telescope fitted with a pair of hori
zontal cross hairs at the focus may be used as a telemeter, and when accompanied
by a graduated staff, called a stadia, affords a means of measuring distance (up
to certain limits) with a close degree of accuracy; the method consists in observing
the number of divisions of the scale subtended by the hairs when the stadia
is held perpendicular to the line of sight of the telescope, it being evident
that the closer the distance the fewer divisions will appear between them. The
f acility with which distances can be measured by this method makes it most important
that all telescopes of theodolites, transits, and plane tables be fitted as telemeters
and that stadia rods be provided for all surveying work.
Speaking approximately, it may be said that the number of divisions intercepted
between the cross hairs will vary directly as the distance of the stadia rod. This
would be exactly true if we looked at the object through an empty tube, directly
between the hairs. Since, however, the rays from the stadia are refracted by the
object glass before they are intercepted by the wires, the statement, to be absolutely
exact, must be slightly modified; but for practical surveying work it may be accepted
as given.
418. There are two methods of installing the telemeter cross hairs — the first, in
which they are immovably secured in the telescope and always remain at the same dis
tance apart, and the second, in which the distance of the cross hairs is made variable,
being under the control of the observer. The former is generally regarded as the
preferable method, and when it is employed it is evident that the subtended height
of the stadia bears a constant ratio to the distance of the staff from the telescope.
It proves most convenient in practice to space the hairs so that this constant ratio
is some even multiple of 10, for facility in converting scale readings into distance;
it is also advantageous to mark the stadia in the unit of the chart scale and decimals
thereof; for example, if the ratio of stadia height to distance were 100, and the
stadia were marked in meters and decimals, a reading of 2.07 would at once be con
verted into a distance of 207 meters. Any units and any ratio may, however, be
employed, and for any given setting of cross hairs it is very easy to graduate a stadia,
by experiment, for any desired units; for example, if it is required to mark the
stadia in feet, set up and level the telescope, measure off a distance of exactly 100
feet from it, hold up an unmarked staff and mark upon it the points intersected by
the cross hairs; the interval between these marks will represent 100 feet of the
scale; divide this length into 100 parts, each of which will represent a distance of
one foot, and mark the whole staffon the same scale; then if the stadia be held up
at any distance, the cross hairs will intercept a number of divisions corresponding
to the number of feet of distance.
When the cross hairs are movable the ratio becomes variable, but the principle
of measuring remains the same — namely, the distance of the staff from the telescope
is equal to the existing ratio multiplied by the distance intercepted on the scale.
4:19. The stadia is made of alight, narrow piece of wood and is usually hinged
for convenience in transporting. Ordinarily the background of the scale is painted
white, while ^the main divisions are marked in red, with minor divisions in black,
and geometrical figures are employed to facilitate the reading of fractional parts of
the scale. Devices are furnished by which the man holding the stadia may know
when it is vertical — an essential condition for accuracy of measurements.
4:20. The use of the telemeter and stadia for measuring distances is limited to
the distance at which the scale divisions can be accurately read through the tele
scope. f For fairly close work and with the class of telescope usually supplied with
surveying instruments, 400 meters represents about the greatest distance at which
it can be employed. With this limitation, the character of the survey determines
the nature of its employment. In a careful survey its greatest use would be in
connection with the theodolite or plane table in putting in shore lines, contour lines,
MARINE SURVEYING. 195
and topography generally. In a survey where only approximate results are sought
it might afford the best means for the measurement of the base.
421. If the telemeter be applied to a theodolite, transit, or plane table which is
fitted with a graduated vertical arc or circle, it is possible to measure the distance to
the stadia not only in a horizontal but also in a vertical direction. In this case the
vertical angle must be observed as well as the stadia reading. Tables are computed
giving the solution of the triangles involved when the stadia rod is held vertical.
422. In making a survey with the ordinary resources of a ship, the principle of
the telemeter and stadia may be profitably employed, using a sextant and improvised
staff. In this case it is usual to have the stadia of some convenient fixed length —
as, for example, 10 feet — and of slight width and thickness; this is held at right
angles to the line of sight from the observer, who notes the angle subtended by the
total length; tables are prepared by which the distance corresponding to each angle
is given.
423. THE SEXTANT. — This instrument is of the greatest value in hydrographic
surveying. It is fully described elsewhere in this work and its adjustment explained.
(Chap. VIII.)
Sextants are manufactured of a form especially adapted to surveying work;
they are smaller and lighter than those usually employed in astronomical observa
tions, but have a longer limb, by which angles may be measured up to 135°; the
vernier is marked for quick reading and has no finer graduation than half minutes;
the telescope has a large field.
This instrument is principally employed in measuring the horizontal angles by
means of which soundings are plotted. It may, however, be put to various uses when
making an approximate survey, as has already been explained. It should be remem
bered, in measuring terrestrial angles with a sextant, that rigorous methods require
a reduction to the horizontal if either of the objects has material altitude above the
horizon.
424. THE LEVEL. — This is an instrument for the accurate measure of differences
of elevation. It consists of a telescope, carried in a Y-shaped rest, which is mounted
upon a tripod and leveled in a manner similar to a theodolite; but it differs from that
instrument in that the telescope is not capable of motion about a horizontal axis
and in having no graduated circles for measurements of altitude and azimuth. The
principle of its use contemplates placing the line of collimation of the telescope in a
truly horizontal plane and keeping it so fixed.
425. It is principally employed in marine surveying to determine heights and
contour lines — the latter being lines of equal elevation above the sea level — and for
locating benchmarks for tidal observations. (Chap. XX.) In connection with it is
used a graduated staff called a leveling rod, carrying a conspicuous mark, adjustable
in height, called a target. To ascertain the difference of level between any two
points, set up the level with the telescope horizontal at some place between them;
let an assistant take the leveling rod to one of the points, and, while holding it on the
ground in a truly vertical position, move the target, under the direction of the
observer at the telescope, to a point where it is exactly bisected by the horizontal
cross hair; the height of the target on the staff — that is, the height of the cross hair
above the level of the first point — is then accurately read with a vernier; now,
without moving the level, shift the rod to the^second point and again adjust the
target and read it. It is evident that a comparison of the reading at the first posi
tion with that at the second will give the difference of height at the two points.
The difference that can be read from one location of the instrument is limited by
the length of the rod; but by making a sufficient number of shifts any difference
may be measured.
The work of the level may be performed equally well by a theodolite whose
telescope is adjusted to the true horizontal.
426. HELIOTROPE AND HELIOGRAPH. — These are instruments sometimes
employed in surveying, by means of which the sun's rays may be reflected in any
given direction; the object of their use is to render conspicuous a_ station which is
to be observed at a distance and which would not otherwise be distinguishable.
The instruments vary widely in form of construction and, in the absence of those
made for the purpose, substitutes may easily be devised.
196
MARINE SURVEYING.
427. ASTRONOMICAL TRANSIT INSTRUMENTS. — Various instruments are employed
for the astronomical determinations necessary in a marine survey. Among these are
the zenith telescope and portable transit. While differing in detail they consist essen
tially of a telescope mounted upon a horizontal axis that is placed truly in the prime
vertical, thus insuring the revolution of the line of collimation in the meridian; a
vertical graduated circle and vernier are supplied, affording a measure of altitude;
in the focus are a number of equidistant vertical cross hairs or lines; a small lamp
is so placed that its rays illuminate the cross hairs and render possible observations
at night. Latitude is obtained by observing the meridian altitude of stars; hour
angle (and thence longitude) by observing the times of their meridian transit, which
is taken from the mean of the times of passing all of the vertical cross hairs.
Excepting in surveys of a
most accurate nature, the astro
nomical determination of position
by the sextant and artificial hori
zon is regarded as satisfactory.
428. THE THREE -ARMED
PROTRACTOR, OR STATION
POINTER. — This is an instrument
whereby positions are plotted
on the principle of the three-
point problem," of which an ex
planation is given in article 152,
Chapter IV. It consists (fig. 64)
of a graduated circle with three
arms pivoted at the center; each
arm has one edge that is a true
rule, the direction of which always
passes through the center of tne
circle. The middle arm is immov
ably fixed at the zero of the scale;
the right and left arms each re
volve about the center on their
own sides, and are provided with
verniers giving the angular dis
tance from the middle arm. The
protractor being set for the right
and left angles, it is so moved that
the three arms pass through the
respective stations, when the cen
ter marks the position of the ob
server. Center pieces of various
forms are provided, being cylin
drical plugs made to fit into a
socket at the pivot, and by em
ploying one or the other of them
FIG. G4. the true center may be pricked
with a needle, dotted with a pen
cil, or its position indicated by cross hairs. Adjustable arms are provided which
can be fitted to the ends of the ordinary arms when working with distant signals.
The most valuable use of the three-armed protractor is in plotting the positions
of soundings taken in boats, where sextant angles between signals are observed.
It may occur, however, that certain shore stations will be located by its use.
429. As this instrument is not made with both right and loft arms capable of
being set to small angles down to 0°, the manufacturers make protractors with
either small right or small left angles. Surveying parties should be equipped with
both. In default of a three-armed protractor, a piece of tracing paper may be made
to answer its purpose. To use the tracing paper, draw a line, making a dot on it
to represent the center station, and with the center of an ordinary protractor on
MARINE SURVEYING.
197
FIG. 65.
the dot, lay off the two observed angles right and left of the line; then, laying this
on the plan, move it about till the three lines pass exactly through the three stations
observed. The dot from which they were laid off will be on the position of the observer,
and must be pricked lightly through or marked underneath in pencil.
430. THE BEAM COMPASS. — This instrument (fig. 65) is employed in chart
drafting and performs the functions of compasses and dividers when the distance
that must be spanned is beyond the limits of those instruments in their ordinary
form. It consists of an angular bar of wood or metal upon which two instruments
termed beam heads are fitted in such a manner that the bar may slide easily; through
them. A clamping screw attached to one side of the beam head will fix it in any
part of its course along the beam. Upon
each head a socket is constructed to carry
a plain point, exchangeable for an ink or a
pencil point. To secure accuracy the
beam head placed at the end of the beam
has a fine adjustment, which moves the
point a short distance to correct any error
in the first rough setting of the instrument.
This adjustment generally
consists of a miBed-head
screw, which passes through
a nut fixed upon the end of
the beam head, which it car
ries with its motion.
431. PROPORTIONAL
DIVIDERS. — These are prin
cipally employed for reduc
ing or enlarging drawings in
any given proportion. They
consist (fig. 66) of two narrow
flat pieces of metal called legs, which turn upon a pivot whose position
is movable in the direction of their length. The ends of both legs are
shaped into points like those of ordinary dividers. When the pivot is
fixed at the middle of the legs, any distance measured by the points
at one end is just equal to that measured by those at the other; for
any other location of the pivot, however, the distances thus measured
will not be equal, but with a given setting of the pivot any distance
measured by one end bears a fixed ratio to that measured by the other.
The path of travel of the pivot is graduated so that the ratio may be
given any desired value. Being adjusted in this respect, if a distance
is taken off a chart with the legs at one end of the instrument, then
those at the other end will show the same distance on the scale of a
chart enlarged or reduced in the proportion represented by the ratio
for which the pivot was set.
METHODS EMPLOYED IN A HYDROGRAPHIC SURVEY.
432. Before commencing a survey a general inspection of the field
is made; a base line is located and its extremities marked by signals;
certain other positions, known as main triangulation points, are selected
FIG. 66. and also marked with signals, being so chosen that, starting with the
base and proceeding thence from one to another of these points, a
series of well-conditioned triangles or quadrilaterals may cover the field of survey.
The base line is measured with the greatest degree of accuracy which the resources
of the survey render possible. Each extremity of the base line and each other main
triangulation point is occupied by an observer with a theodolite, who measures the
angles at each station between all the other stations which are in sight. ^ An astro
nomical determination is made of the latitude and longitude of some point of the
survey (frequently one of the extremities of the base) and of the true azimuth of
some known line (frequently the base line). Data are now at hand for the location,
upon the chart of the base line and main triangulation points.
198 MARINE SURVEYING.
If the survey is one of considerable extent, it is expedient to measure a check base
near the end of the triangulation. A comparison between the measured length of
this base and its length as computed through the chain of triangles will show the
degree of accuracy and afford a means of reconciling discrepancies. The position of
a second observation spot may be determined for a similar purpose.
The primary triangulation gives a skeleton of the field, but the points thus
determined are not usually close enough together to afford a basis for ail the detail
work that must be done. A second system of points is therefore selected and signals
erected thereon, and the position of these points is determined by a series of angles
from the main triangulation points and from one another. This is known as the
secondary triangulation. The points thus located are used in the plotting of the
topography and hydrography. It is not essential that their determination be as
accurate as that of main triangulation points.
The topography is put in, and includes the delineation of the features of the
land — shore line, lighthouses, beacons, contour lines, peaks, buildings, and, in
short, everything that may be recognized by the navigator and utilized by him in
locating the ship's position.
The hydrographic work is taken up and the depth of water and character of
bottom determined as accurately as possible for the complete water area, especial
care being taken to develop all shoals and dangers to navigation and to locate all
aids to navigation, such as buoys, lightships, and beacons.
One or more tidal stations are established where observations are taken, con
tinually and at frequent intervals, of the height of the tide and direction and velocity
of the tidal and other currents, whence data are derived for the reduction of all sound
ings to the plane of reference and for the information about tides and currents which
is to appear upon the chart.
Observations are made to determine the magnetic variation and dip, and the
intensity of the earth's magnetic force.
433. The foregoing represent, in outline, the various steps that must be taken
in the accumulation of the data necessary for the construction of a complete hydro-
graphic chart. In the following paragraphs the details of the various operations will
be more f ully set forth.
The navigator who is called upon to conduct a marine survey without having
available the time, instruments, and general facilities necessary for the most thorough
performance of the work must exercise his discretion as to the modifications of method
that he will make, and call upon his ingenuity to adapt his means to the particular
work in hand.
434. THE BASE LINE. — As the base line is the foundation for all distances on
the chart, the correctness of the results of the survey will depend largely upon the
degree of accuracy with which it is measured. The triangulation merely affords a
measure of the various distances as compared with the distances between the two
initial points from which it began; if that initial distance is 1,000 feet, we have cer
tain values for the. sides of the various triangles; if the same base line is 2,000 feet,
the value of each side becomes twice as great as it was before; with the same triangu
lation, therefore, distances vary directly with the length of the base line; it may
thus be seen that if an error exists in measurement which is only a small fraction
of the total length, the error will become much more material as the more distant
points of the survey are reached. In a base line 1,000 feet long, if a mistake of 10
feet be made all distances measured upon the chart will be in error 1 per cent, and
a point plotted by triangulation 10 miles from the observation spot (the point at
which plotting begins), would be out of its correct position one-tenth of a mile.
It is ^important that the base line should be as long as possible, consistent with
the distribution and distances between the surrounding objects which must be
depended upon as triangulation stations for its expansion. The position of the line
must be such as to afford favorably conditioned triangles and quadrilaterals with
adjoining main triangulation points, and its extremities must be visible from those
points and from each other. The character of the ground and the facility for meas
uring will of course form an important consideration in the choice.
435. In measuring a base by tape, chain, or similar means, a number of suc
cessive fleets are made with the measure, whatever its nature, the distance traversed
MARINE SURVEYING. 199
being appropriately marked after each fleet, while an observer, with a theodolite or
transit, insures the measurement being made accurately along the line.
436. The most careful measurements are made with a steel tape 300 feet long,
stretched along a series of supports at equal intervals along the base line, the points
of support being made exactly horizontal by a level. A good form of support is a
stake driven vertical with one side on the base line and a nail, for supporting the
tape, driven horizontally into the stake at the established level. The stakes falling
at the ends of tape lengths should be set slightly less than 300 feet apart, sawed on
at the established level, and have strips of zinc tacked on then- tops. The end of
each fleet is marked by a scratch mark cut in the strip of zinc at an even hundredth
of a foot-division on the tape, and the corresponding tape reading recorded. Tapes
for base-line measurement are usually subdivided to hundreclths of a foot for a
distance of 10 feet from each end of the tape. The tape is stretched to a uniform
tension by a spring balance. The temperature of the tape at each fleet should be
observed, and the mean temperature, for the entire measurement of the base deduce.
Tapes for base-line measurements are usually standardized lying flat, and at a
temperature of 62° Fahrenheit. To reduce the measured length of the base line
to the true length the f ollowing corrections to the measured length must be applied :
Temperature correction Ct = + (<*Tm - T0) L,
where a = coefficient of expansion.
Tm = mean temperature at measurement.
T0 = standard temperature.
L = measured length.
Correction for sag C.= ~^C~w ) •
where L = measured length.
w = weight per inch of tape.
d = distance between supports in inches.
P = tension in pounds.
By this method of measurement the horizontal distance between the ends of
the base line may be readily found to within 1 part in 250,000, and by application
of superior apparatus, of several measures, and greater care — hence, at an increased
cost — the probable uncertainty may be reduced to 1 part in 500,000, but this degree
of accuracy would not be necessary except in very extended systems of triangulation.
437. A second method of base measurement is with the surveyor's chain.
This depends for accuracy upon the surface traversed being plane and level, a con
dition that is weh1 fulfilled on a sandy beach, where the chain is nearly as accurate
as the tape and much more rapid. A surveyor's chain is usually 100 feet long; the
exact value of its length must be obtained by comparison with a standard, and a
correction applied for expansion or contraction due to temperature. The ends of
the fleets are marked by steel pins driven into the ground; the alignment is kept
by the theodolite.
438. Where neither chain nor tape is available substitutes may be improvised
from sounding wire taken from the deep-sea sounding machine, or failing this, from
well-stretched cod line.
Measurements made by the telemeter and stadia afford a close approxima
tion to the true result, and if these instruments are not at hand the sextant angle
of a rod of fixed length can be employed. The masthead height of the vessel may
be used in determining the length of base line on this principle, either by making
the ship itself mark one of the extremities and observing the masthead angle from
the other extremity, or by simultaneously observing the masthead angle from both
ends of a shore base, and also the three horizontal angles of the triangle formed by
the ship and the two base stations. The latter plan is far preferable where accuracy
is sought, as, if the angles are all taken by different observers at the same instant
(whicn can be marked by the hauling down of a flag), the error arising from the
motion of the ship about her anchor is eliminated, and, moreover, the data furnished
offers a double solution of the triangle and the mean may be taken as giving a closer
result.
200 MARINE SURVEYING.
439. A crude method of estimating distance is by means of the velocity of
sound, though this would never be used where close results are expected. Fire a gun
at one end of the distance and at the other note by the most accurate means available
the time between seeing the flash and hearing the report. Repeat several times in
each direction. The mean number of seconds and tenths of a second multiplied by
the velocity of sound per second at the temperature of observation (art. 314, Chap.
XI) gives the approximate distance.
440. When for any reason the existing conditions do not permit of a direct
measurement being made along the line between the two base stations, recourse
must be had to a broken base, that is, one in which the length of the base is obtained
by reduction from the measured length of two or more auxiliary lines. Necessity
for resorting to a broken base arises frequently when the two stations are situated
on a curving shore line and the straight line between them passes across water, or
where wooded or unfavorable country intervenes, or where a stream must be crossed.
The most common form of broken base is that in^which the auxiliary lines run from
each extremity of the base at an acute angle and intersect; in addition to measuring
each of these lines the angle formed by their intersection or else the angles formed
by them with the base line must be observed and the true length of the base deduced
by solution of the triangle. The form that is most frequently used where only a
short section of the base is incapable of measurement (as is the case where a deep
stream flows across) is that of an auxiliary right triangle whose base is the required
distance along the base line and altitude a distance measured along a line perpen
dicular thereto to some convenient point; by this measured distance and the angles
which are observed, the triangle is solved and the length of the unmeasured section
determined.
441. In a survey of considerable extent, where good means are at hand for the
correct determination of latitude and longitude, a base line actually measured upon
the earth may be dispensed with, and, instead of that, the positions of the two
stations which are most widely separated may be determined astronomically and
plotted; the triangulation is then plotted upon any assumed scale, and when it has
been brought up to connect the two stations the true value of the scale is ascertained.
This is called the method of an astronomical base.
442. SIGNALS. — All points in the survey whose positions are to be located from
other stations, or from which other positions are to be located, must be marked by
signals of such character as will render them distinguishable at the distance from
wnich they are observed. The methods of constructing signals are of a wide variety.
A vessel regularly fitted out for surveying would carry scantlings, lumber, bolts,
nuts, nails, whitewash, and sheeting for the erection of signals ; however meager the
equipment, the whitewash and sheeting (or some substitute for sheeting, preferably
half of it white and half dark in color) should be provided, if possible, before begin
ning any surveying work. Regular tripod signals, which are quickly erected and
are visible, under favorable circumstances, for many miles, are almost invariably
employed to mark the main triangulation stations; among other advantages the
tripod form permits the occupation with the theodolite of the exact center of the
station, and avoids the necessity for the reduction which must otherwise be applied.
Signals on secondary stations take an innumerable variety of forms, the requirement
being only that they shall be seen throughout the area over which they are to be
made use of; a, whitewashed spot on a rock, a whitewashed trunk of a tree, a white
washed cairn of stones, a sheeting flag, a piece of sheeting wrapped about a bush,
or hung, with stones attached, over a cliff, or a whitewashed barrel or box filled with
rocks or earth and surmounted by a flag, suggest some of the secondary signals
that may be employed; sometimes objects are found that are sufficiently distinct in
themselves to be used as signals without further marking, as a cupola or tower, a
hut, a lone tree, or a bowlder; but it is seldom that an object is not rendered more
conspicuous by the flutter of a flag above it, or by the dead-white ray reflected from
a daub of whitewash.
For convenience, each signal is given some short name by which it is designated
in the records.
For the sake of economy in both time and labor, steel towers, such as are used
to support windmills, are being extensively employed by hydrographic parties for
MARINE SURVEYING. 201
surrey signals. They are very easily erected and dismounted, easily transported,
offer little resistance to gales of wind, and are more permanent and satisfactory than
signals of wood.
4:13. THE MAIN TEIAXGULATIOX. — The points selected as stations for the main
trian oblation mark in outline -the whole area to be surveyed ; they are close enough
together to afford an accurate means of plotting all intermediate stations of the
secondary triangulation; and they are so placed with relation to one another that
the triangles or quadrilaterals derived from them are well conditioned. The points
are generally so chosen that small angles will be avoided. In order to fulfill the
other conditions, it frequently becomes necessary to carry forward the triangulation
by means of stations located on points a considerable distance inland, such as moun
tain peaks, which would not otherwise be regarded as properly within the limit* of
the survey.
Great care should be taken in observing all angles upon which the main triangu
lation is based; the best available instrument should be employed; angles taken
with a theodolite or transit should be repeated, and observed with telescope direct
and reversed, and the mean result taken; if the sextant is used, a number of separate
observations of each angle should be taken and averaged for the most probable
value. It must be remembered that while, in any other part of the work, an error
in an angle affects only the results in its immediate vicinity, an error in the main
triangulation goes forward through all the plotting that comes after it.
It occurs frequently that the. purposes of the survey are sufficiently well fulfilled
by a graphic plotting of the mam triangulation, but where more rigorous methods
prevail, tne results are obtained by calculation. The sum of the angles of each
triangle is taken, and if it does not exactly equal 180° the values are adjusted to
make them comply with this condition. In cases where the triangulation stations
form a series of quadrilaterals, the angles of each quadrilateral are adjusted so as to
form a perfect geometrical figure. Allowance is made for the curvature of the earth
where tne area of triangles is sufficiently large to render it expedient to do so. The
lengths of the various sides and the relative latitudes and longitudes of the several
stations are then computed. Each station may then be plotted in its latitude and
longitude on a polyconic projection, and a delineation of the triangulation system
may thus be obtained free from the accumulated errors of a graphic plotting.
" 444. THE SECONDARY TRIANGULATION. — The points of the secondary triangu
lation are located, as far as possible, by angles from the main triangulation stations;
these angles, having less dependent upon them, need not be repeated. A graphic
plotting of these stations, without calculation, will suffice.
4:4:5. ASTRONOMICAL WORK. — This comprises the determination of the correct
latitude and longitude of some point of the survey, and of the true direction of some
other point from the observation spot, thus furnishing an origin from which all posi
tions and all directions can be determined either graphically or by computation.
The methods of finding latitude, .longitude, and the true bearing of a terrestrial
object are fully set forth hi previous chapters. The feature that distinguishes such
work in surveying from that of determining the position of a ship at sea lies in the
greater care tnat is taken to eliminate possible errors.
The results should therefore be based upon a very large number of observations,
employing the best instruments that are available, and tne various sights being so
taken that probable errors are offset in reckoning the mean.
4:4:6. By taking a number of sights the observer arrives at the most probable
result of which his instruments and his own faculties render him capable; but this
result is liable to an error whose amount is indeterminate and which is equal to the
algebraic sum of a number of small errors due, respectively, to his instruments
(which must always lack perfection in some details), to an improper allowance for
refraction under existing atmospheric conditions, and to his own personal error.
Aissuming, as we may, that the personal error is approximately constant, these
three causes give rise to an error by which all altitudes appear too great or too small
by a uniform but unknown amount. Let us assume, for an illustration, that this
error has the effect of making all altitudes appear 30* too great; if an observer
attempted to work his latitude from the meridian altitude of a star bearing south,
the result of this unknown error would give a latitude 30* south of the true latitude;
202 MARINE SURVEYING.
if another star to the southward were observed, this mistake would be repeated;
but if a star to the north were taken, the resulting latitude would be 30" to the
north. It is evident, therefore, that the true latitude will be the mean of the results
of observation of the northern and the southern star, or the mean of the average of
several northern stars and the average of several southern stars. A similar process
of reasoning will show that errors in the determination of hour angle are offset by
taking the mean of altitudes of objects respectively east and west of the meridian.
447. It must be remembered that the uniformity of the unknown error only
exists where the altitude remains approximately the same, as instrumental and refrac
tion errors may vary with the altitude ; another condition of uniformity requires that
the instrument and the observer remain the same, and that all observations be taken
about the same time, in order that atmospheric conditions remain unchanged; to
preserve uniformity, if the artificial horizon is used, the same end of the roof should
always be the near one to the observer; in taking the sun, however, as the personal
error may not be the same for approaching as for separating limbs, every series of
observations should be made up of an equal number of sights taken under each
condition.
448. With all of this in mind, we arrive at the general rule that astronomical
determinations shall be based upon the mean of observations, under similar conditions,
of bodies whose respective distances from the zenith are nearly equal, and which
bear in opposite directions therefrom.
449. This condition eliminates the sun from availability for observations for
latitude, though it properly admits the use of that body for longitude where equal
altitudes or single a. m. and p. m. sights are taken. Opposite stars of approximately
equal zenith distance should always be used for latitude, circum-meridian altitudes
being observed during a few minutes before and after transit; excellent results are
also obtained from stellar observations for longitude; but very low stars should be
avoided, on account of the uncertainty of refraction, and likewise very high ones,
as the reflection from the index mirror of the sextant may not be perfectly distinct
when the ray strikes at an acute angle.
If there is telegraphic or radio communication, an endeavor should be made
to obtain a time signal from a reliable source, instead of depending upon the
chronometers.
450. TOPOGRAPHY. — The plane table, with telemeter and stadia, affords the
most expeditious means of plotting the topography, and should be employed when
available. Points on shore may also be plotted by sextant angles, using the three-
point problem, or by any other reliable method.
451. HYDROGRAPHY. — The correct delineation of the hydrographic features
being one of the most important objects of the survey, great care should be devoted
to this part of the work. Soundings are run in one or more series of parallel lines,
the direction and spacing of which depend upon the scope of the survey. It is
usual for one series of lines to extend in a direction normal to the general trend of the
shore line. In most cases a second series runs perpendicular to the first, and in surveys
of important bodies of water still other series of lines cross the system diagonally.
In developing rocks, shoals, or dangers the direction of the lines is so chosen as will
best illustrate the features of the bottom. When lines cross, the agreement of the
reduced soundings at their intersection affords a test of the accuracy of the work.
As the depth of water increases, if there is no reason to suspect dangers, the
interval between lines may be increased.
Lines are run by the ship or boat in such manner as to follow as closely as possible
the scheme of sounding that has been laid out. The position is located by angles
at the beginning of each line, at each change of course, at frequent intervals along
the ^ line, and at the point where each line is finished. Soundings taken between
positions are plotted by the time intervals or patent log distances.
452. There are a number of methods for determining positions while sounding,
which may be described briefly as follows:
By two sextant angles. — Two observers with sextants measure simultaneously
the angles between three objects of known position, and the position is located by
the three-point problem. This is the method most commonly employed in boat
work, and has the great advantage that the results may be plotted at once on the
MARINE SURVEYING.
203
working sheet in the boat and the lines as run thus kept nearly in coincidence with
those laid out in the scheme. A study of the three-point problem (art. 153, Chap.
IV) will give the considerations that must govern in the selection of objects.
By two theodolite angles. — Two stations on shore are occupied by observers with
theodolites, and at certain instants, indicated by a signal from the ship or boat, they
observe the angular distance thereof from some known point. The intersection
of the direction lilies thus given is at the required position. This method is expedi
tious where the signals are small or not numerous. Its disadvantage is that the
plotting can not be kept up as the work proceeds.
By one sextant and one theodolite angle. — An observer ashore occupies a station
with a theodolite and cuts in the ship or boat, while one on board takes a sextant
angle between two objects, of which one should preferably be the occupied station.
It is plotted by laying off the direction line from the theodolite and finding with a
three-armed protractor or piece of tracing paper at what point of that line the
observed angle between the ob
jects is subtended. Its advantages
and disadvantages are the same as
those of the preceding method.
In running lines of soundings
offshore, where signals are lost
sight of, the best method is to get
an accurate departure, before drop
ping the land, by the best means
that offers, keeping careful note
of the dead reckoning, and on run
ning in again, to get a position as
soon as possible, note the drift and
reconcile the plotting of inter
mediate sounoings accordingly.
Where circumstances require, the
position may be located by astro
nomical observations as usually
taken at sea.
453. A careful record of sound
ings must be kept, showing the
time of each (so that proper tidal
correction may be applied), the
depth, the character of bottom, and
such data as may be required to
locate the position.
454. THE WIRE DRAG.— The
use of the lead in hydrographic
surveying does not absolutely es
tablish a definite available depth,
as pinnacle obstructions may exist which are not detected by that means. This is
particularly true of rocky localities and those of coral formation.
In order to guarantee a certain depth of water for purposes of navigation it has
become the practice to tow through the waters to be examined a line of wire or cable
suspended at that depth.
The drag or sweep consists essentially of a horizontal member, known as the
bottom wire, which is a long steel line composed of 50-foot sections coupled together
with swivels and shackles. It is supported at each terminal from an 80-pound buoy
by a chain stirrup fine whose length may be adjusted from 20 to 50 feet. There
are smaller buoys placed at intervals varying from 150 to 450 feet, according to local
conditions, which support the \yire by means of steel-cable stirrup lines, adjustable
in length like the chain stirrup lines on the terminal buoys. At intermediate 50-foot
connections, cedar toggles or floats, which have a little more buoyancy than is
sufficient to support the wire between the stirrup lines, are attached by means of
snap hooks. To prevent the bottom wire from sagging back as the drag is towed
transversely to its own length by the bridles fastened at the terminals, a leaden
FIG. 67.
204
MAKINE SURVEYING.
weight of 165 pounds is suspended from each of the terminal stirrup lines, and a
weight of 20 pounds from each of the intermediate stirrup lines. The length of the
drag may be varied through a wide range to suit the conditions existing in the
localities to be examined. Any multiple of 50 feet may be used, but it is in general
found best to use, in each division between two towing launches, eight sections with
stirrup-line suppports at their ends, each composed of from three to seven 50-foot
units. The towing launches use tow lines about 200 feet in length bridled to the
terminal stirrup lines with attachments at the top and bottom. During the towing, as
long as the drag is free, the line of supporting buoys will trace out a parabolic curve
on the surface of the water; but, if progress should be interrupted by a pinnacle of
rock rising in its path above the depth to which the drag line is set, the parabolic
curve of the line of buoys will immediately become broken into the form of a V,
whose angle will correspond in position with the position of the pinnacle. . The pres
ence of any such obstruction is also registered by the spring balance usually attached
to the towline at a convenient position near the towing vessel. If the shape of the
obstruction is such as to allow tne drag line to ride upward upon it, as may be with
bowlders and shoals, an additional indication of its presence is afforded by the f ailing
over of the supporting buoys when the suspended stirrup lines are
relieved of strain by the grounding of the weights attached to them.
In such cases a tender should be in readiness to proceed to the
indicated point for the purpose of taking position angles to locate
the spot and also soundings to ascertain the characteristics of the
obstruction. Such localities are plotted upon the chart upon
which the paths of the drag line are being mapped, and later these
areas are again swept with the drag line at a lesser depth;" and
this procedure is continued until the obstruction is cleared by the
dragline, and thus the least depth is proved. The position of the
drag is determined by observers with sextants on board the towing
vessels who simultaneously measure, at frequent intervals, the
values of two angles between two pairs of known objects whose posi
tions are identified upon the plotting chart.
The average speed of towing is about 1J knots per hour, and
the average area explored per working day is 1J square miles,
although a much higher rate of progress is usually attained hi open
areas under favorable conditions.
455. TIDAL OBSERVATIONS. — These should begin as early as
practicable and continue throughout the survey, it being most im
portant that they shall, if possible, cover the period of a lunar month. In the chap
ter on tides (Chap. XX) the nature of the data to be obtained is explained.
456. MAGNETIC OBSERVATIONS. — The feature of the earth's magnetism with
which the navigator is most concerned is the variation, which is set forth on the
chart, and upon the determination of which will depend the correctness of all courses
and bearings on shipboard. It is usually obtained by noting the compass direction
from the observation spot of the object whose true bearing is known by calculation,
and comparing the true and compass bearings; or it may be observed by mounting
the ship's compass in a place on shore free from foreign magnetic influence, and finding
the compass error as it is found on board. Observations for dip and intensity are
also made when the proper instruments are at hand.
457. KUNNING SURVEY. — Where time and opportunity permit only a superficial
examination of a coast line or water area, or where the interests of navigation require
no more, recourse is had to a running survey, in which shore positions are determined
and soundings are made while the ship steams along the coast, stopping only occa
sionally to fix her position, and in which the assistance of boat or shore parties may
or may not be employed.
In this method the ship starts at one end of the field from a known position,
fixed either by astronomical observations or by angles or bearings of terrestrial
objects having a determined location. Careful compass bearings or sextant angles
are taken from this position to all objects ashore which can be recognized, and a
series of direction lines is thus obtained. The ship then steams along tne coast, at a
convenient distance therefrom, keeping accurate account of her run by compass
FIG. 68.
MAKINE SURVEYING. 205
courses and patent log. From time to time other series of bearings or angles are
taken upon those objects ashore which are to be located, the direction lines plotted
from the estimated position of the ship, and the various objects located by the
intersections with their other direction lines. During all the time that the ship is
under way, soundings are taken at regular intervals and plotted from the dead reck
oning. As frequently as circumstances permit, the ship is stopped and her position
located by the best available means, and the intervening dead reckoning reconciled
for any current that may be found.
If a steam launch can be employed in connection with a running survey, it is
usually sent to run a second line inshore of the ship. The boat's position is obtained
by bearings of objects ashore which are located by the ship, or by bearings and mast
head angles of the ship, or by such other means as offer. The duty of the boat is
to take a series of soundings and to collect data for shore line and topography.
If circumstances allow the landing of a shore party, its most important duty is
to mark the various objects on shore by some sort of signals wrhich will render them
unmistakable. Beyond this, it can perform such of the duties assigned to shore
parties in a regular survey as opportunity permits.
CHAPTER XVIII.
WINDS,
458. Wind is air in approximately horizontal motion. Observations of the
wind should include its true direction, and its force or velocity. The direction of the
wind is designated by the point of the compass from which it proceeds. The force
of the wind is at sea ordinarily expressed in terms of the Beaufort scale, each degree
of this scale corresponding to a certain velocity in miles per hour, as explained in
article 68, Chapter II.
459. THE CAUSE OF THE WIND. — Winds are produced by differences of atmos
pheric pressure, which are themselves ultimately, and in the main, attributable to
differences of temperature.
To understand how the air can be set in motion by these differences of pressure,
it is necessary to have a clear conception of the nature of the air itself.
The atmosphere which completely envelops the earth may be considered as a
fluid sea at the bottom of which we live, and which extends upward to a considerable
height, probably 200 miles, constantly diminishing in density as the altitude increases.
The air, or material of which this atmosphere is composed, is a transparent gas,
which, like all other gases, is perfectly elastic and highly compressible. Although
extremely light, it has a perfectly definite weight, a cubic foot of air at ordinary
pressure and temperature weighing 1.22 ounces, or about one seven hundred and
seventieth part of the weight of an equal volume of water. In consequence of this
weight it exerts a certain pressure upon the surface of the earth, amounting on the
average to 15 pounds for each square inch. To accurately measure this pressure,
which is constantly undergoing slight changes, we ordinarily employ a mercurial
barometer (art. 48, Chap. II), an instrument in which the weight of a column of air
of given cross section is balanced against that of a column of mercury having an
equal cross section; and instead of saying that the pressure of the atmosphere is a
certain number of pounds on each square inch, we say that it is a certain number of
inches of mercury, meaning thereby that it is equivalent to the pressure of a column
of mercury that many inches in height, and one square inch in cross section.
All gases, air included, are highly sensitive to the action of heat, expanding or
increasing in volume as the temperature rises, contracting or diminishing in volume
as the temperature falls. Suppose now that the atmosphere over any considerable
region of the earth's surface is maintained at a higher temperature than that of its
surroundings. The warmed air wih1 expand, and its upper layers will flow off to the
surrounding regions, cooling as they go. The atmospheric pressure at sea level
throughout the heated areas will thus be diminished, while that over the circum
jacent cooler areas will be correspondingly increased. As the result of this difference
of pressure, there will be movement of the surface air away from the region of high
pressure and toward the region of low, somewhat similar to the flow of water which
takes place through the connecting bottom sluice as soon as we attempt to fill one
compartment of a divided vessel to a slightly higher level than that found in the
other.
A difference of atmospheric pressure at sea level is thus immediately followed
by a movement of the surface air, or by winds ; and these differences of pressure have
their origin in differences of temperature. If the atmosphere were everywhere of
uniform temperature it would lie at rest on the earth's surfaces-sluggish, torpid,
and oppressive — and there would be no winds. This, however, is fortunately not
the case. The temperature of the atmosphere is continually or periodically higher
in one region than in another, and the chief variations in the distribution of tempera
ture are systematically repeated year after year, giving rise to like systematic
variations in the distribution of pressure.
206
WINDS. 207
460. THE NORMAL DISTRIBUTION OF PRESSURE. — The winds, while thus due
primarily to differences of temperature, stand in more direct relation to differences
of pressure, and it is from this point of view that they are ordinarily studied.
In order to furnish a comprehensive view of this distribution of atmospheric
pressure over the earth's surface, charts have been prepared showing the average
reading of the barometer for any given period, whether a month, a season, or a year,
and covering as far as possible the entire globe. These are known as ispbaric charts,
from the fact that all points at which the barometer has the same reading are joined
by a continuous line or isobar.
The isobaric chart for the year (fig. 69) shows in each hemisphere a well-defined
belt of high pressure (30.20 inches) completely encircling the globe, that in the northern
hemisphere naving its middle line about in latitude 35° North, that in the southern
hemisphere about in latitude 30° South, these constituting the so-called meteorological
tropics. From the summit or ridge of each of these belts the pressure falls off alike
toward the equator and toward the pole, although much less rapidly in the former
direction than in the latter. The equator itself is encircled by a belt of somewhat
diminished pressure (29.90 inches), the middle line of which is ordinarily found in
northern latitudes. In the northern hemisphere the diminution of pressure on the
poleward slope is much less marked and much less 'regular than in the southern
hemisphere, minima (29.70 inches) occurring in the North Atlantic Ocean near
Iceland and in the North Pacific Ocean near the Aleutian Islands, beyond which the
pressure increases. In the southern hemisphere no such minima are apparent, the
pressure continuing to diminish uninterruptedly as higher and higher latitudes are
attained. Along the sixtieth parallel of south latitude the average barometric
reading is 29.30 inches.
461. SEASONAL VARIATIONS OF PRESSURE. — As might be expected from its
close relation to the temperature, the whole system of pressure distribution exnibits
a tendency to foUow the sun's motion in declination, the barometric equator occupy
ing in July a position slightly to the northward of its position in January. In either
hemisphere, moreover, the pressure over the land during the winter season is decidedly
above the annual average, during the summer season decidedly below it ; the extreme
variations occurring in the case of continental Asia, where the mean monthly pressure
ranges from 30.50 inches during January to 29.50 inches during Jul}r. ^Over the
northern ocean, on the other hand, conditions are reversed, the summer pressures
being here somewhat the higher. Thus, in January the Icelandic and the Aleutian
minima increase in depth to 29.50 inches, while in July these minima fill up and are
well-nigh obliterated, a fact which has much to do with the strength and frequency
of the winter gales in high northern latitudes and the absence of these gales during
the summer. Over the southern ocean, in keeping with its slight contrast between
winter and summer temperatures, similar variations of pressure do not exist.
462. THE PREVAILING WINDS. — As a result of the distribution of pressure just
described, there is in either hemisphere a continual motion of the surface air away
from the meteorological tropic — on one side toward the equator, on the other side
toward the pole, the first constituting in each case the trade winds, the second the
prevailing winds of higher latitudes. Upon a stationary earth the direction of this
motion would be immediately from the region of high toward the region of low
barometer, the moving air steadily following the barometric slope or gradient,
increasing in force to a gale where these gradients are steep, decreasing to a light
breeze where they are gentle, sinking to a calm where they are absent. The earth,
however, is in rapid rotation, and this rotation gives rise to a force which exercises
a material influence over all horizontal motions upon its surface, whatever their
direction, serving constantly to divert them to the right in the northern hemisphere,
to the left in the southern. The air set in motion by the difference of pressure is
thus constantly turned aside from its natural course down the barometric gradient
or slope, and the direction of the wind at any point, instead of being identical with
that of the gradient at that point, is deflected by a certain amount, crossing the
latter at an angle which in practice varies between 45° and 90° (4 to 8 compass
points), the wind in the latter case blowing parallel to the isobars. As a consequence
of this deflection the northerly winds winch one would naturally expect to find on
the equatorial slope of the belt of high pressure in the northern hemisphere become
208
WINDS.
FIG. 69.
WINDS. 209
northeasterly — the NE. trade; the southerly winds of the polar slope become south
westerly — the prevailing westerly winds of northern latitudes. So, too, for the
southern hemisphere, the southerly winds of the equatorial slope here becoming
southeasterly — the SE. trades; the northerly winds of the polar slope northwesterly—
the prevailing westerly winds of southern latitudes.
463. The relation here described as existing between the distribution of atmos
pheric pressure and the direction of the wind is of the greatest importance. It may
be briefly stated as follows:
In the northern hemisphere stand with the face to the wind; in this position
the region of high barometer lies on your left hand and somewhat in front of you;
the region of low barometer on your right hand and somewhat behind you.
In the southern hemisphere stand with the face to the wind; in this position
the region of high barometer lies on your right hand and somewhat in front of you ;
the region of low barometer on your left hand and somewhat behind you.
This relation holds absolutely, not only in the case of the general distribution of
pressure and circulation of the atmosphere, but also in the case of the special con
ditions of high and low pressure which usually accompany severe gales.
464. THE TRADE WINDS. — The Trade Wwds blow from the tropical belts of
high pressure toward the equatorial belt of low pressure — in the northern hemisphere
from the northeast, in the southern hemisphere from the southeast. Over the
eastern half of each of the great oceans they extend considerably farther from the
line and their original direction inclines more toward the pole than in midocean,
where the latter is almost easterly. They are ordinarily looked upon as the most
constant of winds, but while they may blow for days or even for weeks with slight
variation in direction or strength, their uniformity should not be exaggerated.
There are times when the trade winds weaken or shift. There are regions where
their steady course is deformed, notably among the island groups of the South Pacific,
where the trades during January and February are practically nonexistent.
They attain their highest development in the South Atlantic and in the South Indian
Ocean, and are everywhere fresher during the winter than during the summer season.
They are rarely disturbed by cyclonic storms, the occurrence of the latter within the
limits of the trade-wind region being furthermore confined in point of time to the
late summer and autumn months of the respective hemispheres, and in scene of
action to the western portion of the several oceans. The South Atlantic Ocean
alone, however, enjo}*s complete immunity from tropical cyclonic storms.
465. THE DOLDRUMS. — The equatorial girdle of low pressure occupies a position
between the high-pressure belt of the northern and the similar belt 01 the southern
hemisphere. Throughout the extent of this barometric trough the pressure, save
for the slight diurnal oscillation, is practically uniform, and decided barometric
gradients do not exist. Here, accordingly, the winds sink to stagnation, or rise at
most only to the strength of fitful breezes, coming first from one point of the compass,
then from another, with cloudy, rainy sky and frequent thunderstorms. The region
throughout which these conditions prevail consists of a wedge-shaped area, the base
of the wedge resting in the case of the Atlantic Ocean on the coast of Africa, and in
the case of the Pacific Ocean on the coast of America, the axis extending westward.
The position and extent of the belt vary somewhat with the season. Throughout
February and March it is found immediately north of the equator and is of inap
preciable width, vessels following the usual sailing routes frequently passing from
trade to trade without interruption in both the Atlantic and the Pacific Oceans.
In July and August it has migrated to the northward, the axis extending east and
west along the parallel of 7° north, and the belt itself covering several degrees of
latitude, even at its narrowest point. At this season of the year, also, the southeast
trades blow with diminished freshness across the equator and well into the northern
hemisphere, being here diverted, however, by the effect of the earth's rotation, into
southerly and southwesterly winds, the so-called southwest monsoon of the African
and Central American coasts.
466. THE HORSE LATITUDES. — On the outer margin of the trades, corresponding
vaguely with the summit of the tropical ridge of high pressure hi either hemisphere,
is a second region throughout which the barometric gradients are faint and undecided,
61828°— 1C 14
210 WINDS.
and the prevailing winds correspondingly light and yariable; the so-called horse
latitudes, or calms of Cancer and of Capricorn. Unlike the doldrums, however,
the weather is here clear and fresh, and the periods of stagnation are intermittent
rather than continuous, showing none of the persistency which is so characteristic
of the equatorial region. The explanation of this difference will become obvious
as soon as we come to study the nature of the daily barometric changes of pressure
in the respective regions, these in the one case being marked by the uniformity of the
torrid zone, in the other sharing to a limited extent in the wide and rapid variations
of the temperate.
467. THE PREVAILING WESTERLY WINDS. — On the exterior or polar side of the
tropical maxima the pressure again diminishes, the barometric gradients beinsj now
directed toward the pole; and the currents of air set in motion along these gradients,
diverted to the right and left of their natural course by the earth's rotation, appear in
the northern hemisphere as southwesterly winds, in the southern hemisphere as
northwesterly — the prevailing westerly winds of the temperate zone.
Only in the southern hemisphere do these winds exnibit anything approaching
the persistency of the trades, their course in the northern hemisphere being subject
to frequent local interruption by periods of winds from the eastern semicircle. Thus
the tabulated results show that throughout the portion of the North Atlantic included
between the parallels 40°-50° North, and the meridians 10°-50° West, the winds
from the western semicircle (South — NNW.) comprise about 74 per cent of the
whole number of observations, the relative frequency being somewhat higher in
winter, somewhat lower in summer. The average force, on the other hand, decreases
from force 6 to force 4* Beaufort scale, with the change of season. Over the sea in the
southern hemisphere such variations are not apparent; here the westerlies blow
through the entire year with a steadiness little less than that of the trades them
selves, and with a force which, though fitful, is very much greater, their boisterous
nature giving the name of the " Roaring Forties" to the latitudes in which they are
most frequently observed.
The explanation of this striking difference in the extra- tropical winds of the two
halves of the globe is found in the distribution of atmospheric pressure, and in the
variations which this latter undergoes in different parts of the world. In the landless
southern hemisphere the atmospheric pressure after crossing the parallel of 30°
South diminishes almost uniformlv toward the pole, and is rarely disturbed by those
large and irregular fluctuations which form so important a factor in the daily weather
of the northern hemisphere. Here, accordingly, a system of polar gradients exists
quite comparable in stability with the equatorial gradients which give rise to the
trades; and the poleward movement of the air in obedience to these gradients,
constantly diverted to the left by the effect of the earth's rotation, constitutes the
steady westerly winds of the south temperate zone.
468. THE MONSOON WINDS. — The air over the land is warmer in summer and
colder in winter than that over the adjacent oceans. During the former season the
continents thus become the seat of areas of relatively low pressure ; during the latter
of relatively high. Pressure gradients, directed outward during the winter, inward
during the summer, are thus established between the land and the sea, which exercise
the greatest influence over the winds prevailing in the region adjacent to the coast.
Thus, off^the Atlantic seaboard of the United States southwesterly winds are most
frequent in summer, northwesterly^ winds in winter; while on the Pacific coast the
reverse is true, the wind here changing from northwest to southwest with the advance
of the colder season.
The most striking illustration of winds of this class is presented by the monsoons
(Mausum, season) of the China Sea and of the Indian Ocean. In January abnormally
low temperatures and high pressure obtain over the Asiatic plateau, high tempera
tures and low pressure over Australia and the nearby portion of the Indian Ocean.
As a result of the baric gradients thus established, the southern and eastern coast
of the vast Asiatic continent and the seas adjacent thereto are swept by an outflowing
current of air, which, diverted to the right of the gradient by the earth's rotation,
appears as a northeast wind, covering the China Sea and the northern Indian Ocean.
Upon entering the southern hemisphere, however, the same force which hitherto
WINDS. 211
deflected the moving air to the right of the gradient now serves to deflect it to the
left; and here, accordingly, we have the monsoon appearing as a northwest wind,
covering the Indian Ocean as far south as 10°, the Arafura Sea, and the northern
coast of Australia,
In July these conditions are precisely reversed. Asia is now the seat of high
temperature and correspondingly low pressure," Australia of low temperature aiid
high pressure, although the departure from the annual average is by no means so
pronounced in the case of the latter as in that of the former. The baric gradients
thus lead across the equator and are addressed toward the interior of the greater
continent, giving rise to a system of winds whose direction is southeast in the southern
hemisphere, southwest in the northern.
The northeast (winter) monsoon blows in the China Sea from October to April,
the southwest (summer) monsoon from May to September. The former is marked
by all the steadiness of the trades, often attaining the force of a moderate gale; the
latter appears as a light breeze, unsteady in direction, and often sinking to a calm.
Its prevalence is frequently interrupted by tropical eye Ionic storms, locally known
as typhoons, although the occurrence of these latter may extend well into the season
of the winter monsoon.
469. LAND AND SEA BREEZES. — Corresponding with the seasonal contrast of
temperature and pressure over land and water, there is likewise a diurnal contrast
which exercises a similar though more local effect. In summer particularly, the land
over its whole area is warmer than the sea by day, colder than the sea by night, the
variations of pressure thus established, although insignificant, sufficing to evoke a
system of littoral breezes directed landward during the daytime, seaward during the
night, which, in general, do not penetrate to a distance greater than 30 miles on and
oft shore, and extend but a few hundred feet into the depths of the atmosphere.
The sea breeze begins in the morning hours — from 9 to 11 o'clock — as the land
warms. In the late afternoon it dies away. In the evening the land breeze springs
up, and blows gently out to sea until morning. In the tropics this process is repeated
day after day with great regularity. In our own latitudes, the land and sea breezes
are often masked by winds of cyclonic origin.
470. A single important effect of the seasonal variation of temperature and
pressure over the land remains to be described. If there were no land areas to break
the even water surf ace. of the globe, the trades and westerlies of the terrestrial circu
lation would be developed in the fullest simplicity, with linear divisions along latitude
circles between the several members — a condition nearly approached in the land-
barren southern hemisphere during the entire year, and in tne northern hemisphere
during the winter season. In the summer season, however, the tropical belt of high
pressure is broken where it crosses the warm land, and the air shouldered off from
the continents accumulates over the adjacent oceans, particularly in the northern
or land hemisphere. This tends to create over each of the oceans a circular or
elliptical area of high pressure, from the center of which the baric gradients radiate
in all directions, giving rise to an outflowing system of winds, whicn by the effect of
the earth's rotation is converted into an outflowing spiral eddy or anticyclonic whirl.
The sharp lines of demarcation which would otherwise exist between the several
members of the general circulation are thus obliterated, the southwesterly winds of the
middle northern latitudes becoming successively northwesterly, northerly, and north
easterly, as we approach the equator and round the area of high pressure by the east;
the northeast trade becoming successively southeasterly, southerly, and southwesterly,
as we recede from the equator and round this area by the west ; similarly for the other
hemisphere.
CHAPTER XIX.
CYCLONIC STOEMS,
471. VARIATIONS OF THE ATMOSPHERIC PRESSURE. — The distribution of the
atmospheric pressure previously described ((hap. XVIII) and the attendant circu
lation of the winds are those which become evident after the effects of many disturbing
causes have been eliminated by the process of averaging, or embracing in the sum
mation, observations covering an extended period of time. The distribution of
pressure and the system of winds which actually exist at a given instant will in
general agree with these in its main features, but may differ from them materially
in detail.
Confining our attention for the time being to the subject of atmospheric pressure,
it may be said that this, at any given point on the earth's surface, is in a constant
state of change, the mercurial barometer rarely becoming stationary, and then only
for a few hours in succession. The variations which the pressure undergoes may
be divided into two classes, viz, periodic, or those which are continuously in opera
tion, repeating themselves within fixed intervals of time, long or short; and non-
periodic or accidental, which occur irregularly, and are of varying duration and
extent.
472. PERIODIC VARIATIONS. — Of the former class of changes the most important
are the seasonal, which have been already to some extent described, and the diurnal.
The latter consists of the daily occurrence of two barometric maxima, or points of
highest pressure, with two intervening minima. Under ordinary circumstances
with the atmosphere free from disturbances, the barometer each day attains its first
minimum about 4 a. m. As the day advances the pressure increases, and a maximum,
or point of greatest pressure, is reached about 10 a. m. From this time the pressure
diminishes, and a second minimum is reached about 4 p. m., after which the mercury
again rises, reaching its second maximum about 10 p. m. " The range of this diurnal
oscillation is greatest at the equator, where it amounts to ten hundredlhs (0.10) of
an inch. It diminishes with increased latitude, and near the poles it seems to vanish
entirely. In middle latitudes it is much more apparent in summer than in winter.
473. NONPERIODIC VARIATIONS. — The equatorial slope of the tropical belt of
high pressure which encircles the globe in either hemisphere is characterized by the
marked uniformity of its meteorological conditions, the temperature, wind, and
weather changes proper to any given season repeating themselves as day succeeds
day with almost monotonous regularity. Here the diurnal oscillation of the barom
eter constitutes the main variation to which the atmospheric pressure is subjected.
On the polar slope of these belts conditions the reverse of these obtain, the elements
which go to make up the daily weather here passing from phase to phase without
regularity, with the result that no two days are precisely alike; and as regards
atmospheric pressure, it may be said that in marked contrast with the uniformity of
the torrid zone, the barometer in the temperate zone is constantly subjected to non-
periodic or accidental fluctuations of such extent that the periodic diurnal variation
is scarcely apparent, the mercurial barometer at a given station frequently rising or
falling several tenths of an inch in twenty-four hours.
474. PROGRESSIVE AREAS OF HIGH AND Low PRESSURE. — The explanation of
this rapid change of conditions is found in the approach and passage of extensive
areas of alternately high and low pressure, which affect alike, although to a different
degree, all the barometers coming within their scope. The general direction of
motion of these areas is that of the prevailing winds; eastward, therefore, in the
latitudes which are under consideration.
Taken in conjunction, these areas of high and low pressure exercise a controlling
influence over the weather changes of the temperate zones. As the low area draws
212
CYCLONIC STORMS.
213
near, the skv becomes overclouded, the prevailing westerly wind falls away, and
is succeeded by a wind from some easterly direction, faint at first, but increasing as
the pressure continues to diminish; the lowest pressure having been reached, the
wind again goes to the westward, the barometer starts to rise, and the weather clears;
all marking the eastward recession of the low area and the approach of the subsequent
high.
The first stage in the development of the low is a slight diminution of the
atmospheric pressure, amounting in general to not more than one or two hundredths
of an inch, throughout an area covering a more or less extensive portion of the earth's
surface, either land or water, but far more frequently over the former than over the
latter. Shortly after the advent of this, initiatory fall the decrease of pressure
throughout some small region within the larger area assumes a more decided character,
the mercury here standing at a lower level than elsewhere and reading successively
higher as we go outward, the region thus becoming, as it were, the center of the whole
barometric depression. A system of barometric gradients is by this means estab
lished, all directed radially inward, and in obedience to these gradients there is a
movement of the surface air toward the center or point of lowest barometer. The
air once in motion, however, the effect of the earth's rotation is brought into play
precisely as in the case of the larger movements of the atmosphere, with the result
that the several currents, instead of following the natural course alon<* these gradients,
are deflected from them, in the northern hemisphere to the right hand., in the southern
hemisphere to the left, the extent of the deflection being from 4 to 8 compass points.
Anticyclonic.
NORTHERN HEMISPHERE.
Cyclonic.
Anticyclonic.
Cyclonic.
SOUTHERN HEMISPHERE.
FIG. 7\
The light arrows show the direction of the gradients; the heavy arrows the direction of the winds.
475. CYCLONES AND CYCLONIC CIRCULATIONS. — A central area of low barometer
will thus be surrounded by a system of winds which constantly draw in toward the
center but at the same time circulate about it, the whole forming an inflowing spiral;
the direction of this circulation being in the southern hemisphere with the motion
of the hands of a watch, in the northern hemisphere opposed to this motion. Where
the barometric gradients are steep, these winds are apt to be strong; where they are
gentle, the winds are apt to be weak; where they are absent, as is the case at the
center or bottom of the depression, calms are apt to prevail.
Around the center of the area of high pressure a similar system of wind will be
found, but blowing in a contrary direction. Here the barometric gradients are
directed radially outward, with the result that in place of the inflowing, we have an
outflowing spiral, the circulatory motion being right handed or with the hands of
a watch in the northern hemisphere, left handed or against the hands of a watch in
the southern.
All these features are shown in the accompanying diagrams (fig. 70), which
exhibit the general character of cyclonic (around the low) and anticyclonic (around
the high) circulations in the northern and the southern hemisphere, respectively.
214
CYCLONIC STORMS.
The closed curves represent the isobars, or linos along which the barometric pressure
is the same; the short arrows show the direction of the gradients, which are every
where at right angles to the isobars; the long arrows give the direction of the winds,
deflected by the earth's rotation to the right of the gradients in the northern hemi
sphere, to the left in the southern.
476. FEATURES OF CYCLONIC AND ANTICYCLONIC REGIONS. — Certain features of
the two areas may here be contrasted. In the anticyclonic, the successive isobars
are as a rule far apart, showing weak gradients and consequently light winds; the
areas themselves are of relatively great extent, and their rate of progression is slow.
During the summer they originate as extensions into higher latitudes of the margins
of the tropical belts of high pressure; during the winter, as offshoots of the strong
anticyclone which covers the land throughout that season. Their approach and
presence is accompanied by polar or westerly winds, temperature below the seasonal
average, fair weather, and clear skies. In the cyclonic area the successive isobars
are crowded together, showing steep gradients and strong winds; they may appear
either as trougn-like extensions into the temperate zone of the polar belt of low
pressure, in which case the easterly winds proper to their polar side are nonexistent,
or (in lower latitudes) as independent areas, sometimes, indeed, as detached portions
of the equatorial low-pressure belt, which move eastward and poleward across the
temperate zone, and are ultimately merged into the great cyclonic area surrounding
the pole. The progress of these independent areas is invariably attended by the
strong and steadily shifting winds, foul weather, and other features which make up
the ordinary storm, at sea. In the trough-like depressions of higher latitudes these
features may or may not be observed, their presence depending upon the depths of
the barometric trough and the steepness of its slopes. In these, moreover, the
cyclonic circulation is never completely developed, the storm winds having rather
the character of right line gales, blowing from an equatorial or easterly direction
until the axis of the trough is at hand, and as this passes shifting by the west at one
bound to a polar direction.
477. CYCLONIC STORMS. — Strong winds are the result of steep barometric
gradients. These may occur with cyclonic or with anticyclonic areas, the latter
being exemplified in the case of the northers in the Gulf of Mexico and the north
westerly winter gales along the Atlantic coast of the United States, which are almost
invariably accompanied by barometers above the average. They are, however, so
much more frequent in the case of areas of low pressure and consequent cyclonic
circulations, with their attendant foul-weather characteristics, that the latter are
generally known 'as cyclonic storms, i. e., storms in which the wind circulation is
cyclonic.
Cyclonic storms may with convenience be divided into two classes: viz, tropical,
or those which originate near but not on the equator; and extra-tropical, or those
which first appear in higher latitudes.
478. TROPICAL CYCLONIC STORMS. — The occurrence of tropical cyclonic storms
is confined to the summer and autumn months of the respective hemispheres, and to
the western part of the several oceans, the North Atlantic, the North Pacific, the
South Pacific, and the Indian Ocean. They are unknown in the South Atlantic
Ocean. -Although these cyclonic storms are all of the same essential characteristics,
they have generally been called hurricanes when occurring in the West Indies and the
region between Samoa and Australia, typhoons when occurring in the region of the
Philippines, and cyclones when occurring in the Indian Ocean and its dependent seas.
The limits of the regions within which these tropical storms originate are defined
by parallels of latitude and meridians of longitude as follows :
Latitude.
Longitude from
Greenwich.
Hurricanes of the West Indies
12° to 28° N
55° to 95° W.
Typhoons of the Philippine region
5 to 20 N
150 to 115 E.
Cyclones of the Bay of Bengal
8 to 22 N
100 to 80 E
Cyclones of the Indian Ocean
4 to 30 S
100 to 40 E
Hurricanes of the Samoan region
10 to 30 S
160 W. to 150 E.
CYCLONIC STORMS.
215
The percentage of frequency of these storms in the different months of the year
is set forth in the following: table:
Jan.
Feb.
Mar.
Apr.
0
2
0
15
6
May.
June.
Julv.
Aug.
25
16
15
0
0
Sept.
Oct.
£ 1 rH rH O l^ CO
*S i— 1 i— 1
±
0
5
4
10
13
Hurricanes of the West Indies
0
2
0
22
29
0
0.4
0
19
17.5
0
I
18
28
1
5
6
6
1
G
9
12
1
0
4
16
19.
0.5
0
32
19
20
0
1.5
31
14
14
1.5
1
Typhoons of the Philippine region. . . .
t yclones of the Bav of Bengal
(Vclones of the Indian Ocean ....
Hurricanes of the Samoan region
The yearly average number of those occurring in the West Indian region is 4, in
the Philippine region 21, in the Bay of Bengal 9, in the Indian Ocean (south of the
Equator) 9, and in the region between Samoa and Australia 4.
4:79. MOTIOX OF THE STORM CEXTER. — In the case of tropical cyclonic storms
there is always a tendency for the barometric depression, impelled by the general
motion of the atmosphere in the trade-wind region, to follow a path which tends at
once westward and away from the equator. This motion continues until the limits
of the trades are reached, where the path ordinarily recurves; and the subsequent
motion of the depression is eastward and toward the pole, the disturbance at the
same time assuming the features of the extra- tropical cyclonic storm.
Rate of progress of the storm center. — Within the tropics in the northern hemi
sphere, the average velocity of the storm center along the path is 11 miles an hour;
and in the latitude of the recurvature of the storm this average is maintained,
although there are numerous instances of wide variations in the rate of progress here,
and sometimes the center becomes stationary for a few days. In higher latitudes, the
rate increases to an average of 16 miles an Sour.
In the southern hemisphere, the average velocity of progress as far as determined
is somewhat less than in the northern; and, in the Indian Ocean, many of the Mauri
tius cyclones have a very small movement of translation, and these are, in conse
quence, designated as stationary cyclones.
The general path of the tropical cyclonic storm in either hemisphere and the
cyclonic circulation of the wind about the storm center are given in figures 73 and
74; that for the northern hemisphere applying to the hurricanes of the West Indies;
that for the southern hemisphere to the hurricanes of the South Pacific Ocean.
480. INDICATIONS OF THE APPROACH OF TROPICAL CYCLOXIC STORMS. — The
premonitory signs of a tropical cyclonic storm comprise, besides those feelings of
personal discomfort which are common within the sphere of atmospheric disturbance
of cyclonic storms in all parts of the world, (1) an unsteady barometer, or even a
cessation of the diurnal range, which is constant in settled weather; (2) a heavy
swell not caused by the wind then blowing; (3) the appearance of the sky arising
from the forms and movements of the clouds. It is upon the concomitance of these
indications, rather than the recognition of any one of them, that reliance should be
placed.
The appearance of the clouds and their value as storm warnings is described as
follows by Faura in the Cyclones of the Far East, by Jose Algue, of the Manila
Observatory :
The best means for determining the center [of a storm] and for following up its movements are the
observations of cirri, little clouds of a very fine structure and clear opal color, "which appear as elongated
feathers. * * * Long before the least sign of bad weather is noticeable and in many cases when the
barometer is still very high — being under the influence of a center of high pressure, which generally
precedes a tempest — these small isolated clouds appear in the upper regions of the atmosphere. They
seem to be piled up on the blue vault of heaven and drawn out in the direction of some point on the
horizon toward which they converge. The first to present themselves are few in number but well defined
and of the most delicate structure, appearing like filaments bound together but whose visibility is lost
before they reach the point of radiation. We often had an opportunity to watch them at the observatory
of Manila, when the center was still 600 miles distant. The best times for observing the cirri are sunrise
and sunset. If the sun is in the east and very near the horizon, the first clouds which are tinged by
the solar rays are the cirro-strati which precede the cyclone, and they are also the last to disappear at
sunset, inasmuch as they overspread the horizon. Such times are the best for determining the radiant
point of the cloud streaks and at the same time for ascertaining the direction in which the center lies. Later
on the delicacy of form, which characterizes this class of clouds in its earlier stages, is lost, and the clouds
216
CYCLONIC STORMS.
appear in more confused and tangled forms, like streamers of feather work, with central nuclei, which
etill maintain this direction, so that the point of radiation can still be detected. In order to ascertain
approximately the direction in which the center is advancing in its movement of translation, it is necessary
FIG. 71.— Average Paths of Hurricanes in the West Indies.
The small circles indicate the points of origin of 130 storms, which comprise all the instances
resulting from the authentic accounts of a period of 35 years.
© June and July storms 0 September storms
© August storms Q October storms
to determine the changes of the radiant point at equal intervals of time and to compare them with the
movements of the barometer. If the point of convergence does not perceptibly change its position, but
remains fixed and immovable for a long time, even for several consecutive days, it is almost certain that
CYCLONIC STORMS.
217
the tempest will break over the position of the observer. In this case the barometer begins to fall shortly
after the first cirrus clouds have been observed and sometimes even before. At first it falls slowly, without
JV-
r-> >
120°
130°
140*
FIG. 72.— Mean Paths of Typhoons.
1. Typhoons in the Marianas.
2. Typhoons formed in the Pacific which, at some distance east of the meridian of Manila, have recurved toward
Japan.
3 and 3a. Typhoons formed in the Pacific which, near the meridian of Manila, have recurved toward Japan.
4. Typhoons of Taiwan or Formosa.
5 and oa. Typhoons of northern Luzon which have recurved in the island or near it in the China Sea.
6. Typhoons which have crossed Luzon northward of Manila and continued to the continent.
7. Typhoons which have crossed Luzon southward of Manila.
8. Typhoons of the Visayas and Mindanao.
9. Typhoons formed in the Pacific which have crossed south of Manila, recurved in the China Sea between latitudes
"10 degrees and 20 degrees, and recrossed north of Manila.
10. Typhoons formed in the China Sea.
11. Typhoons formed in the Sulu Sea and the interisland waters.
completely losing the diurnal and nocturnal oscillatory movements, but changing somewhat the hours
of maximum and minimum. The daily reading is observed to be each day less than that of the preceding
218
CYCLONIC STORMS.
Washington
IN HIGH LATITUDES
Velocity- alon;§ patlx
16 to 30 miles perKcmr
Norfolk
Savsuvnah.
So
30
30°
IN MIDDLE LATITUDES
STORM RECURVING
Velocity along patK
11 miles perliour
day. That part of the horizon in the direction of the storm begins to be covered by a cirrus veil, which
increases slowly until it forms an almost homogeneous covering of the sky. This veil is known by the
name "cirro-pallium" of Poe'y, and da that which^ causes the solar and lunar halos, which are never
absent when a storm approaches. Beneath the veil a few isolated clouds, commonly called "cotton,"
appear. They are much more numerous and larger on the side lying toward the storm, where they soon
appear as a compact mass. At such times the sunrises and sunsets are characterized by the high red
tint which the clouds assume, resembling a great fire, especially in the direction of the cyclone. The
wind remains fixed at one point, showing only a few variations, which are due principally to the squalls,
which continually exert their force within the limits of the storm. The low or ' ' cotton " clouds successively
and from time to time cover the sky, throwing out occasional squalls of rain and wind; but, the squalls
having passed, a lull ensues, the cirrus veil remaining, and like-wise the hurricane bank of clouds, which
seems fixed to the same spot in the direction of the storm. This state of the atmosphere continues until
the bank of clouds invades
QQO 7C)o the point of observation, in
which case the squalls will
be continuous and the wind
will increase in violence each
moment.
The condition of
diminished pressure at
tending a cyclonic
storm gives rise to high
waves which are propa
gated in all directions
from such a storm on
the ocean. These
waves outrun the storm
as^much as a thousand
miles, and, by the di
rection from which they
arrive, indicate the
bearing of the storm's
center.
Although thunder
storms can not be con
sidered as premonitory
signs, it rarely happens
that showers and
squalls are not experi
enced from 24 to 48
hours in advance of the
storm; and the un
settled state of the ba
rometer in the distant
approaches, varying
from 500 to 1,000 miles
in advance of the cen
ter, gives place, at a
distance of 300 to 400
miles, to a slow and steady fall of the mercurial column. At the same time the
direction and velocity of the lower clouds show unmistakable evidence of the
presence of a storm and the bearing of the center. When the storm center is
still far distant, the phenomenon called the "bar of the cyclone ;; may frequently be
seen. This is a dense mass of rain cloud formed about the center of the storm,
giving the appearance of a huge bank of black clouds resting upon the horizon, which
may^ retain its form unchanged for hours. It is usually most conspicuous about
sunrise or sunset. When it is possible to observe this bar, the changes in its position
at intervals of a few hours will enable the observer to determine the direction of
movement of the storm.
481. CHARACTER OF TROPICAL CYCLONIC STORMS. — Within the tropics the
storm area is small, the region covered by violent winds extending in general not
more than 150 miles from the center. The barometric gradients are, however,
exceedingly steep, instances having been recorded in which the difference of pressure
fPorto St."
IN LOW LATITUDES
Velocity along pafh
about 11 miles per tour
20°
80°
70°
FIG. 73.
CYCLONIC STORMS.
219
for this distance amounted to 2 inches. In the typhoons of the Xorth Pacific Ocean
gradients of one inch in 60 miles are not infrequent. The successive isobars are
almost circular. As a consequence of this distribution of pressure the winds on the
slopes of the depression are frequently of great violence, and in the matter of direc-
' tion they are more sym-
I j i i i i i i i i i i i i i i i i i i i •«=• QO metrically disposed about
the center than is the
case with the larger and
less regularly shaped de
pressions of higher lati
tudes. In these low lati
tudes the average values
of the deflection of the
wind from the baromet
ric gradient is in the
neighborhood of six cpm-
10° pass points — to the right
in the northern hemi
sphere, to the left in the
southern.
482. To Fix THE
BEARING OF THE STORM
CENTER FROM THE VES
SEL. — On this assump
tion, the following rules
will enable an observer
to fix the bearing of the
20° storm center from his
vessel:
In the northern hem
isphere, stand with the
face to the wind; the
storm center will bear ten
points to the observer's
right.
In the southern hem
isphere, stand with the
face to the wind; the
storm center will bear ten
30° points to the observer's
left.
On the basis of these
rules the tables hereafter
given (art. 487) show the
bearing of the center
corresponding to a wind
FlQ- 74- of any direction.
483. To Fix THE DISTANCE OF THE STORM CENTER FROM "THE VESSEL. — The
following table, taken from Piddington's " Sailor's Horn Book/' may prove of some
assistance in estimating the distance of the storm center from the vessel:
Average fall of the barometer
per hour.
From 0. 02 to 0. 06 in.
From 0. 06 to 0. 08 in.
From 0. 08 to 0. 12 in.
From 0. 12 to 0. 15 in.
Distance from the storm
center.
From 250 to 150 miles.
From 150 to 100 miles.
From 100 to 80 miles.
From 80 to 50 miles.
The table assumes that the vessel is hove-to in front of the storm and that the
latter is advancing directly toward it.
220 CYCLONIC STORMS.
Inasmuch, as cyclones are of varying area and of different intensities, the lines of
equal barometric pressure (isobars) lie much closer together in some storms than in
others, so that, in the circumstances of an observer on the ocean, the estimation of
the distance of the center by the height of the mercurial column or of its rate of fall
must be somewhat conjectural.
484. To AVOID THE CENTER OF THE STORM. — In the immediate neighborhood
of the center itself the winds attain full hurricane force, the sea is exceedingly
turbulent, and there is danger of being taken aback. Every effort should therefore
be made to avoid this region, either by running or by heaving-to; and if recourse is
had to the latter maneuver, much depends upon the selection of the proper tack;
this being in every case the tack which will cause the wind to draw aft with each
successive shift.
A vessel hove-to in advance of a tropical cyclonic storm will experience a long
heavy swell, a falling barometer with torrents of rain, and winds of steadily increasing
force. The shifts of wind will depend upon the position of the vessel with respect
to the path followed by the storm center. Immediately upon the path, the wind
will hold steady in direction until the passage of the central calm, trie "eye of the
storm," after which the gale will renew itself, but from a direction opposite to that
which it previously had. To the right of the path, or in the right-hand semicircle
of the storm (the observer being supposed to face along the track), the wind, as the
center advances and passes the vessel, will constantly shift to the right, the rate at
which the successive shifts follow each other increasing with the proximity to the
center; in this semicircle, then, in order that the wind shall draw aft with each
shift, the vessel must be hove-to on the starboard tack; similarly, in the left-hand
semicircle, the wind will constantly shift to the left, and here the vessel must be
hove-to on the port tack.
These rules hold alike for both hemispheres and for cyclonic storms in all
latitudes.
Figure 75 represents a cyclonic storm in the northern hemisphere after recurving.
For simplicity the area of low barometer is made perfectly circular, and the center is
assumed to be ten points to the right of the direction of the wind at all points within
the disturbed area. Let us assume that the center is advancing about NNE., in the
direction of the long arrow, shown in heavy full line. The ship a has the wind at
ENE.;tshe is to the left of the track, or technically in the navigable semicircle.
The ship b has the wind at ESE. and is in the dangerous semicircle. As the storm
advances these ships, if lying to, a upon the port tack, b upon the starboard tack, as
shown, take with regard to the storm center the successive positions a, a1} etc., b, 61,
etc., the wind of ship a shifting to the left, of ship b to the right, or in both cases
drawing aft, and thus diminishing the probability of either ship being taken aback,
a danger to which a vessel lying to on the opposite tack (i. e., the starboard tack in
the left-hand semicircle or the port tack in the right-hand semicircle) is constantly
exposed, the wind in the latter case tending constantly to draw forward. The ship b
is continually beaten by wind and sea toward the storm track. The ship a is drifted
away from the track, and, should she be able to carry sail, would soon find better
weather by running off to the westward.
It must not be forgotten that the shifts of wind will only occur in the above order
when the vessel is stationary. When the course and speed are such as to maintain
a constant relative bearing between the ship and storm center, there will be no shift
of wind. jShould the vessel be outrunning the storm, the wind will indeed shift in
the opposite direction to that given, and a navigator in the right semicircle, for
instance, and judging only by the shifts of wind without taking into account his own
run, might imagine himself on the opposite side. In such a case the barometer must
be the guide.
An examination of figure 75 shows how this is. A vessel hove to at the position
marked 6, and being passed by the storm center, will occupy successive positions in
regard to the center from b to 64, and will experience shifts of wind, as shown by the
arrows^ from East through South to SW. On the other hand, if the storm center
be stationary or moving slowly and a vessel be overtaking it along the line from 64
to Z>, the wind will back from SW. to East, and is likely to convey an entirely wrong
impression as to the location and movement of the center.
CYCLONIC STOBMS.
221
485. DANGEROUS AND NAVIGABLE SEMICIRCLES. — Prior to recurving, the winds
in that semicircle of the storm which is more remote from the equator (the right-
hand semicircle in the northern hemisphere, the left-hand semicircle in the southern)
are liable to be more severe than those of the opposite semicircle. A vessel hove to
in the semicircle adjacent to the equator has also the advantage of immunity from
becoming involved in the actual center itself, inasmuch as there is a distinct tendency
on the part of the latter to move away from the equator. For these reasons the more
remote semicircle has been called the dangerous, the less remote the navigable.
486. MANEUVERING. — A vessel suspecting the dangerous proximity of a tropical
cyclonic storm should lie-to for a time on the starboard tack to locate the center by
observing shifts of the wind and the behavior of the barometer. If the former holds
H
steady and increases in force, while the latter falls rapidly, say at a greater rate than
0.03 of an inch per hour, the vessel is probably on the track of the storm and in advance
of the center. In this position the proper step (providing, of course, that sea room
permits) is to run, keeping the wind, in the northern hemisphere, at all times well on
the starboard quarter; in the southern hemisphere, well on the port; and thus
constantly increasing the distance to the storm center. The same rule holds good
if the observation places the vessel at but a scant distance within the forward quadrant
of the dangerous semicircle. Here, too, the natural course will be to seek the navigable
semicircle of the storm, even though such a course involves crossing the track in
advance of the center, always exercising due caution to keep the wind from drawing
too far aft.
222 CYCLONIC STORMS.
The critical case is that of a vessel which finds herself in the forward quadrant
of the dangerous semicircle and at a considerable distance from the track, for here
the shifts of the wind are sluggish and the indications of the barometer are undecided,
both causes conspiring to render the bearing of the center doubtful. If, upon
heaving to, the barometer becomes stationary, the position should be maintained
until indications of a rise are apparent, upon which the course may be resumed with
safety and held as long as the rise continues. If, however, the barometer falls, a
steamer should make a run to the NNE. or NE. (southern hemisphere, SSE. or SE.),
keeping the wind and sea a little on the port (southern hemisphere, starboard) bow,
and using such speed as will at least keep the barometer stationary. Such a step will
in general be attended with the assurance that the present weather conditions will
in any case grow no worse. For a sailing vessel, unable to stand closer to the wind
than six points, the last maneuver will be impossible, and driven to leeward by wind,
sea, and current, she may be compelled to cross the track immediately in advance
of the center, or may even become involved in the center itself. In this extremity
the path of the storm center during the past twenty-four hours should be laid down
on a diagram as accurately as the observations permit, and the line prolonged for
some distance beyond the present position of the center. Having assumed an average
rate of progress for the center, its probable position on the line should be frequently
and carefully plotted, and the handling of the vessel should be in accordance with
the diagram.
487. SUMMARY OF RULES. — The following summary comprises the rules of
maneuvering, so far as they may be made general:
NORTHERN HEMISPHERE.
In the Right or Dangerous Semicircle. — Steamers bring the wind on the starboard
bow, and make as much way as possible; if obliged to heave to, do so head to sea.
Sailing vessels haul by the wind on the starboard tack and carry sail as long as possible ;
if obliged to heave to, do so on the starboard tack.
In the Left or Navigable Semicircle. — Bring the wind on the starboard quarter,
note the course, and hold it; if obliged to heave to, do so on the port tack, unless in
a steamer which behaves better when hove to stern to the sea.
On the Storm Track in Front of the Center. — Bring the wind two points on the
starboard quarter, and, holding this course, run for the Left Semicircle; if obliged
to heave to, do so on the port tack, unless in a steamer which behaves better when
hove to stern to the sea.
On the Storm Track in Rear of the Center. — Avoid the center by the best
practicable route, having due regard to the tendency of cyclones to recurve to the
northward and eastward.
SOUTHERN HEMISPHERE.
In the Left or Dangerous Semicircle. — Steamers bring the wind on the port bow,
and make as much way as possible; if obliged to heave to, do so head to sea. Sailing
vessels haul by the wind on the port tack, and carry sail as long as possible; if obliged
to heave to, do so on the port tack.
In the Right or Navigable Semicircle. — Bring the wind on the port quarter, note
the course, and hold it; if obliged to heave to, do so on the starboard tack, unless in
a steamer which behaves better when hove to stern to the sea.
On the Storm Track in Front of the Center. — Bring the wind two points on the
port quarter, and, holding this course, run for the right semicircle; if obliged to
heave to, do so on the starboard tack, unless in a steamer which behaves better when
hove to stern to the sea.
On the Storm Track in Rear of the Center. — Avoid the center by the best practi
cable route, having due regard to the tendency of cyclones to recurve to the south
ward and eastward.
CYCLONIC STORMS.
223
The application of these rules for the various directions of the wind is shown
in the following table:
Storm Table, Xorthern Hemisphere.
Direction
of wind.
Direction
of center.
Observer facing along storm track.
If wind shifts toward If wind shifts toward ' If wind stead v with
the right. the left. falling barometer.
If wind steady with
rising barometer.
North.
ESE.
g> £ Run SSW. = Run SSW.
Run SSW. ~
XXE.
SE.
rr.^~9-- -±
Run SW. "g Kg.
Run SW. ^ £. =-
Run SW. 5- -: £-
XE.
SSE.
'~K 1='* ^L\~
Run WSW. ZL £. 7"
Run WSW. ?.^r
Run WSW. 5 - ~
EXE. ! South.
-, S^S-SBS
Run West, r r: =
Run West. g'~ c
Run West, o ^ f
East.
SSW.
?8 liffjTg.5.
Run WNW. i.^ =
Run WXW. 1-^
Run WNW. a1! 5
ESE.
SW.
M3&Rg£
Run N W. • - *
RunNW. -'c-~
RunNW. ^-^
SE.
wsw. .
X ^ X ^ /*• ^ JQ
RunXXW. £• s
RunXXW. ^§
RunXXW. S b °
SSE.
West.
5 Sfc* ~ X- ^
5 o* **»*•£ £3 4
Run North. ~ Z
Run North. 9 —
Run North. r~5
South.
WNW.
£~P-P;F^-- RunXXE. 0-
RunXXE. < =
RunXXE. g -
SSW.
NW.
fcs.e-' i*§.
Run XE. < =
Run XE.
RunXE. ^|
sw.
NNW.
5. ** 2 5! c* = £
Run EXE. #J
Run EXE. ~ £
Run EXE. ~^:.
wsw.
North.
§*§.SX ^;
Run East. - *
Run East. e ~
Run East. - m
West.
NNE.
RsH* iT- £
Run ESE. 9-~
Run ESE. ~\
Run ESE. ^
WXW.
NE.
5:1 si" M§- R™SE. ;i
RunSE. -T- ^
RunSE.
NW.
ENE.
, _~~ c^c j RimSSE.
Run SSE. °5
Run SSE.
NNW.
East.
**•£ § Pg 3- Run South. g ~
Run South. § jx;
Run South. § Jf
Courses given are for wind two points on starboard quarter, but it is preferable to take wind broad on quarter if possible.
Storm Table, Southern Hemisphere.
Direction
of wind.
Direction
of center.
Observer facing along storm track.
If wind shifts toward
the right.
If wind shifts toward
the left.
If wind steady with
falling barometer.
If wind steady with
rising barometer.
North.
WSW.
Run SSE. ~
2P 2
Run SSE. ~
Run SSE. ~
XXE.
West.
Run South. £ ^ £-
9- S "z — r" El ^ ^
Run South. ^ £- 2-
Run South. *3 s; £-
XE.
WNW.
Run SSW. 1 x. ~
a ~ 2- ='s P. H- 3
Run SSW. E.^7
Run SSW. i£.-
EXE.
NWT.
RunSW. c^r.6
c ?: ^ < ? ^ = i
RunSW. 3J^ =
RunSW. ^=:d
East.
XXW.
Run WSW. 5*51
Run WSW. 5 -
Run WSW. J.7^ 5
ESE.
North.
Run West. ~~-
^ e-T- x ^ r: ~ 5.
Run West. HT""
Run West. • ~o
SE.
NNE.
Run WNW. % g- °
§. ^- S §• r "J^ 5c -p
Run WNW. S ^g
Run WXW. S" a
SSE.
NE.
RunNW. F~Z
- - ' — — ~ = 1
RunXW. f^j? r-
RunXW. -2
South.
ENE.
Run NNW. 5 r
^ ?.H § S" = r-
RunNNW. < =
Run NNW. 0 r-
SSW.
East.
Run North. ~ =
p 35 5 — cf ?" 2-
Run North.
Run Xorth. ^ 3
SW.
ESE.
Run NNE. ^ V!
(L-< -- p ^ c
Run XXE. ^ =»
Run XXE. g^J
WSW.
SE.
RunXE.
c" | x ex"2
RunXE. cJS
RunNE.
West,
SSE.
Run EXE. §-x
5**^J| ?" g "5
Run ENE. c|
Run EXE. §--5
WXW.
South.
Run East. ^ '£
^ x =" ~ _* c?-
Run East. 2 ^
Run East. ^ :i
NW.
SSW.
Run ESE.
S t^Pi C- - _-
C C - x X
Run ESE.
Run ESE.
NNW.
SW.
Run SE. § Jf
.= 51 ifi
RunSE. §-
Run SE. § $
a Courses given are for wind two points on port quarter, but it is preferable to take wind broad on quarter if possible.
488. EXTRA-TROPICAL CYCLONIC STORMS. — On turning to the cyclones of tem
perate latitudes, we find many features in which they resemhle those of the torrid
zone, but certain other features in which they differ. Their fundamental resemblance
to tropical cyclones is seen in their incurving winds, forming an inflowing left-handed
spiral about the center of low pressure in the northern hemisphere, an inflowing right-
handed spiral in the southern. The intensity of these winds varies with the depth of
the barometric depression. The depression itself, however, in place of covering a few
miles, as is the case in the tropics, will frequently have a diameter of several hundred
or even a thousand miles, and for some distance around the center the gradients will
have a tolerably strong value. For this reason there is less concentration of violence
close to the center, and the calm and clear central space, or "eye," is seldom sharply
developed, although it is not uncommon to discover a gradual weakening or failing
224
CYCLONIC STORMS.
of the winds, and sometimes even an imperfect breaking^ away of the clouds as the
central area passes over the 'observer. The form of tropical cyclones as denned by
their isobaric lines is nearly circular. Extra-tropical cyclones are as a rule less
symmetrical, and their isobars are often elongated into an oval form, the longer axis
of the oval trending (in the northern hemisphere) between north and east — about,
therefore, in the direction of progression. The steepest gradients, and consequently
die strongest winds, are apt to be found on the equatorial and westerly sides of the
depression.
Extra-tropical cyclones generally follow an easterly course, inclining somewhat
toward the pole; but they occasionally turn to one side or the other, become sta
tionary, or even move backward. The velocity of progression varies from 15 to 40
miles an hour. If they exist as independent barometric depressions, with strong
upward gradients on all sides of the center, the cyclonic circulation will be complete,
the wind shifting with the sun for an observer situated in the equatorial semicircle
of the storm, against the sun for an observer situated in the polar semicircle.
Important among these extra-tropical cyclonic disturbances are the pamperos
of the Argentine coast. These storms are primarily caused by the approach and
passage eastward of an area of low pressure, around which the winds circulate spirally
in a right-handed direction. They vary in strength and duration from a squall to a
gale of great violence. Although preceded by the indications which characterize
the approach of cyclonic storms in general, yet they usually break with such sudden
ness, in a shift of wind from the northward to the southwestward, that they may
become particularly dangerous from this cause alone. They usually continue to
blow and die out in the southwest quadrant.
489. STORMS ALONG THE TRANSATLANTIC STEAMSHIP ROUTES. — The storms
which are so frequently met during the winter season along the steamship routes
between America and Europe are not, as a rule, due to central barometric depressions
but to depressions having a trough or V shape, which extend southerly from the
extensive permanent area of low pressure having its center in the vicinity of Iceland.
They are not attended by complete
cyclonic circulations, inasmuch as
the polar gradients which would
otherwise give rise to easterly winds
on this polar side are lacking. Their
approach is heralded by a gradual
hauling of the wind to southward,
which is later followed (at the time
of passage of the central line of the
trough) by a change to NW., accom
panied by heavy rain squalls and a
rapid increase in force. The general
distribution of pressure and the sur
rounding winds are ^ shown in figure 76. The changes in wind and pressure ensue
much more rapidly in the case of a westward-bound vessel than in that of one east
ward bound, the rate at which the observer and the depression approach each other
being^ in the former case the sum of his own westward velocity and the eastward
velocity of the trough, in the latter case the difference of these velocities.
Low
FIG. 76.
CHAPTER XX.
TIDES,
490. DEFINITIONS. — Tidal phenomena present themselves to the observer
under two aspects — as alternate elevations and depressions of the sea, and as recur
rent inflows and outflows of streams. The word tide, in common and general usage,
is made to refer without distinction to both the vertical and horizontal motions of
the sea, and confusion has sometimes arisen from this double application of the term;
in its strict sense, this word may be used only with reference to the changes of eleva
tion, while the recurrent streams are properly distinguished as tidal currents.
The tide rises until it reaches a maximum height called high water or high tide,
and then falls to a minimum level called law water or low tide; that period at high or
low water marking the transition between the tides, during which no vertical change
can be detected, is called stand.
Of the tidal currents, that which arises from a movement of the water in a
direction, generally speaking, from the sea toward the land, is called flood, and that
arising from an opposite movement, ebb; the intermediate period between the cur
rents, during which there is no horizontal motion, is distinguished as slack. Set and
drift are terms applicable to the tidal currents, the first referring to the direction and
the second to the velocity.
Care should be taken to avoid confusing the terms relating to tides with those
which relate to tidal currents.
491. CAUSE. — The cause of the tides is the periodic disturbance of the ocean
from its position of equilibrium brought about through the periodic differences of
attraction upon the water particles of the earth, by the moon, and to lesser degree,
by the sun, on account of their relative periodic movements. The tide-producing
force of the moon upon a particle of unit mass on the surface of the earth is the
difference between the moon's attraction upon the given unit mass and the moon's
attraction upon the entire earth; and it is likewise with the sun, only the magnitude
of the mean tide-producing force is in this case reduced to about two-fifths of the
tide-producing force of the moon, because of the comparative remoteness of the sun
from the earth.
A particle which has a tide-producing body in its zenith or in its nadir experi
ences, as the result of the attraction of the tide-producing body, an effect only in the
vertical direction as il the intensity of gravity were momentarily lessened; and a
particle which has the tide-producing body in its horizon, being then practically at
the same distance from the tide-producing body as the center of the earth, experi
ences, as the result of the attraction of the tide-producing body, an effect which is
practically ah1 in the vertical direction as if the intensity of gravity wTere momentarily
increased. But when the tide-producing body is in any other situation withreference
to an attracted particle, the attraction is partly" directed in a vertical line toward the
center of the earth and partly in a horizontal direction along the surface of the earth.
The vertical components of the attractions of the tide-producing bodies can not
create any sensible disturbance on the existing oceans; but the horizontal components
of such attractions, tending to produce horizontal movements oscillating back and
forth on the surface of the earth, are effective in the production of the tides, and, by
acting upon portions of the oceans that are susceptible of taking up stationary
oscillations in approximate unison with the period of the tide-producing forces, give
rise to the dominant tides.
The peculiarities that characterize the tides of many localities are caused by
modifications resulting from reflections and interferences suffered by the dependent
waves generated by the dominant tides. Theory is not yet sufficiently advanced to
render practicable the prediction of the tides where no observations have been made;
61828°— 16 15 225
226 TIDES.
but by theory, supplemented by the observation of actual tidal conditions in a given
locality during a certain period of time, very accurate predictions of the time and
height of the tides can be mado for that locality.
492. ESTABLISHMENT. — High and low water occur, on the average of the twenty-
eight days comprising a lunar month, at about the same intervals after the transit
of the moon over the meridian. These nearly constant intervals, expressed in hours
and minutes, are known, respectively, as the high water lunitidal interval and low
water lunitidal interval.
The interval between the moon's meridian passage at any place and the time
of the next succeeding high water, as observed on the days when the moon is at full
or change, is called the vulgar (or common) establishment of that place, or, sometimes,
simply the establishment. This interval is frequently spoken of as the time of high
water on full and change days (abbreviated "H. W. F. & C."); for since, on such
days, the moon's two transits (upper and lower) over the meridian occur about
midnight and noon, the vulgar establishment then corresponds closely with the local
times of high water. When more extended observations have been made, the average
of all high water lunitidal intervals for at least a lunar month is taken to obtain what
is termed, in distinction to the vulgar establishment, the corrected establishment of
the port, or mean high water lunitidal interval. In defining the tidal characteristics
of a place some authorities give the corrected establishment, and others the vulgar
establishment, or "high water, full, and change;" calculations based upon the former
will more accurately represent average conditions, though the two intervals seldom
differ by a large amount.
Having determined the time of high water by applying the establishment to the
time of moon's transit, the navigator may obtain the time of low water with a fair
degree of approximation by adding or subtracting 6h 13m (one-fourth of a mean lunar
day) ; but a closer result will be given by applying to the time of transit the mean
low water lunitidal interval, which occupies the same relation to the time of low water
as the mean high water lunitidal interval, or corrected establishment, does to the
time of high water.
493. KANGE. — The range of the tide is the difference in height between low
water and high water. This term is often applied to the difference existing under
average conditions, and may in such a case be designated as the mean range or mean
rise and fall to distinguish it from the spring range or neap range, winch are the ranges
at spring and neap tides, respectively.
494. SPRING AND NEAP TIDES. — At the times of new and full moon the relative
positions of sun and moon are such that the high water produced by one of those
bodies occurs at the same time as that produced by the other, and so also with the
low waters; the tides then occurring, called spring tides, have a greater range than
any others of the lunar month, and at such times the highest high tides as well as
the lowest low tides are experienced, the tidal range being then at its maximum.
At the first and third quarters of the moon the positions are such that the high tide
due to one body occurs at the time of the low tide due to the other, so that the two
actions are opposed ; this causes the neap tides, which are those of minimum range,
the high waters being lower and the low waters higher than at other periods of the
month.
Since the horizontal motion of the water depends directly upon the rise and fall
of the tides it follows that the currents will be greatest at springs and least at neaps.
The effect of the moon's being at full or change is not felt at once in all parts of the
world, and the greatest range of tides does not generally occur until one or two days
thereafter; thus, on the Atlantic coast of North America, the highest tides are
experienced one day, and on the Atlantic coast of Europe two days, afterwards,
though on the Pacific coast of North America they occur nearly at full and change.
495. The nearer the moon is to the earth the stronger is its attraction, and as
it is nearest in perigee, the tides will be larger then on that account, and consequently
less in apogee. For a like reason, the tides will be increased by the sun's action when
the earth is near its perihelion, about the 1st of January, and decreased when near
its aphelion, about the 1st of July.
496. The height of the tides at any place may undergo modification on account
of strong prevailing winds or abnormal barometric conditions, a wind blowing off
TIDES.
227
the shore or a high barometric tending to reduce the tides, and the reverse. The
effect of atmospheric pressure is to create a difference of about 2 inches in the height
of tide for every tenth of an inch of difference in the barometer.
497. PRIMING AND LAGGING. — The tidal day is the variable interval, averaging
24h 50m, between two alternate high or low waters. The amount by which corre
sponding tides grow later day by day — that is, the amount by whicli the tidal day
exceeds 24h — is called the daily retardation. When the sun's tidal effect is such as to
shorten the lunitidal intervals, thus reducing the length of the tidal day and causing
the tides to occur earlier than usual, there is said to be ^priming of the tide; when,
from similar causes, the interval is lengthened, there is saia to be a lagging.
498. TYPES OF TIDES. — The observed tide is not a simple wave ; it is a compound
of several elementary undulations, rising and falling from the same common plane,
of which two can be distinguished and separated by a simple grouping of the
data. These two waves are known as the semidiurnal and the diurnal tides, be
cause the first, if alone, would give two high and two low waters in a day, while
the second would give but one high and one low water in an equivalent period
of time. In nearly all ports these two tides coexist, but the proportion between
them varies remarkably for differ
ent seas. The effect of the com
bination of these two types of
tide is to produce a "diurnal
inequality, both in the height of
two consecutive high or low
waters, and in the intervals of
time between then" occurrence.
The height of the diurnal wave
may be regarded as reaching a
maximum fortnightly, soon after
the moon attains its extreme dec
lination and is therefore near
one of the tropics. The tides
that then occur are denominated
tropic tides.
In undertaking to investi
gate the tides of a port it is im
portant to ascertain as early as
possible the form of the tide ; that
is, whether it resembles the semi
diurnal, the diurnal, or the mixed
tvpe; because not only may this information be of scientific value, but the knowledge
tnus gained at the outset will enable the observer to fix upon the best method of
keeping his record.
499. The type forms referred to are illustrated in the diagram in figure 77,
where the waves are plotted in curves, using the times as abscissas and the heights
as ordinates. In this diagram, the curve traced in the full line is a tide wave of the
semidiurnal type; that traced by the dotted line one of the diurnal; while the
broken line is one of the mixed type, in this case the compound of the two others.
In order to determine the type to which the tide of any port belongs, it is usually
only necessary to make hourly observations for a day or two at the date of the moon's
maximum declination, and to repeat the series about a week later, when the moon
crosses the equator. The reported irregularities of the rise and fall at any place
should not deter persons from careful investigation. When analyzed, even the most
complicated of tides are found to follow some general law.
• 500. TIDAL CURRENTS. — It should be clearly borne in mind by the navigator
that the periods of flood and ebb currents do not necessarily coincide with those of
rising and falling tides, and that, paradoxical though it may seem at first thought,
the inward set of the surface current does not always cease when the water nas
attained its maximum height, nor the outward set when a minimum height has been
reached. Under some circumstances it may occur that stand and slack will be
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FIG. 77.
mixed.
228 TIDES.
simultaneous, while other conditions may produce a maximum current at stand,
with a maximum rate of rise or fall at slack water.
The varying effects which will be produced according to local conditions may
be considered by the comparison of two tidal basins, to one of which the tide wave
has access from the sea by a channel of ample capacity, while the other has an
entrance that is narrow and constricted. In the first case, the process of filling or
emptying the basin keeps pace with the change of level in the sea and is practically
completed as soon as the height without becomes stationary; in this case slack and
stand occur nearly at the same time, as do flood and rise and ebb and fall. In the
second case, the limited capacity of the entrance will not permit the basin to fill or
empty as rapidly as the tide changes its level without; hence there is still a difference
of level to produce a current when the vertical motion in either direction has ceased
on the outside, and for a considerable time after motion in the reverse direction has
been in progress; under extreme conditions it may even occur that a common level
will not be established until mid-tide, and therefore the surface current at some
places will ebb until three hours after low water and flow until three hours after high
water.
Localities that partake of the nature of the first case are those upon open coasts
and wide-mouthed bights. Examples of the latter class will be found in narrow
bays and long channels.
TIMES OF HIGH AND LOW WATER.
501. TIDE TABLES. — The most expeditious, as well as most exact, method of
ascertaining the times of high and low water and other features of the tides will be
by reference to a Tide Table, and every navigator is recommended to provide him
self with such a publication. The United States Coast and Geodetic Survey pub
lishes annually, in advance, tables giving, for every day in the year, the predicted
time and height of the tides at certain principal ports of the world, and from these,
by a simple reduction, the times and lieights at a multitude of other ports may
readily be obtained; data for ascertaining the tidal currents in certain important
regions are also provided. General tide tables are also published by the govern
ments of other maritime nations, and special tables are to be had for many particular
localities.
502. Where no tide tables are available, the method of calculation by applying
the lunitidal interval to the time of the moon's meridian passage must be resorted to.
To do this, find first the time of the moon's meridian passage, upper or lower,
as may be required. The Greenwich mean time of upper transit at Greenwich is
given in the Nautical Almanac; the corresponding time of lower transit is most easily
found by taking the mean of the two adjacent upper transits; to the Greenwich time
of Greenwich transit apply the correction for longitude given in Table 1 1 (using the
daily variation of the moon's meridian passage shown in the Almanac), adding in
west and subtracting in east longitude ; the result is the local mean time of local
transit. Add to this the high-water or low- water lunitidal interval of the port from
Appendix IV, according as the time of high or low water may be required. The
result is the time sought.
The astronomical date must be strictly adhered to, and in so doing it may be
found necessary to employ the time of a lower transit, or the transit of a preceding
day, to find the time of the tide in question.
Appendix IV contains, besides the geographical positions of all the more
important positions in the world, a series of tidal data relating to many of those
places. In such data are comprised the mean lunitidal intervals for high and low
water; also, for places where the semi-diurnal type of tide prevails, the tidal range
at spring and at neap tides, and for those where the tide is of the diurnal type, tjie
tropic range. An alphabetical index is appended to this table.
The corrected establishment taken from the charts may be substituted for the
high-water lunitidal interval of the table; or, with only slight variation in the results,
the vulgar establishment (H. W. F. & C.) may be employed.
TIDES. 229
EXAMPLE: Find the times of the high and low waters at the New York Navy Yard, occurring next
after noon on April 15, 1916.
G.M. T. of Gr. upper transit, 14<i 9^21™ Transit (lower), 14<* 21«» 52°» Transit (lower), 14<* 21»> 52™
G. M. T. of Gr. upper transit, 15 10 05 H. W.Lun.Inf.(App.IV), 8 44 L. W.Lun.Int.(App.IV), 2 49
2)29 19 26 f 15 6 36 f 15 0 41
L.M.T..H.W., -L\pr.lo.6.36 L.M.T..L.W., {Apr. 15,12.41
G.M. T. of Gr. lower transit 14 21 43 I p.m. I p.m.
Corr. for -f 74° Long. (Tab. 11), + 9
L. M. T. of local lower transit 14 21 52
EXAMPLE: Find the time of high water at the Presidio, San Francisco, Cal., on the evening of
February 17, 1916.
G. M. T. of Gr. upper transit, 16<i 10h 37™
G. M. T. of Gr. upper transit, 17 11 23
2)33 22 00
G. M. T. of Gr. lower transit,
Corr. + 122° Long. (Tab .11;,
L. M. T. local lower transit,
H. W. Lun. Int. (App. IV),
• L. M. T., H. W.f
EXAMPLE: Find the time of low water at Singapore on the night of May 21, 1916.
G. M. T. of Gr. upper transit, 20<i 15*> 29»
G. M. T. of Gr. upper transit, 21 16 28
2)42 7 57
G. M. T. of Gr. lower transit, 21 3 59
Corr. for -104° Long. (Tab. 11), — 17
L. M. T. of local lower transit, 21 3 42
L. W. Lun. Int. (App. IV) + 4 02
T \r T T \v /21 7 **
L. M. !.,!>. \N., \May21, 7.44 p. m.
EXAMPLE: Find the time of morning hish water and afternoon low water at Gibialtar on June 19,
1916.
G. M. T. of Gr. upoer transit, 18<* 15* 12™ G. M. T. of Gr. upper transit,
Corr. -f-5° Long. (Tab. 11), + 01 G. M. T. of Gr. upper transit,
L. M. T. of local transit, 18 15 13 2)38 7 17
H. W. Lun. Int. (App. IV), 1 35
G. M. T. of Gr. lower transit, 19 3 39
T \r T TT w 118 16 48 Corr. for +5° Long. (Tab. 11), -f 01
L. M. T., H. W., |June 19j 4 4g a m ^
L. M. T. of local lower transit, 19 3 40
L. W. Lun. Int. (App. IV), 7 55
T \r T w /19 11 35
I* M. T.t 1* W., \June 19, 11.35 p.m.
TIDAL OBSERVATIONS.
503. Since navigators will frequently have opportunity to observe tidal con-
, ditions, either in connection with a hydrographic survey or otherwise, at places
where existing knowledge of the tides is incomplete, an understanding of the methods
employed in tidal observations may be important.
50i . TIDES. — For the proper study of tides, frequent and continuous observa
tions are necessary; it will not suffice to observe the heights of the high and low
waters only, even if they present themselves as distinct phases, but the whole tidal
curve for each day should be developed by recording the height of water at intervals,
which, preferably, should not exceed thirty minutes. Observations, to be complete,
* must cover a whole lunar month; or, if it be impracticable to observe the tides at
night, the day tides of two lunar months may be substituted.
505 . When made for the purposes of a hydrographic survey, the tidal observations
are used to correct the soundings, and care must be taken to make sure that the
gauge is placed in a situation visited by the same form of tide as that which occurs
at the place where soundings are being made. It will not answer, for instance, to
230 TIDES.
correct the soundings upon an inlet bar by tidal observations made within the lagoon
with which this inlet communicates, because the range of the tide within the lagoon
is less than upon the outside coast. A partial obstruction, like a bridge, or a natural
contraction of the channel section, while it may not reduce the total range of the tide
or materially affect the time of high or low tides, will alter the relative heights above
and below at intermediate stages, so that the hydrographer must be careful to see
that no such obstruction intervenes between his field of work and the gauge.
506. TIDAL CURRENTS. — Observations for tidal currents should be made with
the same regularity as for tides; the intervals need not ordinarily be more frequent
than once in every half hour. They should always be made at the same point or
points, which should be far enough from shore to be representative of the conditions
prevailing in the navigable waters. The ordinary log may be employed for measuring
the current, but it is better to replace the chip by a pole weighted to float upright
at a depth of about fifteen feet; the line should be a very light one, and buoyed at
intervals by cork floats to keep it from sinking; the set of the current should be
noted by a compass bearing of the direction of the pole at the end of the observation.
507. RECORD. — The record of observations should be kept clearly and in
complete form. It should include a description of the locality of observation, the
nature of gauge and of instruments used for measuring currents, and the exact position
of both tidal and current stations, together with situation and height of bench mark.
The time of making each observation should be shown, and data given for reduction
to some standard time. In extended tidal observations the meteorological conditions
should be carefully recorded, the instruments used for the observations being properly
compared with standards.
508. There are frequently remarkable facts in reference to tides and currents
to be obtained from persons having local knowledge; these should be examined and
recorded. The date and circumstances of the highest and lowest tides ever known
form important items of information.
509. PLANES OF REFERENCE. — The plane of reference is the plane to which
soundings and tidal data are referred. One of the principal objects of observing
tides when making a survey is to furnish the means for reducing the soundings to
this plane. Four planes of reference are used; namely, mean low water, mean low
water springs, mean lower low Waters, and the harmonic or Indian tide plane.
Mean Low water is a plane whose depression below mean sea level corresponds
with half the mean semidiurnal range, while the depression of mean low water springs
corresponds with half the mean range of spring tide; mean lower low water depends
upon the diurnal inequality in high and low water; the harmonic or Indian tide plane
was adopted as a convenient means of expressing something of an approximation
to the level of low water of ordinary spring tides, but where there is a large diurnal
inequality in low waters it falls considerably below the true mean of such tides.
As these planes may differ considerably, it is important to ascertain which plane
of reference is adopted before making use of any chart or considering data concerning
the tides.
510. The tides are subject to so many variations dependent upon the movements
of the sun and moon, and to so many irregularities due to the action of winds and
river outflows, that a very long series of observations would be necessary to fix any
natural plane. In consideration of this, and keeping in view the possibilities of
repetitions of the surveys or subsequent discoveries within the field of work, it is
necessary to define the position of the plane of reference which has resulted from any
series of observations. This is done by leveling from the tide gauge to a permanent
bench, precisely as if the adopted plane were arbitrary.
511. BENCH MARK. — The plinth of a lighthouse, the water table of a substantial
building, the base of a monument, and the like, are proper benches; and when these
are not within reach a mark may be made on a rock not likely to be moved or started
by the frost, or, if no rock naturally exists in the neighborhood, a block of stone
buried below the reach of frost and plowshare should be the resort. When a bench
is made on shore it should be marked by a circle of 2 or 3 inches diameter with a
•cross in the center indicating the reference point. The levelings between this point
and the gauge should be run over twice and the details recorded. A bench made
upon a wharf or other perishable structure is of little value, but in the absence of
TIDES. . 231
permanent objects it is better than nothing. The marks should be cut in, if on stone,
and if on wood, copper nails should be used. The bench must be sketched and
carefully described, and its location marked on the hydrographic sheet, with a state
ment of the relative position of the plane of reference.
512. The leveling from the bench mark to the tide gauge may be done, when a
leveling instrument is not available, by measuring the difference of height of a number
of intermediate points by means of a long straight-edged board, held horizontal by
the aid of a carpenter's spirit level, or even a plummet square, taking care to repeat
each step with the level inverted end for end. A line of sight to the sea horizon,
when it can be seen from the bench across the tide staff, will afford a level line of
sufficient accuracy, especially when observed with the telescope. It may often be
convenient to combine these methods.
513. TIDE GAUGES. — The Staff Gauge is the simplest device for measuring the
heights of tides, and in perfectly sheltered localities it is the best. It consists of a
vertical staff graduated upward in feet and tenths, and so placed that its zero shall
lie below the lowest tides. The same gauge may also be used where the surface is
rough, if a glass tube with a float inside is secured alongside of the staff, care being
taken to practically close the lower end of the tube so as to exclude undulations;
readings may also be made by noting the point midway between the crest and trough
of the waves.
A staff gauge should always be erected for careful tidal observations, even where
other classes of gauge are to be employed, as it furnishes a standard for comparison
of absolute heights, and also serves to detect any defects in the mechanical details
upon which all other gauges are to a greater or less extent dependent.
514. Where there is considerable swell, and where, from the situation of the
gauge or the great range of the tide (making it inconvenient for the observer to see
the figures in certain positions) the staff gauge can not be used, recourse must be had
to the Box Gauge. This gauge consists of a vertical box, closed at the bottom, with
a few small holes in the lower part which admit sufficient water to keep the level
within equal to the mean level without but which do not permit the admission of
water with sufficient rapidity to be affected by the waves. Within the box is a
copper float; in some cases this float carries a graduated vertical rod whose position
with reference to a fixed point of the box affords a measure for the height of the
water; in other gauges of this class the float is attached to a wire or cord which
passes over pulleys and terminates in a counterpoise whose position on a vertical
graduated scale shows the height of tide.
515. An Automatic Gauge requires a box and float such as has just been described.
The motion of the float in rising and falling with the tide is communicated to a pencil
which rests upon a moving sheet of paper; uniform motion is imparted to the paper
by the revolution of a cylinder driven by clockwork; the motion of the pencil clue to
the tide is in a direction perpendicular to the direction of motion of the paper, and
a curve is thus traced, of which one coordinate is time and the other height, The
paper, which is usually of sufficient length to contain a month's record, is paid out
from one cylinder, passes over a second whereon it receives the record and is rolled
upon a third cylinder, which thus contains the completed tidal sheet.
This gauge, besides giving a perfectly continuous record, has the further merit
of requiring but little of the observer's time. But its indications, both of tune and
heights, should be checked by occasional comparisons with the standard clock and
the staff gauge, the readings of which should be noted by hand at appropriate points
of the graphic record.
A newer type of automatic gauge prints the date, the time, and the stage of
the tide every five minutes on a paper tape.
CHAPTER XXI.
OCEAN CURRENTS.
516. An ocean current is a progressive horizontal motion of the water occurring
throughout a region of the ocean, as a result of which all bodies floating therein are
carried with the stream.
The set of a current is the direction toward which it flows, and its drift, the velocity
of the flow.
517. CAUSE. — The principal cause of the superficial ocean currents is the wind.
Every breeze sets in motion, by its friction, the surface particles of the water over
which it blows; this motion of the upper stratum is imparted to the stratum next
beneath, and thus the general movement is communicated, eachlayer of particles acting
upon the one below it, until a current is established. The direction, depth, strength,
and permanence of such a current will depend upon the direction, steadiness, and force
of the wind; all, however, subject to modification on account of extraneous causes,
such as the intervention of land or shoals and the meeting of conflicting currents.
A minor cause in the generation of ocean currents is the difference in density of the
sea water in different regions, as a result of which a set is produced from the more
dense toward the less dense, in the effort to establish equilibrium of pressure; the
difference of density may be due to temperature, the warmer water near the equator
being less dense than the colder water of higher latitudes; or it may be created by a
difference in the amount of contained saline matter, resulting from evaporation,
freezing, or other causes. Another minor factor that may have influence upon ocean
currents is the difference of pressure exerted by the atmosphere upon the water in
different regions. But neither of the last-mentioned causes may be regarded as of
great importance when compared with the influence, direct and indirect, of the wind.
518. SUBMARINE CURRENTS. — In any scientific investigation of the circulation
of ocean waters it is necessary to take account of the submarine currents as well
as those encountered upon the surface; but for the practical purposes of the navigator
the surface currents alone are of interest.
519. METHODS OF DETERMINATION. — The methods of determining the exist
ence of a current, with its set and drift, may be divided into three classes; namely,
(a) by observations from a vessel occupying a stationary position not affected by the
current; (b) by comparison of the position of a vessel under way as given by obser
vation with that given by dead reckoning; and (c) by the drift of objects abandoned
to the current in one locality and reappearing in another.
520. Of these methods the first named, by observations from a vessel at anchor,
is by far the most accurate and reliable, but being possible only under special circum
stances is not often available. The most valuable information about ocean currents
being that which pertains to conditions in the open sea, the great depths there existing
usually preclude the possibility of anchoring a vessel; ships especially fitted for the
purpose have at times, however, carried out current observations with excellent
results; the most notable achievements in this direction are those of the survey of
the Gulf Stream, made by United States naval officers acting under the Coast and
Geodetic Survey, during which the vessel was anchored and observations were made
in positions where the depths reached to upward of 2,000 fathoms.
521. The method of determining current from a comparison of positions obtained
respectively by observation and by dead reckoning is the one upon which our knowl
edge must largely depend. This method is, however, always subject to some inac
curacy, and the results are frequently quite erroneous, for the so-called current is
thus made to embrace not only the real set and drift, but also the errors of observa
tion and dead reckoning. In the case of a modern steamer accurately steered and
equipped with good instruments for determining the speed through the water as well
as the position by astronomical observations, the current may be arrived at by this
method with a fairly close degree of accuracy. It is not always possible, however,
to keep an exact reckoning, and this is especially true in sailing vessels, where the
conditions render it difficult to determine correctly the position by account; this
232
OCEAN CURRENTS. 233
source of error ma^ be combined with faulty instrumental determinations, giving
apparent currents differing widely from those that really exist.
522. Much useful knowledge regarding ocean currents has been derived from
the observed drift of objects from one to another locality. This is true not only of
the bottles thrown overboard from vessels with the particular object of determining
the currents, but also of derelicts, drifting buoys, and pieces of wreckage, which
fulfill a similar mission. The deductions to be drawn from such drift are of a general
nature only. The point of departure, point of arrival, and elapsed time are all that are
positively known. The route followed and the set and drift of current at different points
are not indicated, and in the case of objects floating otherwise than in a completely
submerged condition account must be taken of the fact that the drift is influenced
by the wind. But even this general information is of great value in researches as to
ocean currents, and navigators who desire to aid in the work of investigation may do
so by throwing overboard, from time to time, sealed bottles containing a statement
of date and position at which they are launched.
523. CURRENTS OF THE ATLANTIC OCEAN. — A consideration of the currents of
the Atlantic most conveniently begins with a description of the Equatorial Currents.
The effect of the northeast and southeast trade winds is to form two great drift cur
rents, setting in a westerly direction across the Atlantic from Africa toward the
American continent, whose combined width covers at times upward of fifty degrees
of latitude. These are distinguished as the Northern or Southern Equatorial Currents,
according as they rise from the trade ^inds of the northern or southern hemisphere.
Of the two, the Southern Equatorial Current is the more extensive. It has its
origin off the continent of Africa south of the Guinea coast, and begins its flow with
a daily velocity that averages about 15 miles; it maintains a general set of west, the
portion near the equator acquiring later, however, a northerly component, while the
drift steadily increases until, on arriving off the South American coast, a rate of 60
miles is not uncommon. At Cape San Roque the current bifurcates, the mam or
equatorial branch flowing along the Guiana coast, while the other branch is deflected
to the southward.
The Northern Equatorial Current originates to the northward of the Cape Verde
Islands and sets across the ocean in a direction that averages due west; though
parallel to the corresponding southern drift, its velocity is not so high.
524. Between the Northern and Southern Equatorial Currents is found the
Equatorial Counter Current setting to the eastward under the propelling force of the
southwest monsoon, which prevails over an elongated area of varying extent lying
north of the equator and "stretching westward from the southwestern part of the
salient extension of the continent of Africa. The extent and strength of this current
thus varies with the seasonal extent of the monsoon area, being a maximum in July
and August, when its effect is apparent to the westward of the fiftieth meridian of
west longitude, while at its minimum, in November and December, its influence is
but slight and prevails for only a limited distance from the African coast.
525. To the westward of the region of the Equatorial Counter Current the
North and the South Equatorial Currents unite. A large part of the combined
stream flows into the Caribbean Sea through the various passages between the
Windward Islands, takes up a course first to the westward and then to the northward
and westward, finally arriving off the extremity of the peninsula of Yucatan; from
here some of the water follows the shore line of the Gulf of Mexico, while another
portion passes directly toward the north Cuban coast; by the reuniting of these two
branches in the Straits of Florida there is formed the most remarkable of all ocean
currents — the Gulf Stream.
From that portion of the combined equatorial currents which fails to find
entrance to the Caribbean Sea a current of moderate strength and volume takes its
course along the north coasts of Porto Rico, Haiti, and Cuba, flows between the
last-named island and the Bahamas, and enters the Gulf Stream off the Florida coast,
thus adding its waters to those of the main branch of the Equatorial Current which
have arrived at the same point bv wav of the Caribbean, the Yucatan Passage, and
the Gulf.
526. The Gulf Stream, which has its origin, as has been described, in the Straits
of Florida, and receives an accession from a branch of the Equatorial Current off
the Bahamas, flows in a direction that averages true north as far as the parallel x>f
234 OCEAN CURRENTS.
31°, then curves sharply to ENE. until reaching the latitude of 32°, when a direction
a little to the north of NE. is assumed and maintained as far as Cape Hatteras; at
this point its axis is about 40 miles, while its inner edge is in the neighborhood of 20
miles off the shore. Thus far in its flow the average position of the maximum current
is from 11 to 20 miles outside the 100-fathom curve, disregarding the irregularities
of the latter, and the width of the stream — about 40 miles — is nearly uniform. From
off Hatteras the stream broadens rapidly and curves more to the eastward, seeking
deeper water; its northern limit may be stated to be 60 to 80 miles off Nantucket
Shoals and 120 to 150 miles to the southward of Nova Scotia, in which latter place
it has expanded to a width of about 250 miles. Farther on its identity as the Gulf
Stream is lost, but its general direction is preserved in a current to be described later.
The water of the Gulf Stream is of a deep indigo-blue color, and its junction
with ordinary sea water may be plainly recognized; in moderate weather the edges
of the stream are marked by ripples ; in cool regions the evaporation from its surface,
due to difference of temperature between air and water, is apparent to the eye; the
stream carries with it a quantity of weed known as "gulf weed," which is familiar
to all who have navigated it waters.
In its progress from the tropics to higher latitudes the transit is so rapid that
time is not given for more than a partial cooling of the water, and it is therefore
found that the Gulf Stream is very much warmer than the neighboring waters of the
seas through which it flows. This warm water is, however, divided by bands of
markedly cooler water which extend in a direction parallel to the axis and are usually
found near the edges of the stream of warm water. The most abrupt change from
warm to cold water occurs on the inshore side, where the name of the Cold Wall has
been given to that band which has appeared to some oceanograDhers to form the
northern and western boundary of the stream.
The investigations of Pillsbury tend to prove that the thermometer is only an
approximate guide to the direction and velocity of the current. Though it indicates
the limits of the stream in a general way, it must not be assumed that the greatest
velocity of flow coincides with the highest temperature, nor that the northeasterly
set will be lost when the thermometer shows a region of cold sea water.
The same authority has also demonstrated that in the vicinity of the iand there
is a marked variation in the velocity of current at different hours of the day, which
may amount to upward of 2 knots, and which is due to the elevation and depression
of the sea as a result of tidal influences, the maximum current being encountered at
a period which averages about three hours after the moon's transit. Another effect
noted is that at those times when the moon is near the equator the current presents
a narrow front with very high velocity in the axis of maximum strength, while at
periods of great northerly or southerly decimation the front broadens, the current
decreasing at the axis and increasing at the edges. These tidal effects are not,
however, observed in the open sea.
The velocity of the Gulf Stream varies with the seasons, following the variation
in the intensity of the trade winds, to which it largely owes its origin. The drift of
the current under average conditions may be stated as follows :
Between Key West and Habana: Mean surface velocity in axis of maximum
current, 2\ knots; allowance to be made by a vessel crossing the entire width of the
stream, 1.1 knots per hour.
Off Fo wey Rocks : Mean surface velocity in axis, 3 .5 knots ; allowance in crossing,
2\ knots per hour.
Off Cape Hatteras: Mean surface velocity in axis, upward of 2 knots; allowance
in crossing the stream, 1J knots per hour between the 100-fathom curve and a point
40 miles outside that curve.
527. After passing beyond the longitude of the easternmost portions of North
America, it is generally regarded that the Gulf Stream, as such, ceases to exist; but
by reason of the prevalence of westerly winds the direction of the set toward Europe
is continued until the continental shores are approached, when the current divides,
one branch going to the northeastward and entering the Arctic regions and the other
running off toward the south and east in the direction of the African coast. These
currents have received, respectively, the designations of the Easterly, Northeast, and
Southeast Drift Currents.
. 528. The effect of the currents thus far described is to create a general circula
tion of the surface waters of the North Atlantic, in a direction coinciding with that
OCEAN CURRENTS. 235
of the hands of a watch, about the periphery of a huge ellipse, whose limits of latitude
may be considered as 20° N. and 40° N., and which is bounded in longitude by the
eastern and western continents. The central space thus inclosed, in which no well-
marked currents are observed, and in the waters of which great quantities of the
Sargasso or gulf weed are encountered, is known as the Sargasso Sea.
529. The Southeast Drift Current carries its waters to the northwest coast of
Africa, whence they follow the general trend of the land from Cape Spartel to Cape
Verde. From this point a large part of the current is deflected to the eastward close
along the upper Guinea coast. The stream thus formed, greatly augmented at certain
seasons by the prevailing monsoon and by the waters carried eastward with the
Equatorial Counter Current, is called the G-uima Current. A remarkable character
istic of this current is the fact that its southern limit is only slightly removed from
the northern edge of the west-moving Equatorial Current, the effect being that the
two currents flow side by side in close proximity, but in diametrically opposite
directions.
530. The Arctic or Labrador Current sets out of Davis Strait, flows southward
down the coasts of Labrador and Newfoundland, and thence southwestward past
Nova Scotia and the coast of the United States, being found inshore of the Gulf
Stream. It brings with it the ice so frequently met at certain seasons off New
foundland.
531. Eennells Current was formerly represented as a temporary but extensive
stream setting at tunes from the Bay of Biscay toward the west and northwest across
the English Channel and to the westward of Cape Clear. The most recent investiga
tions fail to reveal such a feature, but disclose only a narrow current of reaction
moving northward along the coast of France when the winds have forced the waters
above the usual level at the head of the Gulf of Gascoyne.
532. Of the two branches of the Southern Equatorial Current which are formed
by its bifurcation off Cape San Roque, the northern one, setting along the coasts of
northeastern Brazil and of Guiana and contributing to the formation of the Gulf
Stream, has already been described; the other, known as the Brazil Current, flows to
south and west, along the southeastern coast of Brazil, as far as the neighborhood
of the island of Trinidad; here it divides, one part continuing down the coast and
having some slight influence as far as the latitude of 45° S., and the other curving
around toward east.
533. The last-mentioned branch of the Brazil Current is called the Southern
Connecting Current and flows toward the African coast in about the latitude of Tristan
da Cunha. It then joins its waters with those of the general northerly current that
sets out of the Antarctic region, forming a current which flows to the northward along
the southwest African coast and eventually connects with the Southern Equatorial
Current, thus completing the surface circulation of the South Atlantic.
534. There is another current whose effects are felt in the Atlantic. It originates
in the Pacific and flows around Cape Horn, and will be described in connection with
the currents of the Pacific Ocean.
535. CURRENTS OF THE PACIFIC OCEAN. — As in the Atlantic, the waters of the
Pacific Ocean, in the region between the tropics, have a general drift toward the
westward, due to the effect of the trade winds, the currents produced in the two
hemispheres being denominated, respectively, the Northern and the Southern Equa
torial Currents. These are separated, as also in the case of the Atlantic, by an east-
setting stream, about 300 miles wide, whose mean position is a few degrees north of
the equator, and which receives the name of the Equatorial Counter Current.
536. The major portion of the Northern Equatorial Current, after having
passed the Marianas, nows toward the eastern coast of Taiwan in a WNW. direc
tion, whence it- is deflected northward, forming a current which is sometimes
called the Japan Stream, but which more frequently receives its Japanese name of
Kuroshiwo, or "black stream." This current, the waters of which are dark in color
and contain a variety of seaweed similar to "gulf weed/7 carries the warm tropical
water at a rapid rate to the northward and eastward along the coasts of Asia^and its
offlying islands, presenting many analogies to the Gulf Stream of the Atlantic.
The limits and volume of the Kuroshiwo vary according to the monsoon, being
augmented during the season of southwesterly winds and diminished during the prev
alence of those from northeast. The current sets to the north along the east coast
of Taiwan (Formosa), and in about latitude 26° N. changes its course to northeast,
236 OCEAN CURRENTS.
arriving at the extreme southwestern point of Japan by a route to westward of the
Sakishima and Nansei Shoto. A branch makes off from the main stream to fol
low northward along the west coast of Japan, entering the Sea of Japan by the Tsu
shima Kaikyo; but the principal current bends toward the east, flows through
Osumi Kaikyo and the passages between the Tokara Gun to, and runs parallel to the
general trend of the south shores of the Japanese islands of Kiushu, Shikoku, and
Honshu, attaining its greatest velocity between Bungo Suido and Kii Suido, where
its average drift is between 2 and 3 knots per hour. Continuing beyond the south
eastern extremity of Honshu, the direction of the stream becomes somewhat more
northerly, and its width increases, with consequent loss of velocity. In the Kuro-
shiwo, as in the Gulf Stream, the temperature of the sea water is an approximate,
though not an exact, guide as to the existence of the current.
537. Near 146° or 147° E. and north of the fortieth parallel the Kuroshiwo
divides into two parts. One of these, called the Kamchatka Current, flows to the
northeast in the direction of the Aleutian Islands, and its influence is felt to a high
latitude. The second branch continues as the main stream, and maintains a general
easterly direction to the 180th meridian, where it is merged into the north and north
east drift currents which are generally encountered in this region.
538. A cold countercurrent to the Kamchatka Current sets out of Bering Sea
and flows to the south and west clpse to the shores of the Kuril Islands, Hokushu
and Honshu, sometimes, like the Labrador Current in the Atlantic, bringing with it
quantities of Arctic ice. This is often called by its Japanese name of Oyashiwo.
539. On the Pacific coast of North America, from about 50° N. to the mouth
of the Gulf of California, 23° N., a cold current, 200 or 300 miles wide, flows with a
mean speed of three-quarters of a knot, being generally stronger near the land than
at sea. It follows the trend of the land (nearly SSE.) as far as Point Concepcion
(south of Monterey), when it begins to bend toward SSW., and then to WSW., off
Capes San Bias and San Lucas, ultimately joining the great northern equatorial drift.
On the coast of Mexico, from Cape Corrientes (20° N.) to Cape Blanco (Gulf of
Nicoya), there are alternate currents extending over a space of more than 300 miles
in width, which appear to be produced by the prevailing winds. During the dry
season — January, February, and March — the currents generally set toward south
east; during the rainy season — from May to October — especially in July, August,
and September, the currents set to northwest, particularly from Cosas Island and
the Gulf of Nicoya to the parallel of 15°.
540. The Southern Equatorial Current prevails between limits of latitude that
may be approximately given as 4° N. and 10° S., in a broad region extending from
the American continent almost to the one hundred and eightieth meridian, setting
always to the west and with slowly increasing velocity. In the neighborhood of the
Fiji Islands this current divides; one part, known as the Rossel Current, continues
to the westward, following a route marked by the various passages between the
islands, and later acquiring a northerly component and setting through Torres
Strait and along the north coast of New Guinea; the other part, called the Australia,
Current, sets toward south and west, arriving off the east coast of Australia, along
which it flows southward to about latitude 35° S., whence it bends toward southeast
and east and is soon after lost in the currents due to the prevailing wind.
541. The general drift current that sets to the north out of the Antarctic
regions is deflected until, upon gaining the regions to the southwest of Patagonia, it
has acquired a nearly easterly set; in striking the shores of the South American
continent it is divided into two branches.
The first, known as the Cape Horn Current, maintains the general easterly
direction, and its influence is felt, where not modified by winds and tidal currents,
throughout the vicinity of Cape Horn, and, in the Atlantic Ocean, off the Falkland
Islands and eastern Patagonia.
The second branch flows northeast in the direction of Valdivia and Valparaiso,
follows generally the direction of the coast lines of Chile and Peru (though at times
setting directly toward the shore in such manner as to constitute a great danger to
the navigator), and forms the important current which has been* called variously
the Peruvian, Chilean, or Ilumloldt Current, the last name having been given for the
distinguished scientist who first noted its existence. The principal characteristic of
OCEAN CURRENTS. 237
the Peruvian Current is its relatively low temperature. The direction of the waters
between Pisco and Payta is between north and northwest; near Cape Blanco the
current leaves the coast of America and bears toward the Galapagos Islands, passing
them on both the northern and southern sides; here it sets toward WXW. and west;
beyond the meridian of the Galapagos it widens rapidly, and the current is lost in
the equatorial current, near 108° W. As often happens in similar cases, the existence
of a countercurrent has been proved on different occasions; this sets toward the
south, is very irregular, and extends only a little distance from shore.
54:2. CURRENTS OF THE INDIAN OCEAX. — In this ocean the currents to the
north of the equator are very irregular; the periodical winds, the alternating breezes,
and the changes of monsoon produce currents of a variable nature, their direction
depending upon that of the wind which produces them, upon the form of neighboring
coasts, or, at times, upon causes which can not be satisfactorily explained.
543. There is, in the Indian Ocean south of the equator, a regular Equatorial
Current which, by reason of owing its source to the southeast trade winds, corresponds
with the Southern Equatorial Currents of the Atlantic and Pacific. The limits of
this west-moving current vary with the longitude as well as with the season. Upon
reaching about the meridian of Rodriguez Island, a branch makes off toward the
south and west, flowing past Mauritius, then to the south of Madagascar (on the
meridian of which it is 480 miles broad), and thereafter, rapidly diminishing its
breadth, forming part of the Agulhas Current a little to the south of Port Natal.
The main equatorial current continues westward until passing the north end of
Madagascar, where, encountering the obstruction presented by the African con
tinent, it divides, one branch following the coast in a northerly, the other in a southerly
direction. The former, in the season of the southwest monsoon, is merged into the
general easterly and northeasterly drift that prevails throughout the ocean from the
northern limit of the Equatorial Current on the south, as far as India and the adjacent
Asiatic shores on the north; but during the northeast monsoon, when there exists in
the northern regions of the Indian Ocean a westerly drift current analogous to the
Northern Equatorial Currents produced in the Atlantic and Pacific by the northeast
trades, there is formed an e^st-setting Equatorial Counter current, which occupies a
narrow area near the equator and is made up of the waters accumulated at the
western continental boundary of the ocean by the drift currents of both hemispheres.
544:. The southern branch of the Equatorial Current flows to the south and west
down the Mozambique Channel, and, being joined in the neighborhood of Port Natal
by the stream which arrives from the open ocean, there is formed the warm Agulhas
Current, which possesses many of the characteristics of the Gulf and Japan streams.
This current skirts the east coast of South Africa and attains considerable velocity
over that part between Port Natal and Algoa Bay. During the summer months its
effects are felt farther to the westward; during the winter it diminishes in force and
extent. The meeting of the Agulhas Current with the cold water of higher latitudes
is frequently denoted by a broken and confused sea.
Upon arriving at the southern side of the Agulhas Bank the major part of the
current is deflected to the south, and then curves toward east, flowing back into the
Indian Ocean with diminished strength and temperature on about the fortieth
parallel of south latitude, where its influence is felt as far as the eightieth meridian.
A small part of the stream which reaches Agulhas Bank continues across the southern
edge of that bank before turning to the southward and eastward to rejoin the
major part.
545. Along the fortieth parallel of south latitude, between Africa and Australia,
there is a general easterly set, due to the branch of the Agulhas Current already
described, to the continuation of the drift current from the Atlantic which passes to
southward of the Cape of Good Hope, and to the westerly winds which largely prevail
in this region. At Cape Leeuwin, the southwestern extremity of Australia, this
east-setting current is divided into two branches; one, going north along the west
coast of Australia, blends with the Equatorial Current nearly in the latitude of the
Tropic of Capricorn; the other preserves the direction of the original current and
has the effect of producing an easterly set along the south coast of Australia.
54:6. As in the other oceans, a general northerly current is observed to set into
the Indian Ocean from the Antarctic regions.
CHAPTER XXII.
IOE AND ITS MOVEMENT IN THE NOETH ATLANTIC OCEAN.
547. Vessels crossing the Atlantic Ocean between Europe and the ports of the
United States and British America are liable to encounter icebergs or extensive
fields of compact ice, which are carried southward from the Arctic region by the
ocean currents. It is in the vicinity of the Great Bank of Newfoundland that these
APRIL
Limiting lines of the regions
in which icebergs and field ice
have been reported by mariners
in the month of April for the
years 1904 to 1913, inclusive.
masses of ice appear in the greatest numbers and drift farthest southward. The
accompanying charts show the changeable area in which icebergs and field ice have
been reported by mariners in the years 1904 to 1913 in the months of April, May,
and June, when they occur in the greatest number.
238
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 239
. The amount of ice and its location and movement are so variable from year to
year, while the region occupied in its formation and transportation is so vast and
so little under special observation, that no successful system of prediction has as yet
been instituted. The most that can be said now is that after an exceptionally open
winter in the Arctic we may expect the ice to come south earlier and in greater quan
tity. After such a winter the East Greenland current starts the ice stream around
Cape Farewell from one to three months earlier, and this advancing of the season is
reflected by a corresponding advance in the Labrador Current and on the Newfound
land Bank. The greatest calving at the glaciers of Greenland follows the breaking
up of the shore ice, and hence the bergs also start southward earlier and with more
freedom after an open winter.
In April, May, and June, from 1904 to 1913, inclusive, icebergs have been seen
as far south as latitude 37° 50' north and as far east as longitude 38° west. Excep
tional drifts have occurred almost down to latitude 30° north, and between longi
tudes 10° and 75° west, in these months as well as during other seasons of the year.
Between Newfoundland and the fortieth parallel floating ice may be met in any
month, but not often from August to December. On the Great Bank of New
foundland bergs generally move southward. Those that drift westward of Cape
Race usually pass between Green and St. Pierre banks. The Virgin Rocks are
generally surrounded by ice until the middle of April or the beginning of May.
548. THE ORIGIN OF THE ICEBERGS. — -Most of the bergs which annually appear
in the North Atlantic originate on the western coast of Greenland; a few come from
the east coast and from Hudson Bay. A small but productive glacier in southern
Greenland yields the bluish bergs which are so hard to see at night. The largest
bergs come from the glaciers at Umaiiak Fjord and Disko Bay (Lat. 69° to 71°), and
their height above water will rise to 500 feet; but as they lose in mass from that time
forward, we can not expect to find them of such gigantic height when they finally
appear near the Newfoundland Bank.
A huge ice sheet, formed from compressed snow, covers the whole of the interior of
Greenland. The surface of this enormous glacier, only occasionally interrupted by
protruding mountain tops, rises slightly toward the interior and forms a watershed
between the east and west coasts, which is estimated to be from 8,000 to 10,000 feet
above the sea. The outskirts of Greenland, as they are called, consist of a fringe
of islands, mountains, and promontories surrounding the vast ice-covered central
portion and varying in width from a mere border up to 80 miles. Upon the west
side, below the parallel of 73° of latitude, it has an average width of about 50 miles
and extends with little interruption from Cape Farewell to Melville Bay, a distance
of something over 1,000 miles.
Everywhere this mountainous belt is penetrated by deep fiords, which reach
to the inland ice, and are terminated by the perpendicular fronts of huge glaciers,
while in some places the ice comes down in broad projections close to the margin of
the sea. All of these glaciers are making their way toward the sea, and, as their
ends are forced out into the water, they are broken off and set adrift as bergs. This
process is called calving. The size of the pieces set adrift varies greatly, but a berg
irom 60 to 100 feet to the top of its walls, whose spires or pinnacles may reach from
200 to 250 feet in height and whose length may be from 300 to 500 yards, is considered
to be of ordinary size in the Arctic. These measurements apply to the part above
water, which is about one-eighth or one-ninth of the whole mass. Many authors-
give the depth under water as being from eight to nine times the height above; this
is incorrect, as measurements above and below water should be referred to mass and
not to height.
Bergs are being formed all the year round, but in greater numbers during the
summer season; and thousands are set adrift each year.
Once adrift in the Arctic they find their way into the Labrador Current and
begin their journey to the southward. It is not an unobstructed drift, but one
attended with many stoppages and mishaps. Many ground in the Arctic Basin and
break up there: others reach the shores of Labrador, where from one end to the
other they continually ground and float; some break up and disappear entirely,
while others get safely past and reach the Grand Bank. The whole coast of Labrador
is cut up by numerous islands, bays, and headlands, shoals and reefs, which makes the
240
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
journey of all drift a long one, and adds greatly to the destruction of the bergs by stop-
Eages and by causing them to break up. Disintegration is also hastened by their
reaking away from the floe ice, for detached bergs will melt and break up rapidly
even in high latitudes during the summer.
549. THE ICE-BEARING CURRENTS. — The Labrador Current passes to the
southward along the coasts of Baffin Land and Labrador, and, although it occasionally
ceases altogether, its usual rate is from 10 to 36 miles per day. Near the coast it is
very much influenced by the winds, and reaches its maximum rate after those from
MAY
Limiting lines of the regions
in which icebergs and field ice
have been reported by mariners
in the month of May for the
years 1904 to 1913. inclusive.
FIG. 79.
the northward. The general drift of the current is to the southward, as shown by
the passage of many icebergs, although occasions have arisen on which these have
been observed to travel northward without any apparent reason. The breadth and
depth of the current are not known, but it is certain that it pours into the Atlantic
enormous masses of water for which compensation is derived from the warm waters
of the Atlantic and from the East Greenland Current that flows around Cape Farewell.
The flow of the Polar Current down the east coast of Greenland has been abundantly
demonstrated by the drift of vessels that have been beset in the ice pack to the east
ward of Greenland. This current turns around Cape Farewell, with an ice stream
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 241
60 miles wide, and then takes a northwesterly direction along the Greenland coast
as far as the Arctic Circle, where it meets the southerly current from Baffin Bay.
550. DRIFT AND CHARACTERISTICS OF ICEBERGS. — Xot all the bergs made in
any one season find their way south during the following one, for only a small per
centage of them ever reach trans-Atlantic routes. So many delays attend tneir
journey and so irregular and erratic is it that many bergs seen in any one season
may have been made several seasons before. If bergs on their calving at once drifted
to the southward and met with no obstructions their journey of about 1,200 to 1,500
miles would occupy from 4 to 5 months, reckoning tne drift of the Labrador Current
at 10 miles a day, which may be making it too little. Then, if bergs were liberated
principally in July and August they should reach trans-Atlantic routes in December
and January, while we know this to be the rare exception. It is then seen what an
important bearing the shores of Labrador have in arresting their flow, when it is
known that bergs are generally most plentiful in the late spring and early summer
months off the Bank.
It should not be supposed that all bergs follow the same course when set adrift
from their parent glaciers, for, like floating bodies at the head of a river, some will
go direct to the mouth, others will go but a short distance and lodge, others still will
accomplish hah* the journey and remain until another freshet again floats them, so
that in the end the debris will be composed in part of that of several years' production.
Bergs, when first liberated on the west Greenland shore, are out of the strongest
sweep of the southerly current, and they may take some months to find their way
out of Davis Strait, while again others may at once drift into the current and move
unobstructed until dissipated in the Gun Stream. The difference in time of two
bergs reaching a low latitude, which were set adrift the same day, may cover a period
of one or two years.
Field ice also offers an obstruction to bergs, and a close season in the Arctic
may prevent their liberation to a great extent, though, from their deep submersion,
they act as ice plows and aid materially in breaking up the vast fields of ice which
so often close the Arctic Basin.
Ice fields are more affected by wind than bergs. Bergs owe their drift almost
entirely to current, so that they will often be noticed forcing their way through
immense fields of heavy ice and going directly to windward. Advantage is taken of
this by vessels in ice fields, which often moor to bergs and are towed for miles through
ice in which they could not otherwise make any headway. This is accomplished by
sinking an ice anchor into them and using a strong towline, and as the berg advances
open water is left to leeward while the loose ice floats past on both sides. For the
same reason vessels, when beset by field ice, run from the lee of one berg to that of
another, as leads may offer themselves.
Instances are not rare where icebergs were seen to drift toward north, making
15 to 24 miles a day, near the tail of the Bank and to the eastward of Cape Race.
All ice is brittle, especially that in bergs, and it is wonderful how little it takes
to accomplish then" destruction. A blow of an ax will at times split them, and the
report of a gun, by concussion, will accomplish the same end. They are more apt
to break up in warm weather than cold, and whalers and sealers note this before
landing on them, when an anchor is to be planted or fresh water to be obtained. On
the coast of Labrador in July and August, when it is packed with bergs, the noise of
rupture is often deafening, and those experienced in ice give them a wide berth.
When they are frozen the temperature is very low, so that when their surface
is exposed to a thawing temperature the tension of the exterior and interior is very
different, making them not unlike a Prince Rupert's drop. Then, too, during the
day water made by melting finds its way into the crevices, freezes, and hence expands,
and, acting like a wedge, forces the berg into fragments. It is the greatly increased
surface which the fragments expose to the melting action of the oceanic waters that
accounts for the rapid disappearance of the ice after it has reached the northern
edge of the warm circulatory drift currents of the North Atlantic Ocean. If these
processes of disintegration did not go on and large bergs should remain intact, several
years might elapse before they would melt, and thev would ever be present in the
transoceanic routes. In fact, instances are on record in which masses of ice, escaping
the influences of swift destruction or possessing a capability for resisting them, have,
61828°— 16^ 16
242
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
by phenomenal drifts, passed into European waters and been encountered from time
to time throughout that portion of the ocean which stretches from the British Isles
to the Azores.
Icebergs assume the greatest variety of shapes, from those approximating to
some regular geometric figure to others crowned with spires, domes, minarets, and
peaks, while others still are pierced by deep indentations or caves. Small cataracts
fall from the large bergs, while from many icicles hang in clusters from every pro-
JUNE
Limiting lines of the regions
in which icebergs and field ice
have been reported by mariners
in the month of June for the
years 1904 to 1913, inclusive.
FIG 80.
jecting ledge. They frequently have outlying spurs under water, which are as
dangerous as any other sunken reefs. For this reason it is advisable for vessels to
give them a wide berth, for there are cases on record where vessels were seriously
damaged by striking when apparently clear of the berg. Among these is that of the
British steamship Nessmore, which ran into a berg in latitude 41° 50' N., longitude
52° W., and stove in her bows. On docking her a long score was found extending
from abreast her forerigging all of the way aft, just above her keel. Four frames were
ICE AND ITS MOVEMENT IN THE NOETH ATLANTIC OCEAN. 243
broken and the plates were almost cut through. The ship evidently struck a pro
jecting spur after her helm had been put over, as there was clear water between her
and the berg after the first collision.
It is generally best to go to windward of an iceberg, because the disintegrated
fragments will have a tendency to drift to leeward while open water will be found to
windward. Serious injury has occurred to vessels through the breaking up or cap
sizing of icebergs. Often the bergs are so nicely balanced that the slightest melting
of their surfaces causes a shifting of the center of gravity and a consequent turning
over of the mass into a new position, and this overturning also frequently takes
place when bergs, drifting with the current in a state of delicate equilibrium, touch
the ocean bottom.
551. FIELD ICE. — Field ice is formed throughout the region from the Arctic
Ocean to the shores of Newfoundland and yearly leaves the shore to find its way
into the path of commerce. Starting with the Arctic field ice and conning to the
southward, we find this ice growing lighter, both in thickness and in quantity, until
it disappears entirely. Ice made in the Arctic is heavier and has lived through a
number of seasons. After the short summer in high latitudes ice begins to form on
all open water, increasing several feet in thickness each season. Much of this remains
north during the following summer, and, though it melts to some extent, it never
entirely disappears, so that each succeeding winter adds to its thickness.
This continues from year to year until it reaches 12 or 15 feet in thickness, often
more. If it remained perfectly quiet it would be of uniform thickness, increasing
with the latitude, but it is in a state of almost continual motion, often a very violent
one, which causes it to raft and pile until it becomes full of hummocks and other
irregularities. Immense fields are detached from the shore and from other fields,
and under the influence of winds, currents, and tides are set in motion and kept
continually drifting from place to place; after a snow, thaw, or piling the whole
becomes cemented together into solid pieces, when under the influence of a low
temperature. The space of open water between the fields becomes frozen, joining
smaller fields, and making a solid pack which will remain so until the elements again
break it to pieces. Along the shores from headland to headland the bays and inlets
often remain solid for years, almost invariably through the Arctic winter, but in
Baffin Bay and Davis Strait open water can be found at intervals all the year round.
Ice becomes rafted in a variety of ways. If two fields are adrift the one to
windward will drift down on the one to leeward; the one which is rougher on its
surface gives the wind a better hold and drifts the faster; fields may be impelled
towards each other by winds from contrary directions. Ice that is secure to the
shore is rafted on its seaward edge from contact with that which is adrift. Fields
in drifting often have a turning motion, which is caused by contrary currents, or one
variable in strength at different places, or by the friction of a field coming in contact
with another field afloat or one attached to the shore. This rotary motion is especially
dangerous when a vessel finds itself between two fields. A heavy gale will break up
the strongest fields at times and cause them to raft and form hummocks.
Small fragments of bergs find themselves mingled with Arctic fields and become
frozen fast. These, when liberated to the southward, are called growlers, and form
low, dark, indigo colored masses, which are just awash and rounded on top like a
whale's back. They are very dangerous when in ice fields which have become loose
enough to permit the passage of vessels through them, and should always be looked
for; they can be seen apparently rising and sinking as the sea breaks over them.
During the spring and summer months the bergs, aided by a rise of temperature,
so cut up and weaken the ice fields that much ice is loosened and begins drifting out
of the Arctic basin. This is joined by that brought from the waters of Spitsbergen by
the East Greenland Current, near the sixty-third parallel, whence it flows down the
eastern coast of North America, reaching Cape Chidley about October ^or November.
By this time the remaining ice in the Arctic is being cemented into solid fields, while
the ice cap is being daily extended to the southward. As fast as fields are detached
the open water freezes, and these masses are forced to the southward and can not
rejoin the solid pack. With a westerly wind ice formed in Hudson Strait and adjacent
waters is swept out and joins the Arctic ice, differing from it only in being a little
lighter.
244 ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
Ice begins to form at Cape Chidley about the middle of October, at Belle Isle
about November 1, and by the middle of November or 1st of December, the whole
coast is solidly frozen. The dates given are approximate and vary from year to
year, with many marked exceptions.
The string of ice along the coast of Labrador extends from headland to head
land, including the outlying islands, and starting from the heads of the bays works
its way out to seaward, forming by the middle of December an impassable barrier
to the shore which will probably not be permanently broken until the latter part of
April. This ice varies in thickness from 12 feet at the northern extreme to 3 or 4
feet at the southern. During the entire winter the Arctic drift is finding its way
down the coast, and is being continually reinforced by fields broken from the Labrador
ice. These continue to the southward in the Labrador Current on an average of
about 10 miles a day, reaching Belle Isle between the middle of January and the
middle of February.
The best example on record of a continued drift from the Arctic is that of Cap
tain Tyson. On October 14, 1871, he and a party of nineteen others were separated
from the United States surveying ship Polaris^ in latitude 77° or 78° N., just south of
Littleton Island, and, being unable to regain the ship, remained on the floe and
accomplished one of the most wonderful journeys. After a drift of over 1,500 miles,
fraught with danger from beginning to end, they were picked up about six months
later, April 30, 1872, by the Tigress, a sealing steamer from Newfoundland, near the
Strait of Belleisle, in latitude 53° 35' N., and carried safely into port.
Much delay in the southward movement of the drift will be caused by winds
from the southward of west, as field ice is affected more by wind than current.
The prevailing wind and weather will influence the drift very greatly. Strong
northerly or northwest winds will increase its speed, but contrary winds will hold it
back. The string of shore ice keeps the northern ice off the coast and in the current,
At times westerly winds will also send the Labrador ice off the coast and leave it
entirely clear, but this does not happen often. Still the outer Labrador ice is con
stantly being added to the Arctic flow. Frequently the bays remain frozen over
until June; again, they are cleared some years in April, making a large variation.
During the drift the wind from northwest to southwest will clear the ice off the
coast and leave a line of open water, but the ice will be set on the coast by a northeast
wind and be rafted and piled. The appearance of the ice when it reaches Belle Isle
and to the southward would be a fair indication of the weather it had encountered
on its way down. The rougher the ice the more severe the weather. This floating
ice string extends approximately 200 miles offshore in the latitude of Cape Harrison,
and spreads more during its drift, though narrower farther north. One small stream
finds its way through the Strait of Belleisle, while the greater part continues toward
the northern limit of the Gulf Stream. By the middle of January the shores of
Newfoundland and Gulf of St. Lawrence are full of ice, which has been frozen there
and are opened or closed by a favorable or adverse wind. Navigation in the River
St. Lawrence is closed about the middle of November and does not open until about
May. A wind from northwest to southwest will clear the eastern coast of Newfound
land, while the Gulf of St. Lawrence may remain full of ice until the 1st of May.
Even after this date much ice is found in the Gulf until July, and by August or earlier
the field ice is replaced in the Strait of Belleisle by bergs.
In the bight from Cape Bauld to Fogo Island a string of ice is often found joining
these points, hemming in the shore for weeks at a time.
With each northwest or westerly wind the ice is cleared off the Newfoundland
coast, except from some of the deeper bays, and carried out to sea, and frequently
before the Arctic and Labrador ice has passed Belle Isle the Newfoundland ice has
found its way as far south as latitude 45°. In the same way the Labrador ice some
times precedes the Arctic ice, while all may arrive at nearly the same time. Ice
fields of ten lose their identity , as coming from any one particular place, by the constant
intermingling on its southern journey with ice made in a lower latitude.
With easterly winds the field ice and icebergs may block the harbors on the
east coast of Newfoundland until June or even July, but these harbors are usually
open in May.
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 245
Ice leaving the gulf and river St. Lawrence flows southward through Cabot Strait.
This strait is never frozen over completely, but vessels not specially built to encounter
ice can not navigate it safely between the beginning of January and the last of April on
account of the heavy drift ice which blocks the passage. Nearly every spring, from
about the middle of April to the middle of May, a great rush of ice out of the Gulf
of St. Lawrence causes a block between St. Paul Island and Cape Ray. This block,
which sometimes lasts for three or four weeks, and completely prevents the passage
of ships, is known as the bridge. It is recorded that 300 vessels have at one time been
detained by this obstacle.
The ice usually passes out of Cabot Strait in the direction of Banquereau Bank,
with its eastern edge extending halfway between Scatari and St. Pierre Islands.
Its path broadens after it is through the strait and is principally governed by the
winds, but, under the influence of the current alone, it drifts southwest-ward, and in
latitude 45° may be from 10 to 75 miles in width. Much of this ice is very heavy
and prevents the passage through it of all vessels that are not specially built to encoun
ter ice.
Ice fields assume a variety of shapes, depending upon the influence of winds
and currents, and upon their shape on being set adrift. Those loosened in the
Arctic meet with so many vicissitudes that they have entirely lost their original
form when a low latitude is reached, while those from Newfoundland may remain
approximately intact. Their extent is governed by the same rules and varies from
a few scattered pieces to several hundred miles in length.
From off Belle Isle the field ice finds its way south toward the Gulf Stream,
where no definite shape can be given it. In appearance, if heavy ice, it will be white,
covered with snow, and visible at a long distance; even in foggy weather it can often
be seen for some distance. It is full of hummocks and its surface is very uneven;
blocks have been piled upon each other, others stood on end, and the whole mass will
form an impenetrable field, through which vessels can not force their way.
If the ice is lighter the pans will be smoother and more even, the angles ground
down by friction and turned up at the edges like so many large pond lilies. If com
pact, no water is seen; if loose, wide leads may extend through the whole, or a little
water be seen surrounding each cake.
The appearance must decide whether a vessel is warranted in trying to force
her way through. In a smooth sea, where doubt exists, should a vessel go dead slow
into the mass, there will be but little danger in attempting it, and if too heavy she
can haul out. Often the weather edge is the heaviest from being rafted, when to
leeward it may be scattering. An ice field will often form a good lee for riding out a
gale of wind, as it will break the force of the sea. But care is necessary not to lie
too close, for the pans are often given such a force that they will stave in the bows
of the strongest vessel.
A high temperature will soften field ice and make it very rotten, so that the
slightest motion will cause it to fall to pieces. On reaching the waters of the Gulf
Stream or a warmer atmospheric temperature it begins to melt, gets soft and spongy,
and left in a calm will disappear slowly. But, fortunately, there is seldom a time
when there is not a swell on the sea, and this soon breaks the pans into small pieces,
thus bringing a greater surface in contact with the melting agency. A heavy gale
will in a few hours sometimes cause the destruction of a large field by fracture, friction,
and continued motion, just as a calm cold night may unite it in a solid mass. Bergs
plow their way through fields, break them up, and scatter the pieces, as in the Arctic.
Snow preserves them and often gives the pans the appearance of standing well out
of water, and is misleading in this particular. By melting and afterwarcLs freezing
it adds to the thickness of the ice.
552. THE DISAPPEARANCE OF THE ICE. — The advancing ice will have reached,
in the month of April, the northern average limit of the Gulf Stream; and, having
spread itself along this line both east and west of the fiftieth meridian, it enters the
final stage of disintegration and rapid disappearance.
^ After reaching this limit of southward movement, many bergs, on account of
their deep immersion, find their way to the westward, even within the current of the
Gulf Stream, while field ice never follows this course, a condition that is accounted
246
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
for by the fact that the Labrador current here runs under the Gulf Stream, which
spreads itself out on the surface as an eastward-moving current, consisting of streaks
of warm water with colder water between.
The locality in which ice of all kinds is most apt to be found during the months
of April, May, and June lies between latitude 42° and 45° and longitude 47° and 52°
west of Greenwich. Here the Gulf Stream and the Labrador Current meet, and the
movement of the ice is influenced sometimes by the one and sometimes by the other
of these currents.
Stf
General enveloping lines of
the region of icebergs and field
ice, 1904-1913.
FlO. 81.
Besides the three charts of monthly limits for Amil, May, and June, a fourth
chart is presented showing the general limits within which icebergs and field ice hare
been encountered during the same months.
553. SIGNS OF THE PROXIMITY OF ICE.— The proximity of ice is indicated by
the following-described signs :
Before field ice is seen from deck the ice blink will often indicate its presence.
On a clear day over an ice field on the horizon the sky will be much paler or lighter
in color and is easily distinguished from that overhead, so that a sharp lookout should
be kept and changes in the color of the sky noted.
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 247
On a clear day icebergs can be seen at a long distance, owing to their brightness ;
during foggy weather they are first seen through the fog as a black object. In thick
fog the first sight of a berg is apt to be a narrow streak of dark at the water line.
They can sometimes be detected by the echo from the steam whistle or the
fog horn. In that case, by noting the time between the blast of a whistle and the
reflected sound, the distance of tne berg in feet may be approximately found by
multiplying by 550. The absence of echo is by no means proof that no bergs are
near, for unless there is a fairly vertical wall, no return of the sound waves can be
expected.
The presence of icebergs is often made known by the noise of their breaking up
and f ailing to pieces. The cracking of the ice or tne falling of pieces into the sea
makes a noise like breakers or a distant discharge of guns, which may often be heard
a short distance.
The absence of swell or wave motion in a fresh breeze is a sign that there is land
or ice on the weather side.
The appearance of herds of seal or flocks of murre far from land is an indication
of the proximity of ice.
The temperature of the air falls as ice is approached, especially on the leeward
side, but generally only at an inconsiderable distance from it. The fall of the tem
perature of the sea water has been held to indicate the nearness of ice, but in regions
where there is an intermixture of cold and warm currents going on, as at the junction
of the Labrador Current and the Gulf Stream, the temperature of the sea has been
known to rise as the ice is approached. The special temperature studies made during
the ice patrol of 1912 have not settled the question whether icebergs influence the
temperature of sea water to a measurable extent at distances of a mile or so.
A reliable sign of icebergs being near is the presence of calf ice. When such
pieces occur in a curved line, as they may do, especially in calm weather, the parent
berg is on the concave side of the curve.
No ship captain can afford to trust any of the above-named signs to the exclusion
of a good lookout.
CURRENT INFORMATION REGARDING ICE CONDITIONS.— The branch hydrographic
offices receive daily the latest information regarding ice and other obstructions to
navigation, being furnished with the reports of passing vessels and the ice-patrol
ships, as long as such are in service. They also distribute the publications of the
Hydrographic Office dealing with this topic, namely, the Hydrographic Bulletin
(weekly) and the Pilot Chart (monthly), as well as the pamphlet on North Atlantic
Ice Patrols (Reprint No. 24).
APPENDIX I.
EXTBACTS FEOM THE AMERICAN NAUTICAL ALMANAC, FOE THE
YEAE 1916, WHICH HAVE EEFEEENCE TO THE EXAMPLES FOE
THAT TEAE GIVEN IN THIS WOEK.
G. M. T.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Time.
0 ,
m s
0
m s
0
m s
0 ,
m s
SUN, JANUARY, 1916.
Thursday 20.
Monday 24.
Friday 28.
0
-20 20. 8
-10 51. 7
-19 27.4
-11 58. 7
-18 28.2
-12 53. 5
2
20 19. 7
10 53. 2
19 26. 2
12 0.0
18 26. 9
12 54. 5
4
6
20 18. 7
20 17. 6
10 54. 7
10 56. 2
19 25. 0
19 23. 9
12 1.2
12 2.5
18 25. 6
18 24. 3
12 55. 5
12 56. 5
SEMIDIAMETER.
8
20 16. 5
10 57. 7
19 22. 7
12 3.7
18 23. 0
12 57. 4
10
20 15. 5
10 59. 2
19 21. 5
12 5.0
18 21. 7
12 58. 4
/
12
20 14. 4
11 0.7
19 20. 3
12 6.2
18 20. 4
12 59. 4
Jan. 1
16.30
14
20 13. 3
11 2.2
19 19. 1
12 7.4
18 19. 1
13 0.4
11
16.30
21
16.28
16
20 12. 3
11 3.7
19 17.9
12 8.7
18 17. 8
13 1.3
31
16.26
18
20 11. 2
11 5.2
19 16. 7
12 9.9
18 16. 5
13 2.3
20
20 10. 1
11 6.6
19 15. 5
12 11. 1
18 15. 1
13 3.3
22
-20 9. 1
-11 8. 1
-19 14. 3
-12 12.4
-18 13. 8
-13 4. 2
H. D.
0.5
0.7
0.6
0.6
0.7
0.5
SUN, APRIL, 1916.
Sunday 2.
Sunday 16.
Friday 21.
Tuesday 25.
0
+ 4 54. 5
- 3 41. 0
+10 6. 3
+ 0 9.4
+11 50. 5
+ 1 17. 2
+13 10.4
+2 3.3
2
4 56.4
3 39.5
10 8.1
0 10.6
11 52. 2
1 18.2
13 12.0
2 4.2
4
4 58.3
3 38.0
10 9.8
0 11.8
11 53. 9
1 19.3
13 13. 7
2 5.1
6
5 0.3
3 36.5
10 11. 6
0 13.0
11 55. 6
1 20.3
13 15. 3
2 6.0
8
5 2. 2
3 35.1
10 13. 4
0 14.2
11 57. 3
1 21.3
13 16.9
2 6.8
10
5 4.1
3 33.6
10 15. 1
0 15.4
11 59. 0
1 22.4
13 18. 6
2 7. 7
12
5 6.0
3 32.1
10 16. 9
0 16.6
12 0.7
1 23.4
13 20. 2
2 8. 6
14
5 7. 9
3 30.6
10 18. 7
0 17.8
12 2.4
1 24.4
13 21. 8
2 9.5
16
5 9.8
3 29.1
10 20. 4
0 19.0
12 4.1
1 25.4
13 23. 4
2 10.3
18
5 11.8
3 27.6
10 22. 2
0 20.2
12 5.8
1 26.4
13 25. 1
2 11.2
20
5 13.7
3 26.2
10 24. 0
0 21.4
12 7.4
1 27.4
13 26. 7
2 12.0
22
5 15. 6
3 24.7
+10 25. 7
+ 0 22. 6
12 9.1
1 28.4
13 28. 3
2 12.9
H. D.
1.0
0.7
0.9
0.6
0.8
0.5
0.8
0.4
Thursday 13.
Monday 17.
Saturday 22.
Wednesday 26.
0
+ 9 1.7
- 0 35. 6
+10 27. 5
+ 0 23. 8
+12 10. 8
+ 1 29. 4
+13 29. 9
+2 13. 7
2
9 3.5
0 34.3
10 29. 3
0 25.0
12 12. 5
1 30.4
13 31. 5
2 14.5
4
9 5.3
0 33.0
10 31. 0
0 26. 1
12 14. 2
1 31.4
13 33. 1
2 15.4
6
9 7. 2
0 31.7
10 32. 8
0 27. 3
12 15. 9
1 32.4
13 34. 7
2 16.2
8
9 9.0
0 30.5
10 34. 5
0 28.5
12 17. 5
1 33.4
13 36. 3
2 17.0
10
9 10.8
0 29.2
10 36. 3
0 29.6
12 19. 2
1 34.4
13 37. 9'
2 17.9
12
9 12.6
0 27.9
10 38. 0
0 30.8
12 20. 9
1 35.4
13 39. 5
2 18.7
14
9 14.4
0 26.6
10 39. 8
0 32.0
12 22. 6
1 36.4
13 41. 1
2 19.5
16
9 16.2
0 25.4
10 41. 5
0 33.1
12 24. 2
1 37.3
13 42. 7
2 20.3
18
9 18.0
0 24.1
10 43. 3
0 34.3
12 25. 9
1 38.3
13 44. 3
2 21.1
20
9 19.8
0 22.8
10 45. 0
0 35.4
12 27. 6
1 39.3
13 45. 9
2 21.9
22
9 21.6
0 21.6
10 46. 8
0 36.6
12 29. 2
1 40.2
13 47. 5
2 22.7
H. D.
0.9
0.6
0.9
0.6
0.8
0.5
0.8
0.4
NOTE— The Equation of Time is to be applied to the G. M. T. in accordance with the sign as given.
248
EXTRACTS FROM NAUTICAL, ALMANAC.
249
G. M. T.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Tune.
0 /
m s
0
m s
0
m s
0 ,
m s
SUN, APRIL, 1916.
0
2
4
6
8
10
12
14
16
18
20
22
H. D.
Saturd
+ 9 44. 9
9 46.7
9 48.5
9 50.3
9 52.0
9 53.8
9 55.6
9 57.4
9 59.2
10 LO
10 2. 7
10 4.5
0.9
Ay 15.
+ 0 5. 2
0 4.0
0 2. 8
0 1.5
- 0 0.3
+ 0 0. 9
0 2.1
0 3. 3
0 4. 5
0 5. 8
0 7.0
0 8.2
0.6
Wednes
+11 9. 4
11 11. 1
11 12. 8
11 14. 6
11 16. 3
11 18. 0
11 19. 7
11 21. 4
11 23. 1
11 24. 9
11 26. 6
11 28. 3
0.9
dav 19.
-r "0 51. 3
0 52.4
0 53.5
0 54.6
0 55.7
0 56.8
0 57.9
0 59.0
1 0.1
1 1.2
122
1 3.3
0.5
Sunda
+12 30. 9
12 32. 6
12 34. 2
12 35. 9
12 37. 5
12 39. 2
12 40. 8
12 42. 5
12 44. 1
12 45. 8
12 47. 4
12 49. 1
0.8
y23.
-r 1 41. 2
1 42.2
1 43.1
1 44. 1
1 45. 0
1 46.0
1 46. 9
1 47.8
1 48.8
1 49.7
1 50.6
1 51.6
0.5
SEMIDIAMETER.
Apr. 1
11
21
May 1
16.03
15.98
15.94
15.90
SUN, MAY, 1916.
0
2
4
6
8
10
12
14
16
18
20
22
H. D.
Sunds
+18 37. 0
18 38. 2
18 39. 4
18 40. 6
18 41. 8
18 43. 0
18 44. 2
18 45. 4
18 46. 6
18 47. 8
18 49. 0
18 50. 2
0.6
ly 14.
+3 47. 5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
0.0
Mond
+18 51. 4
18 52. 5
18 53. 7
18 54. 9
18 56. 1
18 57. 2
18 58. 4
18 59. 6
19 0.7
19 1.9
19 3.1
19 4.2
0.6
ay 15.
+3 47. 5
3 47.4
3 47.4
3 47.3
3 47.3
3 47.2
3 47.2
3 47.1
3 47.1
3 47.0
3 47.0
3 46.9
0.0
Wedr
+19 19. 1
19 20. 2
19 21. 3
19 22. 4
19 23. 6
19 24. 7
19 25. 8
19 26. 9
19 28. 0
19 29. 1
19 30. 3
19 31. 4
0.6
lesday 17.
+3 45. 7
3 45.6
3 45.5
3 45.3
3 45.2
3 45.0
3 44.9
3 44.8
3 44.6
3 44.5
3 44.3
3 44.2
0.1
Su
+20 10. 6
20 11. 6
nday 21.
+3 35. 6
3 35.2
SEMLDIAMETER.
May 1
11
21
31
15.90
15.86
15.83
15.80
SUN, JUNE, 1916.
0
2
4
6
8
10
12
14
16
18
20
22
H. D.
0
2
4
6
8
10
12
14
Wedne
+22 45. 2
22 45. 7
22 46. 2
22 46. 6
22 47. 1
22 47. 6
22 48. 0
22 48. 5
22 49. 0
22 49. 4
22 49. 9
22 50. 4
0.2
Mond
+23 26. 0
23 26. 1
23 26. 1
23 26. 2
23 26. 3
23 26. 3
23 26. 4
23 26. 4
sday 7.
+1 23. 2
1 22.3
1 21.3
1 20.4
1 19.4
1 18.5
1 17.6
1 16.6
1 15.7
1 14.7
1. 13 8
1 12.9
0.5
ay 19.
-1 3.6
1 4. 7
1 5.8
1 6. 9
1 8.0
1 9.0
1 10.1
1 11.2
Tuesd
+23 13. 0
23 13. 2
23 13. 5
23 13. 8
23 14. 0
23 14. 3
23 14. 6
23 14. 8
23 15. 1
23 15. 4
23 15. 6
23 15. 9
0. 1
Frids
+23 26. 5
23 26. 4
23 26. 3
23 26. 2
23 26. 2
23 26. 1
23 26. 0
23 25. 9
ay 13.
+0 12. 5
0 11.5
0 10.5
0 9.4
0 8. 4
0 7. 4
0 6.4
0 5. 3
0 4.3
0 3. 3
0 2.2'
0 1.2
0.5
ly 23.
— 1 55. 5
1 56.6
1 57.6
1 58.7
1 59.8
2 0.8
2 1.9
2 3.0
Wednes
+23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23. 27 0
23 27. 0
0.0
Tuesd
+23 20. 3
23 20. 1
23 19. 9
23 19. 7
23 19. 4
23 19. 2
23 19. 0
23 18. 8
sday 21.
-1 29. 6
1 30.6
1 31.7
1 32.8
1 33.9
1 35.0
1 36.0
1 37.1
1 38.2
1 39.3
1 40.4
1. 41. 4
0.5
ay 27.
-2 46. 6
2 47.6
2 48.6
2 49.7
2 50.7
2 51.8
2 52.8
2 53.8
Sum
+23 24. 2
23 24. 1
23 23. 9
23 23. 8
23 23. 6
23 23. 5
23 23. 3
23 23. 2
23 23. 0
23 22. 9
23 22. 8
23 22. 6
0.1
lay 25.
-2 21. 2
2 22.3
2 23.4
2 24.4
2 25.5
2 26.5
2 27.6
2 28.6
2 29.7
2 30.8
2 31.8
2 32.9
0.5
SEMIDIAMETER.
June 1
11
21
July 1
15.80
15.78
15.77
15.76
NOTE.— The Equation of Time is to be applied to the G. M. T. in accordance with the sign as given.
250
EXTEACTS FKOM NAUTICAL ALMANAC.
G. M. T.
Sun's
Declination.
Equation
of Time.
Sun's
Declination.
Equation
of Time.
Sun's
Decimation.
Equation
of Time.
Sun's
Declination.
Equation
ofTime.
h
0 ,
m s
o ;
m s
0 ,
m s
0 ,
m s
SUN, JULY, 1916.
0
2
4
6
8
10
12
14
16
18
20
22
H. D.
Wedne
+21 59. 6
21 58. 9
21 58. 2
21 57. 5
21 56. 8
21 56. 1
21 55. 4
21 54. 7
21 54. 0
21 53. 3
21 52. 6
+21 51. 9
0.4
3day 12.
-5 23. 5
5 24.1
5 24.7
5 25.3
5 25.9
5 26.5
5 27.1
5 27.8
5 28.4
5 29.0
5 29.6
-5 30. 2
0.3
Monda
+19 53. 9
19 52. 8
19 51. 7
19 50. 7
19 49. 6
19 48. 6
19 47. 5
19 46. 4
19 45. 4
19 44. 3
19 43. 2
+19 42. 2
0.5
y24.
-6 18. 1
6 18.2
6 18.3
6 18.4
6 18.5
6 18.5
6 18.6
6 18.7
6 18.8
6 18.9
6 19.0
-6 19. 1
0.0
Friday
+19 0. 9
18 59. 8
18 58. 6
18 57. 4
18 56. 3
18 55. 1
18 53. 9
18 52. 8
18 51. 6
18 50. 4
18 49. 2
+18 48. 1
0.6
28.
-6 18. 8
6 18.7
6 18.6
6 18.5
6 18.4
6 18.3
6 18.2
6 18.1
6 18.0
6 17.9
6 17.8
-6 17. 6
0.1
SEMIDIAMETER.
July 1
11
21
31
/
15.76
15.76
15.77
15.79
SUN, OCTOBER, 1916.
0
2
4
6
8
10
12
14
16
18
20
22
H. D.
Sund
-3 9.8
3 11.7
3 13.7
3 15.6
3 17.5
3 19.5
3 21.4
3 23.4
3 25.3
3 27.2
3 29.2
3 31.1
1.0
ay 1.
+10 16. 1
10 17. 7
10 19. 3
10 20. 9
10 22. 5
10 24. 0
10 25. 6
10 27. 2
10 28. 8
10 30. 4
10 32. 0
10 33. 5
0.8
Thurs
-4 42. 7
4 44.6
4 46.5
4 48.4
4 50.4
4 52.3
4 54.2
4 56.1
4 58.1
5 0.0
5 1.9
5 3.8
1.0
day 5.
+11 30.4
11 31. 9
11 33. 4
11 34. 9
11 36.4
11 37. 9
11 39. 3
11 40. 8
11 42. 3
11 43. 8
11 45. 2
11 46. 7
0.7
Mond
-6 14.6
6 16.5
6 18.4
6 20.3
6 22.2
6 24.1
6 26.0
6 27.9
6 29.8
6 31.7
6 33.6
6 35.5
0.9
ay 9.
+12 39. 1
12 40. 5
12 41. 9
12 43. 2
12 44.6
12 45. 9
12 47. 3
12 48. 6
12 49. 9
12 51. 3
12 52. 6
12 53. 9
0.7
Friday 13.
-7 45. 2 +13 40. 8
SEMIDIAMETER.
Oct. 1
11
21
31
/
16.01
16.06
16.10
16.15
NOTE.— The Equation of Time is to be applied to the G. M. T. in accordance with the sign as given.
EXTRACTS FROM NAUTICAL ALMANAC.
SUN, 1916.
251
Dy
Right Ascension of the Mean Sun at Greenwich Mean Noon. ,
Month.
January.
February.
March.
April.
May.
June.
h
m s
h
m s
h
m s
h m s
h m s
h m s
1
18
39 16. 2
20
41 29. 5
22 35 49. 6
0 38 2. 7
2 36 19. 4
4 38 32. 6
2
18
43 12. £
;
20
45 26. 0
22 39 46. 1
0 41 59. 3
2 40 15. 9
4 42 29. 2
3
18
47 9.3
20
49 22. 6
22 43 42. 7
0 45 55. 8
2 44 12. 5
4 46 25. 7
4
18
51 5.9
20
53 19. 2
22 47 39. 2
0 49 52. 4
2 48 9. 0
4 50 22. 3
5
18
55 2.4
20
57 15.7
22 51 35. 8
0 53 49. 0
2 52 5. 6
4 54 18. 8
6
18
58 59. 0
21
1 12.3
22 55 32. 3
0 57 45. 5
2 56 2. 1
4 58 15. 4
7
19
2 55.5
21
5 8.8
22 59 28. 9
1
1 42.0
2 59 58. 7
5 2 12.0
8
19
6 52.1
21
9 5.4
23
3 25.4
1
5 38.6
3 3 55. 2
5 (
5 8.5
9
19
10 48. 7
21
13 1.9
23
7 22.0
1
9 35.2
3 7 51. 8
5 10 5. 1
10
19
14 45. 2
21
16 58. 5
23 11 18.6
1 13 31. 7
3 11 48. 4
5 14 1. 6
11
19
18 41. 8
21
20 55. 0
23 15 15. 1
1 17 28. 3
3 15 44. 9
5 17 58. 2
12
19
22 38. 3
21
24 51. 6
23
19 11.7
1 21 24. 8
3 19 41. 5
5 21 54. 8
13
19
26 34.9
21
28 48. 2
23 23 8. 2
1 25 21.4
3 23 38. 0
5 25 51. 3
14
19
30 31. 4
21
32 44. 7
23 27 4. 8
1 29 17. 9
3 27 34. 6
5 29 47. 9
15
19
34 28.0
21
36 41. 3
23 31 1. 3
1 33 14. 5
3 31 31. 2
5 33 44. 4
16
19
38 24. 6
21
40 37. 8
23 34 57. 9
1 37 11. 0
3 35 27. 7
5 37 41. 0
17
19
42 21. 1
21
44 34.4
23 38 54. 4
1 41 7. 6
3 39 24. 3
5 41 37. 6
18
19
46 17.7
21
48 30. 9
23 42 51. 0
1 45 4. 2
3 43 20. 8
5 45 34. 1
19
19
50 14. 2
21
52 27. 5
23 46 47. 5
1 49 0. 7
3 47 17. 4
5 49 30. 7
20
19
54 10.8
21
56 24. 0
23 50 44. 1
1 52 57. 3
3 51 13. 9
5 53 27. 2
21
19
58 7.4
22
0 20.6
23 54 40. 6
1 56 53. 8
3 55 10. 5
5 57 23. 8
22
20
2 3.9
22
4 17.1
23 58 37. 2
2
0 50.4
3 59 7.0
6 1 20.3
23
20
6 0.5
22
8 13.7
0
2 33.8
2
4 46.9
4 3 3. 6
6 5 16. 9
24
20
9 57.0
22
12 10. 2
0
6 30.3
2
8 43.5
4 7 0.2
6 9 13.5
25
20
13 53. 6
22
16 6.8
0
10 26. 9
2 12 40. 0
4 10 56. 7
6 13 10. 0
26
20
17 50.1
22
20 3.4
0
14 23. 4
2 16 36. 6
4 14 53. 3
6 17 6. 6
27
20
21 46. 7
22
23 59. 9
0
18 20. 0
2 20 33. 1
4 18 49. 8
6 21 3. 1
28
20
25 43. 2
22
27 56. 5
0 22 16. 5
2 24 29. 7
4 22 46. 4
6 24 59. 7
29
20
29 39. 8
22
31 53. 0
0 26 13. 1
2 28 26. 2
4 26 43. 0
6 28 56. 2
30
20
33 36.4
22
35 49. 6
0 30 9. 6
2 32 22. 8
4 30 39. 5
6 32 52. 8
31
20
37 32.9
22
39 46. 1
0 34 6.2
2 36 19.4
4 34 36. 1
6 36 49. 4
CORRECTION TO BE ADDED TO R. A. M. S. AT G.
M. N. FOR TIME PAST NOON.
Time.
QIC
6-
12m
18m
24m
30*
36»
49m
48m
54m
GO*
Time.
h
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
h
0
0 0.0
0 1.0
0 2. 0
0 3.0
0 3. 9
0 4.9
0 5. 9
0 6.9
0 7.9
0 8.9
0 9.9
0
1
0 9.9
010.8
011.8
0 12.8
013.8
014.8
015.8
016.8
017.7
018.7
019.7
1
2
019.7
020.7
021.7
022.7
023.7
024.6
025.6
026.6
027.6
028.6
029.6
2
3
029.6
030.6
031.5
032.5
033.5
034.5
035.5
036.5
037.5
038.4
039.4
3
4
039.4
040.4
041.4
042.4
043.4
044.4
045.3
046.3
047.3
048.3
049.3
4
5
049.3
050.3
051.3
052.2
053.2
054.2
055.2
056.2
057.2
058.2
059.1
5
6
059.1
1 0. 1
1 1. 1
1 2.1
1 3. 1
1 4.1
1 5.1
1 6.0
1 7.0
1 8.0
1 9.0
6
7
1 9.0
1 10.0
1 11.0
1 12.0
1 12.9
113.9
1 14.9
1 15.9
116.9
117.9
118.9
7
8
118.9
119.8
120.8
121.8
122.8
123.8
124.8
125.7
126.7
127.7
128.7
8
9
128.7
129.7
130.7
131.7
132.7
133.6
134.6
135.6
136.6
137.6
138.6
9
10
138.6
139.6
140.5
141.5
142.5
143.5
144.5
145.5
146.5
147.4
148.4
10
11
148.4
149.4
150.4
151.4
152.4
153.3
154.3
155.3
156.3
157.3
158.3
11
252
EXTRACTS FEOM NAUTICAL ALMANAC.
SUN, 1916.
Day
Right Ascension of the Mean Sun at Greenwich Mean Noon.
of
Month
July.
August.
September.
October.
November.
December.
h
na s
h
m s
h
m s
h
m s
h m s
h m s
1
6
36 49. 4
8
39 2.6
10
41 15.8
12 39 32. 4
14 41 45. 6
16 40 2. 3
2
6
40 45. 9
8
42 59. 2
10
45 12. 4
12 43 29. 0
14 45 42. 2
16 43 58. 9
*
6
44 42. 5
8
46 55. 8
10
49 9.0
12 47 25. 6
14 49 38. 7
16 47 55. 4
4
6
48 39. 0
8
50 52. 3
10
53 5.5
12 51 22. 1
14 53 35. 3
16 51 52. 0
5
6
52 35. (
1
8
54 48.9
10
57 2.1
12 55 18. 7
14 57 31. 8
16 55 48. 6
I
5
6
56 32. 2
8
58 45. 4
11
0 58.6
12 59 15. 2
15 1 28.4
16 59 45. 1
7
7
0 28.7
9
2 42.0
11
4 55.2
13
3 11.8
15 5 25. 0
17
3 41.7
8
7
4 25.3
9
6 38.5
11
8 51.7
13
7 8.3
15 9 21. 5
17
7 38.2
3
7
8 21. £
>
9
10 35. 1
11
12 48. 3
13 11 4. 9
15 13 18. 1
17 11 34. 8
10
7
12 18.4
9
14 31. 6
11
16 44. 8
13 15 1. 4
15 17 14. 6
17 15 31.4
11
7
16 14. 9
9
18 28. 2
11
20 41. 4
13 18 58. 0
15 21 11. 2
17 19 27. 9
12
7
20 11. 5
9
22 24. 8
11
24 37. 9
13 22 54. 5
15 25 7. 7
17 23 24. 5
13
7
24 8.1
9
26 21. 3
11
28 34. 5
13 26 51. 1
15 29 4. 3
17 27 21. 0
14
7
28 4.6
9
30 17. 9
11
32 31. 0
13 30 47. 6
15 33 0. 8
17 31 17. 6
15
7
32 1.2
9
34 14.4
11
36 27. 6
13 34 44. 2
15 36 57. 4
17 3
5 14.1
16
7
35 57. 7
9
38 11. 0
11
40 24. 2
13 38 40. 8
15 40 54. 0
17 39 10. 7
17
7
39 54. 3
9
42 7.5
11
44 20. 7
13 42 37. 3
15 44 50. 5
17 43 7. 3
18
7
43 50. 8
9
46 4.1
11
48 17. 3
13 46 33. 9
15 48 47. 1
17 47 3. 8
19
7
47 47. 4
9
50 0.6
11
52 13. 8
13 50 30. 4
15 52 43. 6
17 51 0. 4
20
7
51 44. 0
9
53 57. 2
11
56 10.4
13 54 27. 0
15 56 40. 2
17 54 56. 9
21
7
55 40. 5
9
57 53. 8
12
0 6. 9
13 58 23. 5
16 0 36. 8
17 58 53. 5
22
7
59 37. 1
10
1 50.3
12
4 3.5
14
2 20.1
16 4 33. 3
18
2 50.0
23
8
3 33.6
10
5 46.9
12
8 0.0
14
6 16.6
16 8 29. 9
18
6 46.6
24
8
7 30.2
10
9 43.4
12
11 56. 6
14 10 13.2
16 12 26.4
18 10 43. 2
25
8
11 26. g
10
13 40. 0
12
15 53. 1
14 14 9. 7
16 16 23. 0
18 14 39. 7
26
8
15 23. 3
10
17 36. 5
12
19 49. 7
14 18 6. 3
16 20 19. 5
18 18 36. 3
27
8
19 19. 9
10
21 33. 1
12
23 46. 2
14 22 2. 8
16 24 16. 1
18 22 32. 8
28
8
23 16.4
10
25 29. 6
12
27 42. 8
14 25 59. 4
16 28 12. 6
18 26 29. 4
29
8
27 13. 0
10
29 26. 2
12
31 39. 3
14 29 56. 0
16 32 9. 2
18 30 26. 0
30
8
31 9.5
10
33 22. 7
12
35 35. 9
14 33 52. 5
16 36 5. 8
18 34 22. 5
31
8
35 6.1
10
37 19. 3
12
39 32. 4
14 37 49. 1
16 40 2. 3
18 38 19. 1
CORRECTION TO
BE ADDED TO R. A. M. S
AT G
M. N.
FOR TIME PAST NOON.
Time.
0m
6m
12m
18m
24m
30m
36m
42m
48m
54m
60m
Time.
h
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
h
12
158.3
159.3
2 0.2
2 1.2
2 2. 2
2 3. 2
2 4. 2
2 5. 2
2 6. 2
2 7.1
2 8.1
12
13
2 8.1
2 9.1
210.1
211.1
212.1
213.1
2 14.0
215.0
2 16.0
2 17.0
218.0
13
14
218.0
219.0
220.0
220.9
221.9
222.9
223.9
224.9
225.9
226.9
227.8
14
15
227.8
228.8
229.8
230.8
2 31. 8
232.8
233.8
234.7
235.7
236.7
237.7
15
16
237.7
238.7
239.7
240.7
241.6
242.6
243.6
244.6
245.6
246.6
247.6
16
17
247.6
248.5
249.5
2 50.5
251.5
252.5
253.5
254.5
255.4
256.4
257.4
17
18
257.4
258.4
259.4
3 0.4
3 1\4
3 2.3
3 3.3
3 4. 3
3 5. 3
3 6. 3
3 7.3
18
19
3 7. 3
3 8. 3
3 9.2
310.2
311.2
312.2
313.2
314.2
315.2
316.1
317.1
19
20
317.1
318.1
319.1
320.1
321.1
322.1
323.0
324.0
325.0
326.0
327.0
20
21
327.0
328.0
329.0
329.9
330.9
331.9
332.9
333.9
334.9
335.9
336.8
21
22
336.8
337.8
338.8
339.8
340.8
341.8
342.8
343.7
344. 7
345.7
346.7
22
23
346.7
347.7
348.7
349.7
350.6
351.6
352.6
353.6
354.6
3 55. 6
356.6
23
EXTRACTS FROM NAUTICAL ALMANAC.
MOON, 1916.
253
G. M. T.
Right
Ascension.
Declination.
S. D.
H. P.
G. M. T.
Right
Ascension.
Declination.
S. D.
H. P.
April
15.
May 6.
h
h m s
' '
/
h
h
m s
'
' ! '
0
11 20 23 „,,
+ 0 19. 2 _
15.5
56.9
0
6 15 36
+25 48. 6 .
14. 8 j 54. 2
2
11 24 18 S.
0 10. 2 ~
15.6
57.0
2
6 19 58 ^
25 42. 2 ^
14. 8 54. 2
4
11 28 14 f?
0 39. 8 S
15.6
57.1
4
6 24 19 *}
25 35. 2 ™
14.8
54.2
6
113210^
]
15. C
57.1
6
62840JJ
25 27. 8 78
14. 8 54. 2
8
11 36 7 oq
]
. 38. 9 _
15.6
57.2
8
6 33 0 „
25 20. 0 _
14.8
54.2
10
12
11 40 5 5?
11 44 3 !r!
0 C R zy/
2 8. 6 „
2 38. 3 5!
15.6
15.6
57.3
57.3
10
12
6 37 19 ™
6 41 38 2
25 11. 6 I
25 2.8 ~
14.8
14.8
54.1
54.1
14
1148 2™
3 8.0^
15.7
57.4
14
64556^
2453.5 f7
14.8
54.1
16
11 52 2 0<
3 37. 7 „
15.7
57.5
16
6 50 13 „
24 43.8..
14.8
54.1
18
11 56 3 S
, ,_ K 298
•4: /. O „-_
15.7
57.5
18
65430^? 2433.6^
14.8
54.1
20
12 0 5r!f
4 37. 2 ^
15.7
57.6
20
6 58 45 5! 24 22. 9 ZT!
14.8
54.1
22
12
4 7 ™
' 243
5 6'9296
15.7
57.6
22
7
3 o r; 24 11. s :;t
zo-± no
14.8
54.1
July
10.
October 10.
0
14 35 34 9a_ -20 37.9 _
16.0
58.7
0
0 16 45 ,„ + 6 59. 3 _
16.0 f 58.6
2
14 40 19 f£
20 57. 8 _
16.0
58.8
2
0 21 0 f??
7.28,73
16.0
58.5
4
14 45 6 tr
17. 2
16.1
58.9
4
0 25 15 S
7 58. 0 ±
16.0
58.5
6
14 49 55 5?
o
36. 2 10
16.]
58.9
6
0 29 30 ™.
'
i
3 27. 1 =
16.0
58.5
zyi
186
^00
2SS
8
14 54 46 „,
21 54.81Q
16.1
59.0
8
0 33 45 „
8 55. 9 „
15.9
58.4
10
14 59 39 ;:
22 12 8
16.]
59.1
10
0 38 1 2
9 24. 5 f:
15.9
58.4
12
15 4 35 f:
22 30. 4 JS
16.1
59.2
12
o 42 16 rr
9 52. 9 ^
15.9
58.3
14
15 9 32 ™
2*47.4™
16.2
59.2
14
04633^
10210^
15.9
58.3
16
15 14 31 „
23 3.91(;
16.2
59.3
16
0 50 49 ^
10 48. 9 0_
15.9
58.2
18
15 19 33 *
23 19. 8 U
16.2
59.4
18
0 55 6 ._
11 16. 5 ?£
15.9
58.2
20
15 24 36 JJ
23 35. 2 J2
16.2
59.5
20
0 59 23 Zl
11 43. 8 ™
15.9
58.1
22
15 29 41 J?
23 50. 0 ! .
16.2
59.5
22
1
3 4irr°
12 10. 8 f ?
15.9
58.1
24
15 34 48 J°
-24 4. 2 "z 16. 3 59. 6
24
1
7 59 *>* 4-12 37. 6 ^
15.8
58.0
TIME OF TRANSIT, MERIDIAN OF GREENWICH.
h m
h
m
h m
h m
Feb. 16
10 37
May 20
15
29 „
June 18
15 12 .,
July 10
7 40 An
17
11 23 4f
21
16
28 „
19
16 5 r:
11
8 40 b(
Apr. 14
9 21 44
22
17
21 S
20
16 53 *
18
15 33 ._
15
10 5 ^
23
18
10 4'
21
17 40 4
19
16 20 *
JUPITER, 1916.
GREENWICH MEAN TIME.
Date.
Ascension.
Apparent
Declination.
Transit,
Meridian
of Green
wich.
Date.
Apparent
Right
Ascension.
Apparent
Declination.
Transit,
Meridian
of Green
wich.
Noon.
Abo*.
Noon.
Noon.
h m s
o /
h m
h m s
0 1
h m
Apr. 15
16
0 56 28 _.
0 57 22 „
+ 4 51. 5
4 57. 0 J!
23 20
23 17
Sept. 15
16
2 11 38 t.
2 11 22 "
+11 41. 1
11 39. 5
16
14 33
14 28
July 25
2 8 20 ,
+11 35. 9 ?!
17 54
17
2 11 5 J
f
m .
11 37. 9
16
17
14 24
26
9 C 49 ^
** 22
+1137.6 ;
17 51
18
2 10 48
i
s
11 36. 2
I/
17
14 20
Polar Semidiameter: July 1, 0'.30; Aug. 1, 0' .33;
Hor. Parallax: Apr. 1, 0'.26; May 1, 0'.27; July 1
Sept. 1, 0'.36; Oct. 1, 0'.39; Nov. 1, 0'.39; Dec. 1, 0'.37; Dec. 32, 0'.34.
O'.OS; Aug. 1, O'.OS; Sept. 1,0'.03; Oct. 1,,0'.04; Nov. 1, 0'.04; Dec. 1, 0'.04;
Dec. 32, (X.03.
VENUS, 1916.
GREENWICH MEAN TIME.
Apr 16
438 4267
+2514.7no
3 1
June 1
7 17 48 w
+24 48. 5
93
2 39
Semidameter: Jan. 1, 0'.IO; Feb. 1, 0'.ll; Mar. 1, OM3; Apr. 1, OM6; May 1,
0'.22; Junel,0'.34;
Julvl,0'.49
Hor. Parallax: Jan. 1, 0'.IO; Feb. 1, 0'.ll; Mar. 1, 0'.13; Apr. 1, 0'.16; May 1
,0'.22; June 1,0'
35
July 1,0'. 50.
253a
EXTKACTS FEOM NAUTICAL, ALMANAC.
OtOCOCNlO CN CO OS
CO 3 CN -Ji ?O CO ^ (TO CO CN ip rH rH rH
•I -2ny
00 CO -if O ••*< CN CN G5 OS t~
CO ^F CN •"?* iO CO CO CO CN
Ot^- COOOCNtOt- CN CD CO t^"cb i-HCO'OOCN
CO to rH cd CO ^lOCNt^CN CN CN CO OS" TJ*
CO t^ CO CO O
OO CO CO rH t'* r— OS CO »ft CO TPt^tOOOCO CN^COrHCO
O rH CO CO T)5 to CN t^ CN CN CN CO O5 •*
OtOCStrH rH (NrHCN rH COCOrH
03 co t-- oso
Tl^ rH CO f>^ t'»
CN CN Tf >O CO
co oco t>.o>o
rH S CM 5? fo CO
^'^co'tocp
IO rH rH rH CN
~co"w oo" 06 1- r- rH to o co
•OI>OS"3 COcOtOOCN
'cOCSl^CN CN(NO(5C5-^
OS OC1 1^- CO O>
~CO~l>~f-^CO O5~
rH 03 tO CO CD
•OS to Tji t - CO CO
COtOOSCOOS OrHCOrH<
rHOStOCOCO rHrHtOrJtOO -rPCOCOCCtO OCNO'Ol-- lO-fCOtOCO
oi c>5 oo oo co s d
OOCOOJCOOS OCNtOrHI
++ I ++ I + I ++
O 00 CO"CN CO OSO^ftOOO CNtOrHCOCO OSCOOO-^CO
XDCC'rHCOCO •o'lOCNt^gJ rHCNl^COCO ^rHCOt^CD
+1+1+ T77++ TTTi+ ++TTT ++77+
CN (N CN CN CN
CO CO CO CO CO
'28 '39(1
lrH-^OSt>- rHCOOCNOS OrHC^'rr'CN -^tOOSOCCN
COCNtOrH tOtOCNCOlO ^tOlOCOlO CNCOTfiTfilO
. CS'CO'CN t-H rH rO~-^ h- CO CO OS OS O
'I '08(1
COCNtOrH lOiOrHCOtO GO I
"I 'AON
^COt^-r^CN ddcO-^O ^COrHOrH
CN CN OCS
CO CO "9« U3 •
•I -any
^4 r-I OJ OO
CO CO CO "3 C
rHI>. TJ1 CO CO
$$$$&
rHr-CSt^O OOrHt-O'
t^ OCOt^iOCN CJStoOOscO t>-OOOOCOCO OcOt>-(
OrHOSrHtO CO CN OS OS, OS OS CO <
•I udy
f OS 00 OO t- CN'cb CO rH rj<
tOrHCC IOCOI>OCO
I O tOO O1OOSOO i
OrHTTitOO OrfitOCOO OOrHCOCNt^
iiOCNt^CO t^iOCOcO>O COI>.CSrHOC tocOOCOCN~
1-3-43^0005 cdoOrHcdco oscdosdcd coooocNrH
t- O CO rH t^- IO OS CO 00 CO CN~F^CN~O~tO OO^OO~O t- rH~
'co'So CN oTcN^to TJI oo coocTco ~CN"VO~
SO tO-^f rH
!5§5S'd c^^^^06
IrHCOCO O3«OOSO3>O edl^todoO rHCOCOr)5<
ICNtOrH Tt^tOrHCNtO COTt<tOCO^ CNCO*^1^!
CO
:OOOrHrH rH
O O O I-H
>-l i-H (N CO
IO •«< CN CN TH
OrHCNCN CN
CN COCO^f
M^ liiii Illll
<1OOOO
CO CO COCO CO
EXTRACTS FROM NAUTICAL ALMANAC.
TABLE IV.
PROPORTIONAL PARTS.
253b
Interval
2 hours.
0
10
20
30
40
50
60
70
80
90
100
110
120
Interval
24 hours.
m
h m
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
1
0
0
0
0
0
0
0
1
1
1
2-
1
I
1
12
OA
3
0
0
0
1
1
1
2
' 2
2
2
ks
2
I
3
Z4
36
4
0
0
1
1
1
2
2
2
3
3
3
4
4
48
5
0
0
1
1
2
2
2
3
3
4
4
5
5
1 0
6
0
0
1
2
2
2
3
4
4
4
5
8
6
12
7
0
1
1
2
2
3
4
4
5
5
6
6
7
24
8
0
1
1
2
3
3
4
5
5
6
7
7
8
36
9
0
1
2
2
3
4
4
5
6
7
8
8
9
48
10
0
1
2
2
3
4
5
6
7
8
8
9
10
2 0
11
0
1
2
3
4
5
6
6
7
8
9
10
11
12
12
0
1
2
3
4
5
6
7
8
9
10
11
12
24
13
0
1
2
3
4
5
6
8
9
10
11
12
13
36
14
0
1
2
4
5
6
7
8
9
10
12
13
14
48
15
0
1
2
4
5
6
8
9
10
11
12
14
15
3 0
16
0
1
3
4
5
7
8
9
11
12
13"
15
16
12
17
0
1
3
4
6
7
8
10
11
13
14
16
17
24
18
0
2
3
4
6
8
9
10
12
14
15
16
18
36
19
0
2
3
5
6
8
10
11
13
14
16
17
19
48
20
0
2
3
5
7
8
10
12
13
15
17
18
. 20
4 0
21
0
2
4
5
7
9
10
12
14
16
18
19
21
12
22
0
2
4
6
7
9
11
13
15
16
18
20
22
24
23
0
2
4
6
8
10
12
13
15
17
19
21
23
36
24
0
2
4
6
8
10
12
14
16
18
20
22
24
48
25
0
2
4
6
8
10
12
15
17
19
21
23
25
5 0
26
0
2
4
6
9
11
13
15
17
20
22
24
26
12
27
0
2
4
7
9
11
14
16
18
20
22
25
27
24
28
0
2
5
7
9
12
14
16
19
21
23
26
28
36
29
0
2
5
7
10
12
14
17
19
22
24
27
29
48
30
0
2
5
8
10
12
15
18
20
22
25
28
30
6 0
31
0
3
5
8
10
13
16
18
21
23
26
28
31
12
32
0
3
5
8
11
13
16
19
21
24
27
29
32
24
33
0
3
6
8
11
14
16
19
22
25
28
30
33
36
34
0
3
6
8
11
14
17
20
23
26
28
31
34
48
35
0
3
6
9
12
15
18
20
23
26
29
32
35
7 0
36
0
3
6
9
12
15
18
21
24
27
30
33
36
12
37
0
3
6
9
12
15
18
22
25
28
31
34
37
24
38
0
3
6
10
13
16
19
22
25
28
32
35
38
36
39
0
3
6
10
13
16
20
23
26
29
32
36
39
48
40
0
3
7
10
13
17
20
23
27
30
33
37
40
8 0
41
0
3
7
10
14
17
20
24
27
31
34
38
41
12
42
0
4
7
10
14
18
21
24
28
32
35
38
42
24
43
0
4
7
11
14
18
22
25
29
32
36
39
43
36
44
0
4
7
11
15
18
22
26
29
33
37
40
44
48
Find the correction to be applied to the right ascension and declination of Jupiter on April 15, 1916, at
llh 55m 30s a. m. local mean time, in Long. 81° 15' W.
(Problem page 107.)
G.M.T.=15d5h20m.5.
Difference of R. A. in 24h=54. Difference for Dec. in 24h=55.
With differences of 54 for R. A. and 55 for Dec. as arguments at top of page and the G. M. T. as argument
at right-hand side of page.
Corr. R. A., for 50; 5h 12m= 11s Corr. Dec., for 50; 5h 12m= I'.l
Corr. for 54= +0S.8 Corr. for 55= -fOM
Corr. for 5h 20m.5= +0S.3 Corr. for 5h 20m.5= O'.O
Total
1M
Total
-f-0'.l +0'.l
R. A. (correction) -f!2M
Dec. (correction) +1/2
APPENDIX II.
A COLLECTION OF FOEMS FOE WOEKING DEAD BECKONING AND VAEI-
OUS ASTEONOMICAL SIGHTS, WITH NOTES EXPLAINING THEIB
APPLICATION UNDEE ALL OIECUMSTANCES.
(The figures in parenthesis refer to the Notes following these forms.)
FORM FOB DAY'S WORK, DEAD RECKONING.
Time.
Compass Course.
Var.
Dev.
Lee
way.
Total
error.
True Course.
Patent
log.
Dist.
N.
S.
E.
W Difl.(i)
Long.
I
Latitude.
o /
Longitude.
Left at departure (or noon) (2) N. or S. (2) E. or W.
Run to. . . N. or S. E. or W.
By D. R. at
Run to
By D. R. at
N. or S.
N. or S.
N. or S.
E. or W.
E. or W.
E. or W.
FORM FOR TIME SIGHT OF SUN'S LOWER LIMB (SUMNER LINE).
h. m. s.
W. T. . . ..
Obs. alt. Q
c-w +
Corr. ± .
Chro. t
h
C. C. ±
/ //
(io) G. M. T
(3) S. D. +
(6)Eq. t. ±
(<)I. C. -t-
G. A. T.
+
/ //
dip - .'...
P& f —
/ 1!
Corr. ± .. ..
O I If
h
Li
log sec
p
log cosec
2)
£]
log cos
Si-h
log sin
h. m. s.
2)
GAT
L A.T.i
log sin 5 £1
(h. m. s.~j
< T\ r ffntr . J IT? n
,*• w
Dec.
H. D. ±
G. M. T.
Corr.
Dec.
N.orS.
N. or S.
(8)L,
Sfh
h. m. s.
G. A. T.
L. A.T.j
Eq. t.
H. D. ±
G. M. T.
Corr. ±
Eq. t.
log sec
log cosec
log cos
log sin
log sin i tt
(h. m. s.j
Long., lo'"f"",',\E.orW.
2)-
254
FORMS FOB WORK.
FORM FOB TIME SIGHT OF A STAB (SUMNEB LINE).
h. m. t. • • »
255
W. T.
C-W +
Chro. t.
C.C. ±
(10) G. M. T.
R. A. M. S. +
Red. (Tab. 9) +
G. S. T.
R. A. *
(11) H. A. from Gr.
Obs. alt. *
Corr. ±
(<) I. C
dip
ref.
E. or W.
Corr. ±
h. m s.
R.A.
Dec.
N. or S.
2).
Gr. H. A.
(u) H. A.,
h. m. 8.
log sec
log cosec
log cos
log sin
E. or W.
E. or W. log sin
(8) Li
Sfh
Gr. H. A.
H.A.,
h. m. s.
log sec
log cosec
log cos
log sin
log sin £ h
2).
Long.i
h. m. s.
E. orW.
Long.
E. or W.
FOBM FOB TIME SIGHT OF A PLANET (SUMNEB LINE).
ft. m. s.
W.T.
C-W +.
Chro. t.
C.C. ±
. M. T.
R. A. M. S. + .
Red. (Tab. 9) +.
G. S. T.
R. A. *
Obs. alt. *.
Corr. ±.
(M) par. +.
(4) I. C. +.
dip
(ii) H. A. from Gr E. or W. ref.
h. m. s.
R.A.
H. D. ±.
G. M. T
Corr. ±.
R. A.
h. m. 8.
Dec.
•
H.D. ±.
G. M. T
Corr. ±.
Dec.
.N. or S.
.X.orS.
Corr. ±
For the remainder of the work, by which the hour angles and thence the longitudes are found, employ the method
given under " Form for Time Sight of a Star (Sumner Line)."
61828°— 16 17
256
FORMS FOR WORK
FORM FOR TIME SIGHT OF MOON'S LOWER LIMB (SUMNER LINE).
ft. 771. S. "in ^ m^ g^
W. T. Obs. alt. (£ (16) R. A. 0«)
Dec. N orS.
c-w +..' ~
Chro. t. . (»)S.D 4- H. D. +
H. D. ±
C. C. ± . Aug 4- TO.
fn
(*)I.C. 4- - G.M.T. ±
G.M.T. ±
(10\ P \T T
R.A.M.S. + + ... *.
, ,,
Red. (Tab. 9)4- — -— Corr. ±
Corr ±
G. S. T. dip — ft. m. s
0 / II
Dec. N or S
i a
(") H A from Gr E orW 1st corr ± (5)
Approx. alt.
p & r (Tab 24)4-
-
h
For the remainder of the work, by which the hour angles and thence the longitudes are found,
under "Form for Time Sight of a Star (Sumner Line)."
FORM FOR MERIDIAN ALTITUDE OF SUN'S LOWER LIMB.
0 ' " ' " ft. m.«.
Obs. alt. 0 ... (3) S. D. +. ... L. A. T.
employ the method given
Dec N or S.
Corr. ± (4) I.C. 4- Long.
h 4- G.A.T. .
H.D. ±
h.
0 / // t It
(17) z N or S dip GMT
d N.orS. p. & r. —
i n
_
Lat. N.orS. -
0 1 II
Dec. N or S
Corr. ± .
FORM FOR MERIDIAN ALTITUDE OF A STAR.
Obs.alt. * (4) i.e. +
Dec. N. or S.
Corr. ± . — —
h din —
— <— ref. —
d N.orS. -
Lat. .. N.orS. ' "
Corr. ±
FORM FOR MERIDIAN ALTITUDE OF A PLANET.
0 ' " ' " h. m.
Obs. alt. ^< . (14) par 4- G M T Gr trans
0 1 II
Dec N or S
Corr. ± (4) I.C. + Corr. for Long. ±
lt
ft + . L M T localtrans.
H.D. ±
ft.
. o r n i it
GMT
d N.orS. ref. —
1 !•
Lat. N.orS. -.
Dec. ...N.orS.
Corr.
(")*
d
FORMS FOR WORK.
FORM FOR MERIDIAN ALTITUDE OF MOON'S LOWER LIMB.
•
Obs. alt. £
257
h. m.
G. M. T., Gr. trans. (ie)Dec.
Corr. for Long. (Tab. 11) ±
N.orS. («)S.D.
N. or S. Aug.
(«)I. C.
N. or S.
dip
1st corr
Approx. Alt.
p.<frr.(Tab.24)
L. M. T., local trans.
Long.
G. M. T.. local trans.
H. D. ±.
G.M.T. ±.
Cora. ± .
m
Dec.
N.orS.
ALTERNATIVE FORM FOR MERIDIAN ALTITUDE OF A BODY. (»)
± 90° 00' 00" Rules for tignt.
Corr. ±
Constant ±
Obs. Alt. ±
Lat.
W. T.
C-W ±
Chro. t.
C. C. ±
(") G. M. T.
(•) Bq. t. ±
G. A. T.
Long.i ±
Case I Lat <fe Dec same name Lat greater . ... +90"+Dec —Corr — Alt
Case II Lat & Dec same name Dec greater 90°+Dec +Corr ^Alt
Case III Lat and Dec. opposite names +90°— Dec.— Corr —Alt
Case IV Lower tran^''' o-oo°— . r><v» j-Pni^ a. Ait
N. or S.
FORM FOR LATITUDE SIGHTS OF SUN'S LOWER LIMB (SUMNEB LINE).
h. m. s. ° ' " ••*•* " m, 9.
Obs. alt. Q Dec. N.orS. TCn. t
Corr. ±
H. D. 4- H.D. ±
h
h. h.
G.M.T G.M T
m s D -f
' " t.
(*) I. C. +..
4-
0 ' " m. *
Dec N.orS. Eq. t. .
/ n
L. A. T.i
PO*
(*) Long., ±
L.A.T.I
k
• i
ti
o &r
*
Reduction to Meridian,
it
(**) a
—
° ' " TTT
Corr i
•^••••••••B
h. m. s.
h. m. s.
0 / //
<t>' 4>" Method.
//
log sec
d
log tan log cosec .
• i a » t a
h h
(»)9>i"
...N.orS. log tan log sin
(*)a*i» ± afj*±
T
Hi H»
91
^™o"^^T^ e / //
Lat.j
...N.orS.
C /
tt
(17) z\ N.orS. z*
d N or S d
Lat.i N.orS. Lati N.orS.
h
log sin
94' ' •
N or S log tan log sin
pi*
...N.orS. log cos
I^t..~
V nr S
258
FORMS FOE WORK.
FORM FOB LATITUDE SIGHTS OF A STAB (SUMNEB LINE).
h. m. s.
W.T.
c-w +
Chro. t.
C. C. ±
(10) G. M. T.
R. A. M. S. +
Red.(Tab.9) +
G. S. T.
R. A.*
(11) H. A.fromGr E.orW.
(*) Long.i E.orW.
h. m. s.
(si) Long.2
h. m. s.
h. m. s.
E.orW.
E.orW.
E. or W.
Obs.alt.* .
Corr. ±.
h
dip
ref.
Corr. ±.
h. m. s.
R.A.
Dec.
N.orS.
For the remainder of the work, by which the latitudes are found from either the <p' <p" formula or the reduction to the
meridian, employ the methods given under " Form for Latitude Sights of Sun's Lower Limb (Sumner Line) ."
FOBM FOB LATITUDE SIGHTS OF A PLANET (SUMNEB LINE).
h. m. s.
W.T.
c-w +.
Chro. t.
C. C. ±.
. M. T.
R.A. M.S. +.
Red.(Tab.9) +.
G. S. T.
R. A.*
h. m. s. ° ' "
Obs.alt.:>|c R.A. Dec. N.orS.
a. r"*"1 "
h H.D. ± H.D. ±
' " G. M. T G. M. T
(M)par. +
(*) I.C. + *.
(n) H. A. from Gr
(») Long.!
h. m. s.
E.orW.
dip -.
E.orW. ref. -.
E. or W.
Corr. ±.
h. m. s.
o r ff
R.A,
Dec.
N.orS.
("-I) Long.a
h. m. s.
E.orW.
E.orW.
For the remainder of the work, by which the latitudes are found from either the <p' <?" formula or the reduction to the
meridian, employ the methods given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Line)."
FORMS FOE WORK.
FORM FOB LATITUDE SIGHTS OF MOON'S LOWER LIMB (StJMNER LINE).
h. m. 8.
W.T.
C-W +
Chro. t.
C. C. ±
(») G. M.T.
R. A. M. 8. +
Red. (Tab. 9) -f
G. S. T.
R.A.C
(«) H. A. from Gr E.orW.
(») Long.i E.orW.
h. m. t.
(») S. D.
Aug.
dip
h. TO. *.
Long.,
E. or W.
E.orW.
1st Corr.
Approx. alt.
p. &r. (Tab. 24)
P«) R. A.
(") Dec.
H.D. + H.D.
m.
G.M.T. ± G.M.T.
Con.
R. A.
h. m. i.
259
.N.orS.
Corr. ±
Dec.
h. TO. *. I
"o"i",i "[E.OTW.
For the remainder of the work, by which the latitudes are found from either the 9' <p" formula or the reduction to the
leridian, employ the methods given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Line)."
FORM FOR FINDING THE TIME OF HIGH (OR LOW) WATER.
d. h. m.
G. M. T. of Greenwich transit
Corr. for Long. (Tab. 11) ±
L. M. T. of local transit
Lunitidal int. (App. IV)
L. M. T. of high (or low) water
260
FORMS FOE WORK.
FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE
SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF THE SUN'S LOWER LIMB.
(SINE— COSINE FORMULAE)
h. m. s.
W. T.
Dec. . N. or8. Eq. t.
c-w +
g
- II D ± n D
Chro. t.
A.
A.
C C ±
GMT G. M T
(10) G. M. T.
Corr ± . . Corr.
j.
(6) Eq. t. ±
^^7^"""^"'
G. A. T.
d 4_; Eq. t.
T
Long, of assumed Pos.
E. or W.
L. A. T.-»«
A. TO. S. ° ' "
— « log cos
"
L ah log sin ... -t log cos
Obs. alt. Q
o / n
d i log sin .... i log cos
<*
1C 4-
(Sum) log A dr log B .
• - ±
Corr. (Tab. 46) ±
A ± B ±
Obs h
A ± ... .
Calculated h
nat. sin — A 4- B
Alt. Diff
FORM FOR FINDING THE
SUMNER LINE BY T
W. T.
CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING
HE METHOD OF SAINT HILAIRE FROM A SIGHT OF THE SUN'S LOWER
(COSINE— HAYERSINE FORMULA.*)
h.m.s. ° ' " w.
Dec. . . N. or S. Eq. t. . . .
DOWN TH1
LIMB.
*.
C— W. + .
H. D. ±
"J1™
H D db
Chro. t
.. . A
A.
C C d;
GMT G M. T
» //
(io) GMT
Corr -t- Corr. ±
'
C6) Eq t ±
m
•••••
GAT
d 4- Ea t
Long, of as-\ .
E or W
L. A. T.=-<
A. m. s. ° '
log hav Obs alt Q
//
L
O / ft
log cos I. C. +
d
log cos Corr. (Tab. 46). ±
log hav 9 (Sum) Obs A
nat hav 9 1 Calculated A
T rt
nat hav Alt Diff.
'
-
nat hav (Sum)
Calculated A \ '
=90°— 3 > '
1 Sine— cosine formula: sin A =sin L sin d -f cos L cos d cos t
A + B
2 Cosine— haversine formula: hav s =har (L~d) + cos L cos d hav t
=hav (L~d) + hav 9
FORMS FOE WORK.
261
FOBM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN THE
SUMNEB LINE BY THE METHOD OF SAINT HILAIBE FBOM A SIGHT OF THE SUN'S LOWEB LIMB.
("MHAVEBSINE FORMULA.')
h. TO. 8.
W T
Dec. N or S. Eq t
C— W -f .
1
Chro t
H. D. -J- . H D i
c c ±
h h
G. M. T. GMT
(») G. M. T.
C) Ea t ± ..
in .
Pnrr 4- COIT 4-
GAT
Long of as- 1
m. s.
E. or W. Dec N orS Eq t
sumed Pos. /
L. A T.— i
0 t It
••H
— (*)P. D. ....
co. L.
coL-f-PD nat hav
co L. P.D. nat hav ....
nat hay A ... (Diff'4
log hav A .. \
log hay t /
0 ' " log hay B (Sum)
Obs Alt Q nat hav B •»
1C + nat hav (co L— P D ) /
Corr. (Tab. 46) ± of >...-. /c««\
Obs h ° ' "
Calculated h z .
Alt. Diff. Calculated h\
FOBM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN
THE SUMNEB LINE BY THE METHOD OF SAINT HILAIBE FBOM A SIGHT OF A STAB.
(SINE-COSINE FORMULA.*)
h. m. s.
C-W -f
I. C. -f . . ..
______
Corr. (Tab. 46) —
A. T7l. S
R V
c c. ±
Obs. h
______
(io\ GMT
o / //
t
log cos i
RAMS +
L i log sin i
Red (Tab 9) +
d i log sin i
log cos
GST
(Sum) log A ... i
log B i
R A *
A ±
B ± . .
0 / H
A_i_
(ll) H A 3k from Gr E or W
Calculated h
(s) Long of assumed Pos E or W
Obs h
.
1 ' 7"'
Alt Diff nat sin«= A-f B
jo/ n
V
1 Haversine formula: hav z = {hay (co. L + P. D.)— hav (co. L— P.D.)>hav t + hav (co. L— P.D.)
= hav B + hav (co.L— P.D.) ; where hav B=»hav A hav t, and hav A=hav (co.L+
P. D.)-hav (co. L— P. D.)
» Sine— cosine formula: sin h =sin L sin d + cos L cos d cos t
A + B
i
262
FORMS FOB WORK.
FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE
SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A STAR.
h. m. s.
(COSINE-HAVERSINE FORMULA.1)
h. m. s.
W. T.
t ...
. . . log hav
Dec. (d)
C-W +
o /
L
//
log cos
h. m. s.
R. A.
Chro t
d
log cos
TT
C C ±
log hav 6 (Sum )
Of//
Obs alt *
(io) GMT
nat hav 6 ........"i
1C +
RAMS +
L~d
... nat hav /
Corr. (Tab 46) —
Red (Tab 9)+
z . . .
... nat hav (Sum)
Obs. h
G. S T.
R. A.*
Calcu- ^ ° '
latedft J
//
.... =90°-z
(") H. A. * \ E orW
from Gr. i
C25) Long, of \ EorW.
Alt. diff
assumed PosJ
t
N. orS.
FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN
THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A STAB.
h. m. s.
(») (HAVERSINE FORMULAE)
O / //
h. m. g.
W T
. Dec. N. or S.
R A
C W +
(6) P. D.
Chro. t.
... co. L.
o / //
Obs. alt *
C C ± ...
co. L+P. D nat hav
I. C +
(io) G M. T.
. .. co. L— P. D nat hav
Corr (Tab 46)
R. A. M. S. + .
. ... nat hav A
... (Diff.) Obs h
Red.(Tab.9)+
loghavA
1 Calculated h
G. S. T.
h. m. s.
.. t ........ log hav
AH. diff.
R A #
log hav B
(Sum)
(") H.A. sjcfronn
Gr J
E or W nat hav B
1"
(25) Long, of as- \
sumed Pos /
0 / /•
E. or W. co L — P D nat hav
I
z nat hav
(Sum)
O 1 It
Calculated h 1
=90°- z f
i Cosine— haversine formula: hav z =hav (L~d) + cos L cos d hav t
=hav (L~d) + hav d
> Haversine formula: hav 2 = {hav (co. L + P. D.)— hav (co. L-P. D.)} hav t + hav (co. L-P. D.)
= hav B + hav (co. L— P. D.); where hav B=hav A hav t, and hav A=hav (co. L+
P. D.)-hav (co. L-P. D.)
FORMS FOR WORK.
263
FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING
DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A PLANET.
ft. m. s.
W.T.
C-W +.
Chro. t.
C. C. ±,
(") G. M. T.
R.A. M. S.-f.
Red.(Tab.9)+.
G.S.T.
R.A.*
R.A.
H. D.
G. M. T.
Corr.
R. A.
Gr.
.E. orW.
(*) Long, of as-\
surned Posj E. or W.
(SINE-COSINE FORMULA')
ft. m. s.
Calculated h
Dec.
N. or S.Obs. alt.
a.
H D ±
•••••
1C +
ft.
GMT
ft.
Corr (Tab 46)
Corr. ±
.... Obs. ft
d
-j. Calculated ft
Alt. Diff . .
O 1 II
log cos i
. . . . . log sin ...
4j log COS
.......... log sin ....
-£ log COS . ...
(Sum) log A
4- log B 4-
A ±...
B ±
m t II
A ±
=A+B
FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING
DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A PLANET.
(COSINE-HAVERSINE FORMULA.*)
h. m. e. h. m. s. h. m, f. ° ' "
C-W -f ... .
O 1
L
log cos H. D. 4-...
s. "
H. D. ±
Chro. t.
d
... log cos . G. M T.
h. h.
G. M. T
C C ±
log hav B (Sum) Corr i
Corr ±
no) GMT
nat hav 6 \ R A
d 4-
R.A M.S. -f
L^d
... nat hav . . /
Red.(Tab.9)+
... 2 ....
nat hav (Sum)
G.S.T.
0 /
//
Obs alt.
Calcu- \
I. C. -f. ..
R. A. ^c
lated/U
,=90°_2
Corr. (Tab. 46)—
fu) tl. A. 5|<f rom^
Gr. /
E. orW.
Obs h
(») Long, of as-\
pnmpfl Pop.)
E. or W.
Calcu- i
lated hi
f
Alt. Diff.
1 Sine — cosine formula: sin ft =sin L sin d + cos L cos d coe t
A + B
* Cosine — haversine formula: hav z =hav (L~<i) -f cos L cos d hav t
=hav (L~d) + hav 6
264
FOEMS FOR WORK.
FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN THE
SUMNER LINE BY THE METHOD OF SAINT 111 LA IRK FROM A SIGHT OF A PLANET.
h. TO. 8.
(») (HAVERSINE FORMULA.)1
o / n
C-W + .
n
H. D ±
co. L— P. D nat hav
Chro. t.
h
G. M. T.
nat hav A. .
(Diff.)
C. C. ±
log hav A
~L~
(M) G M. T*
0 / //
Dec
A. TO. *.
N. or S. t log hav
R A. M S. +
(*) P. D
log hav B
Sunn
Red. (Tab. 9) +
nat havB.
G. 8. T
o / n
co. L + P.D
O / /f
co. L — P. D nat hav
R. A. *
co.L-P.D
s nat hav
Sum)
(u) H A sfcfromGr. ...
h. m. 8.
. E. or W. R.A.
(*) Long, of AS-\
sumed Pos /
— ^^— —
s.
E or W H D ±
0 1 II 0 f ft
Calculated h\ Obs alt
t
h.
G.M.T.
=90°— z /
Obs h I 0 +
8.
Corr ±
Corr.-\
Alt Diff (Tab 46 w
h. TO. S.
R A
Obs h
» Haversine formula: hav z - -{hav (co. L + P. D.)- hav (co. L-P. D.)} hav t + hav (co. L-P. D.)
— hav B -f hav (co. L— P. D.); where hav B=hav A hav t, and hav A— hav (co. L4-
P. D.)-har (co. L-P. D.)
FORMS FOR WORK. 265
NOTES RELATING TO THE FORMS.
1 . It is not necessary to convert departure into difference of longitude for each course; it will suffice to make one conversion for
the sum of all the departures used in bringing forward the position to any particular tune.
2. In D. R. it will be found convenient to work Lat. and Long, in minutes and tenths, rather than in minutes and seconds.
3. If upper limb is observed, the correction for S. D. should be negative, instead of positive.
4. A positive I. C. has been assumed for illustration throughout the forms; if negative, it should be included with the mintu
terms of the correction.
5. To obtain p, subtract Dec. from 90° if of same name as Lat.; add to 90° if of opposite name
fi. Sign of Eq. t. that of application to mean time.
7. If G. A. T. is later than L. A. T., Long, is west; otherwise it is east.
8. If Lat. is exactly known, a second latitude need not be employed.
9. »s and»r- & may be obtained by applying half the difference between LI and L2 with proper sign, to «i and «i— h , respectively.
10. The G. M. T. must represent the proper number of hours from noon, the beginning of the astronomical day; to obtain this
it may be necessary to add 12*> to the Chro. t.
11. H. A. from Greenwich is the difference between G. S. T. and R. A., and should be marked W. if the former is greater:
otherwise, E.
12. Local H. A. is marked E. or W., according as the body is east or west of the meridian at time of observation.
13. Subtract local hour angle from Greenwich hour angle to obtain longitude; that is, change name of local hour angle and
combine algebraically.
14. The forms include a correction for the parallax of a planet, but in most cases this is small, and may be omitted. When
used, take hor. par. from Naut. Aim. and reduce to observe altitude by Table 17. The semidiameter of a planet may be disregarded
in sextant work if the center of the body is brought to the horizon line.
15. If upper limb is observed, the corrections for S. D. and Aug. should be negative, instead of positive.
16. R. A. and Dec. are to be picked out of Naut. Aim. for nearest hour of G. M. T. , and to be corrected for the number of minutes
and tenths.
17. Mark zenith distance N. or S. according as zenith is north or south of the body observed; mark Dec. according to its name,
subtracting it from 180° for cases of lower transit; then, in combining the two for Lat., have regard to their names.
18. This form enables "Constant " to be worked up before sight is taken, and gives latitude directly on completion of meridian
observation. Longitude and altitude at transit must be known in advance with sufficient accuracy for correcting terms.
19. The details of obtaining Dec. at transit and correction for altitude are shown in the meridian altitude forms for each of the
various bodies.
20. In an a. m. sight subtract L. A. T. from 24> to obtain t; in a p. m. sight L. A. T. is equal to t .
21. If Long, is exactly known, a second longitude need not be employed.
22. Mark <£" N. or S. according to name of Dec., and subtract it from ISO0 when body is nearer to lower than to upper transit;
mark <t>' N. or S. according as zenith is north or south of the body; then combine for Lat. having regard to the names
23. Take a from Table 26 and af» from Table 27.
24. Add for upper, subtract for lower transits.
25. Subtract longitude from Greenwich hour angle to obtain local hour angle; that is, change name of longitude and combine
algebraically.
26. Add for west, subtract for east longitude.
27. As the trigonometric functions are all haversines in this solution, the abbreviation, hav, might be omitted, and the abbre
riations, nat. and log, might be employed to indicate the natural haversine and the log haversine, respectively.
APPENDIX III.
EXPLANATION OF CERTAIN EULES AND PRINCIPLES OF MATHEMATICS
OF USE IN THE SOLUTION OF PROBLEMS IN NAVIGATION,
DECIMAL FRACTIONS.
Fractions, or Vulgar Fractions, are expressions for any assignable part of a unit ; they are usually
denoted by two numbers, placed one above the other, with a line between them ; thus i denotes the
fraction one-fourth, or one part out of four of some whole quantity, considered as divisible into four
equal parts. The lower number, 4, is called the denoniinator of the fraction, showing into how many
parts the whole is divided ; and the upper number, 1, is called the numerator, and shows how many of
those equal parts are contained in the fraction. It is evident that if the numerator and denominator be
varied in the same ratio the value of the fraction will remain unaltered ; thus, if both the numerator
and denominator of the fraction J be multiplied by 2, 3, 4, etc., the fractions arising will be f, T\, -^,
etc., all of which are evidently equal to J.
A Decimal Fraction is a fraction whose denominator is always a unit with some number of ciphers
annexed and the numerator any number whatever ; as •&, y^, -j-Jthr, etc. And as the denominator of
a decimal is always one of the numbers 10, 100, 1000, etc., the necessity for writing the denominator,
may be avoided by employing a point ; thus, -^ is written .3, and -^ is written .14 ; the mixed number
3^, consisting of a whole number and a fractional one, is written 3.14.
In setting down a decimal fraction the numerator must consist of as many places as there are
ciphers in the denominator ; and if it has not so many figures the defect must be supplied by placing
ciphers before it ; thus, -^=.16, T^fTr=.016, Tinnn7==- 0016, etc. And as ciphers on the right-hand side
of integers increase their value in a tenfold proportion, as 2, 20, 200, etc., so when set on the left handx
of decimal fractions they decrease their value in a tenfold proportion, as .2, .02, .002, etc. ; but ciphers
set on the right hand of these fractions make no alteration in their value; thus, .2 is the same as
.20 or .200.
The common arithmetical operations are performed the same way in decimals as they are in inte
gers, regard being had only to the particular notation to distinguish the integral from the fractional
part of a sum.
ADDITION OP DECIMALS. — Addition of decimals is performed exactly like that of whole numbers,
placing the numbers of the same denomination under each other, in which case the separating decimal
points will range straight in one column.
EXAMPLES.
Miles. Feet. Inches.
Add: 26.7 1.26 272.3267
32. 15 2. 31 . 0134
143. 206 1. 785 2. 1576
.003 2.0 • 31.4
Sum: 202.059 7.355 305.8977
SUBTBACTION OP DECIMALS. — Subtraction of decimals is performed in the same manner as in whole
numbers, observing to set the figures of the same denomination and the separating points directly
under each other.
EXAMPLES.
From: 31.267 36.75 1.254 1364.2
Take: 2.63 .026 .316 25.163
Difference: 28.637 36.724 .938 1339.037
MULTIPLICATION OF DECIMALS. — Multiply the numbers together as if they were whole numbers,
and point off as many decimals from the right hand as there are decimals in both factors together ; and
when it happens that there are not so many figures in the product as there must be decimals, then
prefix such number of ciphers to the left hand as will supply the defect.
EXAMPLE I. EXAMPLE II.
Multiply 3. 25 by 4. 5
3.25
4.5
Answer : . 0102
Answer : 14. 625
1625
1300
In one of the factors is one decimal, and in the
other two ; their sum, 3, is the number of decimals
of the product.
266
Multiply . 17 by .06
.17
.06
In each of the factors are two decimals; the pro
duct ought therefore to contain 4 ; and, there being
only three figures in the product, a cipher must be
prefixed.
RULES AND PRINCIPLES OF MATHEMATICS.
267
EXAMPLE III.
Multiply 0.5 by 0.7
0.5
0.7
Answer:
0.35
EXAMPLE IV.
Multiply .18 by 24
Answer:
4.32
DIVISION OF DECIMALS. — Division of decimals is performed in the same manner as in whole num
bers. The number of decimals in the quotient ^ must be equal to the excess of the number of decimals
of the dividend above those of the divisor; when the divisor contains more decimals than the dividend,
ciphers must be affixed to the right hand of the latter to make the number equal or exceed that of the
divisor.
EXAMPLE I.
Divide 14.625 by 3.25
3.25)14.625(4.5
13 00
1625
1625
In this- example there are two decimals in the
divisor and three in the dividend; hence, there is
one decimal in the quotient.
EXAMPLE II.
Divide 3.1 by .0062
Previous to the division affix three ciphers to
the right hand of 3.1, to make the number o-f deci
mals in the dividend equal the number in the
divisor.
.0062)3.1000(500
3 10
000
EXAMPLE III.
Divide 17.256 by 1.16
1.16)17.25600(14.875+
11 6
565
464
1016
928
880
812
680
580
100
By pursuing the operation further the quotient
may be carried out as many decimal places as
desired.
MULTIPLICATION OF DECIMALS BY CONTRACTION. — The operation of multiplication of decimal fractions
may be very much abbreviated when it is not required to retain any figures beyond a certain order or
place; this will constantly occur in reducing the elements taken from the Nautical Almanac from Green
wich noon to later or earlier instants of time.
In multiplying by this method, omit writing down that part of the operation which involves
decimal places below the required order, but mental note should be made of the product of the first
discarded figure by the multiplying figure, and the proper number of tens should be carried over to
insure accuracy in the lowest decimal place sought.
EXAMPLE: Required the reduction for the sun's decimation for 7h.43, the hourly difference being
58". 18, where the product is required to the second decimal.
By ordinary method.
58".18
7h.43
17454
23272
40726
432".2774
By contraction.
58". 18
7h.43
1.74
23.27
407.26 „
432."27
In the contracted method, for the multiplier .03 it is not necessary to record the product of any
figures in the multiplicand below units; for the multiplier .4, none below tenths; but in each case
.observe the product of the left-hand one of the rejected figures and carry forward the number of tens.
268
RULES AND PRINCIPLES OF MATHEMATICS.
RULES AND PRINCIPLES OF MATHEMATICS.
REDUCTION OP DECIMALS. — To reduce a vulgar fraction to a decimal, add any number of ciphers to
the numerator and divide it by the denominator; the quotient will be the decimal fraction. The decimal
point must be so placed that there may be as many figures to the right hand of it as there were added
ciphers to the numerator. If there are not so many figures in the quotient place ciphers to the left hand
to make up the number.
EXAMPLE I.
Reduce ^ to a decimal.
50)1.00
.02 Answer.
EXAMPLE II.
Reduce f to a decimal.
8)3.000
.375 Answer.
EXAMPLE III.
Reduce 3 inches to the decimal of a foot.
Since 12 inches=l foot this fraction is -j^.
12)3.00
.25 Answer.
EXAMPLE IV.
Reduce 15 minutes to the decimal of an hour.
Since 60m = lh, this fraction is £$.
60)15.00
.25 Answer.
EXAMPLE V.
Reduce 17m 22f to the decimal of an hour.
22m
22- = — =0m.37.
60
17h.37
17=i 37 = =0h.289-f Answer.
Any decimal may be reduced to lower denominations of the same quantity by multiplying it by the
number representing the relation between the respective denominations.
EXAMPLE VI. Reduce 7.231 days to days, hours, minutes, and seconds.
32m.640
Om.640
60
38". 400
Answer: 7d 5h 32m 38«.4.
5h.544
GEOMETRY.
Geometry is the science which treats of the description, properties, and relations of magnitudes, of
which there are three kinds; viz, a line, which has only length without either breadth or thickness; a
surface, comprehended by length and breadth; and a solid, which has length, breadth, and thickness.
A point, considered mathematically, has neither length, breadth, nor thickness; it denotes position
simply.
A line has length without breadth or thickness.
A surface has length and breadth without thickness.
A solid has length, breadth, and thickness.
A straight or right line is the shortest distance between two points on a plane surface.
A plane surface is one in which, any two points being taken, the straight line between them lies
wholly within that surface.
Parallel lines are such as are in the same plane and if extended indefinitely never meet.
A circle is a plane figure bounded by a curved line of which every point is
equally distant from a point within called the center. The bounding curve of
the circle is called the circumference.
The radius of a circle, or semidiameter, is a right line drawn from the
center to the circumference, as AC (fig. 82); its length is that distance which
is taken between the points of the compasses to describe the circle.
A diameter of a circle is a right line drawn through the center and termi-
fjs nated at both ends by the circumference, as ACB, its length being twice that
of the radius. A diameter divides the circle and its circumference into two
equal parts.
An arc of a circle is any portion of the circumference, as DFE.
The chord of an arc is a straight line joining the ends of the arc. It divides
the circle into two unequal parts, called segments, and is a chord to them both;
thus, DE is the chord of the arcs DFE and DGE.
A semicircle, or half circle, is a figure contained between a diameter and the arc terminated by that
diameter, as AGB or AFB.
FIG. 82.
RULES AND PRINCIPLES OF MATHEMATICS. 269
Any part of a circle contained between two radii and an arc is called a sector, as GCH.
A quadrant is half a semicircle, or one-fourth part of a whole circle, as CAG.
All circles are supposed to have their circumferences divided into 360 equal parts, called degrees;
each degree is divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called
seconds; an arc is measured by the number of degrees, minutes, and seconds that it contains.
A sphere is a solid bounded by a surface of which every point is equally distant from a point within,
which, as in the circle, is called the center. Substituting surface for circumference, the definitions of the
radius and diameter, as given for the circle, apply for the sphere.
An angle is the inclination of two intersecting lines, and is measured by the arc of a circle inter
cepted between the two lines that form the angle, the center of the circle being the point of intersection.
A right angle is one that is measured by a quadrant, or 90°. An acute angle is one which is less than
a right angle. An obtuse angle is one which is greater than a right angle.
A plane triangle is a figure contained by three straight lines in the same plane.
When the three sides are equal, the triangle is called equilateral; when two of them are equal, it is
called isosceles. When one of the angles is 90°, the triangle is said to be right-angled. When each angle
is less than 90°, it is said to be acute-angled. When one is greater than 90°, it is said to be obtuse-angled.
Triangles that are not right-angled are generally called oblique-angled.
A quadrilateral figure is one bounded by four sides. If the opposite sides are parallel, it is called a
parallelogram. A parallelogram having all its sides equal and its angles right angles is called a square.
When the angles are right angles and only the opposite sides equal, it is called a rectangle.
In a right-angled triangle the side opposite the right angle is called the hypotenuse, one of the other
rides is called the base, and the third side is called the perpendicular. In any oblique-angled triangle,
one side having been assumed as a base, the distance from the intersection of the other two sides to the
base or the base extended, measured at right angles to the latter, is the perpendicular. In a parallelo
gram, one of the sides having been assumed as the base, the distance from its opposite side, measured
at right angles to its direction, is the perpendicular. The term altitude is sometimes substituted for
perpendicular in this sense.
Every section of a sphere made by a plane is a circle. A great circle of a sphere is a section of the
surface made by a plane which passes* through its center. A small circle is a section by a plane which
intersects the sphere without passing through the center.
A great circle may be drawn through any two points on the surface of a sphere, and the arc of that
circle lying between those points is shorter than any other distance between them that can be measured
upon the surface. All great circles of a sphere have equal radii, and all bisect each other.
The extremities of that diameter of the sphere which is perpendicular to the plane of a circle are
called the poles of that circle. In the case of a small circle the poles are named the adjacent pole and
the remote pole. All circles of a sphere that are parallel have the same poles. All points in the circum
ference of a circle are equidistant from the poles. In the case of a great circle, the poles are 90° distant
from every point of the circle.
Assuming any great circle as a priinary, all great circles which pass through its poles are called its
secondaries. All secondaries cut the primary at right angles.
USEFUL FORMULAE DERIVED FROM GEOMETRY. — In these formulae the following abbreviations are
adopted:
6, base of triangle or parallelogram. r, radius of sphere or circle.
h, perpendicular of triangle or parallelogram. d, diameter of sphere or circle.
/, height of cylinder or cone. A, major axis of ellipse.
it, ratio of diameter to circumference a, minor axis of ellipse.
( = 3. 141593 ) . s, side of a cube.
Area of parallelogram = b X h.
Area of triangle = £ b X h.
Area of any right-lined figure = sum of the areas of the triangles into which it is divided.
Sum of three angles of any triangle = 180°.
Circumference of circle = 2?rr, or ltd.
Tfd2
Area of circle = nr*, or -7-.
Angle subtended by arc equal to radius = 57°. 29578.
ird?
Volume of sphere = ~~g~«
Surface of sphere = nd2, or 4irr*.
t 11- *^a
Area of ellipse = —^ .
Volume of cube = s3.
Volume of cylinder = Area of base X I.
Volume of pyramid or cone = Area of base X IT.
f JVLJL-N VJ.jr.L,.Cja
-, or Pe
c h
rpendicular
ypotenuse
.g
TRIGONOMETRIC FUNCTIONS.
The trigonometric functions of the angle formed by any two lines
are the ratios existing between the sides of a right triangle formed by
letting fall a perpendicular from any point in one line upon the
other line; no matter what point is chosen for the perpendicular
nor which line, the ratios, and therefore the respective functions,
will be the same for any given angle.
Let ABC (fig. 83) be a plane right triangle in which C is the
right angle: A and B, the other angles; c, the hypotenuse; a and
6 the sides opposite the angles A and B, respectively. In considering
the functions of the angle A, its opposite side, a, is regarded as the
perpendicular, and its adjacent side, 6, as the base; for the angle B, 6
is the perpendicular and a the base. Then the various ratios are
designated as follows:
Qf the Je A abbreviated sin A;
, is called the cosine of the angle A, abbreviated cos A;
, ,
c hypotenuse
a or perpendicular ig called ^ t ent of the ang]e A abbreviated tan A;
b base
, is called the cotangent of the angle A, abbreviated cot A;
i, or-
a perpendicular
or
. — — > is called the secant of the angle A, abbreviated sec A;
.
° or Jwotenus€L, is called the cosecant of the angle A, abbreviated cosec A;
a perpendicular
1— cosine A, is called the versed sine of A, abbreviated vers A.
1— sine A, is called the co-versed sine of A, abbreviated covers A.
£ (1— cosine A) is called the haversine of A, abbreviated hav A.
The following relations may be seen to exist between the various functions:
1
sin A
6 c
= 1 -*-- = -*- = sec A;
cos A
sin A a b
Hence the cosecant is the reciprocal of the sine, the secant is the reciprocal of the cosine, the cotan
gent is the reciprocal of the tangent, and the tangent equals the sine divided by the cosine.
The complement of an angle is equal to 90° minus that angle, and thus in the triangle ABC the
angle B is the complement of A. The supplement is equal to 180° minus the angle.
From the triangle ABC, regarding the angle B, we have:
sin B = — = cos A;
C
tan B = — = cot A;
sec B = — = cosec A<
RULES AND PRINCIPLES OF MATHEMATICS.
271
Hence it may be seen that the sine of an angle is the cosine of the complement of that angle; the
tangent of an anjjle is the cotangent of its comple
ment, and the secant of an angle is the cosecant of
its complement.
The functions of angles vary in sign according
to the quadrant in which the angles are located.
Let A A' and BBX (fig. 84) be two lines at right
angles intersecting at the point O, and let that point
be the center about which a radius revolves from
an initial position OB, successively passing the points
A, B', A'. In considering the angle made by this
radius at any position, P', P", P'", P//x/, with the
line OB, its position of origin, the functions will
depend upon the ratios existing between the sides
of a right triangle whose base, 6, will always lie
within BB/, vnd whose perpendicular, a, will always
be parallel to A A', while its hypotenuse, c (of a con
stant length equal to that of 'the radius), will de
pend upon the position occupied by the radius.
Now, if OB and OA be regarded as the positive direc
tions of the base and perpendicular, respectively,
and OBX and OA' as their negative directions, the
sign of the hypotenuse being always positive, the
sign of any function may be determined by the signs
of the sides of the triangle upon which it depends. FlG g4
For example, the sine of the angle P"OB is -, and since a is positive the quantity has a positive
value; its cosine is -, and as b is measured in a negative direction from O the cosine must therefore be
negative.
In the first quadrant, between 0° and 90°, all quantities being positive, all functions will also be
positive.
In the second quadrant, between 90° and 180°, sin A ( =- J is positive; cos A ( =- J has a nega
tive value because b is negative; tan A ( =r j is also negative because of 6. The cosecant, secant, and
cotangent have, as in all^ cases, the same signs as the sine, cosine, and tangent, respectively, being the
reciprocals of those quantities.
In the third quadrant, between 180° and 270°, sin A ( =- J and cos A ( =- j are both negative,
because both a and 6 have negative values; tan A ( =rj is positive for the same reason.
In the fourth quadrant, between 270° and 360°, sin A (=£) is negative, cos A (=-) is positive,
and tan A ( =^ j is also negative.
From a consideration of the signs in the manner that has been indicated, the following relations
will appear:
sin A = sin (180° - A) = — sin (180° + A) = - sin (360° — A) = — sin (— A),
cos A = — cos (180° — A) = — cos (180° + A) = cos (360° — A) = cos (— A),
tan A = — tan (180° — A) = tan (180° + A) = — tan (360° — A) = — tan (—A),
sin A = cos (90° — A) = - cos (90° -f A) = - cos (270° — A) = cos (270° + A).
Any similar relation may be deduced from the figure.
It is of great importance to have careful regard for the signs of the functions in all trigonometrical
solutions.
LOGARITHMS.
In order to abbreviate the tedious operations of multiplication and division with large numbers, a
series of numbers, called Logarithms, was invented by Lord Napier, by means of which the operation of
multiplication may be performed by addition, and that of division by subtraction. Numbers may be
involved to any power by simple multiplication and the root of any power extracted by simple division.
In Table 42 are given the logarithms of all numbers, from 1 to 9999; to each one "must be prefixed
an index, with a period or dot to separate it from the other part, as in decimal fractions; the logarithms
of the numbers from 1 to 100 are given in that table with their indices; but from 100 to 9999 the index
is left out for the sake of brevity; it may be supplied, however, by the general rule that the index of the
logarithm of any integer or mixed number is always one less than the number of integral places in the
natural number. Thus, the index of the logarithm of any number (integral or mixed) between 10 and
61828°— 16 18
272 RULES AND PRINCIPLES OF MATHEMATICS.
100 is 1; from 100 to 1000 it is 2 ; from 1000 to 10000 it is 3, etc.; the method of finding the logarithms
from this table will be evident from the rules that follow:
To find the logarithm of any number less than 100, enter the first page of the table, and opposite the
given number will be found the logarithm with its index prefixed. Thus, opposite 71 is 1.85126, which
is its logarithm.
To find the logarithm of any number between 100 and 1000, find the given number in the left-hand col
umn of the table of logarithms, and immediately under 0 in the next column is a number, to which must
be prefixed the number 2 as an index (because the number consists of three places of figures), and the
required logarithm will be found. Thus, if the logarithm of 149 was required, this number being found
in the left hand column, against it, in the column marked 0 at the top (or bottom) is found 17319, pre
fixing to which the index 2, we have the logarithm of 149 = 2.17319.
To find the logarithm of any number between 1000 and 10000, find the three left-hand figures of the given
number in the left-hand column of the table of logarithms, opposite to which, in the column that is
marked at the top (or bottom) with the fourth figure, is to be found the required logarithm, to which
must be prefixed the index 3, because the number contains 4 places of figures. Thus, if the logarithm
of 1495 was required, opposite to 149, and in the column marked 5 at the top (or bottom) is 17464, to
which prefix the index 3, and we have the logarithm, 3.17464.
To find the logarithm of any number above 10000, find the first three figures of the given number in the
left-hand column of the table, and the fourth figure at the top or bottom, and take out the corresponding
logarithm as in the preceding rule; take also the difference between this logarithm and the next greater,
and multiply it by the remaining figure or figures of the number whose logarithm is sought, pointing off
as many decimal places in the product as there are figures in the multiplier. To facilitate the calcula
tion of the proportional parts several small tables are placed in the margin, which give the correction
corresponding to the difference, and to the fifth figure of the proposed number. Thus, if the logarithm
of 14957 was required, opposite to 149, and under 5, is 17464; the difference between this and the next
greater number, 17493, is 29; this multiplied by 7 (the last figure of the givt:n number) gives 203;
pointing off the right-hand figure gives 20.3 (or 20) to be added to 17464, which makes 17484; to this,
prefixing the index 4, we have the logarithm sought, 4.17484. This correction, 20, may also be found
by inspection in the small table in the margin, marked at the top 29; opposite to the fifth figure of the
number, 7, in the left-hand column, is the corresponding correction, 20, in the right-hand column.
Again, if the logarithm of 1495738 was required, the logarithm corresponding to 149 at the left, and
5 at the top, is, as in the last example, 17464; the difference between this and the next greater is 29;
multiplying this by 738 (the given number excluding the first four figures) gives 21402; crossing off the
three right-hand figures of this product (because the number 738 consists of three figures) , we have the
correction 21 to be added to 17464; and the index to be prefixed is 6, because the given number consists
of 7 places of figures; therefore the required logarithm is 6.17485. This correction, 21, may be found as
above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7£ nearly), to
which corresponds 21, as before.
To find the logarithm of any mixed decimal number, find the logarithm of the number, as if it were
an integer, by the preceding rules, to which prefix the index of the integral part of the given number.
Thus, if the logarithm of the mixed decimal 149 5738 was required, find the logarithm of 1495738, with
out noticing the decimal point; this, in the last example, was found to be 17485; to this prefix the index
2, corresponding to the integral part 149; the logarithm sought will therefore be 2. 17485.
To find the logarithm of any decimal fraction less than unity, it must be observed that the index of the
logarithm of any number less than unity is negative; but, to avoid the mixture of positive and negative
quantities, it is common to borrow 10 in the index, which, in most cases, may afterwards be neglected
in summing them with other indices; thus, instead of writing the index — ], it is written + 9; instead
of — 2 we may write + 8; and so on. In this way we may find the logarithm of any decimal fraction
by the following rule: Find the logarithm of a fraction as if it were a whole number; see how many
ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder
will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 — 10; the logarithm of
0.25 is 9.39794 — 10; the logarithm of 0.0000025 is 4.39794 - 10, etc. In most cases the writing of — 10
after the logarithm may be dispensed with, as it will be quite apparent whether the logarithm has a
positive or a negative index.
To find the number corresponding to any logarithm, seek in the column marked 0 at top and bottom
the next smallest logarithm, neglecting the index; write down the number in the side column abreast
which this is found, and this will give the first three figures of the required number; follow the line
until the logarithm next smaller than the given one is found, and the fourth figure of the required
number will be at the top and bottom of the column in which this stands; take the difference between
this next smaller logarithm and the next larger one in the table, and also the difference between the
next smaller logarithm and the given one; entering the small marginal table which has for its heading
the first-named difference, and finding in the right-hand c lumn of that table the last-named difference,
there will appear abreast the latter, in the left-hand column, the fifth figure of the required number.
Where it is desired to determine figures beyond the fifth for the corresponding number, the difference
between the next lower logarithm and the given one may be divided by the difference between the
next lower and next higher ones, and the quotient (disregarding the decimal point, but retaining any
ciphers that may come between the decimal point and the significant figures) will be the fifth and suc
ceeding figures of the number sought. Having found the figures of the corresponding number, point
off from the left a number of figures which shall be one greater than the index number, and there place
a decimal point. In this operation of placing the decimal point, proper account must be taken of the
negative value of any index.
Thus, if the number corresponding to the logarithm 1.52634 were required, find 52634 in the column
marked 0 at the top or bottom, and opposite to it is 336; now, the index being 1, the required number
must consist of two integral places; therefore it is 33.6.
If the number corresponding to the logarithm 2.57345 were required, look in the column 0 and find
in it, against the number 374, the logarithm 57287, and, guiding the eye along that line, find the given
BULES AND PRINCIPLES OF MATHEMATICS.
273
logarithm, 57345, in the column marked 5; therefore th£ mixed number sought is 3745, and since the
index is 2, the integral part must consist of 3 places; therefore the number sought is 374.5. If the index
be 1 the number will be 37.45, and if the index be 0 the number will be 3.745. If the index be 8,
corresponding to a number less than unity, the number will be 0.03745.
Again, if the number corresponding to the logarithm 3.57811 were required, find, against 378 and
under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being
11, and the difference between 57807 and the given logarithm, 57811, being 4; in the marginal table
headed 11, find in the right-hand column the number 4, and abreast the latter appears the figure 4,
which is the fifth figure of the required number; hence the figures are 37854; pointing off from the
left 3 -f 1 = 4 places, the number is 3785.4.
If the given logarithm were 5.57811, since the index 5 requires that there shall be six places in the
whole number, it is desirable to seek accuracy to the sixth figure. The logarithmic part being the
same as in the example immediately preceding, it is found as before that the first four figures are 3785,
the difference between the next lower and next greater logarithms is 11, and between the next lower
logarithm and the given one is 4; divide 4 by 11 and the quotient is .36; drop the decimal point, annex
and point off, and the number required is found to be 378536.
It may be remarked that in using five-place logarithm tables it is not generally to be expected that
results will be exact beyond the fifth figure.
To show, at one view, the indices corresponding to mixed and decimal numbers, the following
examples are given:
Mixed number. Logarithms.
40943.0.. Log. 4.61218
4094.3 Log. 3.61218
409.43 Log. 2.61218
40.943 Log. 1.61218
4.0943 Log. 0.61218
Decimal number. Logarithms.
0. 40943 Log. 9. 61218—10
0.040943 Log. 8.61218-10
0.0040943 Log. 7. 61218-10
0.00040943 Log. 6.61218-10
0.000040943 Log. 5. 61218-10
To perform multiplication by logarithms, add the logarithms of the two numbers to be multiplied and
the sum will be the logarithm of their product.
EXAMPLE I.
Multiply 25 by 35.
25.. ..Log. 1.39794
35 Log. 1.54407
Product, 875 Log. 2.94201
EXAMPLE II.
Multiply 22.4 by 1.8.
22.4 Log. 1.35025
1.8 Log. 0.25527
Product, 40.32.. ..Log. 1.60552
EXAMPLE III.
Multiply 3.26 by 0.0025.
3.26 Log. 0.51322
0.0025 Log. 7.39794
Product, 0. 00815 Log. 7.91116
EXAMPLE IV.
Multiply 0.25 by 0.003.
0.25 Log. 9.39794
0.003 Log. 7.47712
Product, 0.00075 Log. 6.87506
In the last example, the sum of the two logarithms is really 16.87506—20; this is the same as
6.87506—10, or, remembering that the quantity is less than unity, simply 6.87506.
To perform division by logarithms, from the logarithm of the dividend subtract the logarithm of the
divisor; the remainder will be the logarithm of the quotient.
EXAMPLE I.
Divide 875 by 25.
875.. ..Log. 2.94201
25 Log. 1.39794
Quotient, 35 Log. 1.54407
EXAMPLE II.
Divide 40.32 by 22.4.
40.32.... ..Log. 1.60552
22.4 Log. 1.35025
Quotient, 1.8 Log. 0.25527
EXAMPLE III.
Divide 0.00815 by 0.0025.
0.00815 .. ..Log. 7.91116
0.0025 Log. 7.39794
Quotient, 3. 26 Log. 0.51322
EXAMPLE IV.
Divide 0.00075 by 0.025.
0.00075 .. ..Log. 6.87506
0.025 Log. 8.39794
Quotient, 0. 03 Log. 8. 47712
In Example III both the divisor and dividend are fractions less than unity, and the divisor is the
lesser; consequently the quotient is greater than unity. In Example IV both fractions are less than
unity; and, since the divisor is the greater, its logarithm is greater than that of the dividend; for this
reason it is necessary to borrow 10 in the index before making the subtraction, that is, to regard the
logarithm of .00075 as 16.87506 — 20; hence the quotient is less than unity.
274
KULES AND PRINCIPLES OF MATHEMATICS.
The arithmetical complement of the logarithm of a number, usually called the cologarithm of the
number, and denoted by colog, is the remainder obtained by subtracting the logarithm of the number
from the logarithm of unity. It is therefore the logarithm of the reciprocal of the number; and, since the
effect of dividing by any number is the same as that of multiplying by its reciprocal, it follows that, in
performing division by logarithms, we may either subtract the logarithm of the divisor or add the arith
metical complement of that logarithm. As the addition of a number of quantities can be performed
in a single operation, while in subtraction the difference between only two quantities can be taken at a
time, it is frequently a convenience to deal with the arithmetical complements rather than with the
logarithms themselves.
EXAMPLE III.
40.32X.00815
Simplify the expression, 22.4X.0025 '
40.32 Log. 1.60552
.00815 Log. 7.91116
22.4 Log. 1.35025 Colog. 8.64975
.0025 Log. 7.39794.. ..Colog. 2.60206
Result, 5.868 __ Log. 0.76849
EXAMPLE I.
Divide 875 by 25.
875 Log. 2.94201
25 Log. 1.39794 Colog. 8.60206
Quotient, 35 Log. 1.54407
EXAMPLE II.
Divide 0.00075 by 0.025.
0.00075 Log. 6.87506
0.026 Log. 8.39794 Colog. 1.60206
Quotient, 0.03 Log. 8.47712
To perform involution by logarithms, multiply the logarithm of the given number by the index of the
power to which the quantity is to be raised; the product will be the logarithm of the power sought.
EXAMPLE I.
Required the square of 18.
18 Log. 1.25527
2
Answer, 324 Log. 2.51054
EXAMPLE II.
Required the square of 6.4.
6.4.. ..Log. 0.80618
2
Answer, 40.96 Log. 1.61236
EXAMPLE III.
Required the cube of 13.
13 Log. 1.11394
3
Answer, 2197 Log. 3. 34182
EXAMPLE IV.
Required the cube of 0.25.
0.25 Log. 9.39794
3
Answer, 0.015625 Log. 8.19382
In the last example, the full product of the multiplication of 9.39794—10 by 3 is 28.19382—30, which
is equivalent to 8.19382—10.
To perform evolution by logarithms divide the logarithm of the number by the index of the power;
the quotient will be the logarithm of the root sought. If the number whose root is to be extracted is a
decimal fraction lees than unity, increase the index of its logarithm by adding a number of tens which
shall be less by one than the index of the power before making the division.
EXAMPLE I.
Required the square root of 324.
324 Log. 2)2.51055
Answer. 18. ._ Log. 1.25527
EXAMPLE II.
Required the cube root of 2197.
2197 Log. 3)3.34183
Answer, 13 Log. 1.11394
EXAMPLE III.
Required the square root of 40.96.
40.96 Log. 2)1.61236
Answer, 6.4 Log. 0.80618
EXAMPLE IV.
Required the cube root of 0.015625.
0.015625 Log. 8.19382
Add 20 to the index 3)28.19382
Answer, 0.25 Log. 9.39794
In the last example the logarithm 8.19382— 10 was converted into its equivalent form of 28.19382—30,
which, divided by 3, gives 9.39794—10.
To find the logarithm of any function of an angle, Table 44 must be employed. This table is so
arranged that on every page there appear the logarithms of all the functions of a certain angle A,
RULES AND PKINCIPLES OF MATHEMATICS. 275
together with those of the angles 90° —A, 90°-{-A, and 180° — A; thus on each page may be found the
logarithms of the functions of four different angles. The number of degrees in the respective angles
are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding
appear in one column at the left of the page and in anothei at the right; the names of the functions
to which the various logarithms correspond are printed at the top and bottom of the columns. The
invariable rule must be to take the name of the function froffrlhe top~~6r "the bottom of the page,
according as the number of degrees of the given angle is found at the top or bottom; and to take the
minutes from the right or left hand column, according as the number ot degrees is found at the right
or left hand side of the page; or, more briefly, take names of functions and number of minutes,
respectively, from the line and column nearest in position to the number of degrees.
Taking, as an example, the thirty-first page of the table, it will be found that 30° appears at the
upper left-hand corner, 149° at the upper right-hand, 59° at the lower right-hand, and 120° at the lower
left-hand corner. Suppose that it is desired to find the log. sine of 30° 10'; following the rule given, we
find KX in the left-hand column and Sine at the top ot the page, and abreast one and below the other is
the required logarithm, 9.70115. But if the log. sine of 59° 10' were sought, as 59° appears below and at
the right of the page, the logarithm 9.93382 would be taken from the column marked Sine at the bottom
and abreast 10/ on the right. It may also be seen that log. sin 30° 10/=log. cos 59° 5(K=log. cos
120° 10/=log. sin 149° 50/=9.70115, the equality of the functions agreeing with trigonometrical
deductions; (in this statement numerical values only are regarded, and not signs; the latter must, of
course, be taken into account in all operations) .
EXAMPLE I.
Required the log. sine, cosecant, tangent, cotan
gent, secant, and cosine of 28° 37'.
Log. sin 9. 68029 Log. cot 10. 26313
Log. cosec 10. 31971 Log. sec 10. 05658
Log. tan 9. 73687 Log. cos 9. 94342
EXAMPLE II.
Required the log. sine, cosecant, tangent, cotan
gent, secant, and cosine of 75° 42'.
Log. sin 9. 98633 Log. cot 9. 40636
Log. cosec 10. 01367 Log. sec 10. 60730
Log. tan 10. 59364 Log. cos 9. 39270
When the angle of which the logarithmic function is required is given to seconds, it becomes
necessary to interpolate between the logarithms given for the even minutes next below and next above;
this may be done either by computation or (except in a few cases) by inspection of the table.
To interpolate by computation, let n represent the number of seconds, D the difference between the
logarithms of the next lesser and next greater even minute, and d the difference between the logarithm
of the next lesser even minute and that of the required angle. Then,
It should be noted when the number of seconds is 30, 20, 15, or some similar number, permitting
the reduction of the fraction JL to a simple value, such as £, £, J, as the interpolation by this method
may thus be made with greater facility.
Haying obtained the difference of the logarithm from that of the next lower even minute, it must
be applied in the proper direction — that is, if the function is such that its logarithm increases as the
angle increases, the logarithmic difference must be added; but if it decreases, then that difference must
be subtracted.
For example, let it be required to find the log. sin and log. cosec of 30° 107 19". The log. sin of
30° 107 is 9.70115; the difference between this logarithm and that of the sine of 30° IV (9.70137) is + 22,
which is D. Hence,
and the required logarithm is 9.70122. The log. cosec of 30° 107 is 10.29885; the difference, D, between
that and log. cosec 30° IV (10.29863) is —22. In this case
therefore, log. cosec 30° 107 19"= 10. 29878.
The method of interpolating by inspection consists in entering that column marked " Diff." which
is adjacent to the one from which the logarithmic function for the next lower minute is taken, and
finding, abreast the number in the left-hand minute column which corresponds to the seconds, the
required logarithmic difference; and the latter is to be added or subtracted according as the logarithms
increase or decrease with an increased angle. Thus, if it be required to find log. sin 30° 107 19", find as
before log. sin 30° 10/=9. 70115, then, in the adjacent column headed "Diff." and abreast the number
of seconds, 19, in the left-hand minute column will be found 7, the logarithmic difference; fedd this, as
the function is increasing, and we have the required logarithm 9.70122. If log. cosec 30° l(Y 19// be
sought, find log. cosec 306 10/= 10. 29885; then in the adjacent difference column, which is the same as
was used for the sines, find as before the logarithmic difference, 7; and since this function decreases as
the angle increases, this must be subtracted; therefore, log. cosec 30° 10' 19"= 10. 29878.
This method of interpolation by inspection is not available in that portion of the table where the
logarithmic differences vary so rapidly that no values will apply alike to all the angles on the same
page; on such pages the difference for one minute is given in a column headed "Diff. 1'," instead of
the usual difference for each second; in this case the interpolation must be made by^computation, the
given difference for one minute being D. In other parts of the table the interpolation by inspection
may be liable to slight error because of the variation in logarithmic difference for different angles on
the* same page; but the tabulated values are sufiiciently accurate for the usual calculations in navigation.
276
RULES AND PRINCIPLES OF MATHEMATICS.
It will be evident that while the methods explained have contemplated entering the tables with a
smaller angle and interpolating ahead, it would be equally correct to enter with a greater angle and
nterpolate back for the proper number of minutes, making the requisite change in the sign of the
icorrection.
EXAMPLE I. EXAMPLE II.
Required the log. sine, cosine, and tangent of
42° 57' 06".
Log. sin
Log. cos
Log. tan
For 42° 57'
d
For 42° 67' 06"
9. 83338
9. 86448
9. 96890
+1
—1
+3
9. 83339
9. 86447
9. 96893
Required the log.
of 175° 32' 36".
secant, cosecant, and cotangent
Log. sec
Log. cosec
Log. cot
For 175° 32'
d
For 175° 32' 36"
10. 00132
11. 10858
11. 10726
— I
+97
+98
10. 00131
11. 10955
11. 10824
It should be observed that, for uniformity and convenience, all logarithms given in Table 44 have
been increased by 10 in the index, and it is understood that —10 ought properly to be written after
each; thus all logarithms under 10.00000 represent functions whose value is less than unity, and all
over 10.00000 those greater than unity; for example, 11.10726 is the logarithm of a number in which
the decimal point should be placed after the second figure from the left.
To find the angle corresponding to any logarithmic function, the process is the reverse of the one just
described. Find, in the column marked with the name of the function, either at top or bottom, the
two logarithms between which the given one falls; write down the degrees and minutes of the lesser of
the two corresponding angles, which will be the degrees and minutes of the angle required. Call the
difference between the two tabulated logarithms D, and the difference between the given logarithm and
that which corresponds to the lesser angle, d; then if n represents the number of seconds, we have:
Or, the same may be obtained by inspection (except where, as before explained, the differences
for seconds are not tabulated ) by finding, in the ' ' Diff . ' ' column adjacent to that from which the logarithm
was taken, the logarithmic difference, d, and noting the number of seconds abreast which it stands in
the left-hand minute column.
Interpolation may be also made in the reverse direction from the next greater even minute.
Thus, if it be required to find the angle corresponding to log. sin 9.61400, we find log. sin 24° 16' ,
9.61382, and log. sin 24° 17', 9.61411; hence D=29, and d=18;
n=4§X 60=37;
and the angle is 24° 16' 37". Or, in adjacent column headed "Diff.," 18 would be found abreast 38,
39, or 40 (seconds) in the left-hand minute column — a correspondence sufficiently close for navigation
work.
If the angle were known to be in the second quadrant, we find log. sin 155° 43', 9.61411, and log.
sin 155° 44', 9.61382; here D=29, and d=ll;
therefore, the angle is 155° 43' 23". Or, in adjacent "Diff." column find, abreast 11, 23 or 24 seconds.
EXAMPLE I. EXAMPLE II.
Find angles less than 90° corresponding to log.
cot 10.33621, log. sec 10.11579, and log. cos 8. 70542.
Log. cot 10.33621
Log. sec 10.11579
Log. cos 8. 70542
u
24 45
8
15
40 00
4
22
87 05
116
28
Find angles in second quadrant corresponding to
log. tan 10.15593, log. sin 8.87926, and log. cosec
10.04944.
Log.
Log.
Log.
tan
sin
cosec
10. 15593
8. 87926
10. 04944
o
r
d
//
124
175
116
55
39
49
19
69
3
42
25
27
given
The Hour Columns in Table 44 give the measure in time corresponding to twice the angular distance
a in arc. Thus, abreast the angle 13° 00' stands in the P. M. column lh 44m 00s, corresponding in
time to 2X13° 00'; and in the A. M. column 10h 16m 00s, which is the same subtracted from 12h. These
columns are of use in working the various formulae which involve functions of half the hour angle.
Interpolation for values intermediate to those given in the tables is made on the same principle as for
the angular measure; this operation may be performed by inspection by the use of the small tables at
the bottom of each page, where n, the number of seconds of time, is given in bold-faced type, and d, the
logarithmic difference for the respective columns, appears below.
EXAMPLE I.
Given t=lh 48m 44", find log. cot J t.
log. cot. i t
For lh 48m 40',
Diff. for 4% Col. B
For lh 48m 44',
10. 61687
28
EXAMPLE II.
Given log. sin J t, 9.91394, find the Hour A. M.
corresponding.
For 9. 91389, 4h39m12«
Diff. for 5, Col. C 5
log. cot i t 10. 61659
For 9.91394,
4 39 07
RULES AND PRINCIPLES OF MATHEMATICS. 277
MISCELLANEOUS USEFUL DATA.
Earth's Polar radius=6,356,5S3.8 meters.
Earth's Equatorial radius=6,378,206.4 meters.
Earth's Compression=oqo A^
Earth's Eccentricity =0.0822719 log 8. 9152513.
Number of feet in o'ne statute mile=5280 log 3. 7226339.
Number of feet in one nautical mile=6080.27 log 3. 7839229.
Sine of 1"= 0.00000485 log 4. 6855749.
Sine of 1/=0.0002U089 log 6. 4637261.
The Napierian base £=2.7182818 log 0. 4342945.
The modulus of common logarithms =0.4342945 log 9. 6377843.
French meter in English feet, 3.2808333 log 0. 5159842.
French meter in English statute miles, 0.000621370 log 6. 7933503.
French meter in nautical miles, 0.000539568 log 6. 7320613.
1 pound Avoirdupois =7, 000 grains Troy.
French gramme=0. 00220606 Imperial pound Troy.
French kilogram me=0. 0196969 English cwts.
Cubic inch of distilled water, in grains=252.458. ]
Cubic foot of water, in ounces Troy =908. 8488.
Cubic foot of water, in pounds Troy=75.7374. \ Bar. 30.00 in.; ther. 62° F0
Cubic foot of water, in ounces Avoirdupois=997.1369691.
Cubic foot of water, in pounds A voirdupois=62. 3210606. J
Length of pendulum which vibrates second at Greenwich, 39.1393 inches.
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
The following table contains the latitude and longitude of a large number of places, together with
lunitidal intervals and tidal ranges at the more important ones. It is arranged geographically and followed
by an alphabetical index.
The geographical position generally relates to some specified exact location, and is based upon the
best available authority. The tidal data relate to the waters adjacent to the point whose latitude and
longitude are given, being abstracted from the Tide Tables published by the United States Coast and
Geodetic Survey.
The high-water and low- water lunitidal intervals represent the mean intervals between the moon's
transit and the time of next succeeding high and low waters throughout a lunar month. The spring
and neap ranges are the differences in height between high water and low water at spring and at neap
tides. For those places where the tide is chiefly of a diurnal type, and where there is usually but one
high and one low water during a lunar day, the tidal values are bracketed; in such cases the lunitidal
intervals are for the semidiurnal part of the tide (which, however, is only appreciable for a few days
when the moon is near the equator), and the range given in the column headed "Spg." does not, as in
other cases, apply to the spring tide, but to the greatest periodic daily range, which usually occurs a day
or two after the moon attains its extreme of declination, and is therefore near one of the tropics. As those
places where the diurnal type predominates seldom experience large tidal effects, the general data
furnished regarding such tides will suffice for the ordinary purpose of the navigator. The method of
finding the time of high or low water from this table is illustrated in article 504, Chapter XX.
278
APPENDIX IV. [Page 279
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA.
P
Place.
Lat. N.
Long.W.
Lon.Int.
Range.
H. W.
L.W.
Spg. Xeap.
Labrador.
Salisbury Island: E. pt
ft. m.
ft. m.
A
ft.
63 27 00
63 06 00
62 37 00
62 35 00
62 48 00
62 50 00
62 30 00
62 07 00
61 18 00
60 10 00
60 40 00
60 52 00
60 33 00
61 21 00
61 40 00
60 00 00
59 48 00
59 07 00
57 35 00
57 00 00
56 32 45
55 27 04
55 13 33
54 55 50
54 26 55
54 00 05
53 50 00
53 42 37
53 34 25
53 26 00
52 40 07
52 21 16
52 15 36
52 06 00
51 53 00
51 38 48
50 42 10
49 59 54
49 53 00
49 45 29
49 35 40
49 41 20
49 36 50
49 15 20
49 04 20
48 42 01
48 30 15
48 16 55
47 53 10
48 08 58
47 42 45
47 48 30
47 34 02
46 39 24
46 37 04
46 43 20
46 49 34
47 17 55
47 00 26
46 56 30
76 30 00
77 50 00
78 08 00
77 33 00
74 00 00
75 20 00
74 03 00
72 25 00
70 02 00
67 05 00
67 50 00
64 40 00
64 12 00
65 00 00
64 30 00
64 28 00
64 07 15
63 20 00
61 20 00
62 07 00
61 40 13
60 12 34
59 OS 01
57 56 40
57 12 40
56 31 31
56 23 00
56 59 50
55 58 39
55 35 48
55 44 29
55 38 03
55 32 20
55 41 00
55 22 10
55 25 12
55 35 30
55 21 33
55 37 17
53 10 56
53 45 00
54 47 35
54 12 00
53 25 12
53 37 45
53 04 42
53 02 40
53 23 35
53 23 20
52 47 42
53 08 11
52 47 20
52 40 54
53 04 30
53 31 55
53 22 10
54 11 42
53 58 43
55 08 49
55 32 00
XnTtino'harn Tslp.nd • S pt
8 58
2 46
13.5
6.1
Digges Island: W extreme
Cape Wostenholme
Charles Island* E pt
W pt
Cape Weggs
Prince of Wales Sound: Center of ent
Cape of Hopes Advance
Akpatok Island* E pt
Green Island: XE. pt
Button Islands* N pt ...
Cape Chiolleio-h
Resolution Island: S. pt., Hutton h'dl'd. .
E. pt., C. Resolution. .
Black Head
Eclipse Harbor* E side
8 00
7 00
1 48
0 48
5.0
5.2
2.0
2.1
Xachvack Bav: Islands off entrance
Saddle Island'. .
Port Manvers: Entrance.
Xain: Church
7 00
5 30
0 48
11 43
6.5
6.9
3.0
3.2
Hopedale Harbor: Hill to E'd
Aillick Harbor* Cape Mokkivik
Cape Harrison* N extreme
Indian Harbor: Obsy
6 10
12 23
7.0
3.2
Outer Gannet Island: Summit
Greadv Harbor
Cartwfieht Harbor: Caribou Castle
Indian Tickle* Summit
6 27
0 15
6.0
2.8
Roundhill Island* Summit
Occasional Harbor: E. summit of Twin I.
Cape St Lewis: SE pt . . . .
6 38
6 30
0 26
0 18
5.0
3.5
2.3
1.6
Battle Islands: XE extreme SE I
Table Head
Belle Isle* Lighthouse
Newfoundland.
Cape Bauld: Lighthouse
Bell Island: S end... .
Cape St John* Gull Inland light
Tilt Cove, Union Copper
Mine
Funk Island" Summit
Offer Wadham: Lighthouse
Toulinguet Inlands* Lityhthoii<se
Seldom-come-bv Harbor* Ship Hill
Cape Freeh- Gull I
Greenspond Inland
Cape Bona vista* Lighthouse
Cat'ilina Harbor* Green I li^hthou^
Bonaventu^e Head
Hearts Content* Lighthouse
7 23
1 11
4.1
1.9
Baccalieu Island* Lighthouse
Harbor Grace* Lighthouse on beach
7 15
1 03
3.3
1.5
Cape St Francis* Li^hthou^e
St. Johns Harbor: Chain Rock Battery. . .
Cape Race: Lighthouse
Cape Pine* Li^hthou^
7 12
6 50
1 01
0 38
3.3
6.5
1.5
3.0
Trepassev Harbor* Shingle Xeck
6 50
8 20
0 38
2 08
6.6
7.2
3.1
3.3
Cape St Marv: Lighthouse
Little Placentia Harbor: W. side Coopers
Cove
' Burin Icland* Lifrhthou<;e
! Launt Gr. Laun R. C Church..
8 05
1 53
7.0
3.2
Page 280] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
o
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Labrador. Newfoundland.
St. Pierre: U. S. Coast Survey Station
Brunet Island: Mercers Bd. lighthouse. . .
Boar Islands: Burgoo I light-house
h. m.
8 23
8 53
8 22
8 50
h. m.
2 11
2 41
2 10
2 38
A.
6.6
6.5
6.2
6.0
ft.
3.1
3.0
2.9
2.8
46 46 51
47 15 30
47 35 13
47 39 50
47 37 00
47 52 30
48 33 48
49 55 20
50 38 30
50 41 50
51 02 00
51 17 25
51 24 10
51 38 00
51 58 00
51 27 35
51 22 45
51 22 26
51 27 22
51 21 40
50 47 30
50 46 44
50 31 10
50 14 00
50 09 30
50 11 00
'50 06 00
50 12 27
50 05 40
49 19 35
46 48 23
46 47 59
45 29 57
45 23 30
48 31 25
49 06 00
49 15 40
48 51 37
48 45 15
49 05 20
49 23 45
48 29 30
48 24 00
48 12 00
48 01 00
48 04 24
48 01 07
47 14 00
47 05 00
47 03 46
46 33 56
46 27 15
46 11 36
47 50 40
47 37 40
47 16 30
47 14 23
47 16 03
56 10 36
55 51 40
57 36 52
58 24 10
59 18 00
59 23 40
59 13 10
57 50 00
57 17 07
57 25 00
57 03 50
56 44 45
56 33 40
55 53 52
55 50 20
56 51 05
57 08 00
57 10 04
57 13 21
57 46 00
58 51 30
58 59 20
59 20 25
59 45 00
59 57 00
60 08 00
61 44 00
63 27 03
66 22 44
67 21 55
71 12 19
71 13 10
73 34 08
75 42 59
68 27 40
66 46 00
65 19 30
64 12 00
64 09 35
61 42 30
63 35 46
64 08 00
64 18 00
64 46 30
65 19 00
66 22 10
64 29 20
65 02 00
64 47 33
63 58 49
63 41 35
61 57 35
63 06 58
61 08 32
61 24 30
61 41 20
61 49 38
62 12 25
La Poile Bay: Gr. Espic Church..
Cape Ray: Lighthouse
Codroy Island: S. side Boat Harbor
8 50
2 32
4.3
2.1
Cape St. George: Red L, SE. pt
Cow Head: N W. extreme
9 40
3 13
4.9
2.5
PortSaunders: Two Hills Pt
Rich Point: Lighthouse
F6rolle Pena: New Ferolle Pt.
Flower Cove: Capstan Pt
Green Island: 150 fms. from NE. end
Cape Norman* Lighthouse
Chateau Bay S pt Castle I
Amour Point: Li<*hthouse
Wood Island: S pt
Greenly Island: Lighthouse
Bradore Bay: Obs. Spot, Jones Pt
Old Fort Island: Center..
Great Mekattina Island: SE.pt
Mokattina Harbor: S. point of Dead Cove.
Little Mekattina L: S. pt. C. McKinnon.
St Mary Reefs
South Makers Ledge
Cape Whittle
R. and G. of St. Lawrence.
Natashquan Point: S ed<Te
1 25
6 45
4.0
2.0
C learwater Point: SW extreme
CUOUSB! Island: Lighthouse
1 43
1 48
6 07
7 05
7 18
0 54
8.1
10.8
14.6
6.0
8.0
10.8
Point do Monts: Lighthouse
Quebec: Mann's Bastion, Citadel
Qiiobno: Bomier's Hill Obsy
Montreal: St. James Cathedral
Ottawa: Dominion Observatory
Father Point: Lighthouse.
1 52
1 46
1 33
1 25
7 33
7 13
6 50
6 40
12.0
10.5
6.4
5.5
8.9
7.8
4.7
4.1
Cape Chatto: Extreme
Cape Magdalen : Lighthouse
(,'npo Rosier: Lighthouse
Cape Ga^p6: Lighthouse
Anticosti Island: Heath Pt. lighthouse. . .
SW. pt. lighthouse
Bonaventuro Island: E. pt
1 20
1 25
6 35
6 40
3.6
4.9
1.8
2.5
*
I
I.eander Shoal
Macquereau Point
1 55
2 20
3 10
2 00
4 16
7 33
8 07
9 10
8 25
10 59
4.7
4.8
8.1
4.0
2.3
2.3
2.4
4.1
2.0
1.2
Chaleur Bay: Carlisle
Dalhousie I
Miscou Island: Birch Pt. lighthouse
Miramichi Bay: Portage I., N. pt.
Point Earn men SIP: Lignthoiiso
North Point: Lighthouse .
4 20
5 15
8 17
11 07
11 00
11 55
2 20
4 23
2.4
1.8
1.4
6.4
1.2
0.9
0.7
3.2
l M
h
*t
Malpeque Bay: Rovalty Pt .
East Point: Lighthouse
Charlottetown: Blackhouse Pt. light
Gt Bird Rock* Lighthouse
l
¥
East Island * E extreme
Entry Island: Lighthouse..
Amherst Hbr : N. side of entrance
Deadrnan Rock: W. pt
APPENDIX IV. [Page 281
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
I
Place.
Lat. X.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
St. Paul Island: Lighthouse, NE. end
Lighthouse, SW. end —
Cape North: Lighthouse
h. m.
8 30
A. m.
2 12
£7
ft.
1.4
47 13 50
47 11 20
47 01 45
46 21 00
46 12 25
46 02 15
45 54 34
45 28 00
46 00 00
43 58 14
45 40 50
45 52 00
45 41 42
45 30 48
45 19 49
45 11 58
45 06 15
45 00 35
44 39 38
44 26 10
44 34 00
44 29 00
44 21 45
44 12 00
44 02 00
43 48 30
43 37 15
43 23 19
43 23 34
43 47 28
44 05 20
44 14 57
44 41 34
45 14 55
45 19 00
45 18 40
45 35 34
45 19 30
45 14 20
45 03 40
45 04 00
45 04 06
44 57 40
44 45 52
44 30 38
44 30 07
45 11 05
44 54 15
44 48 55
44 43 01
44 22 03
44 14 29
43 58 08
44 48 23
44 25 29
44 06 06
43 47 03
43 45 53
43 42 26
60 08 32
60 09 50
60 23 27
60 27 00
60 12 50
59 40 25
59 59 26
61 03 00
61 36 00
59 44 15
62 42 10
61 52 00
61 29 10
61 01 47
60 55 41
61 08 14
61 32 40
61 52 45
63 35 22
63 33 30
63 54 00
64 06 00
64 17 35
64 18 00
64 37 30
64 47 15
65 15 45
65 37 11
66 00 52
66 09 21
66 12 40
66 23 38
65 47 20
65 00 45
64 57 00
63 48 30
64 46 55
65 32 00
66 03 20
66 27 40
66 49 00
67 02 52
66 54 10
66 44 00
66 47 00
67 06 13
67 16 50
66 59 14
66 57 04
67 27 22
67 51 51
68 11 58
68 07 44
68 46 59
69 00 19
69 06 52
68 51 28
69 18 59
69 45 32
8 35
8 25
8 10
2 17
2 13
2 05
3.1
6.0
5.0
1.6
3.7
3.1
M
c
0
ti
£
0
St. Anns Harbor: E. pt. entrance
Sydney Harbor: Lighthouse
Scatari Island: Lighthouse, NE. pt ..
Louisburg: Lighthouse, NE. pt
7 45
7 55
9 05
1 35
1 47
2 47
5.0
5.0
3.5
3.1
3.1
1.8
Madame Island * S pt
Port Hood ' Just-au-corps I
Sable Island: Lighthouse, E end
Pictou: Customhouse
9 34
9 20
9 26
7 55
7 43
7 45
3 13
3 00
3 10
1 47
1 36
1 38
3.9
2.8
3.1
5.0
6.5
6.6
2.0
1.4
1.6
3.1
4.0
4.1
Nova Scotia.
Cape St. George
North Canso: Lighthouse, NW. entrance.
Arichat Harbor: R. C. Church steeple
Cape Canso: Cranberry I., lighthouse
White Head Island: Lighthouse .
Green Island: Lighthouse....
Wedge Island : Lighthouse . . .
Halifax: Dockyard observatory..
7 34
146
5.2
3.2
Sambro Island* Lighthouse
Margaret Bay: Shut-in I
7 32
1 30
7.1
4.4
Tancook Island
Lunenburg: Battery Pt light
7 39
1 36
7.0
4.3
Cape La Have: Black Rock.
Coffin Island" Lighthouse
Little Hope Island* Lighthouse
Shelburne Hbr. : Two lights, McNutts 1 . .
Cape Sable: Lighthouse
8 17
9 35
10 00
2 05
3 23
3 41
8.5
12.8
16.0
5.2
9.5
11.8
Seal Island: Lighthouse
Yarmouth : Cape Fourchu light
Cape St. Mary
Bryer Island : Lighthouse
10 29
10 49
11 07
4 36
4 41
5 27
20.8
27.5
33.0
15.4
20.4
24.4
Annapolis Harbor: Prim Pt. light.
Haute Island: Lighthouse
Cape Chignecto ..
Rurntcnat TTpad: Lighthouse ,
0 27
7 27
50.5
37.4
Cape Enrag£: Lighthouse
tf
^
/
9
a
2
«'
c
"3
Cape Quaco : Lighthouse ....
11 21
11 07
11 04
11 09
11 00
5 56
4 58
5 26
5 08
5 00
30.0
23.9
24.5
23.3
24.9
22.2
17.7
18.2
17.1
18.2
St. Johns: Partridge I. light. . .
Cape Lepreau : Lighthouse
L'Etang Harbor: S. pt. tower
St. Andrew: S pt. li<>ut
Campo Bello Island: Lighthouse, N. pt. .
Grand Manan Island : Lighthouse, NE.pt.
Gannet Rock* Lighthouse NE pt
11 02
5 21
22.5
16.7
Machias Island* Lighthouse
10 51
11 36
11 09
4 56
5 40
5 05
18.0
23.3
20.9
13.2
17.1
15.2
Calais: Astronomical station
Eastport: Cong. Church..
Quoddy Head* Lighthouse
Machias- Town Hall
11 02
4 59
15.5
11.3
Petit Manan Island : Lighthouse
Bakers Island: Lighthouse
Mount Desert Rock* Lighthouse
Bangor* Thomas Hill
0 23
11 35
11 09
10 45
6 47
5 22
4 55
4 31
15.1
11.7
11.0
10.2
11.0
8.6
8.1
7.5
Belfast: Methodist Church
Rockland : Episcopal Church
Matinicus Rock : Lighthouse
Monhegan Island * Lighthouse
Seguin Island * Lighthouse
Page 282] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP NORTH AMERICA— Continued.
1
6
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.w.
Spg.
Neap.
Maine.
Bath: Winter St. Church
ft. TO.
12 13
ft. m.
6 16
ft.
7.9
ft.
5.8
43 54 55
43 54 29
44 18 52
43 39 28
43 37 23
43 33 51
43 27 24
43 07 17
43 03 32
43 04 56
43 04 16
42 56 15
42 58 02
42 48 30
42 48 55
42 41 07
42 39 43
42 38 21
42 36 46
42 36 07
42 32 48
42 31 00
42 30 20
42 22 48
42 22 22
42 21 28
42 19 41
42 16 11
41 58 44
42 00 12
41 43 20
42 02 23
41 40 17
41 33 34
41 16 55
40 37 05
41 17 01
41 28 08
41 28 51
41 20 55
41 24 52
41 38 10
41 26 30
41 26 58
41 29 07
41 38 34
41 50 21
41 21 40
41 09 10
41 18 14
41 04 16
41 19 31
41 21 16
41 12 23
41 08 29
41 10 25
41 16 17
41 19 22
69 49 00
69 57 44
69 46 37
70 15 18
70 12 30
70 12 11
70 19 46
70 28 37
70 41 49
70 44 22
70 42 34
70 50 12
70 37 25
70 52 28
70 49 10
70 46 00
70 40 55
70 34 31
70 39 59
70 39 58
70 51 23
70 53 03
70 50 03
71 07 46
71 03 05
71 03 50
70 53 26
70 45 35
70 39 12
70 36 04
70 16 52
70 03 40
69 57 01
69 59 39
70 05 57
69 36 33
69 57 57
70 45 29
70 36 01
70 50 08
70 57 01
70 55 36
71 13 30
71 24 00
71 19 40
71 15 39
71 23 59
71 28 55
71 33 08
71 51 32
71 51 27
71 54 49
72 04 47
72 06 26
72 08 44
72 12 43
72 20 37
72 55 09
Brunswick* College spire
Augusta: Baptist Church
2 54
11 06
10 18
4 51
4.9
10.1
3.6
7.3
Portland : Customhouse ....
Portland. Head lighthouse
Cape Elizabeth* Lighthouse (west)
Wood Island* Lighthouse
11 12
4 51
10.2
7.5
Boon Island • Lighthouse
WTiale Back: Lighthouse
5
K
Portsmouth: Navy-yard flagstaff
11 23
5 09
10.5
7.7
Fort Constitution
Hampton* Baptist Church
Isles of Shoals* White I lighthouse
11 19
11 23
4 58
5 10
10.0
9.1
7.3
6.6
Newburyport : Academy
Massachusetts.
Plum I. lighthouse
Ipswich: Lighthouse (rear)
11 17
11 13
5 04
5 00
10.1
10.1
7.4
7.4
Annisquam Harbor: Lighthouse
Cape Ann: Thatchers I. lighthouse (N.). .
Gloucester" Universalist Church
Ten-pound I lighthouse
11 02
4 49
10.2
7.5
Beverly: Hospital Pt lighthouse
Salem: Derby 8 Wharf lighthouse
11 16
11 09
5 03
4 57
10.6
10.6
7.7
7.7
Marblehead: Lighthouse
Cambridge: Harvard Observatory
Boston: Navy-yard flagstaff
11 27
5 17
11.0
8.1
Pt.at.ft "HVmfifi
Little Brewster I. lighthouse
Minots Ledge: Lighthouse
11 09
4 56
10.9
8.0
Plymouth: Pierhead.
Gurnet lighthouse
11 23
11 36
5 11
5 25
10.8
11.6
7.9
8.5
Barnstable: Lighthouse
Cape Cod: Highland slight house
Chatham: Lighthouse (south)
12 11
12 00
0 04
5 57
5 48
6 00
4.6
4.3
3.8
3.4
3.1
2.3
Monomoy Point : Lighthouse
Nantucket: South Church
Nantucket Shoals: Lightship
Sankaty Hpad " Lightboiipp
Tarpaulin Cove: Lighthouse
7 51
11 34
7 31
7 36
7 57
7 40
7 40
7 48
7 53
8 12
7 32
7 33
8 49
8 20
9 09
9 26
9 26
9 40
1 51
4 33
1 20
0 59
1 18
1 05
1 09
1 00
0 40
0 57
1 17
1 25
2 38
2 03
3 03
3 32
3 04
3 35
2.8
2.0
3.7
4.3
5.2
4.5
4.7
4.4
5.2
5.4
3.8
3.7
3.2
2.3
3.2
2.9
3.0
2.5
1.7
1.2
2.2
2.6
3.1
2.6
2.8
2.6
3.6
3.4
2.3
2.2
2.1
1.5
2.1
1.9
2.0
1.7
Vineyard Haven: W. Chop lighthouse...
Gay Head: Lighthouse.. .
Cutty hunk: Lighthouse... . ,.
New Bedford: Baptist Church
Sakonnet Point: Lighthouse
Rhode Island.
Beaver Tail : Lighthouse
Newport: Flagstaff, torpedo station
Bristol Ferry: Lighthouse..
Providence: Brown University Obsy
Point Judith: Lighthouse
Block Island : Lighthouse (SE.)
Watch Hill Point: Lighthouse
Montauk Point: Lighthouse
'*
fc
•d
a
es
fl
0
0
w
Stonington: Lighthouse
New London: Groton Monument
Little Gull Island: Lighthouse
Gardners Island: Lighthouse, N. pt
Plum Island: Lighthouse, W. pt
Say brook: Lighthouse, Lynde Pt
10 29
11 08
4 11
4 54
4.3
7.0
2.8
4.9
New Haven: Yale University Obsy. .
APPENDIX IV. [Page 283
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
l
Place.
Lat. N.
Long. W.
Lion. Int.
Range.
H. W.
L. W.
Spg.
Neap.
N
A
«
6
1
j
1
8
•
•
i
f
i
m
I~*
« s
if
*s
I!
jf
|
1
E
K
E
•
I
j
c
a
0
h
0
£
M
fa
0
BJ
1
E
i
0
•
Bridgeport Harbor* Lighthouse
A. TO.
11 09
11 03
7 48
7 19
5 13
8 44
h. m.
5 04
4 56
1 38
1 20
0 46
2 49
ft.
8.4
8.2
3.0
2.2
2.8
5.3
6
5.7
2.0
1.4
1.8
3.4
41 09 24
41 02 56
40 51 03
40 37 57
42 39 13
40 42 02
40 42 44
40 36 20
40 27 42
40 28 15
40 23 48
39 45 52
39 30 22
39 21 59
38 47 20
38 55 59
39 58 02
39 53 14
39 44 27
38 46 42
37 54 40
37 23 46
37 07 22
39 17 48
38 58 53
38 02 19
38 52 30
38 55 14
38 53 20
37 00 06
3649 33
37 32 16
36 55 35
36 17 58
36 03 24
36 22 36
35 49 07
35 15 17
35 06 32
35 06 21
34 37 22
34 43 05
33 34 26
33 22 08
33 13 21
33 01 06
32 41 43
32 46 34
32 26 02
32 05 33
32 01 20
32 04 52
31 23 28
31 21 54
31 08 02
31 08 51
73 10 49
73 25 11
72 30 16
73 13 08
73 46 42
73 58 51
74 00 24
74 03 15
74 00 09
73 50 09
73 59 10
74 06 24
74 17 08
74 24 52
74 34 36
74 57 39
75 16 39
75 10 32
75 33 03
75 05 03
75 21 23
75 41 59
75 54 24
76 36 30
76 29 08
76 19 20
76 59 45
77 03 57
77 00 36
76 18 24
76 17 46
77 26 04
76 00 27
76 13 23
76 36 31
75 49 51
75 33 49
75 31 J6
75 59 11
77 02 24
76 31 29
76 39 48
77 49 12
79 16 49
79 10 55
79 22 19
79 52 54
79 55 49
80 40 27
80 33 15
80 50 37
81 05 26
81 17 01
81 25 39
81 23 30
81 29 26
Norwalk Island* Lighthouse
Shinnecock Bav: Lighthouse . ...
Fire Island : Lighthouse
Albany: New Dudley Observatory
New York: Navy-yard flagstaff
City' Hall
Fort Wadsworth: Lighthouse
7 41
7 30
1 38
1 23
5.4
5.6
3.5
3.6
Sandy Hook: Lighthouse (rear)
Lightship
Navesink Highlands: N. lighthouse
Barnegat Inlet: Lighthouse
7 50
7 48
9 59
1 43
1 42
3 57
2.7
4.2
4.7
1.7
2.7
3.0
Tuckers Beach: Lighthouse. .
Absecon Inlet: Lighthouse
Five Fathom Bank: Lightship
Cape May: Lighthouse
8J6
1 28
0 53
12 00
8 17
1 47
8 58
8 02
6 40
1 50
5.6
6.2
7.0
6.7
5.4
3.6
4.4
5.2
4.9
3.5
Philadelphia, Pa.: University Obsy
Navy-yard flagstaff,
League I
Wilmington Del * Town Hall .
Cape Henlopen* Lighthouse..
Assateague Island: Lighthouse... .
Hog Island: Lighthouse
Cape Charles: Lighthouse
8 03
6 34
4 39
0 31
7 42
2 19
044
10 53
6*2
1 56
3.0
1.4
1.0
1.7
3.5
2.0
1.0
0.8
1.1
2.5
Baltimore: Johns Hopkins Obsy
Annapolis: Naval Academy Observatory.
Point Lookout* Lighthouse
Washington, D. C.: Navy-yard flagstaff...
Naval Observatory. .
Capitol dome
Old Point Comfort' Lighthouse
844
9 05
4 30
7 53
2 17
2 47
11 55
1 43
3.0
3.2
4.3
3.2
2.0
2.1
2.9
2.1
Norfolk* Navy-vard fla°rstaff
Richmond, Va. : Capitol
Cape Henry Lighthouse
Elizabeth City* Courthouse
Edenton : Courthouse
Currituck Beach: Lighthouse
7 37
1 26
3.4
2.2
Bodie Island: Lighthouse
Cape Hatteras: Lighthouse
Ocracoke* Lighthouse
7 00
0 45
2.2
1.5
Newbern* Episcopal spire
Cape Lookout * Lighthouse
6 29
7 21
0 20
1 08
4.4
3.3
3.0
2.3
Beaufort N C * Courthouse
Frying-Pan Shoals : Lightship
Georgetown* Episcopal Church
8 39
3 38
4.3
2.9
Lighthouse North I
Cape Romain* Lighthouse
6 59
0 50
5.9
4.1
Charleston * Lighthouse Morris I
St Michael's Church
7 20
8 10
1 10
2 06
6.0
8.5
4.2
5.9
Beaufort S. C : Episcopal Church
Port Royal: Martins Industry lightship...
Tvbee Island * Lighthouse . . .
7 10
8 13
7 30
7 40
7 30
8 00
1 04
3 07
1 24
1 44
1 27
1 57
7.9
7.6
8.4
7.5
7.5
7.8
5.5
5.3
5.8
5.2
5.3
5.4
Georgia.
Savannah : Exchange spire
Sapelo Island : Lighthouse
Darien* Winnowin0* House
St Simon* Lighthouse
Brunswick: Academv
Page 286] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP NORTH AMERICA— Continued.
o
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Belize.
Sand-Fly Cays' Hut S end
ft. m.
ft. TO.
ft.
ft.
16 57 50
16 48 50
17 29 20
16 57 40
16 47 45
16 48 10
16 30 54
16 14 15
15 54 00
15 49 45
15 38 00
15 24 20
15 52 20
15 57 45
16 08 00
15 47 11
15 48 45
15 38 00
15 55 45
16 03 40
15 58 00
16 18 00
16 24 20
16 28 00
18 44 00
17 24 21
15 53 00
16 00 00
15 51 50
15 48 50
15 23 40
15 00 04
16 03 30
15 52 00
15 51 00
15 08 50
15 07 00
14 21 12
16 54 00
15 47 45
14 21 33
14 08 00
14 30 00
13 34 30
13 22 54
12 31 40
12 24 00
12 10 00
12 22 35
12 20 39
11 59 00
12 17 30
12 09 17
10 56 15
10 02 00
10 00 16
88 06 05
88 05 36
88 11 20
88 13 48
88 15 15
88 37 40
88 22 13
88 35 51
88 56 20
88 46 22
89 01 36
89 09 15
88 33 22
88 38 50
88 20 15
88 04 31
87 27 46
86 55 00
85 59 18
86 59 15
86 32 09
86 34 27
86 18 41
85 55 00
84 02 00
83 56 25
85 27 10
85 03 00
84 38 33
84 17 10
83 42 36
83 09 22
83 08 20
82 23 27
82 18 07
82 42 08
82 20 00
82 45 57
80 51 27
79 50 53
80 15 20
81 08 21
81 07 21
80 05 05
81 21 26
81 43 06
81 27 53
81 49 54
83 23 10
83 37 12
83 41 57
82 58 35
83 03 35
83 42 15
83 48 30
83 00 57
South Water Cay Center
Belize* Fort George li^ht
8 00
1 50
1.5
0.8
North. Standin0' Creek * Entrance . . .
Sittee Point- Cay
Cockscomb Mount: Summit, 4,000 feet...
Placentia/ Point' Huts on point
Icacos Point' S extreme
Sarstoon River* Entrance
Dulce River' Entrance ^V side
9 00
2 50
2.0
1.1
Guat.
Dulce Gulf* Fort St Philip
Izabal
Hospital Bight: Hut, N. pt. of entrance..
Cape Three Points: NW. extreme
Honduras.
Seal Cays: S Cay
Omoa : Entrance
Cape Triunfo: Bluff pt
Con^rehoy Peak * Summit 8 040 feet
Truxillo* Fort
Utilla Island* S Cay
Hog Islands: Highest hill on W islet ..
Roatan: Center of Coxen Cay ...
7 35
1 23
3.5
1.8
Port Royal, NW. pt. of George
Cay
Bonacca Island: Summit, 1,200 feet
8 50
2 38
1.5
0.8
Misteriosa Bank' S Point
Swan Islands: Light on W. pt. of west
island
Great Rock Head: Bluff extreme
Cape Camaron
Brewers Lagoon: E.side of entrance. . . .
Patuca River: E side of entrance
Carataska Lagoon: E. side of entrance
Cape Gracias-d-Dios : Lighthouse
10 20
4 07
2.0
1.1
Nicaragua.
Caxones Reef: Great Hobby Islet
Gorda Bank* Gorda Cay
Farrall Rock: Center
Half moon Cay Center
Alargate Reef- E pt
Miskito Cays: S end
Miskito Shore.
Rosalind Bank* NW extreme
Serranilla Bank: Beacon Cay
4 00
4 00
10 13
10 13
2.0
2.0
1.1
1.1
Serrana Bank: Little Cay
Quita Sueno Bank: S. extreme of reef
Spit at N W end
Roncador Cay: S. pt. . . .
Old Providence: Isabel House
St. Andrews Island : S W. cove, Entrance I .
Courtown Cays* Middle Cay
4 00
10 13
1.0
0.5
Albuquerque Bank' Smith Cay
Pearl Cays: Colombilla Cay
1 50
8 03
2.0
1.1
Pearl Cays Lagoon: Mosquito Pt
Bluefields: Schooner Pt
1 40
7 52
2.0
1.1
Little Corn Island : Gun Pt
Great Corn Island : Wells N. of Quin Bluff.
Greytown : Lighthouse
1 35
1 00
7 47
7 13
2.0
1.5
i.i
0.8
Mount Cartago- Peak 11 100 feet
B
0
Port Limon: Monument, Park, opp. P. O.
1 00
7 13
1.6
0.9
APPENDIX IV. [Page 287
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP NORTH AMERICA— Continued.
i
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.w.
Spg.
Neap.
«
i
8
i
i
Carreta Point: Extreme
h. m.
&. m.
A-
ft.
9 38 30
9 26 16
9 25 00
9 14 24
9 20 17
9 14 53
9 17 00
9 10 30
9 06 00
9 19 27
9 22 39
9 22 09
9 33 20
9 34 00
8 53 52
8 46 30
82 39 06
82 20 40
82 19 28
82 19 36
82 14 29
82 07 48
83 03 00
81 54 06
81 33 57
80 00 22
79 57 13
79 54 42
79 39 13
78 57 00
77 40 53
77 32 15
Almirante Bay: Tirbi Pt., Extreme
Columbus I., Lime Pt
Shepherd I., Summit. . . .
Bocaa del Toro, Radio
Tel. Sta
0 42
Crawl Cay Channel : Crawl Cay
Blanco Peak: Summit, ll,740*feet
Chiriqui Lagoon: Valiente Peak, Summit.
Escudo de Veragua: NW. Pt. of Island . . .
Chagres : San Lorenzo Castle
Toro Point: Lighthouse
Colon : Lighthouse
0 06
6 18
1.1
0.6
Porto Bello: Ft. St. Geronimo .
Gulf of San Bias: Cape San Bias
Caledonia Harbor: Dobbin Cay. .
11 30
5 17
1.5
0.8
Port Carreto: Peak
WEST COAST OF NORTH AMERICA.
«
i
X
Point Barrow: Highest lat. of Alaska ....
Icy Cape : Extreme
71 23 30
70 16 00
68 52 00
67 09 00
66 14 30
66 32 00
65 35 30
65 33 30
65 16 40
64 26 00
63 26 00
63 34 30
61 40 00
63 16 00
60 18 00
60 13 00
60 25 22
58 48 31
57 30 24
55 54 59
56 34 23
52 56 01
51 59 04
51 23 39
51 49 18
52 10 36
57 07 19
53 52 54
54 13 30
54 26 12
55 20 45
55 19 17
55 07 36
55 03 17
54 58 25
54 55 30
156 27 00
161 47 30
166 06 00
163 34 00
161 45 00
163 36 00
168 40 00
168 00 00
166 46 30
165 05 00
162 02 30
162 42 30
166 15 00
168 41 00
172 02 00
172 36 00
166 08 30
160 50 00
157 58 30
160 34 54
169 39 50
Long E.
173 12 24
177 30 00
179 12 06
LongW.
176 52 00
174 15 18
170*17 52
166 31 44
162 38 00
162 18 00
160 38 39
160 31 14
159 56 06
159 23 05
159 22 18
159 15 03
11 41
5 33
0.6
0.2
Cape Lisburne : 849 feet
Cape Krusenstern: Extreme
Chamisso Island: Summit.
7 45
1 50
2.0
0.6
Cape Espenberg : Extreme
Diomede Island: Fairway Rock
Cape Prince of Wales: W. pt
Port Clarence: Point Spencer
6 10
[205]
[805]
1 10
[8 25'
[1 20;
1.1
[2.11
[4.5J
0.9
Cape Nome : Extreme
St. Michael: Fort
Stuart Island : W. pt
Cape Romanzof : Extreme
St. Lawrence Island : E. pt
St. Matthew Island : SE pt
4 40
11 00
3.1
1.6
Pinnacle Islet: Summit, 930 feet
Nunivak Island : Cape Etolin
Hagenmeister Island
Cape Menchikof : Extreme
PortMoller
St. George Island: S. side
Attu Island : Chichagof Harbor
3 35
3 30
9 48
9 43
5.7
5.2
2.9
2.7
Aleutian Inlands.
Kiska Island: Kiska Harbor, Ast. sta
Amchitka Island: Constantiue Harbor....
Adakh Island : Bay of Islands .
3 25
9 38
5.0
2.6
Atka Island : Nazan Bay (church)
Pribilof Island: St. Paul I., village
4 17
3 50
12 13
10 29
9 58
6 10
2.7
2.9
5.7
1.4
1.5
2.8
Unalaska Island: C. S. station, Ihuliuk. .
Sannakh Reefs: S edge .. ..
Sannakh Island: NE.°end
Unga Island
2 40
8 55
8.2
4.1
Popof Island: Humboldt I
Nagai Island : Sanborn Harbor
Koniushi Island: NW. harbor. .
NE. harbor
Simeonof Island : Simeonof Harbor
2 20
8 33
7.5
3.8
61828°
Page 288] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OP NORTH AMERICA— Continued.
i
Place.
Lat. N.
Long.W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Alaska.
Cape Strogonof * Extreme
ft. m.
ft. m.
ft.
ft.
56 48 00
56 19 20
56 05 13
55 45 24
55 48 22
57 47 57
60 20 43
59 27 22
60 20 45
59 33 42
58 36 57
57 02 52
58 18 00
56 27 00
54 15 25
54 10 30
52 56 31
52 09 07
51 54 00
53 02 00
53 22 20
54 13 00
54 02 14
54 05 50
49 15 22
49 13 46
48 54 41
48 47 23
49 27 31
49 22 07
49 35 31
49 47 20
49 52 45
49 59 55
50 11 21
50 06 31
50 29 25
50 32 26
50 46 41
50 54 47
50 50 49
50 42 36
50 35 02
49 36 29
49 15 43
49 12 50
49 10 15
48 25 26
48 25 50
48 17 53
48 33 30
54 33 20
54 17 17
50 33 58
50 31 09
50 24 15
50 02 42
49 24 39
158 46 00
158 24 24
156 39 19
157 27 04
155 42 51
152 21 21
146 37 38
146 18 45
141 00 12
139 46 16
137 40 06
135 19 31
134 24 00
132 23 00
133 02 00
133 05 10
132 09 06
131 03 20
131 01 26
131 31 00
131 51 00
131 37 00
132 11 16
132 26 10
125 55 43
124 50 07
125 16 54
125 13 14
126 24 53
126 31 58
126 36 58
126 56 31
126 59 21
127 08 56
127 37 24
127 56 46
128 03 05
127 35 44
128 26 11
127 55 29
127 39 23
127 24 33
126 56 56
124 50 44
124 07 32
123 48 11
123 56 02
123 23 31
123 26 48
123 31 47
124 27 37
130 26 09
130 21 33
126 16 06
126 03 47
125 38 26
125 14 34
123 28 46
OTngnilt Bay Anchorage
Anowik Island* S end
1 45
7 58
8.1
4.0
Lighthouse Rocks
Chirikof Island .
Kodiak Island, St. Paul Harbor: Cove
NW of village
0 16
0 50
6 24
7 05
9.0
10.1
4.5
5.1
Port Etches
Middleton Island ....
Mount St Elias* Summit
Yakutat Bay ' Port Mulgrave
e 34
6 41
9.5
5.0
Lituya Bay
Sitka* Middle of parade ground
0 06
0 45
0 30
6 17
6 56
6 39
9.9
18.6
17.7
5.2
9.7
9.2
Juneau
Wrangell • Ast station .
North Island • N pt
Queen Cnarlotte Is.
Cape Knox ' Extreme .'
Port Kuper* Sansum I
0 00
6 12
11.5
6.1
Forsyth Point* Extreme
St James Cape* S extreme
Cumshewa Harbor: N. side of entrance...
Skidegate Bay • Rock on bar
0 07
6 19
12.8
6.7
Rose Spit Point: Extreme
Masset Harbor: Masset village
Cape Edenshaw: Extreme
Hecate Bay Observatory Islet
12 15
0 45
6 08
7 20
10.0
12.4
5.8
7.1
Vancouver Island.
Stamp Harbor* Observatory Islet
Island Harbor* Observatory Islet
Cape Beale ' Lighthouse
12 20
12 05
6 15
5 56
9.9
10.3
5.7
5.9
Hesquiat Harbor* Boat Cove
Estevan Point* S extreme...
Nootka Sound : Friendly Cove
12 05
5 55
9.8
5.6
Port Langford : Col wood Islet
Esperanza Inlet: Observatory Rock
11 55
11 50
11 47
5 45
5 38
5 34
9.7
9.3
9.3
5.5
5.3
5.3
Kyuquot Sound : Shingle Point
Nasparti Inlet: Head Beach
Cook Cape* Solander I
North Harbor* Observatory Rock
Hecate Cove: Kitten Islet
Cape Scott: Summit.......
Bull Harbor, Hope Island : N . pt. Indian I .
Port Alexander: Islet in center. .
0 10
0 32
0 30
0 55
4 45
4 52
6 22
6 44
6 42
7 08
11 00
11 18
10.7
11.6
11.5
12.8
10.6
10.2
5.6
6.1
6.0
6.7
6.6
6.4
Beaver Harbor: Shell Islet
Cormorant I.: Yellow Bluff in Alert Bay.
Baynes Sound* Beak Pt
Nanoose Harbor* Entrance Rock
Nanaimo: Lighthouse
"R fin son's TToiisfi
4 40
[2 171
[2 00]
11 05
[8311
[814]
9.8
[5.71
[5.8J
6.1
Victoria : Lighthouse
Esquimalt : Fisgard I. light «.
Race Island' Lighthouse
Port San Juan: Pinnacle Rock
Port Simpson : Methodist Church Spire . . .
Prince Rupert Hbr. : Fairview Obs. Spot. .
Port Harvey Tide Pole Islet
0 15
0 50
1 55
2 30
3 40
4 45
5 38
20
24,17
14.1
16.0
15.7
7.2
9.0
6.5
16
7.4
8.3
7.7
4.8
5.6
g
d
£
s
8 10
8 47
10 00
10 15
11 58
Port Neville: Robber's Nob
Knox Bay, Thurlow Island: Stream at
head of bay
Valdes Island : S. pt
Howe Sound: Plumper Cove
:?. I
APPENDIX IV. [Page 289
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA— Continued.
I
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg-
Neap.
Washington. Brltlsb Col.
Atkinson Point' Lighthouse
ft. m.
5 20
5 28
5 11
ft. m.
11 35
12 01
11 23
h
8.2
7.0
ft.
4.9
5.0
4.4
49 19 42
49 16 18
49 07 04
49 13 01
49 00 00
49 00 00
48 09 19
47 10 20
47 35 54
48 06 56
48 19 07
48 10 52
48 08 24
48 23 30
46 43 00
46 16 29
47 33 43
47 15 32
46 11 19
44 40 35
43 20 36
42 50 22
41 44 36
41 03 01
40 48 11
40 41 37
40 26 18
38 57 12
37 59 39
37 47 28
37 47 30
37 52 24
38 05 56
38 03 05
37 41 51
37 20 49
37 21 03
37 19 58
37 10 49
36 57 31
36 35 21
36 37 55
35 39 50
34 26 49
34 26 10
34 15 46
33 42.14
34 03 05
32 39 48
123 15 54
123 11 26
123 11 27
123 53 52
123 04 52
122 44 56
122 40 34
122 35 51
122 19 59
122 44 58
122 50 36
123 06 31
123 24 07
124 44 06
124 04 25
124 03 11
122 37 59
122 26 26
123 49 42
124 04 40
124 22 31
124 33 30
124 12 10
124 09 03
124 09 41
124 16 26
124 24 25
123 44 27
123 01 24
122 25 43
122 27 49
122 **-**
**•*,
122 16 24
122 09 23
123 00 07
121 56 26
121 36 40
121 53 39
122 23 39
122 01 29
121 52 59
121 56 02
121 17 06
120 28 18
119 42 42
119 15 56
118 17 41
118 14 32
117 14 37
117 09 41
117 07 32
120 21 55
119 58 29
119 33 51
119 23 04
119 02 29
119 31 19
118 24 05
Vancouver, Burrard Inlet: Govt. Re
serve, English Bay
Fraser River* Garry Pt
New Westminster: Military barracks
Point Roberts : Parallel station
Semiamoo Bay : Parallel station
4 59
11 10
7.1
4.6
Admiralty Head : Lighthouse
Steilacoom : Methodist Church
4 46
4 22
3 47
3 40
2 42
2 10
0 08
11 04
10 33
9 32
9 28
8 34
8 23
6 16
11.0
9.2
6.2
5.6
5.0
5.3
7.1
7.2
6.0
4.0
3.7
3.3
3.4
4.1
Seattle' C S ast station
Port Townsend * C S ast station
Smith Island: Lighthouse..
New Dungeness: Lighthouse
Port Angeles : Ediz Hook lighthouse . .
Cape Flattery: Lighthouse
Cape Shoal water: Lighthouse
Cape Disappointment: Lighthouse
12 22 i 6 19
4 27 10 35
4 32 10 45
0 15 6 42
11 50 ! 5 37
11 55 ! 5 49
7.7
9.4
9.8
7.8
7.3
6.0
4.5
6.1
6.4
4,7
4.3
3.5
Bremerton' Navy-yard flagstaff
Tacoma- St Luke's Church
Astoria: Flagstaff
Oregon.
Yaquina Head : Lighthouse
Cape Arago, or Gregory: Lighthouse
Cape Blanco : Lighthouse
Crescent City : Lighthouse
11 33
11 27
11 57
11 33
11 00
10 36
11 23
12 07
11 43
5 15
5 11
5 45
5 19
4 50
4 21
5 08
5 34
5 07
5.8
5.7
5.7
5.3
4.7
4.1
5.1
5.1
4.9
3.4
3.3
3.3
3.1
3.0
2.6
3.2
3.2
3.1
California. >
Trinidad Head : Lighthouse
Eureka: Methodist Church
Humboldt' Lighthouse
Cape Mendocino* Lighthouse
Point Arena: Lighthouse
Point Reyes: Lighthouse. ..
San Francisco: Davidson Observatory...
Presidio
Berkeley Univ. Obsy
Mare Island: Chronom. and Time Sta.,
Navy-yard
•5
Hi
1 OO
10 40
7 15
7 48
4 25
5.6
5.6
4.5
3.7
3.7
2.9
Benicia* Church
Farallon Islet' Lighthouse
Santa Clara: Catholic Church
Mount Hamilton: Obs. peak
San Jose : Spire
Pigeon Point : Lighthouse
Santa Cruz : Warehouse flagstaff
10 54 4 27
10 43 4 24
5.2
4.8
3.3
3.1
Monterey: C. S. azimuth station
Point Pinos: Lighthouse
Piedras Blancas: Lighthouse
Point Conception: Lighthouse
Santa Barbara: N. tower, Mission Church.
San Buenaventura: C. S. ast. station
Pt. Fermin, San Pedro Bay: Lighthouse..
Los Angeles: Courthouse
9 37 ! 3 io
9 53 3 21
9 36 3 13
4.8
4.9
5.5
2.2
2.2
2.5
Point Loma' Lighthouse
9 29 3 07
9 32 3 20
5.2
5.1
2.3
2.3
San Diego: C. S. ast. station
32 43 06
32 31 58
34 04 19
33 56 30
34 03 12
34 00 25
33 28 16
33 14 55
33 23 09
Mexican Boundary: Obelisk
San Miguel Island : Seal Pt
9 23
3 02
4.9
2.2
Santa Rosa Island: E. pfc
Santa Cruz Island : NE pt
9 29 3 06
4.9
2.2
Anacapa Island: E. pt .
Santa Barbara Island : Summit
San Nicolas Island: Summit
9 20
9 28
3 04
3 08
4.9
5.1
2.2
2.3
Santa Catalina Island : Ca talma Peak
Page 290] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OP NORTH AMERICA— Continued.
I
Place.
Lat.N.
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Lower California.
Ensenada Harbor: Head of bay, close to
beach. • ....
h. 771.
9 28
h. m.
3 06
ft.
5.0
ft.
2.2
31 51 10
31 33 04
30 57 39
30 28 58
30 22 16
29 47 20
29 25 29
29 10 50
28 56 06
28 40 16
28 14 26
28 03 52
28 18 08
27 39 35
27 06 10
26 45 45
26 42 49
26 18 56
26 03 18
24 58 00
24 47 31
24 38 23
24 18 12
24 20 17
23 27 14
22 53 07
23 03 35
23 32 48
24 03 52
24 15 31
24 10 10
24 24 10
24 52 03
25 29 23
25 59 37
26 00 41
26 30 44
26 53 37
27 10 21
27 26 06
28 00 07
28 25 04
28 47 40
28 49 11
28 56 39
29 13 52
29 33 08
29 57 27
30 25 16
31 02 57
31 46 10
31 00 54
30 16 05
29 54 12
29 16 12
28 45 '55
28 45 28
28 03 22
27 50 28
116 38 05
116 40 51
116 17 28
116 06 46
115 59 07
115 48 12
115 12 14
118 18 30
114 31 06
114 14 15
114 06 21
115 11 32
115 36 10
114 54 27
114 17 25
113 16 25
113 35 04
112 41 44
112 17 52
115 51 54
112 18 25
112 08 54
111 42 54
111 30 21
110 14 07
109 54 50
109 40 43
109 28 57
109 50 29
110 20 34
110 20 41
110 20 35
110 41 47
111 01 43
111 06 53
111 21 03
111 27 14
111 58 04
112 05 39
112 19 56
112 47 36
112 51 59
113 12 48
113 00 05
113 34 35
113 40 00
113 35 19
114 25 49
114 39 47
114 52 10
114 43 31
113 16 30
112 53 26
112 45 04
112 28 51
112 21 46
111 58 37
111 16 00
110 54 28
San To mas* NW shore of cove
Colnett Bay: Head of bay
9 27
3 05
5.8
2.6
San Martin Island* Hassler Cove
Port San Quentin • Sextant Pt
9 23
3 00
4.9
2.2
San Geronimo Island: Bight at E. end. . .
Canoas Point* High bluff .
Guadeloupe : North pt
La Playa Afaria* Mound on W side
9 15
2 53
7.6
3.4
Santa Rosalia Bay Obs spot Cairn
Lagoon Head* Highest pt of crater.
Cerros Island * SE extremity
9 05
2 42
7.8
3.5
San Benito Island : Summit of W. island. .
San Bartolome"* N side of entrance
9 00
2 37
8.2
2.8
Asuncion Island* Summit of island
San Ignacio Point* Extreme
Abreojos Point: Extreme of rocky ledge..
San Domingo Point: Edge of cliff
9 00
2 48
6.7
2.3
San Juanico Point* Knoll
8 29
2 17
5.7
1.6
Alijos Rocks* South Rock
Cape San Lazaro* Extreme
Magdalena Bay: Obs. spot (post) N. of
Port Magdalena
8 25
2 12
5.5
1.5
• Cape Tosco * Extreme . ...
El Conejo Point: Extreme
Todos Santos: Foot of hill, Lobos Pt
San Lucas: Steep sand beach, NW. pt. of
bay
San Jose" del Cabo: NE. side of entrance. .
Arena Point* Extreme
8 36
2 20
4.5
1.2
Arena de la Ventana* Extreme
Pichilinque Bay: SE. pt. of San Juan,
Nepomezeino I
La Paz: Obs. spot, El Mogote.
9 40
3 34
5.4
1.3
Lupona Point: Extreme
San Evaristo: 3m. S. of S. Evaristo Hd. .
San Marcial Point* Extreme
Salinas Bay: Beach, NE pt of bay
Loreto: Cathedral
Pulpito Point: Summit
Muleje: Equipalito Pt
San Marcos Island: S. sand spit
Santa Maria Cove: Beach on NW. shore. .
San Carlos Point: Extreme
Santa Teresa Bay: Beach on N side
11 50
5 47
11.2
2.6
Las Animas: Low pt
Raza Island: Landing place, S. side
Angeles Bay: Bight on NW. shore
Remedies Bay: Beach on W. shore
Mejia Island: S. side
San Luis Island: SE. side
San Firmin: Beach, N. of bight
San Felipe Point: Peak, 1,000 feet
Philips Point: Beacon
Georges Island: NE. shore
Mexico.
Cape Tepoca: Hill, 300 feet
Libertad Anchorage: Beach
Patos Island: SE. end
Tib uron Island: SE. end
Kino Point: 0.2 mile N. 88° W. of mound. .
San Pedro* N side of bay
Guaymas: Lighthouse
11 30
5 26
5.0
1.2
APPENDIX IV. [Page 291
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA— Continued.
j
o
i
g
Place.
Lat. X.
Long. TV.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Claris Island: NW part
ft. m.
ft. 771.
ft-
ft.
26 58 59
26 41 09
26 16 35
25 33 56
25 23 06
25 11 42
24 38 52
23 10 40
22 30 26
21 32 30
21 30 45
20 45 50
20 36 26
20 25 00
19 34 48
19 17 15
18 42 57
18 59 41
18 20 55
10 17 00
19 13 25
19 03 15
17 58 21
17 40 15
17 37 50
17 31 28
17 16 13
16 49 10
16 19 37
15 39 09
15 40 41
15 44 58
15 52 17
16 09 36
14 17 44
13 55 15
13 34 20
13 28 50
13 20 00
13 17 09
12 27 54
11 14 45
11 03 10
10 36 46
9 43 45
8 10 13
8 04 30
7 43 32
7 24 20
5 32 57
8 57 06
8 47 45
7 27 40
4 03 00
8 39 00
8 54 30
8 56 32
8 12 30
8 28 50
109 57 17
109 40 48
109 17 30
109 10 23
108 49 00
108 23 37
107 59 37
106 26 47
105 44 25
105 18 40'
106 33 14
105 33 37
105 16 00
105 39 21
105 08 54
110 49 22
110 56 53
112 04 07
114 44 17
109 13 00
104 43 26
104 19 50
102 07 06
101 40 25
101 33 23
101 27 14
101 04 32
99 55 50
98 35 05
96 30 43
96 15 04
96 08 10
95 46 43
95 12 16
91 55 36
90 49 45
89 50 26
89 19 20
87 51 00
87 47 06
87 12 31
85 53 00
85 43 38
85 42 46
85 00 46
82 14 32
81 43 30
81 31 58
81 41 51
86 59 17
79 32 09
79 33 16
79 59 25
81 36 00
79 41 45
79 31 15
79 07 55
78 54 40
78 05 35
Santa Barbara* NW side of bay
A^iabampo* SE side of entrance
Topolobampo: SE. end of Santa Maria I..
Navachista* W side of creek
Playa Colorado* N side of entrance
^.Itata* N side of entrance
10 07
9 08
3 59
2 51
5.8
3.8
1.4
0.9
Mazatlan* Lighthouse
Palenita \~illage* Boca Tecapan
San Bias* Customhouse
9 08
2 52
3.2
1.0
Maria Madre Island* SE extreme
Mita Point* Extreme
Penas Anchorage* Mouth of Rio Real
Cape Corrientes* Extreme ..."
Perula Bay Smooth Rock .
9 07
2 53
2.5
1.1
San Benedicto Island: S. extreme ...
Socorro Island: SE. part
Roca Partida* Summit
Clarion Island* S end
Clipperton Island* Summit
Navidad Bay: W. end of sandy beach
Manzanilla Bay: Flagstaff, U.S. consulate.
Sacatula River: Beach, W. side of bay
Isla Grande: Tripod on NW. summit
9 07
2 54
1.9
L3
Sihuatanejo Point* Tree on beach
8 50
2 38
2.0
0.9
Morro Petatlan: Junction of stony and
sandv bea.ch.es
Tequepa Harbor* Limekiln
Acapulco* Lighthouse .
Maldonado* El Recordo Pt ....
Port \ngeles : Lighthouse
Sacrificios Point: Highest pt. of cape. . . .
Port Guatulco* Cross
Morro Ayuca: Summit of N. edge of cape.
Salina Cruz* Lighthouse
Champerico: Inshore end of iron wharf...
San Jose de Guatemala: Lighthouse
2 50
2 50
2 55
3 05
3 15
9 02
9 02
9 08
9 18
'9 28
8.5
9.0
9.5
10.0
10.5
4.6
4.9
5.1
5.4
5.7
1 Contra! America.
\caiutla* Lighthouse
Libertad* Lighthouse
La Union1 Lighthouse
Chicarene Point' Extreme
Corinto* Lighthouse
2 55
3 00
2 50
2 45
9 08
9 12
9 02
8 58
10.5
10.0
9.5
9.0
5.7
5.4
5.1
4.9
San Juan del Sur: Signal station
Salinas Bay: Salinas Islet
Port Culebra: Extremity of Mala Pt
Ballena Bay: N. Estero'Toussa
Parida Anchorage* S pt of Deer Id
3 15
9 28
10.5
5.7
Port \uevo* Entrada Pt
Bahia Honda: W. end of Centinela I. . . .
Coiba (Quibo) Island: Observation pt
Cocos Island: Head of Chatham Bay. . . .
Panama : Cathedral, S. tower
3 10
9 22
11.0
5.9
3 00
3 00
3 10
9 14
9 13
9 22
16.0
15.4
13.0
8.7
8.3
7.0
Taboga Island : Church ....
Cape Mala: Extreme
Malpelo Island* Summit
Point Cham6* Extreme
3 30
9 42
15.0
8.1
Flamenco Island: N Pt
Chepillo Island: Center
3 05
3 00
9 18
9 13
16.0
15.7
8.7
8.5
Rev Island: Cocas Pt. extreme
Darien Harbor: Graham Pt
Page 292] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS.
I
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
ii
•d
•
•
M
J
3
A
i
cS
A
w
Memory Rock* Center . . . .
ft. ra.
7 40
h. m.
1 28
ft.
3.2
ft.
1.7
26 56 53
26 41 18
25 51 30
26 31 10
27 15 42
26 02 00
25 34 30
22 45 10
22 22 30
21 42 00
22 01 15
22 14 02
22 20 44
22 31 15
22 51 00
23 32 15
23 06 00
25 00 00
25 31 20
25 05 37
24 43 45
25 49 40
25 49 12
24 06 15
23 50 50
23 56 40
23 37 45
22 06 40
22 32 40
22 47 30
22 51 00
23 05 30
22 34 38
22 16 30
21 40 30
20 56 00
21 30 40
21 37 30
21 30 00
21 54 00
21 29 33
21 30 55
21 06 30
20 35 00
20 02 00
20 15 00
20 21 46
20 41 41
20 47 19
21. 04 24
21 09 00
21 07 00
21 07 30
21 07 15
21 18 30
21 32 44
21 40 02
22 08 45
22 11 14
22 29 10
22 09 44
22 38 41
79 06 54
79 00 38
77 10 45
76 57 36
78 23 48
79 06 00
79 18 26
78 06 02
77 34 26
75 44 39
75 10 34
75 45 17
75 28 20
• 75 51 41
74 51 54
75 46 24
74 59 00
76 13 00
76 51 48
77 21 58
77 46 45
77 53 55
77 57 06
74 26 00
75 07 27
74 28 20
74 50 08
74 20 37
74 22 54
74 20 21
74 22 48
73 49 15
73 38 03
72 47 03
73 50 29
73 40 17
73 42 33
72 28 18
72 12 51
72 07 14
71 31 12
71 07 29
70 29 54
69 21 24
68 47 24
74 08 01
74 29 13
74 53 44
75 34 21
75 36 59
75 47 18
75 47 40
75 '52 18
76 06 27
76 35 34
77 15 18
77 08 04
77 37 33
77 39 23
78 09 11
78 35 54
79 13 44
Htihaniii Island * W pt
Abaco Island. * Lighthouse
Little Guana, Cay Lighthouse
Walker Cay * Highest part
Great Isaac Cay* Lighthouse
Gun Cay Lighthouse
8 20
2 08
3.0
1.5
Ginger Cay Center
Cay Lobos" Lighthouse
St Domingo Cay Center
Cay Verde* Hill at S end
Ragged Island * Gun Pt
Nairn Cay E pt
Nurse Channel Cay Beacon
Long Island* S pt
Great Exuma Island* Beacon
Clarence Harbor: Lighthouse
8 20
7 00
2 08
0 48
4.1
4.0
2.1
2.1
Eleuthera Island: Lighthouse
Royal Island: Eastern Pass.. . . ..
Nassau: Lighthouse
7 20
7 40
1 08
1 28
4.0
3.0
2.1
1.5
Andros Island : Lighthouse .
Great Stirrup Cay Lighthouse
Little Stirrup Cay W end
San Salvador (Cat I.) : Lighthouse
7 00
0 48
4.0
2.1
Concepcion Island* W bay
Watlings Island: Hinchinbroke Rock
Rum Cay: Harbor Pt
Castle Island: Lighthouse
Fortune Island: S end
Crooked Island: Moss flagstaff
Bird Island: Lighthouse
Samana Cay: W. pt
Plana Cay NW pt
Mariguana Island: SE.pt
7 20
1 08
3.0
1.5
Hogsty Reef* NW Cay
Inagua Island: Lighthouse.
7 50
1 38
3.5
1.8
Little Inagua Island* NW pt
W. Caicos Cay: Hill SE end
French Cay: W. pt
Fort George Cay: Old magazine
Caicos Island: Parsons Pt S islet
Turk Island: Lighthouse
7 30
1 18
3.0
1.5
Square Handkerchief Bank: NE. breaker.
Silver Bank* E extreme
Navidad Bank* Center of E side
Cape Maysi: Lighthouse
5 40
11 53
2.8
1.6
Port Baracoa: Lighthouse
Port Cayo Moa: Carenero Pt
Nipe Bay: Extremity of Carenero Pt
Lucrecia Point: Lighthouse
Port Sama: E. side of entrance
Peak of Sama: Summit, 885 feet
Port Naranjo* E side of entrance
Gibara: Lighthouse
6 20
0 08
2.4
1.4
Port Padre* Guinchos Pt
Port Nuevitas: NW. corner R. R. station.
Maternillos Point: Lighthouse
7 00
0 48
2.2
1.2
Cay Verde: NW. end
Cay Confites * S pt
Paredon Grande Cay: Lighthouse. . .
7 20
1 08
2.8
1.6
San Fernando : NW. corner Old Spanish
Fort No 1
Cayo Frances* Lighthouse
i
APPENDIX IV. [Page 293
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
1
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
ci
i
5
Isabella deSagua: SE. corner of church ..
Cav Sal ' Lighthouse
h. m.
h. m.
ft.
ft.
22 56 30
23 56 30
23 12 34
23 14 10
23 02 43
23 01 54
23 09 26
23 09 04
23 09 11
22 59 11
23 00 00
22 29 32
21 52 01
21 53 55
22 14 36
21 55 00
21 35 30
22 41 09
21 57 45
22 01 49
22 08 36
22 06 52
21 48 16
21 37 24
20 42 23
20 20 26
20 02 55
19 50 32
19 53 31
19 56 57
19 57 29
19 54 42
19 53 04
19 57 00
19 54 08
20 01 01
19 45 15
19 39 10
19 17 45
18 33 00
17 55 05
18 11 31
18 23 00
18 26 24
18 30 34
18 29 25
18 27 45
18 12 20
17 55 56
17 55 56
17 26 30
17 06 20
15 53 00
18 35 52
19 12 29
19 22 12
19 48 51
19 54 00
19 46 20
19 46 19
80 00 32
80 27 51
80 29 26
81 07 20
81 12 02
81 43 18
82 21 29
82 20 38
82 21 01
83 09 13
83 13 00
84 14 17
84 57 09
84 56 16
83 34 24
83 31 18
83 09 13
82 17 42
81 07 18
80 26 32
80 27 05
80 27 11
79 58 58
78 51 13
77 59 45
77 07 33
77 34-50
77 43 33
Bahia de Cadiz Cay ' Lighthouse. .
Piedras Cav ' Lighthouse
Cardenas * Cross on Cathedral
Matanzas * Summit of peak
8 30
8 18
2 18
1 56
2.2
1.3
1.2
0.7
Habana * \Iorro lighthouse
Transit pier, Casa Blanca Ob
servatory
Flagstaff Cabanas Fortress
Bahia Honda : SE . corner Morillo Fort
Gobernadora Pt. : Lighthouse
Dimas • N\7 corner of warehouse
Cape San Antonio ' Lighthouse
8 30
2.18
1.5
0.9
Radio tower
La Caloma: SW. corner of warehouse
San Felipe Cays- SW pt
Isla de Pinos* Port Frances . .
Batabano • Lighthouse
Piedras Cay : Lighthouse
Cienfuegos: Colorados Pt. light
4 47
11 00
2.0
1.1
Cathedral tower
Flagstaff Punta Gorda
•.
Casilda* Observation pier
Jucaro' Observation pier
1
Santa Cruz del Sur: Observation pier
Manzanillo' Observation pier
Niniie^O' Siigar mill Rmokestarlc
Cape Cruz* Lighthouse
Point Mota
Chirivico * Damas Cay . ...
Santiago * Lighthouse
75 52 03
75 09 28
75 09 28
75 07 33
75 03 08
74 50 49
79 46 07
80 07 17
81 23 17
75 44 24
76 11 08
76 26 31
76 54 22
77 12 52
77 39 52
77 56 16
78 10 52
78 08 54
76 50 35
76 50 38
75 58 20
77 26 28
78 39 04
68 18 50
69 19 23
69 12 12
70 41 27
71 40 15
71 46 40
72 12 07
8 20
7 50
2 30
2 00
2.2
2.6
1.1
1.3
Guantanamo Bay * Fisherman Pt
Lighthouse
Naval Station flagstaff.
Port Escondido • Inner Entrance Pt
Port Baitiqueri* Barlovento Pt
Cayman Brae • E pt
Little Cayman: w pt
Grand Cayman: Fort George, W. end. . . .
Formigas Bank : Shoal spot
[1.3]
Jamaica.
Morant Point : Lighthouse
fLll
Port Antonio • Folly Pt Light
Port Maria • N W wharf
St Ann Bay* Long wharf
[1.2]
Falmouth : Fort
Montego Bay : Fort
St. Lucia: Fort
Savanna-la-Mar: Fort
Kino'ston' Port Royal flagstaff
PortRoval: Fort Charles, flagstaff
ri.il
Morant Cays: NE. Cay
1 Isl. of Haiti.
Pedro Bank' Portland Rock E end
Baxo Nuevo' Sandy Cay
Cape Enganoi Extreme.. . .
Samana Town: Obs. spot
9 00
2 48
3.0
1.5
Cape Cabron* East extreme
Port Plata: Lighthouse
Monte Cristi" Cabra Island
.Manzanillo Point
6 50
0 39
5.5
2.9
Cape Haitien ° Town fountain
1
Page 294] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
i
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Island of Haiti.
Port Paix: Wharf.
ft. m.
ft. m.
ft.
ft.
19 57 06
19 49 15
19 27 12
18 56 00
18 48 50
18 33 31
18 39 15
18 36 48
18 25 00
18 11 08
18 13 25
17 46 08
17 36 55
17 37 37
17 28 22
18 08 55
18 12 13
18 27 54
18 11 57
18 05 17
18 12 37
18 24 51
18 28 23
18 23 01
17 57 10
18 18 56
18 05 54
18 20 23
18 18 08
18 25 04
18 30 39
18 45 11
18 36 30
17 45 09
17 44 43
18 35 37
18 16 42
18 13 06
18 04 07
17 53 58
17 39 10
17 29 10
17 18 12
17 13 38
17 07 52
17 35 50
17 00 00
17 06 54
16 55 18
16 42 12
15 59 50
16 25 09
16 11 57
16 13 14
16 13 56
16 19 56
16 10 17
15 52 59
15 51 32
72 50 00
73 23 07
72 43 52
73 18 20
72 39 13
72 21 00
74 06 52
74 25 50
75 01 57
73 44 08
72 30 45
71 41 06
71 31 10
71 41 10
71 38 30
71 02 25
70 32 53
69 52 59
68 45 41
67 50 50
67 09 17
67 09 42
66 07 26
65 37 07
66 54 13
65 13 40
65 25 26
64 55 47
64 42 03
64 36 47
64 21 48
64 24 58
64 10 45
64 42 16
64 41 14
63 28 13
63 16 00
63 04 39
63 05 45
62 51 30
63 15 16
62 59 09
62 43 14
62 35 25
62 37 29
61 49 54
61 46 07
61 55 11
62 19 10
62 13 24
61 44 09
61 32 15
61 29 40
61 32 05
61 33 15
61 00 44
61 06 45
61 19 15
61 35 55
St. Nicholas Mole: Fort George, flagstaff. .
Gonaives: Verreur Pt
Gonave Island: W. pt
Arcadins Islands: Lighthouse
Port au Prince* Fort Islet light
[1.2]
Jeremie' Fort - . .
Cape Dame Marie : Extreme
Navassa Island: NW. extreme
Aux Cayes: Tourterelle Bat'y
Jacmel: Wharf
[2.5]
False Cape: Extreme
Beata Island: NW. pt
Fraile Rock: Center
Alta Vela: Summit
Avarena Point: Extreme
Salinas Point (Caldera) : Extreme
Sto Domingo City : Lighthouse
[2.2]
Saona Island : Pt. Catuano
Mona Island: Lighthouse
Porto Rico.
Mayaguez* Mouth of Mayaguez R
7 04
2 00
2.0
1.0
Aguadilla: Columbus Monument
San Juan : Morro lighthouse ....
8 21
2 20
1.3
0.9
Cape San Juan: Lighthouse..
Guanica: Meseta^Pt. lighthouse
1 0]
Culebrita Island: Lighthouse
[731]
[735J
[711]
[130]
[140]
[058]
101
1.1;
[1.2]
Vieques (Crab) Island: Port Ferro light..
St. Thomas: Fort Christian, SW. bastion. .
St. John Island: Ram Head
Tortola: Fort Burt
Virgin Gorda: Vixen Pt
Anegada* W pt
E extreme of reefs
St. Croix, Christiansted: SW. bastion of
fort
St. Croix, Lang's Observatory.
Sombrero : Lighthouse
Dog Island: Center
Anguilla: Customhouse
St. Martin : Fort Marigot light
St Bartholomew: Fort Oscar
[1.5]
Saba: Diamond Rock..
St. Eustatius: Fort flagstaff
St. Christopher: Basseterre Church
Bobby Island : Center
Nevis : Fort Charles
Barbuda: Flagstaff , Martello Tower
Antigua, English Harbor: Flagstaff, dock
yard
[2.0]
Sandy Island: Lighthouse
Redonda Islet: Center. .
Montserrat: Plymouth Wharf
Guadeloupe, Basseterre: Light on mast. . .
Port Louis: Light on mast. .
Gozier Islet: Lighthouse
Manroux Id. : Lighthouse. . .
Point a Pitre: Jarry Mill
Desirade: E. pt
[1.3]
Petite Terre: Lighthouse
Marie Galante: Lighthouse
Saintes Islands: Tower on Chameau Hill . .
APPENDIX IV. [Page 295
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
0
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
Dominica, Prince Ruperts Bay: Sand
beach W of church. . .
ft. m.
4 00
ft. m.
10 12
ft.
1.5
ft.
0.8
15 34 34
15 17 27
15 42 00
14 35 44
14 43 54
14 46 13
14 23 23
14 01 54
13 05 43
13 02 45
13 09 40
13 09 19
13 00 25
12 03 02
11 10 08
11 25 02
11 19 00
10 59 43
10 57 45
11 47 57
11 56 16
12 02 06
11 59 30
12 06 58
12 06 15
12 31 05
61 28 14
61 23 52
63 37 46
61 04 30
61 11 09
60 53 20
60 52 33
61 00 48
59 37 16
59 31 50
59 26 04
61 14 34
61 14 09
61 45 06
60 42 38
63 05 48
63 36 00
63 48 00
65 26 38
66 12 31
66 39 10
68 14 10
68 39 19
68 55 48
68 56 17
70 02 34
Roseau: Flagstaff , Fort Young
Aves Island • Center ,
Martinique, Fort de France: Fort St.
Louis light
St. Pierre: Ste. Marthe Bat
tery
Caravelle Pen.: Lighthouse.
Cabrit Islet: Summit
3 50
10 02
1.1
0.6
St Lucia, Port Castries: Lighthouse
Barbados, Bridgetown: Flagstaff, Rick-
ett's Battery
2 50
9 02
3.0
1.5
S Point' Lighthouse
Ragged Point: Lighthouse .
St Vincent, Kingstovm : Lighthouse . . .
2 50
9 05
1.6
0.8
Bequia Island, Admiralty Bay: Church. .
Grenada: St. George Lighthouse
2 30
3 50
8 42
10 02
1.5
2.1
6.8
1.1
Tobago Rocky Bay Lighthouse
Testigos Islets: Center of Testigo Grande.
Sola Island: Center . ...
Pampatar, Margarita I.: San Carlos Castle.
Tortugas Island: S. end of W. Tortugillo
Islet
Orchila Island: S. side
Roques Islands: Pirate Cav
Bonaire Island: Lighthouse
Little Curacao Island: Lighthouse
Curacao Island : Fort Nassau
Lighthouse
Oniba Island : Lighthouse
1
NORTH AND EAST COASTS OF SOUTH AMERICA.
Colombia.
Caribana Point: Extreme . . ...
8 37 30
9 24 00
9 24 00
10 25 50
11 00 15
10 07 00
11 15 28
11 33 30
12 12 34
12 23 09
12 04 00
10 57 30
11 48 56
12 11 00
12 29 15
11 27 56
10 47 00
11 10 00
10 29 53
10 36 57
10 35 00
10 34 06
10 49 30
10 13 30
10 27 20
10 40 00
10 42 00
76 52 55
76 10 45
75 48 00
75 32 50
74 57 55
74 49 51
74 14 33
72 54 50
72 09 42
71 45 42
71 07 55
71 37 00
70 17 21
70 04 55
70 57 00
69 34 20
68 19 55
68 22 54
68 00 55
66 56 06
66 06 15
66 04 13
66 09 25
64 44 00
64 11 33
64 17 55
63 50 25
Fuerte Island: N. extreme
. . . |
Cispata Port: Zapote Pt
Cartagena: Lighthouse
Savanilla: Lighthouse
Magdalena River: NW. pt. of Gomez I. . .
Santa Marta: Lighthouse
1
Rio de la Hacha : Li^ht on church
i
Cape La Vela: Sand beach inside cape. . .
Bahia Honda: E. pt., S. side
j
Espada Point: Extremet
1 Venezuela.
Maracaibo : Zapara I lio'ht .
5 05
11 17
2.5
1.5
Estangues Point: 500 ft. from extreme
Cape San Roman* Extreme
Marjes Islets* N islet
Vela de Coro: Lighthouse
Tucacas Island: Ore house
St Juan Bay Cay
Puerto Cabello: Lighthouse
La Guaira: Lighthouse
6 00
12 12
2.8
1.7
Cape Codera* Morro
Corsarios Bay: W pt
Centinela Islet: Center.
Barcelona* Morro
Cumana: Lighthouse
Escarceo Point" Extreme
Chacopata* Morro
Page 296] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued.
i
Place.
Lat. N. ,
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Venezuela.
Esmeralda Islet' Center .
A. ra.
Ji. m.
ft.
ft.
1-0 40 00
10 40 15
10 42 00
10 43 27
10 45 00
10 44 19
10 43 48
10 38 15
8 39 25
10 38 37
10 40 03
10 50 02
10 03 29
10 16 59
6 49 20
5 58 30
5 49 30
5 44 50
5 16 50
5 02 40
4 56 20
4 49 30
4 23 20
4 20 45
2 46 30
1 40 17
Lat. S.
0 17 00
1 26 59
0 35 03
2 10 11
2 31 48
2 16 22
2 41 55
2 53 20
3 42 05
4 25 35
5 03 15
5 29 15
5 45 05
. 5 46 41
6 56 30
7 06 35
8 00 50
8 03 22
8 20 45
8 43 40
9 39 35
10 30 30
10 58 20
11 09 45
11 27 40
12 12 05
12 33 40
13 00 37
12 52 48
13 22 37
13 56 42
14 17 40
63 31 55
63 18 00
63 14 00
63 09 43
62 41 55
62 44 29
61 50 50
61 51 18
60 10 15
61 30 35
61 45 54
60 54 10
61 55 41
61 28 12
58 11 30
57 00 30
55 08 48
54 00 30
52 34 53
52 21 11
52 20 26
51 55 36
51 50 36
51 27 46
50 54 46
49 56 46
48 23 30
48 30 01
47 20 54
44 25 56
44 18 45
43 37 30
42 18 02
41 40 35
38 28 25
37 44 55
36 02 52
35 15 52
35 11 55
35 12 43
34 49 30
34 53 04
34 50 36
34 51 57
34 56 05
35 05 06
35 44 54
36 21 51
37 04 00
37 12 36
37 24 00
37 45 46
38 02 16
38 32 06
38 41 28
38 54 38
39 07 05
39 00 45
Carupano: Lighthouse
Pt Herman Vasquez
Puerto Santo Bay: Sand spit S. of Morro.
Tres Puntas Cape* Extreme
Unare Bay: Obs. spot, 200 yds. S. of Morro.
Pena Point' Extreme
Pato Island* E pt
Mocomoco Pt ' Extreme
Port of Spain* King's Wharf light
4 20
10 30
3.2
1.9
Trinidad.
Chacachacare Island: Rocks off SW. pt. .
Galera Point: NE. extreme, lighthouse...
Icacos Point* Lighthouse
San Fernando* Pierhead
Demerara* Georgetown lighthouse
4 18
9 50 8. 6
3.9
Oulana.
Nickerie River* Lighthouse .
Paramaribo* Stone steps . .
5 50
12 66 9. 5
4.3
Maroni River* W lighthouse
Salut Islands: Lighthouse
Enfant Perdu Islet* Lighthouse
i
Cayenne: Lighthouse
4 27
10 30
6.0
2.7
Connetable Islet* Center
Carimare Mount* Summit
Orange Cape * Extreme
Brazil.
May e Mountain: Summit
North Cape: Extreme
Cape Magoari: Extreme
Para: Customhouse
11 50
5 37
11.0
5.2
Atalaia Point* Lighthouse
Itacolomi Point* Lighthouse
Maranhao Island: Landing place
6 50
5 35
5 05
0 38
11 47
11 17
16.5
13.1
11.7
7.9
6.2
5.6
Santa Anna Island * Lighthouse
Tutoya* Entrance
Paranahiba River' Amarfao Village
Ceara* Lighthouse .
5 25
5 50
11 37
12 00
8.2
8.0
3.9
3.8
Jaguaribe River: Pilot station
Caicara: Village
Cape St Roque: Extreme
4 05
10 17
8.8
4.2
Rio Grande do Norte* Lighthouse
Natal* Cathedral
Parahiba River: Lighthouse at entrance..
Parahiba* Cathedral
Olinda: Lighthouse.
Pernambuco: Picao lighthouse
' 4 33
10 50
7.0
3.3
Cape St Augustine: Lighthouse
Tamandare* Village
Maceio' Lighthouse
4 20
4 17
10 32
10 29
8.5
7.8
4.1
3.7
San Francisco River: Lighthouse at en
trance
Cotinguiba River : Lighthouse at entrance .
Vaza Barris River: Semaphore at en
trance
Real River* Lighthouse
Conde* Village
Garcia d'Avila* Tower
Bahia* Santo Antonio lighthouse
4 10
10 22
7.6
3.6
Itaparica: FortonN.pt
Morro de Sao Paulo: Lighthouse
3 50
3 50
10 00
10 00
6.0
6.3
2.9
3.0
Camamu : Village
Contas * Church
APPENDIX IV. [Page 297
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued.
*j
Place.
Lat. S.
Long.W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
j
Ilheoe : Church
h. m.
3 35
ft. TO.
9 47
t<
ft
14 47 40
14 56 40
15 13 27
15 21 00
16 17 20
16 25 38
17 21 40
17 31 45
17 43 30
17 57 31
18 06 15
20 19 23
20 38 25
20 49 00
20 57 35
21 38 40
22 02 00
22 23 45
22 26 00
22 37 00
22 46 00
23 00 42
22 53 15
23 01 43
22 54 46
22 54 24
23 03 40
22 32 00
23 03 40
23 04 20
22 57 20
23 09 20
23 00 30
23 09 50
23 12 20
23 25 55
23 32 57
23 45 15
23 58 30
23 47 20
24 03 06
23 56 00
24 06 30
24 10 32
24 28 45
24 42 35
25 06 40
25 30 55
25 31 20
25 26 30
25 44 10
25 50 15
26 14 17
26 46 45
27 01 35
27 18 00
27 25 30
27 22 55
27 50 27
27 36 00
27 56 40
28 38 00
29 20 20
32 06 40
39 03 25
39 01 45
39 01 15
39 16 45
39 02 05
39 04 15
39 13 15
39 12 00
39 14 36
38 41 46
39 31 16
40 16 36
40 23 46
40 40 45
40 46 35
41 02 21
40 59 00
41 47 35
41 43 15
41 59 45
41 54 05
42 00 00
42 01 15
42 54 05
43 09 19
43 10 21
43 08 45
43 11 01
43 33 24
43 59 26
44 02 29
44 08 24
44 19 04
44 05 45
44 42 04
45 04 04
45 03 50
45 00 39
45 15 20
45 21 04
46 15 57
46 19 09
45 40 49
46 47 44
46 41 04
47 32 54
47 51 50
48 19 53
48 31 03
48 43 14
48 23 14
48 25 51
48 39 29
48 36 59
48 36 44
48 22 20
48 34 25
48 26 09
48 35 16
48 34 14
48 33 44
48 49 45
49 43 39
52 07 44
Olivenca* Center of village
Una* Center of village
Comandatuba * Center of village
Santa Cruz : Church
3 25
9 37
6.0
2.9
Porto Seguro* Matriz Church
Prado' River entrance
Alcobaca* Center of village .
Caravellas' Center of village
3 10
3 15
9 23
9 27
6.4
7.5
3.1
3.6
Abrolhos Island* Lighthouse
Porto Ale°re' Center of village
E^piritu Santo Bay Lighthouse
2 50
9 00
4.0
1.9
Guarapiri Islets' E islet
Benevente: Village
2 40
8 52
5.0
2.4
Itapemirim: Moscas Islet
Sao Joao da Barra: Lighthouse
Cape St Thome* Extreme
Macah£* Fort at entrance
2 20
8 30
9.2
4.4
Sant^. Anna TslfVnH • Summit
Barra Sao Joao * Village
Busios: Church....
Cape Frio : Lighthouse
Port Frio* Village
2 30
8 42
4.9
2.3
Maricas Islands* S islet
Rio de Janeiro: Fort Villegagnon Light. .
National Observatory
Raza Island* Lighthouse
2 50
9 00
4.2
2.0
Petropolis* Center of town
Cape Guaratiba* Summit
MaVambaya Island: Summit of SW. end..
Mangaratiba : Village
Palmas Bay: Beach at head of bay
Angra dos Reis* Landing place
Ilha Grande* Lighthouse
Parati* Fort
1 35
7 47
5.3
2.5
Ubatuba: Cathedral .... •
Porcos Grande Islet: Summit
Busiofl Tslpts* Siirnrriit
St Sebastian Island* Boi Pt li^ht
Villa Nova da Princessa* Center
Santos: Moela I lighthouse. .
Quay
2 50
9 00
5.6
•2.8
Alcatrazes Island* Summit 880 ft
Conceicao* Church
Quemada Grande Island: Summit, 623 ft .
leruaDe* Ouav
L
1
Bom Abrigo Islet : Lighthouse
Ilha do Mel: Lighthouse
Parana ona* Quay
2 55
9 05
6.4
3.1
Antonina* Quav
Coral Islet* Center . ..
Itacolomi Islet* Center
Sao Francisco* Center of town
Itapacaroya* Church
Cambria: Church
Ajrvoredo Island * Lighthouse
Anhatomirim* Li^hthou^e
Sta Catherina Island * Rapa Pt
2 35
8 47
5.9
2.8
Naufragados light.
Nossa Senhora do De^erto* Quay
Coral Island* Summit 230 feet
Cape St Martha * Lighthouse
Torres Point* Extreme
Rio Grande do Sul: Lighthouse
4 00 10 12
i. 8 1 6. 9
Page 298] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued.
|
8
Place.
Lat. S.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Uruguay.
Castillos* Beuna Vista Hill 184 feet
ft. m.
8 20
ft. m.
2 08
ft.
2.0
ft.
0.9
34 21 19
34 40 01
35 01 39
34 58 15
34 56 55
34 54 33
34 28 20
34 10 50
34 36 30
34 54 30
35 15 45
35 26 50
36 18 24
36 53 00
38 05 30
38 57 00
38 43 50
39 26 30
39 57 30
40 32 52
40 36 10
41 02 00
41 11 00
40 49 00
41 41 10
42 14 15
42 46 15
42 57 00
42 45 40
43 20 45
44 30 40
45 04 00
45 03 00
45 10 10
47 06 20
47 45 05
47 57 15
49 15 20
50 08 30
50 58 27
51 33 21
52 18 35
54 40 35
54 43 24
54 45 16
54 53 45
54 48 02
55 17 00
55 19 00
55 35 30
55 48 54
55 58 41
55 51 20
55 43 15
55 52 30
56 28 50
55 24 50
54 45 40
54 24 48
53 47 16
54 09 14
54 53 16
54 57 10
55 55 04
56 12 15
57 52 27
58 15 40
58 22 14
57 54 15
57 10 45
57 05 28
56 44 15
56 38 54
57 30 01
61 59 15
62 15 27
62 03 22
62 07 46
62 09 30
62 10 12
62 45 11
63 08 16
64 54 41
65 12 29
64 27 56
63 37 16
64 28 20
64 59 00
65 03 36
65 22 10
65 36 01
65 52 30
66 32 36
65 51 46
65 54 45
65 45 40
67 42 30
68 23 00
69 09 47
69 00 31
68 22 12
65 05 53
63 47 00
64 03 00
64 45 45
65 13 48
66 49 00
67 10 00
67 19 00
66 43 48
67 16 15
67 34 00
68 04 40
69 17 30
68 41 30
70 01 30
71 36 10
72 10 20
Cape Santa Maria : Lighthouse
Lobos Island* Center
Maldonado* Lighthouse . ...
Flores Island * Lighthouse
Montevideo* Cathedral, SE. tower
2 00
6 30
8 12
0 00
3.5
4.0
2.3
2.7
Colonia* Lighthouse
Martin Garcia Island : Lighthouse
Argentina.
Buenos Ayres: Cupola of customhouse —
La Plata: National University Obsy
6 43
12 15
2.1
1.4
Indio Point: Lighthouse
Piedras Point: Extreme
Cape San Antonio : Lighthouse . . ... ...
9 50
3 35
5.3
3.5
Madanas Point: Lighthouse
Cape CorrienteB : E . summit
Port Belgrano: Anchor-Stock Hill
6 00
0 00
15.8
8.2
Argentina : Fort.
Labyrinth Head : Summit
Union Bay: Indian Head
San Bias Harbor: SW. end of Hog Islet...
San Bias Bay: Summit of Rubia Pt
Rio Negro* Main Pt
10 50
4 38
14.7
7.7
Bermeja Head: E. summit
Port San Antonio: Point Villarino
10 35
4 23
23.5
12.3
San Antonio Sierra: Summit
Port San Jose: San Quiroga Pt
Delgado Point: SE. cliff.
Cracker Bay : Anchorage
Port Madryn: Anchorage off cave bluff. . .
Chupat River: Entrance
7 05
0 52
13.2
6.9
Port St. Elena: St. Elena pen
3 50
10 03
16.8
8.8
Leones Island: SE. summit
Melo Port: W. pt
Port Malaspina: S. pt
Cape Three Points : NE . pitch
Port Desire* Largest ruin
0 00
6 12
18.3
9.6
Sea Bear Bay Wells Pt .
Port San Julian* Sholl Pt
10 35
9 20
9 00
8 40
8 18
4 20
4 19
4 23
3 08
2 47
2 28
2 06
10 33
10 32
29.5
39.6
40.0
45.6
38.7
9.9
7.8
15.4
20.7
20.9
23.9
20.2
5.2
6.0
Port Santa Cruz* Mount at entrance
Coy Inlet: Height S. side of entrance
Gall egos River: Observation mound
Cape Virgins: SE. extreme.
Cape San Diego : Extreme.
Staten Island, Cape St. John: Light
house "W pt
Port Cork: Observation
mark summit
Cape St. Bartholomew:
Middle pt
Good Success Bay: S. end of beach
Lennox Cove: Bluff, N. end of beach
Goree Road* Guanaco Pt
0
3 50
10 03
6.7
5.2
Wollaston Island* Middle Cove
Barneveldt Islands: Center
Cape Horn* South summit, 500 ft
Hermite Island: St. Martin Cove
4 07
10 02
4.8
3.8
False Cape Horn * S extreme
Ildefonso Islands* Highest summit
Diego Ramirez Island: Highest summit. .
York Minster Rock* Summit, 800 ft . .
3 50
10 03
5.0
3.9
Cape Desolation • S summit
Mount Skyring' Summit 3 000 ft
APPENDIX IV. [Page 299
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA.
j
Place.
Lat. 8.
Long.W.
Lun. Int.
Range.
H.W.
L.W.
SK.
Neap.
3
Noir Inland' SE extreme
h. m.
2 20
1 50
A. m.
8 33
8 03
ft.
4.8
4.7
6
3.7
54 30 00
53 IS 30
52 55 30
52 46 15
52 42 50
52 23 55
52 39 00
52 32 00
52 17 54
52 28 40
52 28 00
52 38 IS
52 46 20
52 49 IS
53 10 10
53 33 30
53 38 12
53 47 00
53 53 43
53 51 45
53 41 45
53 43 57
53 42 00
53 37 10
53 34 20
53 31 45
53 32 10
53 30 50
53 30 05
53 25 00
53 18 45
53 15 30
53 13 40
53 06 30
53 11 40
53 06 35
52 55 46
53 01 00
52 55 00
52 42 00
52 44 58
51 IS 29
49 25 19
49 12 40
49 07 30
48 51 20
52 37 18
52 24 00
52 16 10
51 51 50
50 42 00
50 17 20
50 02 00
50 00 IS
4948 00
48 06 15
48 02 20
47 39 30
46 49 31
46 5S 57
46 49 10
46 35 00
46 04 00
73 00 00
74 18 15
74 36 30
74 46 50
74 42 20
68 25 45
68 34 00
68 45 20
68 57 10
69 24 00
69 33 00
70 14 16
70 25 25
70 37 51
70 54 24
70 34 27
70 58 31
70 55 03
71 17 15
71 55 30
71 59 41
7 04 45
7 10 42
7 19 30
7 27 10
7 34 15
7 32 25
7 38 00
7 47 30
7 47 55
73 00 30
73 12 05
73 21 30
73 15 30
73 17 45
73 16 15
73 44 28
73 59 33
74 17 45
74 13 30
74 38 14
74 04 00
74 17 39
74 23 27
landfall Island: Summit of Cape Inman.
Cape Deseado: Peaked summit
Apostle Rocks: W. rocks
Cape Pillar- N cliff
0.32
8 19
8 20
8 24
8 35
6 45
2 07
2 08
2 12
2 25
4.0
39.4
39.0
30.0
39.0
3.1
20.6
20.4
15.7
20.4
Dungeness Point: Lighthouse
Cape Espiritu Santo: NE. cliff
Catharine Point: NE. extreme
Cape Possession : Lighthouse
Cape Orange: N. extreme
Delcyada Point' Lighthouse
S 47
9 23
"i6"24*
11 03
2 40
3 20
"4*24"
5 03
39.0
21.0
"*8."6*
5.0
20.4
11.0
"4.*2
2.6
Cape Gre°orv • Lighthouse
Cape St. Vincent :^W. extreme
Elizabeth I -land- \E bluff
Sandv Point : Lighthouse
Cape St. Valentine: Summit, at extreme.
Port Famine : Observatory
11 58
12 21
0 28
5 58
6 21
6 53
6.0
8.0
7.0
3.1
4.2
3.7
Cape San I^idro* Extreme
Cape Froward* Summit of bluff
Mount Pond ° Summit
Port Gallant' Wigwui Pt . .
1 20
7 40
8.0
4.2
Charles Island: White rock near NW. end.
Rupert Island : Summit
ICunel Bav : Entrance
Tillv Bar: Sarah I
Boria Bav Bluff on W shore
1 54
8 11
5.5
2.9*
Cape Quod' Extreme
Barcelo Bav Entrance
Swallow Bav: Shag I
1 53
8 08
5.0
3.9
Cape Notch : Extreme
Playa Parda Cove: Summit of Shelter I. .
Pollard Cove* Entrance
1 31
7 44
4.5
3.5
Port \n°osto- Hav Pt
1 09
7 21
4.0
3.1
St \nne Inland' Central summit
Half Port Bav Point
Upright Porf Fntrance
Port Tamar: Mouat Islet
0. 55
7 07
6.0
4.6
Port Churruca : Summit of Blanca Pen. . .
Valentine Harbor: Observation mount...
Cape Parker* W summit
Mercv Harbor' Summit of Battle I. .
Mavne Harbor* Observation spot
Port Grappler" Observation spot
Port Rio trio * Vitalia I
Eden Harbor • Observation spot
74 25 10
74 20 55
74 23 10
75 06 00
74 55 00
75 13 20
75 -27 45
74 51 30
75 22 00
75 13 20
75 34 00
75 40 30
75 28 20
75 10 00
75 18 20
75 25 30
75 37 55
75 31 30
75 12 00
Halt Bav Observation islet
Westminster Hall Islet* E summit
Evangelists.5 Island : Lighthouse
0 55
7 08
4.4
3.4
Cape Victorv Extreme
Cape Isabel* W extreme
Cape Santia°t}* Summit
Molvneux Sound • Romalo I ....
Cape Tres Puntas- Summit 9 000 ft
Port Henrv Observation spot
0.30
6 45
4.5
3.5
Mount Cor^o' SW" summit
Rock of Dundee* Summit .....
Santa Barbara Port: N. extreme obs. pt. .
Guaineco Islands: Speedwell Bav, hill,
\E pt
0 15
6.30
5.3
4.1
Port Otwav Observation spot
0 10
6 25
5.3
4.1
Capp TVps \foTites* FxlTfTTip
Christmas Cove' SE extreme
Hellvpr "Rooks- Midd-lp
1 1
Page 300] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMEBIC A— Continued.
i
Place.
Lat. 8.
Long.W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
j Chile.
Cape Taytao* W extreme
ft. m.
0 00
A. m.
6 13
ft.
4.4
£
45 53 20
44 55 50
44 09 00
43 49 15
43 43 05
43 19 30
43 16 25
43 11 30
42 46 45
42 29 15
42 22 45
42 11 15
41 28 36
41 46 20
41 49 58
40 46 19
40 43 18
40 35 52
40 21 04
40 11 47
39 51 37
39 23 00
38 21 22
37 35 20
37 22 30
37 05 20
36 59 07
36 42 00
36 36 45
34 46 02
33 34 13
33 38 30
33 26 42
33 01 08
33 01 52
32 46 00
32 07 55
31 51 45
31 39 30
31 17 05
30 50 45
30 14 00
30 15 14
29 56 15
29 56 24
29 55 10
29 34 40
29 15 45
29 00 50
28 27 20
28 05 45
28 04 30
27 54 10
27 39 20
27 20 00
27 03 15
27 03 15
26 51 05
26 34 30
26 20 00
26 16 12
26 09 15
75 06 00
75 08 45
74 07 45
74 00 30
74 42 15
73 42 25
74 24 15
72 48 30
72 31 25
73 45 05
73 38 10
72 35 55
72 56 15
73 07 55
73 51 12
73 51 00
73 49 50
73 45 00
73 45 20
73 41 50
73 26 25
73 14 00
73 58 06
73 39 55
73 40 00
73 11 13
73 32 30
73 07 27
73 02 49
72 06 12
71 38 00
69 56 30
70 41 32
71 38 52
71 38 42
71 32 56
71 33 22
71 34 51
71 35 20
71 39 21
71 39 00
71 39 00
71 31 09
71 21 00
71 21 53
71 22 21
71 33 20
71 34 38
71 36 40
71 15 45
71 12 48
71 11 32
71 09 38
71 03 26
70 58 45
70 52 54
70 53 45
70 51 55
70 44 25
70 37 25
80 11 43
70 43 57
Socorro Island* S extreme
Mayne Mountain: Summit, 2,080 ft ....
Port Low ' Huacanec I S end
0 15
12 10
6 10
6 00
Guafo Island * S extreme
6.1
3.1
Port San Pedro* Cove on S shore
Cape Quilan* SW extreme
Corcovado Volcano: Summit, 7,527 ft
Minchinmadiva Volcano: S. summit,
8 000 feet
•
Castro : Extreme of point
0 01
6 21
18.0
9.1
Dalcahue* Chapel
Comau Inlet* Morro Comau
Port Montt * Lt on end of pier
0 31
1 10
0 04
21.0
14.8
5.9
14.5
7.5
3.0
Port Calbuco: La Picuta
7 35
6 20
Ancud : Ahui Pt. light
Condor Cove : Landing
Ranu Cove : Anchorage
Muilcalpue Cove* Landing place
Milagro Cove * Landing place
Laruehuapi Cove * Landing place
0 00
10 25
10 18
10 20
10 15
10 10
10 05
10 10
10 04
10 05
9 57
9 44
6 13
4 13
4 05
5 07
4 02
3 55
3 50
3 55
3 51
3 53
3 48
3 34
7.2
5.6
4.9
3.3
4.9
5.3
4.9
6.0
5.3
5.0
4.1
4.0
3.7
2.8
2.5
1.7
2.5
2.7
2.5
3.0
2.7
2.5
2.1
2.0
Valdivia : Niebla Fort light
Queule Bay: Choros Pt
Mocha Island: Lighthouse
Lebu River: Tucapel Head
Yanez Port: Anchorage
Lota: Lighthouse
Santa Maria Island : Lighthouse
Talcahuano: Fort Galvez. . .
Light on Quinquina I
Llico : Village
Port San Antonio : Village
Aconcagua Mountain* Summit
Santiago* Observatory
Valparaiso : Playa Ancha Pt. light
9 37
3 26
3.9
2.0
Site of old Fort San Antonio . .
Quintero Point: Summit
9 35
9 30
9 26
3 25
3 20
3 16
4.1
3.9
4.2
2. i
2.0
2.1
Pichidangui: SE. pt. of island
Tablas Point: SW. extreme..
Chuapa River* S entrance pt
Maitencillo Cove* N head
Talinay Mount: Summit
Lengua de Vaca: Lighthouse
Port Tongoi: Obs. spot. W. of village
Coquimbo: Tortuga Pt light
9 15
8 58
3 05
2 48
4.1
4.9
2.1
2.5
Smelting works, N. of town. .
N. islet. .
Pajaros Islets* Lighthouse
Choros Islands: SW. pt. of largest island. .
Chanaral Island: Lighthouse
Huasco: Light on mole
8 23
8 50
2 10
2 38
4.9
4.9
2.5
2.5
Herradura de Carrizal : Landing place . . .
Port Carrizal: Middle Point
Matamoras Cove : Outer pt. S. side
Salado Bay Summit of Caches Pt
Copiapo: Landing place
8 21
8 50
2 08
2 37
5.0
4.9
2.5
2.5
Caldera: Lighthouse
Light on mole head.
Cabeza de Vaca Point: Extreme
Flamenco: SE. corner of bay
9 00
9 05
2 47
2 52
5.0
4.9
2.5
2.5
Chanaral Bay: Observation pt
St. Felix I.: Peterborough Cathedral Rock
Pan de Azucar Island: Summit
APPENDIX IV. [Page 301
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
j
Place.
Lat. S.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Cblle.
Lavata: Cove near SW. pt
h. TO.
9 10
ft. 771.
2 57
t*
ft.
2.5
25 39 30
25 31 00
25 25 20
25 07 00
25 05 25
24 34 30
24 15 00
23 53 00
23 38 50
23 33 05
23 28 30
23 26 42
23 06 30
22 34 00
22 06 00
21 55 50
21 28 00
21 05 30
20 57 40
20 51 05
20 12 30
19 05 01
19 36 30
19 19 00
18 45 40
18 28 43
17 58 35
17 42 00
17 37 00
17 01 00
17 00 00
16 42 20
16 23 50
16 13 30
15 48 00
15 33 15
15 20 56
14 57 00
14 41 00
14 09 50
13 50 00
13 48 00
13 45 00
13 38 20
13 01 00
12 48 00
12 31 00
12 11 30
12 04 03
12 08 15
11 47 10
11 27 10
10 49 45
10 06 15
9 38 35
9 15 30
9 04 40
8 46 30
8 34 50
8 05 40
7 42 40
7 23 40
70 44 03
70 41 18
70 34 10
70 30 16
70 29 50
70 36 29
70 33 00
70 32 28
70 25 18
70 26 55
70 34 56
70 37 11
70 31 39
70 17 42
70 13 40
70 11 17
70 02 45
70 12 12
70 10 26
70 14 40
70 11 20
70 10 30
70 15 21
70 17 50
70 21 50
70 20 00
70 52 31
71 22 31
71 20 01
72 02 53
72 07 16
72 27 16
73 16 41
73 41 31
74 27 16
74 51 01
75 09 36
75 30 46
75 49 56
76 16 36
76 27 31
76 18 31
76 10 00
76 24 15
76 31 06
76 38 11
76 48 56
77 02 31
77 15 44
77 14 45
77 16 11
77 50 04
77 43 42
78 10 02
78 21 33
78 30 03
78 35 57
78 45 16
78 56 53
79 06 46
79 26 00
79 33 15
San Pedro Point: Summit
PortTaltal- Lighthouse
9 20
9 35
9 30
3 07
3 22
3 17
4.9
5.0
4.9
2.5
2.5
2.5
Grande Point: Outer summit
Paposo Road: Huanillo Pt
Reyes Head : Extreme pitch
Cobre Bay: Pt. W. of village
Jara Head: Summit
Antofagasta* Lighthouse
9 05
2 52
4.7
2.4
Chimba Bay: E pt of large island
Moreno Mountain : Summit
Constitution Cove: Shingle pt. of island..
Mexillones Mount: Summit
9 35
9 44
8 55
3 22
3 31
2 42
3.9
4.0
4.8
2.0
2.0
2.4
Port Cobija: Landing place
Tocopilla: Extremity Point
San Francisco Head: W pitch
Loa River: Mouth
Lobos Point: Outward pitch
9 00
2 47
4.9
2.5
Pabellon de Pica: Summit
Pata^hfi Point' FiTtrflrnfi
Iquique: Lighthouse
8 35
2 22
5.0
2.5
Mexillon Bav : Landing place
Pisagua: Pichalo Pt. extreme
8 32
2 20
5.0
2.5
Gorda Point: W. low extreme
Lohos Point* Summit
Arica* Iron church
7 49
1 37
5.6
2.8
Schama Mount: Highest summit
Coles Point: Extreme...... ..
1
Ilo: Mouth of rivulet . .
7 55
1 43
5.3
2.7
Port Mollendo: Lighthouse
Islay Customhouse
7 39
1 27
6.2
3.1
Quilca: W. head of cove
Pescadores Point: SW extreme
Atico : E . cove
Chala Point: Extreme
Lomas* Fla^taff on pt
San Juan Port: Needle Hammock
6 47
0 35
3.9
2.0
Nasca Point: Summit
Mesa de Dona Maria: Central summit
Carrfitfl, Mount: Summit
San Gullan Island : N. summit".
Paraca Bay* N extreme of W pt
Pisco' Lighthouse
6 16
0 04
3.8
1.9
Chincha Islands: Boat slip, E. side N. id..
Frayles Point: Extreme . .
A«ia Roolt' Summit,
Chilca Point- SW pitch
Morro Solar* Summit
San Lorenzo Island: Lighthouse
Callao: Palominos Rock Li°lit..
5 47
12 00
3.5
1.8
Pescadores Islands: Summit of largest
Pelado Island' Summit
Supe: W end of village. ...
Huarmey: W end of sandy beach
5 08
11 21
2.1
1.1
Colina Rpdonrla' Summit
Samanco Bav Cross Pt
Chimbote: Village, N. part
Chao Islet' Center
4 50
11 03
2.0
1.0
Guanape Inlands* Summit of highest
Huanchaco Point * SW extreme
Malabrigo Bav : Rocks
4 19 10 32
2.1
1.1
Pacasmavo' Lighthouse
Page 302] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OP SOUTH AMERICA— Continued.
i
6
Place.
Lat. S.
Long. W.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
*
Eten Head : Lighthouse .
h. 771.
4 04
h. m.
10 17
ft.
2.5
ft.
1.3
6 55 50
6 46 00
6 46 45
6 26 45
5 55 30
5 05 02
4 40 50
4 16 40
3 30 42
3 10 40
2 12 24
2 44 30
2 12 00
1 16 55
1 03 30
0 56 50
0 35 25
0 .21 30
Lat N.
0 50 10
0 40 00
1 03 30
1 36 00
1 49 36
2 37 10
2 58 10
3 49 27
4 17 06
5 28 46
6 41 19
6 49 45
79 51 30
79 57 55
80 42 54
80 51 56
81 09 19
81 07 17
81 17 01
81 12 01
80 28 12
80 .25 29
79 52 19
79 53 45
80 59 00
81 03 55
80 55 55
80 42 50
80 25 24
.80 30 37
80 05 40
80 07 55
79 42 00
79 03 30
78 45 29
78 24 24
78 11 16
77 11 45
77 29 44
77 33 28
77 30 31
77 40 55
Lambayeoue* Beach opposite
Lobos de Afuera Island: Cove on E. side. .
Lobos de Tierra Island: Central summit. .
A cniia "Point • "W fliff siiniTnit
Paita Cathpflral
Parinas Point* Extreme
Cape Blanco: Under middle of high cliff. .
Tumbez* Malpelo Pt
Guayaquil River: t Light on Santa Clara I.
Guayaquil Concejo* S pt of city
4 00
7 00
10 13
1 00
10.0
11.0
5.1
5.6
Ecuador.
Puna* M^aTidinfipa Pt liffht
Point Santa Elena * Veintemilla light
3 00
9 13
7.9
4.0
Plata Isle* E pt
Cape San Lorenzo: Marlinspike Rock
Manta Bay Lighthouse
3 10
9 23
7.5
3.8
Caraoues Bay* Punta Playa
Cape Pasado : Extreme
3 15
9 28
9.9
5.0
Point Gal era* N extreme
Cape San Francisco* 'SW extreme
Esmeralda River* Lighthouse
Colombia.
Mangles Point: S. pt. of creek entrance. . .
Tumaco: S. pt. of El Morro I
3 35
9 48
13.2
7.1
Guascama Point* Extreme
Gorgona Island* Watering Bay
Buenaventura* Basin Pt
6 00
12 13
13.2
7.1
Chirambiri Point* N extreme
Cape Corrientes: SW. extreme
3 40
3 30
9 53
9 43
13.1
13.3
7.0
7.2
Cupica Bay: Entrance to Cupica River..
Cape Marzo* SE extreme
ISLANDS IN THE ATLANTIC OCEAN.
Fseroe Islands, Strom Islet: Thorshaven
Fort flagstaff
62 02 26
C2 18 20
61 23 00
57 35 52
39 40 07
39 27 00
38 32 09
38 31 45
38 34 30
38 25 00
38 40 30
39 05 24
38 38 20
37 44 16
37 49 20
36 56 00
37 16 44
6 43 08
7 00 36
6 45 30
13 42 21
31 08 00
31 08 49
28 34 00
28 37 39
28 44 00
28 28 12
28 13 00
28 00 45
27 13 45
25 40 40
25 08 21
25 10 00
24 47 06
Halderoig Islet: Halde-
roig Church
Rockall Islet: Summit, 70 feet
Corvo Island: S pt
Azores Islands.
Flores Island: Santa Cruz Fort
Fayal Channel: N Magdalen Rock
Fayal Island, Horta: Castle of Santa Cruz.
Caldera: Summit 3,351 ft. . .
Pico Island: Summit..
11 30
5 18
3.9
1.8
St. George Island: Lighthouse .
Graciosa Island: Santo Fort light
Terceira Island: Monte del Brazil, near
Angra
0 20
6 32
4.4
2.0
St. Michael Island : Customhouse, Ponta
Del°*ada
Pt Arnel light
0 15
6 27
5.7
2.6
Santa Maria Island : Villa do Porto light. .
Fonnigas Islands * Highest rock
APPENDIX IV. [Page 303
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS IN THE ATLANTIC OCEAN— Continued.
o
Place.
Lat. X.
Long. W.
Lun. Int. Range.
H. W.
L. W.
Spg.
Neap.
Madeira Is.
Porto Santo Island * Lighthouse
ft. m.
0 40
A. 771.
6 52
ft.
6.6
&
33 03 15
32 35 45
32 37 43
32 43 14
32 45 00
32 48 07
30 08 00
29 23 50
28 57 24
28 50 56
28 45 25
28 03 00
28 10 42
28 07 06
28 35 25
28 28 12
28 16 35
28 08 00
27 46 30
28 50 06
17 06 50
17 04 00
16 53 14
16 49 00
16 38 00
16 34 00
16 50 50
16 34 00
16 13 20
16 11 00
16 09 10
15 07 30
15 18 06
14 53 40
14 53 00
14 50 30
32 19 22
32 19 37
32 15 05
32 21 40
0 55 30
Lat.S.
3 51 30
3 50 30
7 55 20
15 55 00
20 27 42
20 30 32
37 19 00
37 02 48
40 19 11
16 16 20
16 33 30
16 54 53
16 39 31
16 57 30
17 16 05
15 54 00
13 29 31
13 33 07
13 52 05
13 49 13
14 31 35
15 25 11
15 2;4 56
16 08 11
16 15 09
16 38 02
17 05 55
17 54 22
17 47 01
24 59 15
25 17 00
24 59 30
24 47 08
24 38 08
24 16 00
22 54 55
22 55 42
22 55 44
22 42 00
22 57 20
23 12 42
23 47 06
23 31 45
24 30 38
24 40 00
64 49 35
64 49 15
64 49 40
64 38 40
29 22 28
33 49 29
32 25 29
14 24 35
5 43 03
28 46 57
29 14 56
12 23 00
11 18 39
9 56 11
Desertas • Chao I Sail Rock
Madeira Island • Funchal light ....
0 35
6 47
6.6
3.0
Fora I lighthouse..
Pico Ruivo, summit,
6 056 ft
Par'go (W.) Pt
Salvage Islands: Lighthouse, Gran Sal
vage I
Alegranza Island: Del^ada Pt light.
Canary Island*.
Lanzarote Island: Port Naos li^ht
0 50
7 00 8.5
3.9
Pe.chinguera Pt. light..
Lobos Island : Martino Pt. light
Fuerta Ventura Island: Jandia Pt. light..
Gran Canaria' Tsleta Pt liorht
0 40
6 50
9.3
4.3
Palmas li^ht
Teneriffe Island • An«-a Pt lio-ht
Santa Cruz, Br. con
sulate..
1 15
7 27
7.8
3.6
Summit of peak, 12,180
Gomera Island : Port Gomera
Ferro Island* Port Hierro .
Palma Island: Li°-ht, NE. pt
0 20
6 30
. 8.6
4.0
San Antonio Island : Bull Pt light
Cape Verde isi.i mis.
Summit, 7,400ft. . .
St. Vincent Island: Porto Grande light...
St Lucia Island* N pt
5 50
12 00
3.3
1.5
Raza Island' E pt
St Nicholas Island' Lighthouse
Sal Island • N pt li^ht .
S pt
7 30
1 20
4.4
2.0
Boavista Islana: NW pt
NE. pt
Lighthouse
Mayo Island' English Road
St Jago Island' Reta Pt lio-ht
Porto Praya, S. light....
Fogo Island: N S da Luz village
5 50
12 00
4.8
2.2
Brava Island: Lighthouse
Ireland Island: Dock yard clock tower...
Bastion C
7 04
0 52
4.0
2.6
liermu-
da Is.
Hamilton Island • Gibbs Hill lio-ht
St Davids Island* Lio-hthouse
St. Paul Rocks: Summit, 64 ft
Rocas Reef: NW sandy islet...
5 05
5 00
5 20
3 00
3 35
3 40
11 18
11 13
11 30
9 10
9 48
9 53
10.0
6.0
2.0
2.8
3.5
4.0
4.6
2.7
0.9
1.3
1.6
1.8
Fernando Noronha: The Pyramid.
Ascension Island : Fort Thornton
St. Helena Island : Obs. Ladder Hill
Martin Vaz Rocks' Largest islet
Trinidad Island: SE.pt
Inaccessible Island * Center
Tristan da Cunha Islands: NW. pt
12 50
5 40
5.2
2.4
Gough Island* Penguin Islet
61828°—
Page 304] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS IN THE ATLANTIC OCEAN— Continued.
|
o
O
Place.
Lat. S.
Long. W.
Lun. Int.
Range.
H.W.
L. W.
Spg.
Neap.
II
8 "8
Port Egmont: Observation spot
ft. m.
7 20
h. m.
I 08
ft.
10.7
ft.
5.6
51 21 26
51 04 11
51 32 20
51 41 10
51 40 40
54 04 45
53 48 00
59 34 00
55 57 00
60 54 00
60 46 00
62 55 36
54 16 00
60 04 52
58 30 56
58 08 04
57 51 30
57 41 48
38 15 00
43 25 00
27 45 00
26 33 00
44 25 00
45 53 00
60 35 00
Long. E.
6 14 00
Mare Harbor: Observation spot
Port Louis: Flagstaff, govt. house
5 31
11 27
4.3
2.2
Port Stanley: Governor's house.
South Georgia Island* N cape
Sandwich Islands: S. Thule
Traverse I. volcano...
New S Orkney Is * E pt Laurie I
E. summit Corona
tion I., 5,397 ft....
New S. Shetland Islands, Deception Is
land * Port Foster .
Bouvets Island (Circumcision) : Center —
ATLANTIC COAST OF EUROPE.
Great Britain.
Greenwich' Observatory
Lat. N.
51 28 38
51 45 34
52 12 52
51 22 28
51 08 23
50 54 47
50 44 15
50 46 35
50 48 03
50 53 45
50 42 07
50 39 42
50 34 30
50 31 10
50 13 18
50 20 02
50 10 49
50 08 30
49 57 40
50 02 44
50 04 10
49 53 33
50 33 00
51 04 00
51 12 05
51 27 24
51 27 48
51 36 50
51 37 52
51 41 00
51 43 15
52 24 20
52 45 00
53 18 30
53 18 54
Long. W.
0 00 00
1 15 06
Long. E.
0 05 41
1 26 48
1 22 22
0 58 18
0 13 00
Long. W.
1 05 15
1 05 58
1 24 00
1 33 04
1 35 25
1 17 47
2 27 30
3 38 28
4 09 27
4 15 53
5 01 00
5 12 06
5 39 18
5 44 45
6 20 38
5 01 55
4 12 30
4 40 35
2 35 55
3 09 42
3 56 00
4 40 59
5 10 30
5 40 15
4 05 40
4 47 50
4 42 00
4 37 01
1 10
7 46
18.8
12.6
Oxford' University Observatory
Cambridge* Observatory
North Foreland* Lighthouse
11 24
11 09
10 35
11 10
5 53
5 43
4 23
4 58
16. 8
19.8
21.5
19.8
8.4
10.0
11.0
10.1
South Foreland* Lighthouse
Dungeness* Lighthouse
Beachy Head* Lighthouse
Southsea Castle: Lighthouse .
Portsmouth: Observatory
11 31
0 35
11 05
4 19
6 48
4 53
13.2
12.8
12.2
6.7
6.5
6.2
Southampton* Royal Pier light
Hurst Castle: W. light
Needles Rocks: Old lighthouse
St. Catharine: New lighthouse
Portland : Notch Bill light
6 29
5 25
5 20
0 09
11 38
11 33
6.7
14.9
15.3
1.0
6.8
7.0
Start Point: Lighthouse ...
Plymouth: Breakwater light
Eddystone * Lighthouse
Falmouth* St Anthony Pt light
Lizard Point: W. lighthouse
4 45
10 58
14.2
6.5
Porthcurnow: SE. cor. telegraph co.'s sta.
Lands End* Lon^ships lighthouse
Scilly Islands: St. Agnes lighthouse
4 15
10 28
15.9
7.3
Trevose Head * Lighthouse
Bideford : High lighthouse
5 45
5 00
7 00
6 45
5 45
5 40
5 41
5 40
7 25
7 24
11 58
11 13
0 48
0 33
11 58
11 53
11 54
11 53
1 13
1 12
22.7
26.9
31.3
36.2
27.1
25.3
24.0
20.9
14.2
14.9
11.4
13.5
15.7
18.1
13. 6
12.7
12.0
10.5
7.1
7.5
Lundy Island: Lighthouse, N. pt
Bristol: Cathedral
Cardiff: Lighthouse, W. pier
Swansea: Lighthouse, W. pier
Caldy Island : Lighthouse
St Anns* Upper lighthouse
Smalls Rocks* Lighthouse
Aberystwith* Lighthouse
Bardsey Island* Lighthouse
South Stack' Lighthouse on rocks
Holyhead' Lighthouse on old pier
10 00
3 48
15.8
7.9
APPENDIX IV. [Page 305
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
1
O
Place.
Lat. X.
Long. w.
Lun. Int.
Range.
II. VT.
L. W.
spg.
Neap.
1 Oreat Britain.
Skerries Rocks: Lighthouse, highest I
Bidstone: Lighthouse on hill
ft. 77?. h. m.
ft.
ft.
53 25 15
53 24 02
53 26 38
53 24 05
53 55 03
54 03 14
54 24 56
54 30 50
54 33 00
54 38 10
55 28 10
55 32 55
55 38 27
55 26 00
55 52 43
55 18 39
55 40 20
56 24 50
56 19 22
56 47 08
57 51 25
58 11 28
58 30 40
58 37 30
58 40 16
58 59 15
59 16 45
59 23 24
59 33 00
59 51 15
60 OS 02
60 09 22
60 27 20
60 44 25
58 41 22
57 51 54
57 28 15
57 08 33
56 28 07
56 26 03
56 11 00
56 02 09
55 57 23
55 46 00
55 37 00
55 20 06
54 58 10
55 00 30
54 55 07
54 41 51
54 07 00
53 39 00
53 34 45
52 29 14
52 05 00
51 56 05
4 36 20
3 10 42
3 02 27
3 04 20
3 00 20
4 49 37
4 22 01
3 37 50
3 36 00
4 51 20
4 38 10
4 41 00
4 49 28
5 07 09
4 17 38
5 48 00
6 30 46
5 28 20
7 06 32
7 39 09
6 38 28
6 22 10
6 16 01
4 59 41
3 22 25
2 57 33
2 22 25
2 22 45
1 36 30
1 16 20
1 16 02
1 08 41
1 29 50
0 47 30
2 55 25
3 46 30
1 46 22
2 '04 06
2 44 53
2 23 06
2 33 22
3 08 05
3 10 47
1 59 00
1 39 00
1 32 00
1 21 30
1 26 00
1 21 30
1 10 19
0 05 00
0 12 00
Long. E.
0 07 10
1 45 24
1 34 30
1 19 10
Liverpool: Rock light
Bidston Observatory. .
11 08
11 00
5 27
4 48
27.6
27.4
14.0
13.9
Morecambe Bay: Fleetwood high light
Calf of Man : Upper lighthouse
Isle of Man : Avre Pt. lighthouse
10 55
4 43
19.7
10.0
St. Bees: Lighthouse
"White Haven • \V pierhead light
11 00
11 05
11 40
4 48
4 53
5 28
25.9
14.8
8.7
13.1
8.9
5.2
Mull of Galloway Lighthouse
Ayr, Firth of Clyde: Lighthouse, X.side
harbor
Troon: Lighthouse, inner pier
Ardrossan: S. breakwater li^ht. ...
11 35
5 23
8.8
5.3
Pladda Island: Lighthouse.
Glasgow: Observatory
0 55
10 20
7 08
4 08
11.2
4.0
6.7
2.4
Cantvre : Lighthouse
Rhvnns of Islay: Lighthouse
Oban' Lighthouse on \ pier
5 10
11 22
12.8
7.7
Skerryvore Rocks: Lighthouse
TtarraTTfiad: Licrhthonsff
5 35
11 47
11.1
4.8
Glas Island: Lighthouse, Scalpay I
Stornowav: Arnish Pt. light..
6 35
0 22
13.4
5.7
Butt of Lewis: Lighthouse. . . .
Cape Wrath: Lighthouse
Dunnet Head : Lighthouse
Kirkwall (Orkneys): New pierhead light.
Startpoint (Orkneys) : Lighthouse
9 57 3 44
9.8
4.2
North Ronaldsay: Lighthouse
i
Fair Isle Skroo: Lighthouse
10 50
9 35
4 37
3 22
5.0
5.2
2.2
2.2
Sumbur^h Head: Lighthouse
Blackness (Shetland Is.): Lighthouse
pier .
Lerwick (Shetland Is ): Fort
10 20
4 17
6.0
2.6
Hillswickness (Shetland Is.): S. extreme.
Balta I. (Shetland Is.): Cairn on E. side. .
Pentland Skerries: Upper lighthouse
9 30
10 00
3 17
3 47
6.4
9.8
2.7
4.2
Tarbertness: Lighthouse
Buchanness* Lighthouse
0 24
0 50
1 56
6 36
7 02
8 08
11.2
11.7
15.5
6.1
6.4
8.5
Aberdeen (Girdleness) : Lighthouse
Buddonness : Upper lighthouse
Bell Rock: Lighthouse
May Island: Lighthouse . .
Inch Keith Rock: Lighthouse
Edinburgh : City observatory
1 58
2 OS
8 11
8 28
16.5
15.0
8.9
7.5
Berwick : Lighthouse
Farn Island: NW. lighthouse
Coquet Island* Lighthouse
Tynemouth : Souter Point lighthouse
North Shields' Lighthouse
3 11
3 12
3 21
4 20
9 31
9 32
9 43
10 36
14.8
14.5
14.2
15.8
7.4
7.3
7.0
8.8
Sunderland: N pierli^ht
Hartlepool: Lighthouse
Flamborough : New lighthouse
Humber River: Killingholme middle
light
Spurn Head : Upper lighthouse ....
5 16
9 47
11 05
11 56
11 29
3 35
4 53
5 44
18.5
6.2
7.8
11.2
10.2
3.6
4.5
6.6
Lowestoft: Lighthouse
Orfordnecs* N lighthouse
Harwich: Landguard Pt. light
Page 306] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
1
8
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
j Oreat Britain*
Cape Clear- Old lighthouse
h. m.
3 50
Ji. m.
10 03
i»
A
51 26 02
51 23 18
51 33 24
51 31 00
51 27 41
51 39 10
51 35 30
51 46 14
51 56 00
51 53 08
52 07 15
52 04 30
52 13 46
52 16 14
52 39 00
52 40 04
52 33 38
53 08 55
53 07 38
53 15 13
53 13 46
53 23 58
53 29 47
53 35 00
53 36 40
53 42 27
53 49 34
53 53 06
53 49 30
54 05 45
54 17 00
54 16 00
54 19 36
54 16 33
54 15 30
54 18 00
54 20 50
54 34 08
54 39 47
55 00 52
55 08 13
55 16 26
55 12 31
55 15 14
55 16 33
55 19 07
55 22 50
55 25 55
55 13 38
55 10 20
54 59 40
55 05 23
55 15 03
55 18 05
54 55 47
54 51 07
54 40 20
54 41 50
54 38 45
54 24 04
9 29 03
9 36 25
9 32 44
9 10 20
9 48 19
9 44 49
10 18 03
10 32 45
10 19 16
10 23 17
10 15 30
10 40 00
10 21 40
9 52 53
9 01 18
8 37 23
9 55 54
9 51 30
9 42 06
9 03 10
9 46 03
10 14 01
10 03 54
10 00 15
10 09 40
10 06 41
9 40 12
9 32 56
9 59 00
10 03 34
10 05 31
9 53 00
9 20 41
8 46 02
8 34 25
8 37 00
8 40 14
8*27 33
8 49 52
8 33 48
8 15 38
8 15 00
7 57 15
7 47 12
7 37 53
7 23 51
7 22 22
7 13 37
6 55 38
7 02 20
7 19 25
7 21 51
6 28 45
6 10 45
5 44 18
5 47 21
5 49 30
5 31 30
5 32 01
5 22 20
Fastnet Rock: Lighthouse
Mount Gabriel: Ordnance survey station .
Castlehaven : Lighthouse
4 10
10 23
10.6
5.3
Mizen Hill: Ordnance survey station. . . .
Bantry Bay: Roancarrig light
Bull Rock: Lighthouse
Skelligs Rocks: Lighthouse
Valentia' Lighthouse
3 30
9 43
10.8
4.6
Port Magee
Dingle Bay Li^ht at entrance
3 40
9 53
10.7
4.6
Blasket Islands: Westernmost rock
Smerwick' Signal tower
3 40
3 50
9 53
10 03
10.7
12.3
4.6
5.3
Limerick : Cathedral
6 00
0 13
18.7
8.0
Shannon River: Loop Head light
Eeragh Island: Lighthouse
Arran Island' Lighthouse
4 15
4 19
10 28
10 19
13.4
15.1
5.7
6.4
Galwav Mutton I light
Golam" Head : Tower
Slyne Head: N lighthouse.
4 16
10 29
13.2
5.7
Clifden Bay: Gortrumnagh Hill
Tully Mountain: Ordnance survey station.
Inishboffin : Lyon Head light
4 20
10 33
12.1
5.2
Inishturk Island : Tower '.
Clew Bay: Inishgort light
Newport : Church
Clare Island : Lighthouse
Blacksod Point: Lighthouse
Eagle Island : W. lighthouse
Broadhaven : Guba Cashel light
4 50
11 03
10.4
4.5
Dounpatrick Head: Ordnance survey
station
Anghris Head: Ordnance survey station. .
Knocknarea: Tumulus
Sligo Bay: Black Rock light
5 10
11 23
11.4
5.3
Knocklane : Ordnance survey station ....
Killybegs (Donegal Bay): St. Johns Pt.
light %
5 03
11 16
11.2
4.8
Rathlin O'Birne Islet: Lighthouse
Aran Island: Rinrawros light
Bloody Foreland: Ordnance survey sta
tion
Tory Island: Lighthouse
I
Horn Head: Ordnance survey station
Melmore Head : Tower
5 28
11 41 11. 6
5.3
Fanad Point: Lighthouse...
Glashedy Island: Ordnance survey station
Malin Head : Tower
Inishtrahull : Lighthouse
Inishowen Head: E. lighthouse
Moville: New Pier
6 55
7 48
0 43
1 35
7.5
8.0
3.4
3.6
Londonderry: Cathedral
Scalp Mountain: Ordnance survey station.
Benbane Head: Summit
Rathlin Island: Altacarry lighthouse
Maiden Rocks: W. lighthouse!
10 30
4 18
6.7
4.5
Lough Larne: Farres Pt. lighthouse..
Belfast Bay: Light, east side
10 42
4 06
9.3
6.3
Mew Islands: Lighthouse
Donaghadeei Lighthouse
11 00
4 48
11.1
7.4
South Rock: Light vessel
APPENDIX IV. [Page 307
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
I
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
II. W.
L. W.
Spg.
Neap.
Great Britain.
Dundmm Bay: St. John Pt. light
h. m.
ft. TO.
Jt.
ft.
54 13 30
54 01 10
53 43 00
53 35 47
53 21 40
53 23 13
53 20 4?
53 20 30
53 18 10
53 15 52
53 10 39
52 57 54
52 41 55
52 32 55
52 20 53
52 20 04
52 18 57
52 12 09
52 06 41
52 07 25
52 15 33
52 08 13
52 04 27
52 13 39
52 03 00
51 59 33
51 56 34
51 52 54
51 49 30
51 50 33
51 47 33
51 36 11
51 34 14
51 31 50
51 28 05
49 43 00
49 10 29
70 22 00
70 04 00
71 11 00
71 06 00
70 40 15
69 39 12
69 36 05
69 19 30
68 24 40
68 09 20
67 53 15
67 23 15
66 56 35
66 25 50
65 28 40
64 32 55
64 10 25
63 48 25
63 38 45
63 27 04
63 13 11
63 07 01
63 03 04
5 39 30
6 04 45
6 15 00
6 00 20
6 03 06
6 20 17
6 13 33
6 09 00
6 07 30
6 06 37
6 04 55
6 00 08
6 13 01
6 48 17
7 07 31
6 28 15
6 33 41
6 12 35
6 37 15
6 55 53
7 06 24
7 10 15
7 33 05
7 54 54
7 32 39
7 35 OS
7 50 34
7 51 10
7 59 00
8 18 20
8 15 14
8 31 58
8 42 51
8 57 10
9 13 27
2 12 00
2 06 44
Long. E.
' 31 07 30
29 45 00
25 40 00
23 59 00
23 40 00
18 57 00
17 50 15
16 OS 00
16 02 30
14 40 40
13 04 30
13 52 30
13 28 50
11 59 50
12 13 30
10 42 10
9 24 50
9 44 45
9 45 20
10 23 30
7 36 05
7 43 35
7 46 04
Carlingford Lough: Haulbowline Rk. It. .
Drogheda : Lighthouse
10 45
10 45
4 33
4 33
15.8
11.6
9.2
6.8
Rockabill : Lighthouse.
Howth Peninsula: Bailey light
10 55
4 43
12.7
7.5
Dublin : Observatory
N. wall light
Poolbeg* Lighthouse
11 00
10 52
4 48
4 27
13.0
10.9
7.6
6.4
Kincrstown* E pier li°iit
Killiney Hill * Ma pas obelisk
Bray Head: Ordnance survey station
10 30
10 10
4 18
3 58
11.8
8.7
6.9
5.1
Wicklow: Upper light
TaraHill: Summit
Bkck Stairs Mountain: Ordnance survey
station
Tory Hill: Ordnance survey station
Wexford* College
7 05
0 53
4.9
2.9
Forth Mount: Ordnance survey station...
Tuskar Rock: Lighthouse
5 30
11 43
8.8
5.1
Great Saltee: S end
Waterford: Hoop Pt light
5 05
11 18
12.3
6.2
Waterford: Cathedral
Great Newton Head: Metal Man Tower...
Dun°rarvan* Ballinacourty li^ht
5 00
11 13
12.4
6.2
Kuockmealdown Mount: "Ordnance sur
vey station
Helvick Head: Ordnance survey station.
Mine Head' Lighthouse . . .
Youghal: Lighthouse
5 02
11 15
12.6
6.3
Capel Island: Tower
Ballycottin: Lighthouse
4 40
10 53
11.8
5.9
Cork Harbor: Haulbowline Coal Wharf. . .
Queenstown: Roches Pt light
4 33
4 30
4 20
10 59
10 43
10 33
11.6
11.4
10.7
5.8
5.7
5.3
Kinsale* Lighthouse S pt
Seven Heads* Tower
Galley Head* Light on summit
Sta^ Rocks* Largest .
Alderney Harbor* Old pier light
6 21
6 09
5 40
0 16
0 00
11 57
17.2
31.2
9.0
7.6
13.6
5.1
St Heliers: Light on Victoria, Pier
Vardo * Fortress ...
> IVorway.
Vadso* Lighthouse
North Cape* Extreme
Fruholm* Lighthouse
Hammerf est * Lighthouse
2 20
1 35
8 40
7 48
8.3
7.8
4.7
4.4
Tromso* Observatory
Hekkin°ren* Lighthouse
Andenes* Lighthouse
0 42
6 55
7.0
4.0
Lodingen (Hjertholm)* Lighthouse .. .
Lofoten Island* Skraaven I light
Glopen li^ht
Grvto * Lighthouse
Stot * Li^hthou^e
Trssnen* Soe Islet light
11 35
5 23
6.9
3.3
Bronnosund* Lighthouse
Villa* Li^hthou^e
Koppem
Agdenes* Li^hthou^e
Trondheim* Mumkholmen flao^taff
11 18
5 04
8.4
4.1
Grip * Church
Christiansund : Storvaden
11 00
4 48
5.0
2.9
Freikallen
Page 308] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
l
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
£
*
8
B
d
W
I
5C
Hestsk i aer * Lighthouse
h. m.
ft. m.
ft.
ft-
63 05 00
62 58 49
62 48 20
62 19 38
62 11 12
61 51 21
61 38 40
61 33 35
61 19 16
60 45 05
60 23 54
60 21 39
60 07 50
59 57 44
59 18 20
59 03 10
58 58 30
58 39 25
58 36 56
58- 25 51
58 06 25
57 58 55
57 58 00
58 07 50
58 04 15
58 15 02
58 24 40
58 51 50
58 59 25
59 00 01
58 59 34
58 58 05
59 01 35
59 10 30
59 23 10
59 25 34
59 29 23
59 39 52
59 40 21
59 54 44
59 09 00
59 07 08
58 59 45
58 54 05
58 56 24
58 54 12
58 32 45
58 20 12
57 53 49
57 40 58
57 18 15
57 06 26
56 54 08
56 40 21
56 14 40
56 18 06
56 02 37
55 52 00
55 41 52
55 36 47
55 23 00
7 29 55
7 12 32
6 36 10
5 16 25
5 07 59
5 15 11
4 47 38
4 46 45
4 47 14
4 42 55
5 18 11
5 19 35
5 01 00
5 03 30
4 52 35
5 24 20
5 45 20
5 33 35
5 49 08
5 58 49
6 34 20
7 03 10
7 29 50
8 00 30
8 03 30
8 31 36
8 47 55
9 36 15
9 45 50
9 45 14
10 03 28
10 09 26
10 31 55
10 36 25
10 32 45
10 29 52
10 19 15
10 38 08
10 36 55
10 43 23
10 50 15
11 24 09
10 47 20
11 00 45
11 10 28
11 00 36
11 02 16
11 13 24
11 28 04
11 53 54
11 54 16
12 14 32
12 29 48
12 51 38
12 51 47
12 27 11
12 41 30
12 49 48
13 11 15
12 59 49
12 49 02
Stemshesten
2Erstenen* Lighthouse
Svinoen Islet
Helliso * Lighthouse
Bergen* Naval School Obsy
10 15
3 55
4.1
2.1
Lorstakken Mountain* Summit
Marstenen Islet* Lighthouse
Furen Islet
Ulsire * Lighthouse
Hvidingso * Lighthouse •
Port Stavanger* Lighthouse . .'..
9 43
3 40
1.9
0.8
Obristadbroekke* Lighthouse
Synesvarde Mountain* Summit
Kompas Mountain* Summit
Lister * Li°rhthouse
Lindesnes * Lighthouse
Ry vin^en Island * Lighthouse
Christianssand * Odderoen light
4 16
10 15
1.1
0.5
Okso * Lighthouse
Hamber0*' Mill
Arendal Inlet: Inner Torungerne light. . .
Jomfruland * Lighthouse
4 17
10 10
1.0
0.7
Lan°"otangen * Lighthouse
Langesund * Church
FrederiksvsBrn * Lookout tower
4 34
10 00
1.3
1.0
Svenor* Lighthouse
Foerder Islet" Lighthouse
Fulehuk* Lighthouse
Basto* Lighthouse
Horten* Church
Holmestrand • Church
Drobak : Church
Oscarsber°" Fort flagstaff
Christiania : Observatory ...
5 22
10 37
1.2
0.9
Stromtangen (Torgauten) : Lighthouse
Fredriksten * Fort clock tower
Torbjornskjser1 Lighthouse
Koster' Lighthouse
Stromstad* Steeple
Nord Koster Islands* Lighthouse
Wadero Island*. Lighthouse .
Hollo Island* Lighthouse
Paternoster Rocks* Lighthouse
Gottenburg* Signal station
Nidingen Islet' Lighthouse
Warberg: Castle tower
Falkenberg: Church
Halmstad: Palace. .
Engelholm: Church. . . .
Kullen Point : Lighthouse
Helsino'borg * Lighthouse
Landskrona* Lighthouse
Lund* Royal Observatory
Malmo* Lighthouse .
Falsterbo : Lighthouse ....
APPENDIX IV. [Page 309
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
i
Place.
Lat. X.
Long. E.
Lun. Int.
Range.
H. W. L. W.
Spg.
Neap.
Sweden.
Trelleborg : Lighthouse
0 / IT
55 22 00
55 25 42
55 22 58
56 00 54
56 10 04
56 09 45
56 11 50
56 55 18
57 26 29
57 57 24
57 45 38
58 08 52
58 17 55
58 44 26
59 20 33
59 51 29
59 45 24
59 45 15
60 10 35
60 15 19
60 20 26
60 22 15
60 22 26
60 31 41
60 40 29
60 43 48
60 55 57
61 18 22
61 32 54
61 43 57
62 02 51
62 23 30
62 38 35
63 11 55
63 35 34
63 39 33
64 28 50
65 19 10
65 18 53
65 31 30
65 48 30
65 02 20
64 20 05
63 14 08
62 20 06
61 28 29
60 43 10
60 26 57
60 24 45
60 13 20
59 50 50
59 31 11
59 46 30
59 46 00
59 56 10
60 09 43
60 06 40
59 58 45
59 58 08
60 00 40
60 06 22
13 09 20
13 49 38
14 11 10
. 14 50 57
14 52 02
15 36 05
16 24 04
18 11 06
18 59 27
19 22 36
16 40 36
16 59 22
16 11 28
17 52 09
18 03 30
17 37 32
18 41 34
19 24 34
18 49 49
18 22 36
18 26 33
18 24 21
18 09 49
18 22 38
17 08 29
17 33 50
17 02 57
17 04 18
17 01 51
17 07 37
17 16 22
17 19 05
18 05 05
19 02 50
20 45 35
20 18 35
21 34 45
21 30 00
22 21 55
23 34 00
24 12 00
24 34 00
23 27 00
20 37 40
21 11 24
21 22 34
21 01 00
22 17 03
19 34 00
19 31 20
19 54 05
20 25 50
21 22 00
22 58 08
24 24 43
24 57 17
25 25 51
25 37 30
26 41 05
27 01 40
26 58 44
h. m. ; Ji. m. ft.
ft.
Ystad : Lighthouse
Sandhcimmaren* Lighthouse .
Hano Island* Lighthouse. .
!
K? rlstuuDD : Lighthouse
Karl^krona: Stumhohn Tower
Oland Island: Light on S. pt
Gottland Island :lloburg light, S. pt. . . .
Ostergarns light . .
Faro Island • Holmadden lio'ht
Sparo Vestervik : Granso light
Haradsskar Islet: Lighthouse.. .
Norrkopings Inlopp : Lighthouse
Landsort: Lighthouse
Stockholm : Observatory
Upsala : Observatory
\orrtelge* Inn
Soderarm* Lighthouse
Svartklubben : Lighthouse
Osthammaj* : Church
Oregrund : Clock tower
Djursten : Lighthouse
Forsmark : Church
Orskar Rock: Lighthouse
Gene- Church
Ego'esrund Islet: Lighthouse
Hamrange : Church . ...
Sodprhamm : Courthouse
Enanger : Church
Hudiksvalls: Courthouse
Gnarp* Church
Sundsvall* Church
Lun°*o: Lighthouse
Skags Head : Lighthouse
Holinogadd : Lighthouse
Umea: Bredekar Light
Bjuroklubb : Lighthouse
Pi tea
Rodkallen* Lighthouse
Maloren • Lighthouse
"
Tornea: Lighthouse
i
\ Russia.
L'leabore: Karlo I. light
Ulko Kalla Rock: Lighthouse
Norrsher Islet: Kvarken light
Kaske: Shelgmnd I. light
Bierneborg: Sebsher light
Xuistad : Ensher light
Abo : Observatory
Aland Island* Shelsher li^ht
Ekkere li°*ht
i
Logsher light
Bogsher: Beacon
L'te Islet* Lighthouse
Gange* Gan^e I light
Rensher: Lighthouse
Helsin^fors ' Observatory
Soder Skars* Lighthouse
Kalboden Island* Li°ht vessel
Rodsher Island * Lighthouse
Holland Island* Lower li°iit
Upper light
i
Page 310] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
I
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
M
Sonxmer Island* Lighthouse
60 12 31
60 14 43
60 11 05
59 58 14
59 59 44
59 56 30
59 46 19
59 53 26
59 55 40
60 02 08
59 28 04
59 49 10
59 41 06
59 42 00
59 27 05
59 26 28
59 36 22
59 27 55
59 21 30
59 18 06
59 05 25
58 55 02
58 23 02
57 54 37
58 05 50
58 23 10
57 03 38
56 57 01
57 48 02
57 48 10
57 24 00
56 31 01
55 43 45
54 53 47
54 57 40
54 38 25
54 43 49
54 42 50
54 19 19
54 09 44
54 16 30
54 21 18
54 24 28
54 23 51
54 12 16
54 33 09
54 36 06
54 49 55
54 45 29
54 35 16
54 32 29
54 25 27
54 11 28
54 14 40
51 10 40
54 05 47
53 58 29
53 50 41
53 25 41
53 55 03
0 f It
27 33 46
27 58 36
29 03 01
29 47 12
29 46 07
30 19 22
30 19 40
29 54 54
29 46 38
28 23 01
28 03 31
26 23 00
25 48 58
25 02 37
24 46 10
24 44 45
24 31 57
24 24 05
24 04 30
23 23 15
22 36 15
22 11 36
21 49 56
22 04 15
23 59 34
24 49 25
24 01 27
24 06 38
23 15 00
22 39 15
21 34 00
20 59 40
21 06 06
20 01 25
19 59 06
19 53 55
20 00 39
20 29 46
19 31 58
19 23 58
19 08 37
18 39 54
18 39 59
18 41 03
18 40 35
18 33 46
18 49 04
18 20 29
17 33 38
16 51 35
16 32 50
16 24 52
16 11 05
15 52 39
15 34 44
15 04 06
14 46 36
14 37 12
14 33 52
14 17 19
ft. TO.
h. m.
ft.
ft-
Vieborg Bay* Nelva I light
Stirsudden: Lighthouse . ....
Kronstadt: Light on Frederikstadt bas
tion
Cathedral
St Petersburg' Observatory
Pulkowa* Observatory
Peter hof • Pier-head light . . .
Oranienbaum • Lighthouse
Seskar Islet : Lighthouse
Narva; Light S. pt. of entrance
Stensher Rock : Lighthouse
Ekholm Islet: Lighthouse
Koksher* Lighthouse
Revel* Light N end of W. mole
Cathedral .
Nargen Island' Lighthouse . .
Surop- W light
Baltic Port: Lighthouse
Odenskholm Island: Lighthouse
Takhkona Point: Lighthouse
Dago Island : Dagerort light
Filzand Island : Lighthouse
S valferort Tzerel : Lighthouse
Kuino: Lighthouse
Pernau: Light at S. entrance
Riga: Ust Dyinski light
Cathedral of St. Peter
Runo Island : Lighthouse
Demesnes: Lighthouse
Windau: Light on S jetty
Libau: Light at entrance of port
Memel: Lighthouse
Germany.
Heiligen Creutz: Church tower
Brusterort: Lighthouse
Pillau: Lighthouse
Fischausen : City Hall tower
Konigsberg: Observatory
Tolkemit: Church tower
Elbing: Church tower
Tiegenort: Church tower
Dantzig: Observatory
Neufahrwasser light
Weichselmunde: Fortress tower
Putziger Heisternest: Church tower
Oxhoft: Lighthouse
Hela: Lighthouse
Rixhoft: Lighthouse
Leba: Church tower
Stopelmunde: Church...
Jershoft: Lighthouse
Rugenwalde: St. Mary's Church
Coslin: St. Mary's Church
Funkenhagen : Lighthouse
Colberg: St. Mary's Church
Gross-Horst: Lighthouse
Cammin: Cathedral tower. .
Wollin : Church tower
Stettin : N. Castle tower
Swinernimde: Lighthouse
APPENDIX IV. [Page 311
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued .
i
Place.
Lat. X.
Long. E.
Lun. Int.
Range.
H.W. j L. W.
Spg-
Neap.
Germany.
Streckelsberg: Survey station near beacon
Usedom: Church tower
ft. m. h. m.
ft.
ft.
54 03 08
53 52 17
53 56 59
54 03 18
54 05 49
54 15 02
54 22 56
54 25 08
54 40 53
54 18 42
54 28 28
54 20 47
54 14 42
54 10 42
54 05 27
54 06 32
54 08 00
53 53 50
53 58 54
53 57 44
54 26 16
54 29 43
54 28 54
54 19 47
54 23 52
54 27 25
54 20 28
54 28 25
54 30 55
54 39 48
54 47 05
54 54 28
54 40 23
54 56 48
54 58 05
55 02 46
55 03 52
55 05 31
55 03 04
54 54 13
54 41 51
54 41 21
54 28 43
54 19 08
54 07 52
54 10 57
53 57 15
53 55 01
53 52 25
53 36 12
53 33 43
53 32 45
53 33 07
53 32 52
52 31 31
52 29 07
53 28 30
53 42 50
53 36 20
53 32 52
53 46 57
53 42 21
14 01 17
13 55 26
13 51 13
13 46 51
13 22 53
13 55 42
13 37 54
13 26 11
13 26 12
13 05 30
12 30 23
12 24 02
12 26 04
12 05 19
12 08 10
11 46 04
11 41 54
11 28 09
11 05 54
10 52 59
11 11 59
11 14 29
11 04 18
10 32 59
10 22 24
10 12 04
10 08 53
9 50 23
9 34 23
9 56 13
9 26 20
9 45 35
10 02 23
9 52 20
9 58 41
9 25 18
9 23 35
8 39 41
8 26 50
8 22 03
8 33 13
8 33 58
9 03 21
8 56 38
8 51 53
7 53 11
8 24 35
8 29 58
8 42 43
9 28 48
9 36 40
9 56 35
9 58 27
9 58 21
13 21 52
13 28 33
9 59 37
8 14 48
8 18 30
8 34 25
8 04 47
8 01 43
i
Lassau: Church tower
1
Wokrastr Church tower
Griefswald: St Nicholas Church
i
Griefswalder Oie: Lighthouse
|
Granitz : Castle tower
Bergen : Church tower
Arkona : Lighthouse
Stralsund : St Mary's Church
Darsserort: Lighthouse
\Vustrow * Church
Ribnitz: Church tower .
(
Warnemunde: Church
Rostock: St Jacob's Church
Diedrichshagen : Survey station
1
Basdorf : Survev station
Wismar: St Nicholas Church
:
Hohenschonberg: Survrey station
Travemunde: Lighthouse
Burg: Church tower
Marienleuchte: Lighthouse ..
Petersdorf: Church tower. .
Hessenstein: Flagstaff of lookout tower. ..
Schonberg: Church
Bulk : Lighthouse
Kiel: Observatory
1
Eckemforde: Church
Schleswig: Cathedral ...
|
Kappeln : Church
Flensber0'* Church
)
Duppel: Survev station
i
Schleimunde: Lighthouse
j
Au°rustenburop: Church
Hu°reberg: Survey station
|
Apeiirade: Church..
Skoorgaarde: Survev station
Ballum : Church
List: E. lighthouse
0 20
6 33
5.2
3.0
Keitum* Church
Fohr: St Nicholas Church
1 35
7 47
7.8
4.5
Galgenberg: Survey station
Husum: Church.
2 10
1 45
1 11
11 29
8 23
7 57
7 24
5 17
10.8
11.0
11.7
8.1
6.2
6.4
6.8
4.7
Tonnin01: Church
Busum : Church
Helgoland* Lighthouse
Scharhorn' Beacon
Neuwerk: Lighthouse
Cuxhaven: Lighthouse . .
0 39
6 51
10.1
5.8
Stade* Church steeple
Steinkirchen : Church
4 00
10 13
8.5
4:9
Altona " Observatory
Hambur°r' Old Observatory
5 00
11 12
6.1
3.5
Imperial Marine Observatory.
Berlin* TJrania Observatory
Treptow Observatory
Harbur°p* Lighthouse
Hohe We0'' Lighthouse
0 25
6 38
10.1
5.7
Landward. en * Church
Bremerhaven: New harbor light
0 54
0 10
7 07
6 23
10.4
9.5
5.8
5.3
Minsener Sand: Light vessel
Schillio'hcm * Lighthouse
Page 312] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
1
6
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Germany.
Wilhelmshaven : Observatory
h. m.
0 04
11 27
h. m.
6 17
5 15
ft.
13.2
8.0
ft.
7.4
4.5
53 31 52
53 47 25
53 46 19
53 45 06
53 43 46
53 42 39
53 40 45
53 22 06
54 33 50
54 59 03
54 56 46
55 07 24
55 29 44
55 35 45
55 38 10
55 41 13
55 05 40
55 19 19
56 02 20
56 07 10
56 11 50
56 44 16
55 58 36
55 38 34
55 55 30
55 57 52
55 55 09
55 40 50
55 09 48
55 00 26
55 02 19
54 44 23
54 51 14
55 02 34
55 16 09
55 17 44
55 29 31
55 34 03
55 18 41
55 03 00
55 03 37.
55 45 32
55 48 02
55 51 44
55 56 58
55 57 06
56 09 26
56 08 00
56 26 36
56 59 54
57 02 54
57 43 46
57 35 06
57 06 50
56 30 48
56 05 27
55 47 17
55 44 50
55 31 52
55 26 26
55 16 11
8 08 47
7 54 09
7 41 45
7 35 41
7 22 03
7 13 58
6 59 53
7 12 25
11 58 03
12 17 16
12 32 40
12 03 07
12 07 36
12 38 24
12 41 26
12 34 41
14 42 00
15 11 39
12 32 02
12 20 50
11 42 50
11 39 15
11 51 36
12 05 02
11 40 29
11 24 06
11 05 07
11 05 04
11 09 32
11 54 59
11 22 23
10 42 13
10 24 11
10 09 16
9 53 50
9 48 09
9 28 40
10 05 29
10 47 47
10 40 02
10 36 48
10 16 20
10 33 37
9 51 19
10 26 51
10 33 00
10 12 50
10 48 32
10 57 40
10 18 53
9 55 22
10 36 38
9 56 44
8 36 10
8 07 23
8 14 52
8 14 36
8 14 43
8 24 12
8 24 03
8 32 38
^Van^eroog * Ligh thouse
Spikeroog* Church.
Langeoo01: Belvedere
Balstrum: Church . . .
Norderney: Lighthouse
11 05
4 53
7.3
4.1
Juist: Church
Emden " City Hall tower
0 24
6 36
8.9
5.0
Falster* Gjedser li^ht
Denmark.
Moen Island: Stege Church spire
Moen lio-ht, SE. pt
PrcBste' Church spire
Kjorge ' Church tower
Amager Island: Hollcenderby Ch. spire..
Nordse Rase light
Copenhagen: University Observatory
Bornholm: Ronne light
9 33
3 21
0.6
0.3
Christianso Island: Great tower
Kronberg: High spire
Nakkehooed: Upper light
Hesselo Island: Lighthouse
Anholt Island: Lighthouse
Spodsbjerg: Lighthouse
Roeskilde: Cathedral
Nykjobing: Church tower
Oddensby : Church tower
Sejro Island: Sejro Point light
Kallundborg: Church
Omo Island : Church
Vordingborg: Waldemar's tower
Veiro Island : Lighthouse
Langeland Island: Fakkebjerg light
.ZEro Island: Church spire
Lyo Island : Church tower
Assens: Church tower
Baago Island : Lighthouse
Kolding: Castle tower
Bogense: Church spire
Nyborg: Church spire
Turo Island : Church spire
Svendborg: Frue Church
Endelave Island : Church tower
Samso Island: Koldby Church tower. . . .
Horsens: Frelser Church spire
Tuno Island : Lighthouse
Samsoe Island: Nordby Church tower. . .
Aarhus: Cathedral spire
Hjelm Islet: Lighthouse
Fornses: Lighthouse
Hals: Church tower
Aalborg: St. Rudolph's Church
Cape Skaw, or Skagen: Old lighthouse. . .
Hirtshals: Lighthouse
5 46
4 18
11 58
10 30
1.0
1.2
.05
.07
Haustholm: Lighthouse
Boobjerg: Lighthouse
Ringkjobing : Church spire
Loune : Church tower
2 35
- 8 47
2.1
1.2
Blaabjerg: Summit, 100 ft
Guldager: Church :
2 35
2 34
8 47
8 46
4.5
4.7
2.6
2.7
Fano Island' Nordby Church
Mano Island : Church spire
APPENDIX IV. [Page 313
MARITIME POSITIOXS AXD TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
j
Place.
Lat. X.
Long. E.
Lun. Int. Range.
H. W.
L. W.
Spg.
Neap.
Holland.
XT ewe Diep: Time-ball station
52 57 50
52 22 30
52 05 10
52 09 20
52 04 40
52 06 16
51 54 29
51 54 30
51 49 19
51 41 48
51 49 08
51 26 33
51 26 24
50 47 56
51 12 28
51 13 17
51 18 47
51 14 13
51 13 50
51 07 53
48 50 11
51 02 09
51 00 18
50 57 45
50 52 10
50 41 57
50 07 05
50 11 42
49 56 06
49 55 04
49 52 28
49 46 05
49 30 04
49 29 01
49 25 32
49 11 14
49 20 18
49 20 28
49 34 19
49 41 50
49 40 29
49 38 54
49 43 22
49 43 17
49 27 13
49 06 28
49 22 27
49 02 54
48 50 07
48 52 13
48 40 18
48 41 05
48 54 33
48 40 23
48 44 45
48 36 57
48 28 31
0 / It
4 46 36
4 53 01
5 07 45
4 29 03
4 18 30
4 15 10
4 10 45
4 28 50
4 07 40
4 26 26
3 58 35
3 35 48
3 34 32
4 21 44
4 24 44
4 24 12
3 06 54
2 55 51
2 55 22
2 45 34
2 20 15
2 22 31
2 06 34
1 51 07
1 35 02
1 33 47
1 49 56
1 30 46
1 05 01
0 57 35
0 42 34
0 22 12
0 04 08
0 06 22
0 13 43
Long. W.
0 21 10
0 27 24
0 31 08
1 16 21
1 15 56
1 43 44
1 38 08
1 57 15
2 22 41
2 31 31
2 48 49
1 48 25
1 26 39
1 36 46
1 49 20
1 58 41
2 19 08
3 05 11
3 52 33
4 01 38
4 34 34
5 03 26
ft. m.
7 17
ft. 772.
1 05
ft.
3.9
ft
Amsterdam : TV church, tower
Utrecht' Observatory
Level en* Observatorv
The Ha^ue • Church tower
Sche venin^en • Lighthouse
Brielle • Lighthouse
2 50
3 35
2 20
3 20
9 02
9 47
8 32
9 32
4.8
6.7
5.2
9.8
2.5
3.5
2.8
5.2
Rotterdam: Time-ball station
Hellevoet^luis' Time-ball station
Willezostadt: Li^hthou^e
Goedereede* Li^ht on church tower
Fiu^hin0'' Time-ball station
Li^ht Westhaven bastion
0 44
6 56
14.7
7.8
Brussels : Xe w observatory
Ilclglum.
Antwerp : Observatory
4 15
10 27
14.8
7.8
Xotre Dame Cathedral
Blankenber°"he * Fort lighthouse
0 05
0 02
6 17
6 32
12.5
16.1
6.7
8.4
Ostend* Lighthouse
Church tower
Xieuport: Templars tower
0 10
6 22
15.7
8.4
Paris: Observatory
• Franco.
Dunkerque' Tower
11 58
11 59
11 39
11 17
11 18
5 58
6 16
6 13
5 51
5 52
16.8
19.0
21.0
21.5
25.2
8.5
9.6
10.7
11.0
12.8
Gravelines' Li^ht on X breakwater
Calais: Li^ht on old fort
Cape Gris Xez: Lighthouse
Bouloone C Alprech: Lighthouse. .
Abbeville: Tower
Caveux : Lighthouse
Dieppe: TV. jettv light
10 54
5 48
27.3
13.3
Ailly Point' Lighthouse
St. Valery en Caux: Light on W. break
water
10 29
10 06
5 33
5 02
26.8
23.3
13.1
11.4
Fecamp* N jetty light
Cape La Heve • S li<*ht
Havre • S jetty li^ht '.
9 03
4 14
22.5
11.0
Hnrifleiir* Hospital jetty light. . ..
Port Corseulles: W jettv light
Point De Ver* Lighthouse
Cape La Hou^ue* Lighthouse
8 13
8 14
2 45
2 37
18.5
17.0
8.2
7.5
Cape Barfleur* Lighthouse.
Cherbourg: Light, W. head of breakwater.
Naval Observatory
7 30
1 44
17.6
7.8
Cape La Hague : Lighthouse
Casqueta Rocks' Light on NW rock
6 20
6 12
0 15
0 07
15.5
26.0
6.9
11.5
Port St. Peter, Guernsey : Light on Castle
Coonet Breakwater
Douvres Rocks' Lighthouse
Cape Carteret * Lighthouse
6 07
0 15
30.8
13.5
Coutance*5 ' Cathedral tower
Granville* Lighthouse
5 50
5 55
5 43
0 09
0 04
0 04
36.7
34.7
36.0
16.0
15.2
15.7
Chausey Is . : Light on SE . end of large id . .
St Malo • Rochebourne light
Cape Frehel * Lighthouse
Heau de Brehat * Lighthouse
5 35
5 00
4 35
4 00
3 35
12 00
11 25
11 00
10 25
10 00
30.4
23.1
22.0
20.6
18.9
13.3
10.6
10.1
9.5
8.7
Morlaix lie Xoire* Lighthouse
De Bas Islet* Lighthouse
\bervrach * Light on Vrach I^let
Ushant* Stiff Point light
Page 314] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
*i
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
France.
Brest : Observatory
t r n
48 23 32
48 19 10
48 02 40
48 02 28
48 00 47
47 47 52
47 43 17
47 38 51
47 44 53
47 18 42
47 29 10
47 19 18
47 32 53
47 39 30
47 17 53
47 18 30
47 19 44
47 16 18
47 17 17
47 13 08
47 00 41
47 02 35
46 43 04
46 29 38
46 20 41
46 14 40
46 09 25
46 00 36
45 56 37
46 02 49
45 41 39
45 35 14
45 34 10
44 50 07
43 29 29
43 29 38
43 23 58
43 22 52
43 23 30
43 20 05
43 19 22
43 22 36
43 24 20
43 28 36
43 29 30
43 26 50
43 23 35
43 31 00
43 32 48
43 38 05
43 34 40
43 47 20
43 39 00
43 29 30
43 27 30
43 23 10
42 52 45
42 12 30
41 09 10
0 t II
4 29 36
4 34 28
4 52 03
4 45 25
4 32 50
4 22 30
3 57 15
3 30 35
3 21 31
3 13 38
3 06 09
2 50 07
2 55 08
2 45 28
2 38 05
2 31 25
2 25 48
2 11 50
2 02 09
1 32 59
2 13 16
2 21 37
2 22 56
1 47 45
1 27 49
1 33 40
1 08 57
1 10 40
0 57 50
1 24 37
1 15 16
1 10 24
1 04 27
0 31 23
1 28 43
1 33 16
1 39 53
1 45 02
1 47 30
1 56 05
2 01 40
3 04 06
3 16 10
3 28 06
3 47 40
4 01 00
4 24 55
5 07 10
5 40 11
5 56 00
7 03 00
7 42 00
8 05 30
8 13 29
8 20 20
8 24 26
9 15 28
8 54 00
8 40 35
ft. ra.
3 23
ft. TO.
9 45
ft.
19.5
ft.
9.0
Brest (approach)' Quelern light
De Sein Islet: Lighthouse ...
3 25
9 53
17.2
7.9
Bee du Raz • Lighthouse
A udierne* Pierhead light
3 04
3 05
3 00
9 31
9 34
9 27
11.1
13.3
13.0
5.1
6.1
6.0
Penmarch Rocks' Lighthouse
Glenan Islands • Light Penfret I
De Groix Island * Lighthouse
3 09
3 25
3 35
3 20
3 45
5 47
9 36
9 50
9 58
9 46
10 08
12 11
13.8
16.6
16.9
16.7
16.6
15.8
6.3
7.7
7.9
7.7
7.7
7.4
Belle Isle* Lighthouse
Port Haliguen • Li°-ht on N jettv
Haedic Island * Lighthouse
PortNavDlo' Lighthouse
Vannes * St Pierre Church
Le Four Rock* Lighthouse
Croisic * End of breakwater
3 25
9 47
16.7
7.7
Guerande * Steeple
Port St Nazaire* Lighthouse
3 35
4 18
5 50
3 05
9 56
10 39
12 28
9 26
16.6
17.0
16.5
16.7
7. 7
7.9
7.7
7.7
Paimbceuf* Steeple .
Nantes- Cathedral
Noir Moutier Island: Lighthouse
Le Pilier Island * Lighthouse
D' Yeu Island : Lighthouse
3 18
3 20
9 40
9 44
14.7
12.7
6.8
5.9
La Chaume • Lighthouse
Point de Grouin du Cou: Lighthouse
Re* Island : Light, NW. pt
Rochelle : E. Quay light
3 27
3 27
3 45
9 22
9 22
9 55
16.6
16.6
16.7
7.7
7.7
7.7
Aix Island : Lighthouse
Rochefort: Hospital
Oleron Island : Light, NW. pt
Point de la Coubre: Lighthouse
Point Cordouan: Lighthouse
3 35
9 53
16.8
7.8
Point de Grave : Lighthouse
Bordeaux: University Obsy., Floirac
6 30
0 12
15.3
7.1
Bayonne* Cathedral
Biarritz' Lighthouse
St. Jean de Luz : St. Barbe Point light. . .
Hendaye* Abbadia Observatory
3 07
9 14
12.3
5.8
Fuenterrabia: Light on Cape Higuera
Port Pasages: Light at entrance
Spain and Portugal.
Sa,n Sebastian: Monte Igueldo light.
2 55
2 50
2 50
2 55
3 05
3 00
3 00
9 05
9 03
9 03
9 07
9 18
9 14
9 14
11.7
12.7
11.8
12.3
14.8
11.7
10.4
5.5
5.9
5.5
5.7
6.9
5.5
4.9
Bilbao: Light on Galea Castle . . .
Castro Urdiales: Santa Ana Castle light...
Santona : Pescador Point light
Santander : Cape Mayor light
San Martin de la Arena: Lighthouse
San Vincent de la Barquera: End of new
mole
Rivadesella: Mount Somos light
Gijon : Santa Catalina light
2 50
2 45
2 45
9 03
8 58
8 58
13.5
12.0
14.4
6.3
4.9
3.9
Aviles: Lighthouse. ...
Rivadeo: Lighthouse.
Estaca Point: Lighthouse
Port Cedeira: Lighthouse.
2 43
2 44
8 56
8 57
14.8
14.9
6.1
6.1
Ferrol: Old naval observatory
Priorino Chico light.
Corufia: Hercules Tower light
2 43
2 42
8 56
8 55
14.8
10.0
6.1
4.6
Cape Finisterre : Lighthouse
Vi^o' Cres I li^ht
Oporto: Light, N. S. de Luz
2 25
8 38
10.0
4.3
APPENDIX IV. [Page 315
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
^
Place.
Lat. X.
Long. W.
Lun. Int.
Range.
H. W.
L. W. Spg.
Neap.
Spain and Portugal.
Coimbra* Royal Observatory
ft. m.
ft. m.
ft.
ft.
40 12 25
40 10 47
39 24 49
39 21 00
38 46 49
38 42 31
38 29 15
37 01 20
37 07 48
36 58 23
37 11 00
37 15 08
36 43 58
36 27 42
36 31 30
36 10 50
35 59 53
36 07 19
36 07 10
36 06 25
8 25 47
8 54 15
9 30 29
9 22 30
9 29 46
9 11 10
8 56 00
8 58 00
8 39 53
7 51 48
7 24 00
6 57 12
6 26 30
6 12 18
6 19 00
6 02 08
5 36 31
5 26 12
5 21 17
5 20 42
Caps Mondego * Lighthouse
2 20
8 35
7.0
3.0
Berlin ^a Island* Lighthouse
Peniche* Lighthouse
2 05
8 15
7.8
3.4
Cape Roca * Lighthouse
Lisbon* Royal Observatory, Tapada
2 20
2 10
8 05
8 20
11.1
11.6
4.8
5.0
Setubal : Lighthouse
Cape St Vincent* Lighthouse
Lagos* Church
1 55
8 08
13.0
5.6
Cape Sta Maria* Lighthouse
Avamonte* Lighthouse
Huelva* Plaza at head of mole
San Lucar* Chipiona li^ht
1 15
7 28
12.3
5.6
Cadiz* Observatory of San Fernando. .
San Sebastian light
1 45
7 58
11.8
5.4
Cape Trafalgar : Lighthouse
Tarif a : Lighthouse
1 32
7 52
5.6
2.6
Algeciras* Verde I li^ht
Gibraltar* Dockvard fla^taff
Europa Pt li^ht
1 35
7 55
3.7
1.7
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS.
| Spain.
Malaga * Lighthouse
36 42 39
36 50 12
36 42 57
37 33 28
37 35 50
37 33 22
37 34 38
38 12 30
38 20 12
38 30 00
38 30 57
38 33 30
38 38 36
38 40 51
38 48 06
38 51 00
39 12 15
39 28 05
39 27 50
39 53 57
40 04 53
40 27 48
40 33 30
40 43 10
41 06 00
41 25 18
41 5004
42 16 15
42 19 10
4 24 38
2 27 50
2 11 12
1 15 12
0 59 09
0 57 58
0 50 20
0 30 12
0 28 48
0 11 42
0 10 06
0 04 02
Long. E.
0 02 52
0 09 17
0 12 02
0 07 30
Long. W.
0 13 37
0 19 48
0 18 50
Long. E.
0 41 19
0 08 56
0 28 48
0 39 45
0 53 55
1 14 42
2 07 00
3 08 28
3 17 10
3 18 55
2 15
8 35
2.9
1.5
Almeria: Lighthouse
Cape de Gata: Lighthouse
Mazarron: Lighthouse
Cartagena: Arsenal gate
Escombrera light
Ponnan* Lighthouse
Santa Pola Bayi Lighthouse
Alicante: N. mole li°iit.
Villajoyose: Lighthouse
Altea: Lighthouse
Calpe : Church tower ...
Morawa: Tower.
Jarea": Cape San Antonio light
Denia: Mole-head light
Cape Cullera: Lighthouse
Valencia: Lighthouse
|
Mole-end light
5 00
11 30
1.5
0.8
Columbretes Islands* Lighthouse
Oropesa Cape * Lighthouse
j
Vinaroz : Mole-head light . . ....
Port Alfaques: Bana light
Cape Tortosa* Lighthouse
Tarragona* E mole li^ht
Barcelona* Roval Academy Obsy
Palamos Bav : Molino Pt. light
Cadaques : Clock tower
Cape Creux* Lighthouse
Page 316] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
1
o
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
France.
Cape Bear: Lighthouse
h. m.
A. m.
ft.
ft.
42 30 59
42 31 18
43 00 47
43 23 50
43 29 17
43 11 57
43 20 43
43 18 18
43 10 21
43 05 10
43 01 01
43 32 51
43 33 51
43 41 32
43 41 58
43 40 30
38 54 10
39 06 34
39 33 00
39 51 53
37 08 09
38 52 34
39 08 44
40 33 50
40 50 25
41 14 36
41 18 24
41 14 15
40 59 52
40 54 55
39 55 47
39 05 15
39 12 35
41 22 10
41 52 50
42 18 14
42 35 10
43 01 45
42 41 47
41 35 45
43 57 17
44 24 15
44 25 09
44 04 00
43 45 15
43 32 36
43 02 57
42 45 14
42 35 06
42 21 28
42 20 15
42 19 13
42 05 38
41 53 34
41 12 27
3 07 30
3 06 50
3 04 08
3 42 08
4 08 32
5 13 51
5 20 46
5 23 39
5 36 42
5 56 06
6 08 39
7 00 54
7 08 02
7 17 15
7 18 42
7 19 41
1 27 25
2 57 20
2 37 00
4 18 20
8 18 44
8 51 08
8 13 29
8 10 00
8 23 56
9 08 42
9 20 28
9 29 40
9 39 14
9 44 22
9 42 52
9 32 35
9 07 20
9 11 15
8 35 45
9 09 04
8 43 25
9 24 10
9 27 00
9 22 05
8 10 22
8 54 19
8 55 20
9 50 48
11 15 20
10 17 45
9 51 07
10 24 38
10 05 50
10 03 54
10 18 39
10 55 24
11 46 50
12 29 06
13 35 15
Port Vendres : Fort Fanal light
Port Nouvelle: S. jetty light
Cette: Light, St. Louis mole
Aigues Mortes: Espignette Pt. light
Planier Rock* Lighthouse
Marseilles • Janet Cliff light
7 31
2 00
0.6
0.3
National observatory
Ciotat* Berouard mole li^ht
Toulon: St Mandrien light
8 22
2 24
0.6
0.2
Grand Riband Island: Lighthouse . . .
Cannes : Lighthouse
Antibes : Garoupe light
Nice : Lighthouse
Villefranche: Mole-head light
Cape Ferret light
Port Ibiza' Lighthouse
M
i
Cabrera Island' Lighthouse
Pi (Majorca) * Lighthouse
Port Mahon (Minorca) ' Lighthouse
Carloforte: Int. Latitude Obsy
Sardinia.
Cape Spartivento: Lighthouse
,
Cape Sandalo : Liejht on San Pietro I
|
Porte Conte : Cape Caccia light .
Port Torres: Lighthouse . . .
Cape Testa: Lighthouse
Razzoli Island : Lighthouse
Caprera Island : Gal era Pt
Cape Figari: Signal station
Cape Tavolara' Lighthouse
Cape Bellavista* Lighthouse
Cape Carbon era* Cavoli I light
Cagliari: Light on mole
Bonifacio* Mount Pertusato light
Corsica.
Ajaccio: Lighthouse..
Corti: Church tower
Calvi: Lighthouse . ...
Cape Corso : Giraglia I . light
Bastia : Lighthouse
Porto Vecchio* Chiape Pt light
Cape Melle* Lighthouse
>>
w
H
Genoa: San Benigno light
Hydro. Institute Obsy
Spezzia: Fort Santa Maria light
Florence: Arcetri Observatory
Leghorn (Livorno): Light on S. end of
curved breakwater
Capraia Island : Cape Ferrajone light
Elba Island, Porto Longone: Cape For-
cado light
Pianosa Island: Light on battery, W.
side of fort. .
Africa Rock: Lighthouse..
Monte Christo Islet: Summit. .
Giglio Island, Cape Rosso: Lighthouse...
Civita Vecchia: Light N. end of break
water
Rome: Royal Observatory at Capitol
Gaeta: Orlando tower
APPENDIX IV. [Page 317
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
o
Place.
Lat. X.
Long. E.
Lun. Int.
Range.
II. W.
L. w.
Spg.
Neap.
£
"3
•4*
M
Ponza Islet: Punto della Guardia light...
Naples' Observatory Capo di Monte
ft. 772.
ft. m.
ft.
ft.
40 52 38
40 51 46
40 50 20
40 32 07
38 28 43
38 42 40
38 16 02
38 16 10
38 06 44
38 07 56
38 00 39
37 57 13
37 47 10
37 16 55
36 04 10
35 54 00
35 51 50
35 29 37
36 41 03
37 03 04
37 12 39
37 29 35
37 30 13
37 50 25
38 11 32
38- 16 03
37 55 27
39 01 29
39 04 38
40 24 41
40 02 48
39 47 43
40 06 23
40 09 06
40 39 36
41 08 19
41 53 17
41 37 39
42 08 14
43 37 14
45 20 30
45 26 02
45 26 11
45 41 06
45 48 33
45 38 45
45 38 54
45 33 00
45 32 34
45 31 54
45 29 24
45 19 16
45 13 45
45 05 00
44 51 49
44 45 30
44 57 24
45 19 36
45 16 18
45 01 30
45 07 12
44 57 36
12 57 17
14 15 26
14 15 37
14 11 40
14 51 40
13 12 00
15 39 11
15 13 42
13 21 29
13 22 29
12 29 50
12 02 55
12 25 59
13 32 27
14 12 55
14 31 30
12 52 09
12 36 12
15 07 45
15 17 37
15 13 20
15 05 19
15 05 00
15 18 30
15 34 33
15 39 15
16 03 45
17 12 09
17 08 07
17 12 23
17 56 55
18 22 17
18 31 25
18 28 45
17 59 37
16 50 52
16 11 13
15 55 34
15 31 36
13 31 18
12 19 09
12 20 24
12 20 32
13 22 54
13 32 10
13 45 44
13 45 14
13 43 18
13 39 32
13 33 48
13 29 30
13 33 42
13 35 39
13 38 00
13 50 43
13 53 36
14 08 42
14 26 41
14 33 42
14 34 36
14 16 30
14 23 30
Lujht on elbow of mole
4 00
10 13
0.7
0.2
Capri Island : Carena Pt. light
Lipari Island: Casa Bianca light
Ustica Island: NE. point light
Faro of Medina* Capo di Faro lio'ht
Milazzo* Lighthouse
Palermo: Roval Observatory
Li^ht on mole head
Trapani : Palumbo Rock light
Maritime Island : Light on SYT. pt
Marsala* \V mole lio'ht
Girgenti: Port Empedoche light
Gozo Island : Lis:ht on N W. pt
Malta Island, Yaletta Harbor: Lighthouse.
Linosa Inland : Landin<* Cove
3 12
9 25
0.7
0.2
Lampedusa Island: Carallo Bianco light. .
Cape Passaro: Lighthouse . . .
Syracuse: Maniace Castle light ....
Augusta Port: Torre d'Avola light
3 00
9 13
0.9
0.3
Catania : Sciari Biscari lio-ht
Royal University Observatory . .
Cape Taormina: Semaphore
1
Messina: San Rarieri li^ht
Cape Peloro: Lighthouse
Cape Spartivento: Lighthouse . .
Cape Colonna: Lighthouse
Cotrone : Mole-head light
Taranto: Cape St. Vi to light
Gallipoli* St Andrea li°ht
Cape Sta. Maria di Leuca: Lighthouse
Cape Otranto: Lighthouse
PortOtranto: Castle
Brindisi: Lighthouse
3 30
9 43
1.8
0.5
Bari: St. Catalolo light
Viesti: Lighten St. Croce Rock .
Manfredonia: Lighthouse
Tremiti Islands: Caprara I. light
Ancona: Monte Cappucini li^ht
Malamocco' Rocchetta Mole li^ht
10 15
4 45
3.3
0.9
Venice: Site of tower of St Mark
Nautical Institute Observatory..
Grado : Church tower
i
i Austria.
Monfalcone: Church tower
Trieste: Imperial Maritime Observatory. .
Theresa Mole li°"ht
i
9 20 3 50
2.0
0.6
Capo d'Istria* Lighthouse
Isola: Lighthouse
Pirano: Lighthouse . ..
Salvore Point' Lighthouse
i
Citta Nuova' Lighthouse
Parenzo* Cathedral tower
,
Rovigno' St Eufemia li^lit
Pola: Imperial Hydro Office Obsv
9 00 3 25
3.4
0.9
Promontore Point* Porer Rock light
Nera Point* Lighthouse
Fiume* Cathedral tower
8 15
2 35
1.2
0.3
Porto Re* Lighthouse
Veglia * Mole head
Prestenizza Point * Li^hthou^e
i
Cherso* Kimen Point li°iit
Page 318] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
j
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
Austria.
Galiola Rock * Lighthouse
ft. 771.
ft. m.
ft-
ft.
44 43 36
44 37 20
44 32 11
44 27 42
44 24 42
44 59 24
44 40 06
44 31 30
44 07 05
44 09 06
43 56 16
43 51 15
43 37 36
43 45 08
43 31 00
43 27 00
43 31 02
43 30 07
43 23 50
43 19 12
43 17 46
43 05 28
43 01 43
43 04 30
43 09 24
43 09 50
43 07 30
43 02 50
42 57 42
42 54 19
42 57 37
42 45 54
42 45 05
42 45 05
42 23 30
42 47 06
42 45 30
42 39 00
42 35 08
42 27 04
42 23 36
42 25 30
42 16 42
42 11 43
42 05 15
41 55 47
41 35 10
41 23 31
41 18 40
41 08 44
41 02 12
40 47 00
40 36 14
40 25 30
40 25 17
40 12 00
40 02 57
39 54 29
14 10 36
14 14 06
14 28 06
14 33 28
14 34 06
14 53 48
14 34 42
15 04 24
15 14 05
14 49 24
15 26 21
15 12 06
15 34 24
15 58 07
15 55 00
16 08 51
16 15 09
16 26 06
16 11 10
16 24 30
17 01 36
15 27 30
15 45 29
16 12 28
16 27 14
16 41 55
17 12 00
17 00 19
17 12 44
16 51 32
16 43 07
17 08 54
16 51 *45
16 29 29
16 15 12
17 22 51
17 46 48
18 03 08
18 10 49
18 25 36
18 32 00
18 46 12
18 50 36
18 56 25
19 04 19
19 12 29
19 27 15
19 24 54
19 27 14
19 26 47
19 26 30
19 20 14
19 19 14
19 27 55
19 17 45
19 38 33
19 47 53
19 54 55
TJnie Island. * Netak Point li°lit
Lussin Piccolo* Manora Observatory
8 10
2 25
1.1
0.3
St. Pietro di Nembo Island : Health office.
Gruizza Rock* Lighthouse
Zengg* Mole-head light
Terstenik Rock* Lighthouse
Carlobago * Lighthouse
Zara * Church tower . .
Blanche Point: Lighthouse
Zara Vecchia : Church tpwer
Port Tajer: Lestrice I. light
Lucrietta Island : Lighthouse
Sebenico* Mount Tartaro
6 10
0 20
1.0
0.3
Rogosnizza Port* Mulo Rock light
Zirona Grande Island: St. George
Church tower
Trani* Cathedral tower
Port Spalato * Cathedral tower
Solta I., Port Olivetto: St. Nicholas tower
Spalato Passage: Speo Pt. light
Makarska * Church tower
Porno Rock * Center
St Andrea Rock: Summit
Lissa Island : Hoste Rock light
4 00
10 30
2.4
0.7
Pakonjidol Rock : Lighthouse
Lesina Island * Port Gelsa light
St Giorgio Pt light
Sabioncello Peninsula: Cape Gomena
light
Sorelle Rocks* Lighthouse
Curzola Island: Porto Bema mole head.
Porto Valle Grande,
church tower
Lagostini Island * Glavat Rock light
Lagosta Island' St George Chapel
Cazza Island* Lighthouse
Pelagosa Rock: Lighthouse
Meleda Island* Port Palazzo Ruin. . .
Olipa Rock: Lighthouse
Pettini di Ragusa Rocks: Lighthouse
Bobara Rock * Summit
Molonta Peninsula* Summit
Ostro Point* Lighthouse
Cattaro* Health office
Budua* Mole-head light
Katie Rock* St Domenica Chapel
Antivari* Pt Valovica light
Dulcigno* W windmill
Cape Rodoni: Guardhouse
| Albania.
Cape Pali* Guardhouse
Durazzo* Lighthouse
Cape Laghi* Ruin
Skumbi River* Pyramid at mouth
Semeny River* Samana Pt light
Vojazza River* Pyramid at mouth
Avlona* Lighthouse
Cape Linguelta * Extreme
Mount Cica* Pyramid
Port Palermo * Pyramid
Cape Kiefali* Pyramid
APPENDIX IV. [Page 319
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
j
Place.
Lat. X.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
5
Saseno Island : Lighthouse
/ f tf
40 30 12
39 51 53
39 39 27
39 29 50
39 16 32
39 39 54
39 37 05
39 11 30
38 56 30
38 47 25
38 40 40
38 22 04
38 11 36
38 15 00
37 38 20
37 47 10
37 15 12
37 03 38
36 54 10
36 48 40
36 47 50
36 57 20
35 28 55
35 20 30
36 29 40
36 34 25
36 15 20
36 40 27
36 59 12
37 06 32
37 00 01
37 08 38
37 26 12
37 07 36
37 25 55
37 38 00
37 39 28
37 44 00
37 57 30
36 47 05
37 18 42
37 31 45
37 44 30
37 56 14
37 58 21
37 38 45
37 52 48
38 01 28
38 28 15
39 10 48
40 37 28
39 52 10
39 50 52
39 31 58
39 12 35
39 06 10
39 03 20
38 32 00
19 16 15
19 26 06
20 07 12
20 17 09
20 24 55
19 43 09
19 56 30
20 12 34
20 45 40
20 44 16
20 42 44
20 43 37
20 29 30
21 43 50
21 18 55
20 55 26
21 01 14
21 34 35
21 40 29
21 42 40
21 58 00
21 56 42
24 09 39
25 09 44
26 59 25
26 24 28
25 13 00
24 23 15
24 40 30
25 23 00
25 14 21
25 14 08
24 56 14
24 32 23
24 23 35
24 44 32
24 19 44
24 04 12
24 42 30
23 05 40
23 08 53
23 25 45
23 25 30
23 38 10
23 43 14
24 02 15
24 03 00
24 16 42
23 36 45
23 27 07
22 58 00
25 03 20
25 14 14
24 59 13
25 50 00
26 34 54
26 31 39
25 35 00
A. m.
h. m.
ft.
ft.
Fano Island : Pt. Kastri light
Port Pagonia: Ruin
Port Gomenitza: Well Dogana
Port Parea : Madonna I
Port St. Spiridione: Convent
Corfu : Lighthouse .
Paxo Island: Madonna I. light
Prevesa; Fort Nuovo minaret
Port Drepano: Observation island ....
Port Vliko: Customhouse
Port Vathi: Lazaretto light
Port Argostoli: St. Theodoro light
Patras1 Lighthouse
3 40
9 53
1.0
0.3
Katakolo: Lighthouse
Zante: Mole fight
Strovathi, or Strivali Island: Stamphani
I. light
Proti Passage: Marathon Pt. ...
Navarin : Lighthouse
Mothoni: Round tower
Koroni Anchorage: Mole light
PetaKdi Bay: Petalidi Pt
Candia Island, Port Suda: Lighthouse. . .
Megalo Kastron : Mole
li^ht . . .
Kandeliusa Island : Lighthouse
Stampali Island, Maltezana Port: Agios
loanes
Christiana Islands* N pt
Milo Island: Summit Mt St Elks
Siphano Island: Lighthouse
Naxos Island, Naxia: Gate on Bacchus I.
Paros Island, Port Trio: Trio Pt
Port Naussa: St. Yanni
Church
Syra* Alole light
Sermo Island* Amyno Pt
Thermia Island: Ruins of Cythnus
Jura Island: North pt
Port St Nikolo: Lighthouse
St Nikalao Island* Port Mandf i
Andros Island, Cape Fasse: Lighthouse...
leraka* Acropolis
Port Kheli* Lighthouse
Poros Island * Lighthouse
.ZEgina* Lighthouse
Pirs&us* Lighthouse
Athens' National Observatory
Cape Colonna* Extreme
Port Raphti* Statue I
Petali Island* Tra^o I peak
Euripo Strait* Lighthouse
i
i
Skiathos Island* Mount Stavros
Salonika* S bastion
Lemros Island* Kastro Castle
Port Moudros* San°Tada Pt
Strati Island* St Strati Church
Mityleni Island, PortSigri: Lighthouse.
Mityleni: Lighten Mit
yleni Pt
Portlero: Sid ero Islet.
Psara Island * Fort
61828°— 16-
Page 320] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
I
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L. W.
Spg.
Neap.
Turkey.
Port Baklar* Cape Xeros
40 32 40
37 16 33
37 41 24
38 19 55
36 55 00
36 48 00
36 39 33
36 26 00
36 05 53
40 02 30
40 24 27
41 01 20
41 01 02
41 00 35
41 00 16
41 21 15
41 52 04
42 27 52
43 10 00
44 10 20
45 09 47
45 16 00
46 28 37
46 58 22
46 34 27
44 36 55
44 29 50
45 21 03
46 45 00
42 58 00
41 39 30
41 01 00
42 01 20
41 18 03
40 38 10
40 23 30
39 50 00
39 01 21
38 50 10
38 25 40
38 21 48
38 12 21
37 02 00
36 52 00
36 35 30
35 30 30
34 29 25
34 52 00
33 54 10
33 34 20
33 16 30
32 54 35
32 47 40
35 07 10
34 33 45
34 54 00
31 15 41
31 31 40
31 29 30
31 21 23
31 11 43
26 45 00
27 36 55
26 58 42
26 17 45
27 18 25
28 18 00
29 06 13
28 16 24
28 08 10
26 10 54
26 41 24
29 01 00
29 00 29
29 01 14
28 58 59
28 42 14
27 58 45
27 35 54
27 58 35
28 39 14
29 41 14
30 14 14
30 45 32
31 58 27
31 33 36
33 36 26
33 36 25
36 28 30
36 46 40
40 55 10
41 38 15
39 46 25
35 13 20
31 25 49
27 46 09
27 47 30
25 58 34
26 47 57
26 57 20
27 09 10
26 47 00
26 47 32
27 27 05
30 45 34
36 10 20
35 46 30
35 44 24
35 51 00
35 28 25
35 21 30
35 14 40
35 08 00
35 05 00
33 57 22
33 01 30
33 38 59
32 18 45
31 51 00
30 19 10
30 06 00
29 51 40
Ji. m.
ft. m.
ft.
ft.
Port Isene: Tower
Samos Island* Fonia Pt light . .
Tchesme": C Ke"cil light .
Kos : Lighthouse .
Marmorice Harbor: Adassi Pt. light
Makry Harbor: Kasil I
Rhodes Port: Arab's Tower light
Port Lindo: Tower
Dardanelles • Hellas Pt light
Gallipoli' Lighthouse
Scutari* Leander Tower light
Constantinople* Seraglio Pt light
St Sophia Mosque
Cape Kara Burnu * Lighthouse
Yuiada Road * Fort Tersana
Russia.
Buro'haz * Lighthouse
Varna Bay * Lighthouse
Kusterjeh* Cape Kusterjeh light
Danube River* Salina light
Fidonisi Island: Lighthouse
Odessa* University Observatory
Nikolaieff* Naval Observatory
Dnieper Bay* Fort Nikolaeo light
Sebastopol* E lighthouse
Balaklava Bay* Hospital
Kertch* Lighthouse
Berdiansk * Breakwater light . .
Saukhoum • Lighthouse - - -
Batoum • Lighthouse
Turkey.
Trebizond * Lighthouse
Sinope * Lighthouse
Bender Erekli* Lighthouse ...
Marmora Island * Lio-ht off E pt
ArtakiBay* Zeitijn Adasi Islet
Tenedos Island* Ponente Pt. light
Port Ajano * Nikolo Rock
Port Ali-Agha* W pt of entrance
Smyrna: English consulate flagstaff
9 15
3 15
2.5
0.7
Vourlah* Customhouse
Sighaiik Harbor* Beacon on islet
Budrum* Lighthouse
Adalia * Lighthouse
Alexandretta : Lighthouse
Latakia * Lighthouse
Tripoli Roadstead: Bluff Islet lio-ht.
Ruad Island * Lighthouse
Beirut* Lighthouse
9 45
3 35
1.2
0.3
Saida (ancient Sidon) * Lighthouse
Sur (ancient Tyre) : Lighthouse
Acre* Lighthouse
Haifa : Lighthouse
Cyprus. 1
Famagusta * Lighthouse
9 40
3 30
1.4
0.4
C Gata* Light
Lamaka * Lighthouse
Port Said * High lighthouse
9 40
3 30
1.0
0.3
• -J
i£
H
River Nile* Damietta Mouth
Rosetta Mouth li^ht
AboukirBay* Nelson I peak
Alexandria* Eunostos Pt light
9 45
3 15
1.1
0.3
APPENDIX IV. [Page 321
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
I
Place.
Lat. X.
Long. E.
Lun. Int. Range.
H.W.
L.W. Spg.
Neap.
Ben Ghazi' Castle
h. m.
9 55
10 00
3 35
h. m.
3 45
3 50
9 57
ft.
1.2
1.9
4.2
({'3
0.5
1.1
32 06 51
32 54 03
34 39 01
35 30 24
35 45 24
36 23 20
36 50 12
37 04 45
36 48 19
37 10 42
37 16 38
•37 31 16
36 57 15
36 54 29
37 05 17
36 46 41
36 47 16
36 47 50
36 33 07
35 44 21
35 43 22
35 11 05
35 58 00
35 53 44
35 47 00
35 47 14
20 02 40
13 10 50
10 41 17
11 05 15
10 50 42
10 37 10
11 07 00
11 03 15
10 18 31
10 17 30
9 53 21
8 56 12
7 46 40
6 53 11
6 28 37
5 06 22
3 04 13
3 02 08
1 20 36
Long. W.
0 41 38
1 07 57
2 25 45
3 03 29
5 16 46
5 48 31
5 55 41
Tripoli Harbor* Lighthouse
Sfax • Ras Tina light
Til lite.
Mehediah * Sidi Jubber
Monastir * Burj el Kelb battery
Ufimmfinipt' "Rav* Castle flao'Staff
i
Kalibia Road • Lighthouse
i
Cape Bon* Lighthouse
Tunis* Goletta light. ...
3 33
9 55
3.0
0.8
Cape Farina * Extreme
Algeria.
Benzert • N Jetty light
Galita Inland • Monte Guardia
Bona * Fort Genois li^ht
Stora* Sin»e I light
Cape Bou^aroni: Lighthouse
Cape Carbon: Lighthouse. . .
Algiers: Lighthouse near Admiralty
2 46
8 58
2.6
1.3
Bouzareah Observatory
Cape Tenez* Lighthouse
Oran* Mers el Kebir li°*ht
Habibas Island* Lighthouse
Zafarin Islands: Light Isabel Segunda I..
Alboran Island : Lighthouse
Morocco.
Ceuta : Lighthouse
1 55
1 30
8 07
7 40
3.3
8.0
1.5
3.7
Tangier* Ca^bah tower
Cape Spartel* Lighthouse
WEST COAST OF AFRICA.
El Araish: S. pt. of entrance
35 12 50
34 04 10
33 36 00
33 08 00
31 30 30
30 38 00
28 45 00
27 56 00
26 07 57
25 07 06
23 36 03
22 12 37
20 46 27
18 18 45
16 01 31
14 44 45
14 43 20
14 40 30
14 38 55
14 39 55
13 39 45
13 28 00
12 35 00
10 36 37
10 03 15
9 30 30
9 16 10
8 57 05
6 09 13
6 48 00
7 33 00
8 35 05
9 43 30
9 50 00
11 02 00
12 56 00
14 29 00
14 50 44
15 58 00
16 48 11
17 05 40
16 02 00
16 30 22
17 32 25
17 30 55
17 25 28
17 26 47
17 24 30
16 40 30
16 35 00
16 44 00
14 42 00
14 04 30
13 44 00
13 26 20
13 18 25
Sali* Fort
1 35
7 45
10.4
4.8
Cape Dar el Beida* Lighthouse
Cape Blanco North* Extreme
Mogador Harbor* English consulate. . . .
1 05
7 17
10.9
5.0
Cape Ghir* Extreme
Cape Noun : Extreme
Cape Juby : Extreme
11 55
11 50
5 43
5 38
8.5
7.3
3.9
3.4
Cape Bojador* Extreme
Penha Grande
Ouro Riyer entrance* Dumford Pt
Pedra de Galha
Cape Blanco* Extreme
1^35
5 23
5.5
2.5
Portendik * Village
St Louis* Lighthouse
Almadie Point* Lighthouse
Cape Verde* Lighthouse
Port Dakar* Lighthouse
CapeAIanoel* Lighthouse
Goree Inland * Fort
Bird Inland* Flagstaff
Bathur^t* Flagstaff
9 00
2 50
5.9
2.7
Nunez Riyer * Sand I
Ponga River entrance: Observation Pt
7 30
1 20
11.4
5.2
"Yfatacon0* Inland* Hou^e
Scarcies "River: W. end of Yellaboi I
Page 322] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF AFRICA— Continued.
j
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
II. W.
L. W.
Spg.
Neap.
Sierra Leone : Light on cape
h. TO.
7 40
h. TO.
1 30
ft.
11.6
ft.
5.3
8 30 00
8 29 57
7 40 36
7 22 45
7 00 08
6 44 30
6 19 10
6 19 00
6 08 06
5 54 08
5 26 25
5 12 42
4 59 15
4 22 10
4 24 47
4 52 18
4 45 00
4 47 45
4 53 00
5 01 00
5 04 48
5 06 20
5 31 50
5 46 00
6 25 15
5 46 01
4 16 40
4 23 07
4 27 00
4 30 40
4 57 53
3 46 10
1 35 00
1 40 42
0 20 30
Lat. S.
1 24 18
0 36 25
3 23 00
4 40 00
4 49 00
5 18 30
5 32 30
6 04 36
6 31 50
8 48 24
12 20 00
12 34 43
13 12 30
13 26 05
15 09 00
15 47 30
16 30 00
18 23 00
22 57 00
26 17 00
26 37 52
26 58 30
13 18 30
13 14 30
13 04 30
12 31 55
11 38 45
11 22 51
10 49 25
10 50 00
10 22 45
10 04 05
9 34 45
9 20 16
9 02 05
7 44 15
7 21 30
2 14 45
2 05 45
1 56 40
1 45 00
1 38 00
1 21 05
1 13 50
0 11 30
Long. E.
0 41 00
3 25 15
5 03 05
6 15 00
7 07 00
7 40 00
7 59 00
8 18 57
8 47 05
9 39 00
7 27 56
6 42 45
5 38 12
8 43 10
10 38 00
11 46 30
11 45 00
12 08 00
12 11 00
12 15 00
12 25 25
13 13 20
13 32 00
13 23 45
12 48 55
12 36 00
12 12 00
11 52 40
11 42 00
11 57 12
14 30 00
14 57 20
15 07 02
15 12 22
N. battery
Sherbro Island : N. island
Sherbro River: Manna Pt
5 50
12 00
10.4
4.8
Gallinas River: W. elbow of Kamasoun I.
Cape Mount: W peak
Cape Mesurado: Lighthouse
Monrovia' Lighthouse
5 40
11 54
6.0
2.5
Marshall: Agent's house
Grand Bassa: Agent's house
Cestos: Factory
Sang win River: Sangwin Pt
Sinon : Bloobarra Pt
4 50
4 30
11 05
10 43
4.8
4.3
2.0
1.8
Cape Palnias : Lighthouse
Tabou River: Tabou Pt
Axirn Bay: Ft. St. Anthony
Cape Three Points: Lighthouse
4 00
10 13
4.7
1.9
Dix Cove: Fort
Tacorady Bay: Tacorady Pt
Chama Bay: Dutch Fort
El Mina Bay: Ft. St. George
Cape Coast Castle: Lighthouse
4 20
10 32
6.0
2.5
Accra: Lighthouse
Volta River entrance : Dolbens Pt
4 20
4 50
10 33
11 05
4.2
3.3
1.8
L3
Lagos River : Lighthouse
Benin River entrance : N . pt . .
Brass River: Entrance (approx.)
Calebar River (New): Rough Corner.
Opobo River: W. pt. beacon (approx.).. .
Quaebo River: Bluff Pt
Calebar River (Old) : Judicial Ho. flagstaff
(Duke Town)
Fernando Po Island: Lighthouse
San Bento River: Joho Pt. (approx )
Princes Island: Diamond Rocks, center
of largest
St. Thomas Island: Ft, San Sebastian
light
Anno Bon Island: Turtle Islet
Cape Lopez : Lighthouse
Mayumba Bay : Lighthouse
4 25
4 13
10 38
10 26
7.0
6.5
2.9
2.7
Loango Bay: Indian Pt. light
Black Point Bay: Sandy Pt
Malemba Bay: Landing Cove
Kabenda Bay: Kabenda Pt. li^ht
Congo River entrance : Shark Pt
4 10
10 25
6.0
2.5
Margate Head : Summit
St. Paul de Loando: Flagstaff, Ft. San
Miguel
3 40
9 53
4.8
2.0
Lobito Point' Extreme
Benguela: Telegraph office
3 30
9 43
5.5
2.3
Elephant Bay: Friar Rocks
St Mary Bay: Bay I .
Little Fish Bay * Lighthouse
Port Alexander* Bateman Pt
Great Fish Bay: Tiger Pt
3 00
9 12
5.7
2.4
Cape Frio' Extreme
Walfisch Bay Lighthouse
Ichabo Island
Angra Pequena: Diaz Pt
Elizabeth Bay: S. pt. of Possession I. ..
2 35
8 47
5.5
2.3
APPENDIX IV. [Page 323
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF AFRICA— Continued.
i
8
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H.W. L. W.
Spg.
Neap.
North Nolloth : Magistrate's house
Hondeklip Bay
h. m,
2 25
ft. 77?.
8 38
ft.
5.3
ft.
2.2
29 15 12
30 18 33
30 33 07
33 07 51
33 48 52
33 56 04
34 21 12
16 52 02
17 16 20
17 27 30
18 01 21
18 22 33
18 28 41
18 29 26
Roodewal Bay ...
Saldanha Bay : Constable Hill
2 20
8 33
5.1
2.1
Table Bay: Robben I. light
Cape Town : Royal Observatory
1 36
7 47
4.6
2.0
Cape of Good Hope: Lighthouse
EAST COAST OF AFRICA AND THE BED SEA.
Simons Bay : Lighthouse
34 10 45
34 23 48
34 46 45
34 49 45
34 23 47
34 11 10
34 04 35
34 06 15
34 12 30
34 01 41
33 57 43
33 50 27
33 36 09
33 28 00
33 23 10
33 05 10
33 01 45
32 42 00
32 02 30
31 48 15
31 38 06
31 26 15
29 52 40
29 50 47
29 00 12
28 32 30
28 09 36
25 58 30
24 05 30
23 45 30
22 05 00
21 31 00
20 38 10
20 10 42
18 52 50
18 01 24
17 51 50
17 15 00
17 06 30
16 33 24
16 20 30
15 08 00
15 02 12
15 00 45
14 58 20
14 53 00
13 23 40
12 55 45
12 19 30
11 09 18
18 27 30
18 50 20
19 38 17
20 00 37
20 48 40
22 09 31
23 03 38
23 24 23
24 50 20
25 42 12
25 37 21
26 17 13
26 54 10
27 03 00
27 20 48
27 49 12
27 55 02
28 22 36
29 06 40
29 21 15
29 33 16
29 48 40
31 03 41
30 00 18
31 51 39
32 27 39
32 38 10
32 35 55
35 29 45
35 31 41
35 29 00
35 29 30
34 53 30
34 46 00
36 11 47
36 58 30
37 01 09
38 04 00
39 06 27
39 49 57
40 03 57
40 36 12
40 48 45
40 45 06
40 45 10
40 40 00
40 46 00
40 31 15
40 40 09
40 43 21
2 35
8 48
5.2
2.2
Cape Hangklip : Extreme
Quoin Point: Extreme
Cape Agulhas* Lighthouse
2 40
8 53
5.2
2.2
Port Beaufort: Flagstaff
St Blaize: Lighthouse
3 18
9 31
5.6
2.0
Knysna Harbor: Fountain beacon
PlpttpTibpro Bay: Summit, of Spal Pt,.
St. Francis: Lighthouse
Cape Recife: Lighthouse
Port Elizabeth : Lighthouse
3 21
9 33
5.4
1.9
Bird Islands: Lighthouse
Port Alfred : Signal staff
Waterloo Bay: Maitland Signal Hill.
Madagascar Reef: Center
Cove Rock: Center . .
East London : Lighthouse .
3 37
9 50
5.0
1.8
Cape Morgan* Extreme
Hole-in-the-Wall
Raine Head' Extreme
Cape Hermes' Extreme
Waterfall Bluff
Port Natal (Durban): Lighthouse
3 58
10 11
5.6
1.6
Govt. Observatory
Dumford Point* Extreme
Cape St Lucia* Extreme
Cape Vidal' Extreme
Delagoa Bay: Pta. Vermelha (Reuben
Pt ) light
5 10
11 22
11.9
3.4
Cape Corrientes: Small rock
Innamban Bav : Barrow Hill light
4 30
10 42
11.0
3.2
Cape St. Sebastian: Extreme
Bazaruto Island' N pt ii^ht
Chuluwan Island* Lighthouse
Sofala: Fort on N. side of entrance
Zambesi River: Kan°"oni Mouth
4 15
10 27
13.5
3.9
.Kiliman River : Lighthouse
Kiliman : Town
Mazemba River* Entrance
Premeira Islands: Center of Casuarina I..
Angoxa Islands* Center of Hurd I
Mafamale Island* Center
Port Mokambo* Mokambo Pt
i
Port Mozambique: St. George I. light
San Sebastian light. . .
Cape Cabeceira' Lighthouse
4 00
10 12
11.8
3.4
Port Conducia* Bar Pt
,
Lurio Bay* Pando Pt
j
Pemba Bay* N pt light
Querimba Isl°nd5'' Ibo I li°*lit
NuTtiba IP! and * E pt
i
!
Page 324] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF AFRICA AND THE BED SEA— Continued.
*;
6
Place.
Lat. S.
Long. E.
LUH. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Cape Delgado: Lighthouse
ft. m.
3 59
ft. m.
10 11
ft.
11.3
ft.
3.3
10 41 20
10 19 22
10 16 31
10 06 43
9 59 30
9 44 22
9 25 36
8 57 15
7 38 10
6 49 41
6 26 10
6 09 43
5 00 35
4 04 30
3 12 48
2 15 42
2 13 35
1 13 00
0 22 35
Lat. N.
1 06 48
1 42 06
2 01 48
2 30 00
10 26 30
11 50 30
12 26 00
12 11 15
12 39 00
11 27 30
11 13 00
10 25 00
11 22 00
12 39 00
14 44 00
15 28 10
15 37 12
18 15 12
19 07 00
20 44 00
23 36 20
24 56 30
26 06 24
26 18 50
26 45 48
27 47 21
28 20 52
29 06 29
29 53 05
28 13 47
27 35 45
27 33 00
26 13 00
24 38 35
24 05 15
22 43 50
21 28 00
20 09 00
19 55 30
19 07 40
18 15 50
40 38 35
40 26 34
40 10 33
40 02 14
39 46 41
39 47 07
39 39 31
39 30 42
39 54 42
39 17 05
38 54 27
39 11 08
39 10 20
39 41 13
40 11 21
40 56 21
40 59 40
41 54 15
42 33 57
44 03 27
44 53 49
45 24 39
46 07 00
51 22 55
51 16 45
52 09 35
52 25 35
53 59 31
49 35 40
47 17 00
44 59 35
43 29 35
43 25 35
40 52 00
39 45 30
39 27 23
38 19 30
37 19 09
37 15 30
36 10 15
35 51 00
34 17 03
34 50 45
33 59 43
33 42 28
33 06 31
32 39 43
32 32 50
33 36 56
35 30 30
35 32 30
36 27 00
37 17 45
38 02 45
39 00 30
39 10 38
40 12 00
40 30 00
41 03 20
41 27 30
Msimbati : Has Matunda
Mikindini Harbor: Kinizi
Mgan Mwania: Madjori Rock
Lindi Riven Fort flagstaff
3 55
10 08
10.9
4.5
Mchinga Bay: Observation spot
Kiswere Harbor: Rustmigi
Kilwa Kisiwani: Fort
Mafia Island: Moresby Pt
Dar-Es-Salaam: Flagstaff
Bagamoyo : French Mission
Zanzibar: English consulate
4 05
10 17
14.5
6.0
Tanga Bay: Lighthouse
Mombasa: Lighthouse
Port Melinda: Vasco de Gama's Pillar
Lamo Bay: Lamo Castle
4 00
10 13
12.1
5.0
Manda Roads: E. side of Manda To to I. .
Port Durnford : Foot Pt
4 30
10 42
11.7
4.9
Kisimayu Bay: S pt of Kisimayu I
Brava- Well
4 15
10 27
7.5
3.1
Meurka Anchorage: S. pt. of town
Magadoxa: Tower.
Murat Hill: Peak
Ras Hafun: E. extreme of Africa
Cape Guardafui: E. pt
6 00
12 12
6.1
2.5
Kal Farun Islet: Center
Abd-al-Kuri Island: NE. pt
Sokotra Island : Tamarida, mosque
7 05
1 17
7.5
3.1
Ras Antareh: Extreme of rocky pt .
Mait Island: Center... . ....
Port Berb era: Lighthouse.. .
Zeyla: Mosque
7 30
7 50
1 18
1 38
8.5
7.2
3.5
3.0
Perim Island: Lighthouse.
Hanfelah Bay: Hanfelah Pt
r
•
i
Disei Island: Village Bay
Massaua Harbor: N. pt. of entrance
0 45
6 57
4.0
1.7
Khor Nowarat: Shatireh Islet
Suakin : Lighthouse
2 10
8 22
1.7
0.7
Makaua Island: S. pt
St. Johns Island: Peak
Daedalus Shoal: Lighthouse.
Kosair Anchorage: SW. angle of fort.
Brothers Island : Lighthouse
6 40
0 28
2.0
0.8
Safajah Island: N. summit
Ashrafi Island: Lighthouse
Ras Gharib : Lighthouse . .
10 35
10 40
10 45
4 23
4 28
4 32
1.5
5.5
6.8
0.6
2.3
2.8
Zafarana: Lighthouse
Suez: Newport Rock
Tor: Ruined fort
Sherm Yahar: Entrance
Sherm Joobbah: Entrance
Sherm We j: Lighthouse. .
Sherm Hassey: Anchorage .
Yembo: Anchorage
Sherm Rabeo'h: Anchorage
Jiddah : Jezirah el Mifsaka I
3 30
9 42
2.0
0.8
Lith: A°ha Islet.
Jelalil: Anchorage
Kunfidah: Islet
Khor Nohud' Entrance
APPENDIX IV. [Page 325
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF AFRICA AND THE RED SEA— Continued.
i
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L. W.
Spg.
Neap.
si
V
a
«
•
M
M
Farisan I. Anchorage: Jebel Mandhakh..
Gizau : Fort
h. m.
ft. TO.
ft.
ft.
16 50 15
16 53 00
15 42 00
15 20 30
14 47 00
14 03 53
13 19 43
41 58 15
42 29 00
42 38 45
42 34 00
42 56 00
42 45 28
43 13 36
Loheiya: Hill Fort
I 15
7 27
2.9
1.2
Kamardn Bay Harbor
Hodeida Road
Jebel Zukur Island : N pt
Mokha: N Fort
11 45
5 33
4.5
1.9
ISLANDS OF THE INDIAN OCEAN.
I^accadlve Islands.
Chitlac Islet- S end
11 40 45
11 35 00
11 27 30
11 13 00
11 06 00
10 47 00
10 32 00
10 06 00
10 03 00
8 16 00
6 55 00
6 59 00
6 25 00
5 26 30
5 01 30
4 25 45
4 44 00
4 10 15
3 41 00
2 57 00
3 16 00
2 10 30
2 07 00
0 14 30
Lat. S.
0 41 30
5 40 56
4 52 26
5 53 00
4 37 15
3 43 06
5 15 00
7 13 37
16 25 12
19 40 22
19 52 36
19 59 45
20 08 46
20 05 39
20 24 20
72 42 54
72- 09 54
72 59 00
72 44 00
72 41 00
73 40 00
72 37 40
72 15 10
73 35 54
73 01 15
72 55 54
73 12 54
72 41 54
73 20 00
72 53 00
72 57 24
73 28 00
73 30 24
73 24 54
73 34 24
72 48 00
73 03 00
73 35 54
73 13 00
73 06 54
53 41 03
53 23 38
55 27 10
55 27 23
55 12 19
71 43 47
72 23 50
59 46 40
63 25 38
57 39 14
57 32 35
57 29 26
57 33 09
57 47 14
Betrapar Islet: N Island
Kittan Islet: S. end. .
10 20
4 00
6.3
3.0
Cardamum Islet : Center
A.rneni Islet' N end
Underut Islet: Center
Cabrut Islet: E end
Seuheli Par: N. islet .
Kalpeni Islet : S . end
j
Mimkoi Island : Lighthouse
11 27
5 15
2.5
1.2
Heawandu Island' S end
Maldlve Islands.
Kee-lah Island: N end
Mah Kundu Island: NE extreme..
Nar Foree Island
Hee-tah-doo Island
To-du Island' Center
Gator Island' Center
Male or Kin0^ Island: Flacrstaff
0.20
6 25
2.9
1.4
Pha-li-du Island: Northern end.
Moluk Island : Center
Himmittee Island
Kimbeedso Island' S end
Esdu Island' NE pt
Wahdu Island: E end . ...
Addu Atoll' Gung I
Amirante Islands: He des Roches, N.
beach
African Islands
Seychelles, Platte I. : S. end
Port Victoria : End of Hodoul
Jetty
4 22
10 35
4.3
1.2
Bird Island : Tree ....
Chagos Archipelago, Peros Banhos: Dia
mond Islet
Diego Garcia: N. end
of Middle I
1 30
1 50
0 20
7 43
8 03
6 32
5.8
4.0
5.5
1.7
1.2
1.6
Cargados Carajos: Establishment I., flag
staff
Rodriguez Island: Mathurina Bay, Point
Venus
Flat Island: Lighthouse
(Mauri
tius I.
Cannonier Point* Lighthouse
Port Louis: Martello tower, Ft. George...
Royal Alfred Obsv
0 48
7 00
1.6
0.3
Grand Port' Fouquet I light
Page 326] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE INDIAN OCEAN— Continued.
I
Place. .
Lat. S.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Reunion Island: St Denis lio'ht
20 51 38
20 53 11
20 59 45
21 19 47
15 51 37
10 21 30
10 06 45
7 00 30
7 06 00
25 39 10
25 12 30
25 03 00
23 38 25
22 05 18
21 54 24
20 18 18
19 49 30
17 53 00
17 29 00
16 12 10
16 07 00
15 46 30
15 43 45
15 11 42
14 40 18
13 59 00
13 55 40
13 27 15
13 23 38
12 49 30
12 27 20
12 03 18
11 57 30
12 23 20
12 44 02
12 49 00
12 56 48
13 21 15
15 15 48
15 54 50
15 27 55
16 14 00
17 00 05
16 42 30
17 23 16
18 09 47
19 55 00
21 58 10
24 46 25
24 59 42
24 58 50
25 01 30
22 22 30
21 29 00
12 26 30
12 47 02
12 16 20
12 25 00
11 34 48
11 40 44
9 46 20
55 26 59
55 36 18
55 16 18
55 28 58
54 28 46
56 32 00
51 10 21
52 44 57
56 22 00
45 06 50
44 17 57
44 07 20
43 38 20
43 15 20
43 20 21
44 19 21
44 31 30
44 02 20
43 45 18
44 29 05
45 17 09
45 43 09
46 18 45
46 57 29
47 24 36
47 58 21
47 48 05
47 59 30
48 17 34
48 38 57
48 45 45
49 11 21
49 17 25
49 35 56
49 45 06
49 54 00
49 56 25
50 01 59
50 31 21
50 16 05
49 49 11
49 50 59
49 50 59
49 56 15
49 32 04
49 25 31
48 52 10
48 14 50
47 10 34
47 07 20
47 04 24
46 59 11
40 24 10
39 40 39
46 32 35
45 16 27
44 24 54
43 47 00
47 24 09
43 19 15
46 31 07
n. TO.
7i. m.
ft.
ft.
Bel- Air light
St. Paul light
St. Pierre light. .
11 50
5 38
3.5
0.6
Tromelin Island: N. end
Agalegas Island : NW. pt
Farquhar Islands: Hall's house
Alphonse Island: SE. part (Trees)
Coetivy Island: N. end
Cape St. Mary: S. extreme
Madaga
Leven Island: Center
Port Machikora: Barracouta I
St. Augustine Bay: Nosi Vei I
5 40
11 52
9.8
2.9
Murderers Bay : Center of Murder I
Cape St. Vincent: Extreme
Mourondava: Village
Tsmano: Village
Kovra Rythi Point: Extreme
Coffin Island: Nosi Vao
Cape St. Andrew: Extreme
Boyanna Bay: Barabata Pt
Cape Tauzon: Extreme.
Majunga (Mojanga): Lighthouse
4 15
11 28
10.9
3.2
Majamba Bay : W pt . .
Narendri Bay: Moormora Pt
PortRadama: Pt. Blair..
Radama Islands: N. pt Nossuvee I.
Baratoube Bay: Ambubuka Pt
Nosi Be": Hellville Jetty
Miaow Islands: N. pt. Great I
Cape San Sebastian: Extreme
Port Liverpool : N. pt. of entrance .
Cape Amber: NE. extreme '.
Port Lady Frances: Sunson Pt...
Port Looke* : Pt. Bathurst
Port Leven: S. pt. Nosi Hau I
Andrava Bay : Berry Head
Vohemar: Flagstaff
Cape East: Ugoncy I
Venangue Be Bay: Entrance
Port Choiseul : Maran Seelzy Village
3 45
9 57
5.1
1.5
Cape Bellone: Extreme
St. Marys Island : Light on Madame I
Port Tan tang: Flagstaff
Fenerive Point: Flagstaff..
Tamatave: Pt. Hastie
4 00
10 12
7.3
2.1
Mahanuru : Town
Matatane : Village
Santa Lucia: N. end of town, Obs. Rock. .
Point Ytapere: Extreme :
Ytapere Bay: N pt
Fort Dauphin : Flagstaff
4 15
10 27
4.7
1.3
Europa Island: Center
Bassas da India: E. pt
Geyser Reef: SE. extreme
Mayotta Island : Zaoudzi
4 00
10 13
11.9
2.0
Johanna Island: Landing place, Pomoni
Harbor. .
Mohilla Island : Numa Choa Harbor
Glorioso Islands: W islet
Comoro Island : Islet in Mauroni Bay
4 45
10 58
10.0
1.7
Assumption Island' Hummock
APPENDIX IV. [Page 327
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE INDIAN OCEAN— Continued.
!
o
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Aldabra Island: West I., E. side entrance
Cosmoledo Islands: Observation islet
Prince Edwards Islands: Marion I., Obs.
spot XE side .
A. 77i. ! ft. m.
ft.
ft.
9 22 35
9 41 20 ;
46 49 30
46 36 00
46 22 00
46 01 00
46 28 18
46 10 40
46 26 00
48 40 00
48 26 45
49 42 00
49 21 22
49 41 00
49 29 00
53 02 45
53 13 00
53 02 50
38 42 51
37 50 00
12 06 22
10 25 19
46 14 52
47 32 25
37 49 15
50 41 30
51 30 15
50 40 00
51 50 00
50 35 00
52 13 00
69 04 00
68 48 20
68 54 00
70 04 31
70 15 00
70 29 50
73 15 30
73 52 00
72 31 45
77 31 53
77 29 15
96 53 02
105 45 57
Penguin Islands Center of S W islet
at
«•
y
Possession Island * N\V pt
Twplvp Inlands' Summit \E T
Navire Bav
Ho0' Island' Summit
East Island • Center
Christmas Harbor . ....
Kerguelen Is.
Blighs Cape
Cape Bourbon
Molloy, Port Royal Sound: U. S. Tr. of
Venus Obs 1874
0 14
6 36
4.6
1.3
Cape Challenger
Balfour Rock
Heard Island: Cape Laurens, NW. end. . .
Sealing station
McDonald Island, Summit
St Pauls Island : Ninepin Rock
10 40
10 50
5 20
7 10
4 28
4 38
11 32
1 00
3.0
3.3
5.1
4 5
0.9
1.0
1.5
1.3
Amsterdam Island: Summit, 2,750 feet
Keeling or Cocos Islands: Direction I
Christmas Island : Flying Fish Cove
SOUTH COAST OF ASIA.
I Arabia.
Aden: Telegraph station . . .
Lat. N.
12 47 16
13 22 00
13 24 50
13 28 45
14 20 10
14 31 15
14 43 50
14 49 00
14 54 40
15 12 00
15 38 00
16 30 00
16 59 00
17 32 45
17 53 15
19 00 25
20 10 00
20 31 30
22 32 40
23 38 00
23 52 00
23 51 30
24 21 50
25 21 00
26 24 13
26 30 00
25 21 34
24 29 02
25 17 24
26 10 55
26 13 56
30 32 00
29 22 56
44 59 07
45 40 50
46 26 35
46 39 00
48 56 45
49 07 35
49 35 05
49 57 05
50 16 35
51 10 30
52 14 20
52 48 00
54 43 29
56 03 05
56 20 35
57 51 35
58 38 35
58 58 35
59 48 35
58 30 50
58 08 00
57 26 00
56 46 12
56 22 56
56 32 22
56 31 29
55 24 12
54 22 14
51 33 32
51 13 46
50 31 18
47 51 23
48 00 55
7 49
1 41
4.9
2.0
Sughra: Sheik's house
Mokateini Black ruin
Howaiyuh* Sheik's house
Banderburnm * SE house of town
Makalleh Bav Flagstaff
8 20
2 07
6.8
2.8
Shahah Roads' Customhouse
Sharmoh* Single house
Kosair" Hi^h house . . .
Sihut* Center of town
Ras Fartak : Extreme pt
Dam°iiot : Town
|
Merbat: Town
8 50
2 38
7.0
2.9
Kuria Maria Is., Hullaniyeh I. : NE. bluff
Ras Sherbedat* Point
Cape Isolette* Islet
Masirah Island' Point Abu-Rasas
Point Ras Ye
9 45
9 15
9 30
3 32
3 03
3 20
9.6
8.9
6.0
4.4
4.1
2.8
Ras-al-Hed * Extreme pt
Maskat (Muscat) : Maskat Pt
Deimaniyeh Islands' E islet
Sueik* Fort
Sohar* SE tower of town hall
Khor Fakan Bav TV end of village
Ras Musendomf N. end of island
Great Quoin I^let' Center
Sharjah' High tower with flagstaff
Abu-Thabi' Fort flagstaff
Al Beda'a Harbor: Nessah Pt., N. extreme
Ras Rakkin* NW pt
Bahrein Harbor* Portuguese fort
5 15
11 30
6.4
3.7
Kuweit Harbor' N end of town
0 05
6 17
8.3
4.8
Page 328] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OP ASIA— Continued.
1
6
Place.
Lat. N.
Long. E.
Lun. Int. Range.
1
H.W.
L.w.
Spg.
Neap.
Persia.
Kahrig Islet: Fort flagstaff .
29 15 25
28 59 07
26 47 40
26 33 37
26 39 12
26 40 49
26 57 27
25 38 19
25 29 45
25 16 43
25 03 17
25 07 19
25 15 52
25 11 55
25 25 19
24 50 03
24 47 37
24 49 50
22 50 00
22 29 20
22 14 00
22 14 00
21 38 00
21 06 00
20 41 20
21 02 21
21 47 00
21 35 54
22 17 00
21 05 20
21 12 19
19 20 10
18 53 45
18 42 08
17 58 00
16 59 30
16 33 26
15 05 12
15 21 24
15 29 25
15 51 10
15 53 20
14 49 00
14 25 00
14 17 28
13 38 15
12 52 17
11 51 10
11 45 00
11 42 00
11 15 10
9 58 00
9 30 00
8 53 20
8 30 47
8. 29 55
8 04 00
8 47 10
9 17 20
o / n
50 21 11
50 50 35
53 23 36
54 02 21
55 16 47
55 54 25
56 17 37
57 45 57
59 40 32
60 37 40
61 26 24
62 19 42
63 28 37
64 37 02
66 35 39
66 39 58
66 58 06
67 01 33
• 69 20 15
69 05 15
68 57 06
68 58 54
69 36 00
70 06 32
70 50 45
71 49 35
72 14 00
72 21 08
72 35 10
72 38 40
72 49 27
72 48 44
72 48 56
72 48 49
73 02 40
73 15 56
73 19 39
73 54 50
73 54 00
73 46 10
73 37 00
73 27 15
74 03 40
74 22 30
74 26 40
74 39 50
74 50 40
75 21 51
75 29 40
75 31 10
75 46 40
76 14 40
76 20 40
- 76 34 00
76 56 45
78 07 47
77 32 35
78 11 26
79 12 50
h. m.
Jt. m.
ft.
ft.
Abu Shahr: Residency flagstaff.
7 12
I 13
2.6
1.5
Shaikh Shu'aib Islet: E. end
Kais Islet: NE pt
0 30
6 40
6.6
3.8
Basidu: Chapel
Hanjam Islet: Ruined mosque
Kasm: Fort
10 50
9 20
4 35
3 05
11.6
7.8
5.3
3.6
Jask Bay: Telegraph office
Kub Kalat: High peak, 1,680 feet
Chahbar Bay : Telegraph office
Gwatar Bay: Islet
Baluchistan.
Gwadar Bay: Telegraph office
9 20
3 05
8.1
3.7
Pasni: Telegraph office
Ormarah: Telegraph office
Sunmiyani: Jam's house
8 50
2 35
8.1
3.8
Cape Monze: Peak
Karachi: Manora light
10 15
4 00
7.3
3.4
India.
Observatory
Mandavi: Lighthouse
Beyt (Bet): Lighthouse
12 05
5 39
10.8
5.2
Dwarka: Lighthouse
Temple spire
Porbandar: Lighthouse
Mangarol: Lighthouse
(
Diu Head: Lighthouse..
Kutpur: Lighthouse
Bhaunagar: Lighthouse. ..
4 27
11 18
29.8
15.1
Perim Island: Lighthouse..
Cambay: Flagstaff
Surat River: Tapti light. . .
Surat : Minaret Adrusah
Bassein : Center of town
Bombay: Colaba Observatory. .
11 26
5 08
12.0
4.9
Kenery Island light
Bankot: Fort Victoria
Ratnagherry: Fort
1
Viziadrug: Fort Flagstaff
1
Cape Ramas: W. bastion of fort
....
Goa: St. Denis Church
Aguada li^ht
10 34
4 10
5.2
2.5
Vingorla: Signal-station light
Vingorla Rocks: Lighthouse
Sedashigar Bay: Oyster Rock light
10 34
4 11
5.0
2.4
Kumpta: Lighthouse
Hinawar: Monument
Kundapur: Lighthouse
Mangalore: Lighthouse
10 50
4 28
6.5
3.4
Kannanur: Lighthouse
Tellicherri: Flagstaff
Mahe: Lighthouse
Calicut: Lighthouse
11 21
11 33
4 59
5 06
2.7
2.1
1.4
1.0
Cochin: Lighthouse
Alipee: Lighthouse
Quilon: Tangacherri Point light
0 18
6 16
2.5
1.3
Trivandninr Observatory
Tiruchendore : Pagoda on pt.
Cape Coniorin: Lighthouse.. .
Tuticorin : Lighthouse
1 52
1 37
7 51
7 36
3.0
2.0
0.8
0.5
Pamban Pass: Lighthouse
j APPENDIX IV. [Page
! MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
329
5
Place.
Lat. X. Long. E.
Lun. Int. Range.
H. W.
L.W. j Spg. Neap.
i
1 -*
es
•o
5
H
>>
l
Manaar: Center of town
ft. TO. ft. m.
ft.
ft.
8 59 00
6 55 40
5 55 30
6 01 25
6 10 10
6 25 00
7 45 00
8 33 30
10 18 00
10 45 28
11 55 40
13 04 08
13 05 15
13 25 15
13 53 08
15 47 00
16 09 45
16 56 21
17 41 34
18 19 00
19 13 00
19 22 30
19 48 17
20 20 20
21 27 15
21 38 40
22 11 10
22 33 25
22 11 00
20 05 00
20 08 53
18 51 00
18 50 30
16 01 30
15 42 14
16 01 30
14 12 30
13 18 40
11 40 40
10 27 00
15 37 26
16 30 01
16 46 00
16 26 00
16 04 45
15 52 00
13 36 40
12 26 15
12 06 00
10 05 05
9 58 00
7 50 00
5 24 45
4 13 05
2 52 10
79 53 52
79 50 40
80 34 12
80 13 04
81 28 15
81 44 00
81 41 00
81 13 42
79 51 30
79 50 47
79 50 10
80 14 55
80 17 27
80 19 12
80 12 30
80 59 00
81 11 00
82 15 05
83 17 42
84 07 30
84 52 06
85 03 29
85 49 09
86 44 00
87 02 20
88 02 00
88 11 07
88 20 12
91 49 00
92 39 00
92 52 40
93 56 30
93 31 00
94 13 16
94 12 00
94 23 00
93 22 30
92 57 10
92 45 15
92 31 10
95 37 32
96 23 00
96 07 30
97 38 00
97 33 05
97 35 00
98 13 00
98 35 59
99 03 00
98 10 15
97 35 00
98 25 30
100 21 44
100 34 15
100 59 12
Colombo' Lighthouse
1 55
7 49
2.0
0.4
Dondra Head : Lighthouse
Point de Galle: Lighthouse
2 02
8 07
1.9
0.4
Great Bassas Rocks: Lighthouse
Little Bassas Rocks: Lighthouse
::::::
Batticaloa: Lighthouse
Trincomali: Dock-yard flagstaff
8 10
1 44
2.0
0.5
Calimere Point: Lighthouse
Negapatam: Lighthouse
8 37 2 37
2.1
0.9
Pondicherri: Lighthouse
Madras* Observatory .
Lighthouse..
8 41 2 26
3.1
1.2
Pulicat' Lighthouse
Armeghon: Lighthouse
1
Kistna: Lighthouse
Masulipatam: Flagstaff
Coconada: Lighthouse
8 42
8 48
2 35
2 34
4.5
4.4
1.9
1.8
Yiza^apatam' Fort flagstaff
Kalingapatam* Lighthouse
Gopalpur: Lighthouse
Gau jam : Fort
Juggernath: Great temple
False Point* Lighthouse
9 21
3 00
6.8
2.6
Balasor River: Chandipur light
Saugor Island: L:ghthouse
Diamond Harbor: Flagstaff
Calcutta: Ft. William semaphore
1 25
1 02
9 06
7 56
11.2
13.1
4.4
5.6
Chittagong River: Lighthouse
Akyab* Oyster Reef light
Old temple
9 40 3 28
7.6
3.0
Ramree Island: S pt
Chedubah Island: NW. peak
Cape Negrais: Extreme
Bassein River* Alguada Reef li^ht
Bassein* Port Dalhousie
3 05
9 55
18.7
7.8
Andaman Is. : Table Id , Lighthouse
Port Cornwallis, Rock in
entrance .
....
9 50
9 40
3 37
3 27
8.6
6.3
2.9
2.1
Port Blair, Lighthouse
Little Andaman Island,
SE pt
Krishna Shoal' Lio'ht vessel
Rangoon River* Grove Pt light
Rangoon: Great Dagon pagoda
4 26
3 07
2 12
11 15
10 49
8 49
16.9
11.7
19.2
7.0
5.0
7.4
Moulinein : Docks
Moulrnein River* ^mherst Pt light
Double Island* Lighthouse
Tavoy River* Lighthouse
10 50
10 40
4 20
4 10
15.6
18.0
5.9
6.9
Mergui : Courthouse
Tena^serim
St. Matthew Island: Hastings Harbor
Pak Chan River* Lighthouse
j
Tongka Harbor, Junkseylon Island:
Lighthouse
Pulo Penan0'* Fort Cornwallis
11 50 5 40
8.8
3.8
Dindins* Channel* Hospital Rock
One Fathom Bank' Lighthouse
5 50
12 00
14.4
6.2
Page 330] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
I
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
II. W.
L.W.
Spg.
Neap.
I
Cape Rachado : Lighthouse
h. m.
ft. m.
ft.
ft.
2 24 08
2 11 30
1 09 57
1 17 33
1 19 57
1 04 20
1 03 13
0 57 10
0 44 30
0 55 50
0 36 52
0 36 30
Lat. S.
0 12 34
0 26 13
0 57 51
Lat. N.
9 15 40
8 02 10
6 46 20
5 45 00
5 34 40
5 15 58
Lat. S.
0 00 32
1 00 55
1 23 13
1 35 33
2 59 26
5 27 00
5 55 02
5 11 24
5 18 50
4 48 35
3 59 25
3 47 22
2 44 54
2 10 35
0 59 56
0 57 53
0 53 58
0 07 41
0 03 13
0 02 56
Lat. N.
0 11 41
0 33 11
0 34 47
1 17 36
1 24 16
1 44 24
2 16 47
2 02 32
2 51 30
3 14 59
4 08 14
4 38 21
101 51 02
102 15 00
103 44 47
103 51 11
104 24 08
104 27 21
104 10 30
104 19 52
104 21 19
104 25 43
104 04 42
104 11 31
104 36 14
104 30 15
105 38 20
92 48 00
93 29 42
93 49 20
95 04 33
95 19 00
97 30 11
103 47 58
104 21 30
103 59 14
103 36 41
104 45 34
105 15 58
104 32 36
103 55 42
102 07 28
103 20 18
101 00 58
102 14 50
101 17 25
100 50 06
100 19 28
100 20 19
98 53 58
99 45 20
98 05 55
98 16 43
99 22 09
99 06 33
97 43 43
97 36 46
97 12 28
98 46 08
97 45 06
97 06 53
95 56 02
97 10 13
96 07 23
95 34 29
Malakka: Stat. St. Pauls Hill
7 20
I 08
10.5
4.5
Singapore Strait: Coney Island light
Singapore: Cathedral tower
10 18
4 02
7.6
3.2
Singapore Strait: Pedra Branca light. . . .
Summit Bintang great
hill, 1,253 feet
Rhio Straits, PuloSauh: Lighthouse.
Terkolei: Lighthouse. .
Little Garras: Lighthouse...
Rhio, Bintang Island : Residency flagstaff.
Pitong Island: Peak
9 40
3 14
7.1
3.1
Abang Besar Island : N. pt
Linga Island : Flagstaff
6 00
12 13
11.5
4.9
Singkep Island : Mountain summit
Menali Island: N. pt
Nicobar Islands, Car Nicobar: N. pt
Nicobar Islands, Nancowry Harbor: Na
val Pt
9 05
2 52
8.3
2.8
Great Nicobar: W. pt.
Galathea Bay
Acheen (Acheh) Head: Pulo Bras light...
N extreme
Sumatra.
10 00
11 50
3 44
5 34
5.2
8.7
2.3
3.7
Diamond Point: Lighthouse. ..
Point Baru or Datu: Extreme
Point Bon or Djabon: Extreme
Moeara-Kompehi: Fort
Djambi: Flagstaff of fort
Palembang: Residency flagstaff
Lampong Bay: Telok JBetong li^ht
Blimbing Bay
5 40
11 52
2.6
0.7
Kroe: Village
Engano Island: Barioe anchorage
Bintoean: River mouth.
Mega Island: N. pt
Benkulen: Lighthouse..
5 50
12 03
4.0
1.1
Bantal: Village
Indrapura Point: Extreme
Pisang: Lighthouse
Padang: Lighthouse
5 35
11 48
5.5
1.4
Siberoet Island: Sigeb Pt
Xatiagam: Village .
Batoe Islands: N. point of Simoe Islet. . .
Summit of Tello
Ayer Bangis: Fort flagstaff
5 29
11 42
2.8
0.7
Natal : Fort flagstaff .
Nias Island: Lagoendi Bay.
Sitoli
Lapan
Siboga* Flagstaff
Singkel* Post office
Bangkaru Islands* Bay
Simaloe Island: NW pt
TampatToewon: Flagstaff
Analaboe ...
Batoe Toetong* Landin0' place
APPENDIX: rv. [Page 331
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA.
i
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Banka Strait.
! Java Head: First Pt. light
ft. 771.
5 30
6 50
ft. m.
11 42
0 37
ft.
2.5
3.8
ft.
0.7
1.1
6 44 30
6 08 46
5 12 17
3 13 05
3 00 48
2 34 18
2 23 20
2 04 03
1 38 26
1 29 00
3 19 10
2 56 52
2 52 05
2 44 40
2 32 12
2 24 30
1 33 24
2 07 00
2 26 30
Lat. N.
0 07 26
0 14 19
0 06 37
0 55 00
0 56 52
1 00 27
1 34 41
2 18 10
2 25 00
2 44 31
1 51 42
4 03 00
4 31 00
Lat. S.
6 04 15
6 01 20
6 07 40
6 35 45
5 56 15
6 43 00
6 51 09
6 51 29
6 57 09
6 42 18
7 12 10
7 37 30
7 02 00
7 02 30
7 43 25
7 49 00
8 12 30
8 47 00
8 32 00
7 40 30
7 25 00
105 11 48
105 26 58
106 27 33
106 13 02
106 27 22
106 50 36
105 44 30
105 09 45
105 46 28
106 57 30
107 12 42
106 54 38
107 00 43
107 38 46
107 37 15
107 03 33
108 55 13
104 17 00
104 34 06
107 13 00
108 01 47
108 37 05
106 45 00
107 32 57
106 24 10
106 18 27
105 35 58
105 52 00
105 22 57
108 38 55
107 21 40
107 42 30
105 53 05
106 08 20
106 48 37
106 49 11
108 22 37
108 34 00
109 08 07
109 41 08
110 25 03
111 20 32
112 43 58
112 55 00
112 41 09
113 53 45
113 41 10
114 26 53
114 22 55
114 25 13
113 15 00
109 02 12
106 24 30
Sunda Strait : Krakatoa I. peak
North Watcher Island : Lighthouse
Lucipara I ' Beacon
Banka Island' Tobol Ali Fort
[9 05]
[252]
[10.1]
Berikat, summit
Nanka I * Lighthouse
i [650]
[0 38]
[9.3]
Banka Island : Mintok light
Blinvu
CrassokPt
Shoahvater Island : Lighthouse
[2 08]
[8 21]
[5.6]
Ciiaspar
Strait.
Pulo Lepar: Lighthouse
Pulo Jelaka : Lighthouse
i
Billiton Island: Tanjong Pandan flagstaff.
Lano'kuas I light
[317]
[9 29]
[6.6]
Gaspar Island • Peak
Carimata Island : Sharp peak
Entrance to China Sea.
Pulo Eu- Center
Pulo Aor • S peak, 1 805 feet
St. Barbe Island: Center of W. side
Direction Island: S. pt
Dato Island: Summit . . .
St Julian Island: Summit '
|
Tamb elan Island: S. pt
1
Tamban I. obs. station.
Victory Island : S. pt
:
Anamba Islands : White rock
. ..j
Pulo Repon
Pulo Domar
St Pierre Rock- S pt
Natuna Islands: Pyramidal rocks
i
Semione I
Anjcr* Fourth. Pt light
7 11
0 58
2.4
0.7
i
Bantam: Flao'staff
Batavia: Observatory
[11 58]
[546]
[3.0]
Buitenzorg: Palace tower
Boompjeo Island: Racket I. light
Cheribon' Lighthouse
Te°al' Flagstaff
Pekalongan' Light W of entrance
Samarang' Lighthouse
[6 00]
[12 13]
[4.0]
Remban°" Residency flagstaff
Surabava: Time-ball station
12 07
11 44
5 54
5 31
4.9
6.2
1.7
2.3
Paeuruan: Lighthouse
Madura Island : Lighthouse
Soemenep flagstaff
Besuki' Lighthouse
Cape Sedano' NE pt of Java
Banjuwan°i' Fort
10 00
3 45
7.8
2.6
Bantenan: S pt of Java
Barung Island: S. pt
Kambangan Island: Lighthouse ...
8 33
2 21
5.2
1.8
Cape Anjoe- Extreme
Page 332] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
j
Place.
Lat. S.
Long. E.
- Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Smaller Dutch East Indian Islands.
Karimon Djawa Island: Flagstaff
Ji. m.
h. m.
ft.
ft.
5 52 57
5 51 18
5 32 28
5 05 46
8 05 30
8 21 00
8 42 30
8 23 00
8 34 15
8 32 00
8 12 30
8 27 00
6 31 00
7 30 00
7 35 00
6 05 50
6 07 00
5 15 00
6 17 00
6 43 00
5 28 30
8 16 15
8 50 55
8 04 45
7 48 00
8 20 30
8 33 00
8 34 00
8 12 00
8 34 00
9 00 00
10 09 54
10 46 00
10 29 00
9 35 03
7 53 00
7 38 00
8 12 00
8 14 00
7 03 00
6 44 00
5 32 50
7 55 00
7 04 00
6 35 00
7 05 00
5 20 00
5 56 00
5 20 00
4 44 00
4 33 00
4 03 05
4 31 53
3 22 48
2 55 52
3 41 00
1 44 00
1 48 12
2 28 00
1 30 00
1 11 21
2 04 00
110 25 29
112 39 10
114 23 42
114 35 00
115 03 48
115 28 00
115 08 47
116 27 30
116 04 09
117 20 33
117 57 00
118 43 55
118 43 00
117 56 00
117 22 00
118 56 50
122 40 00
123 32 00
123 59 00
126 43 30
127 30 00
120 29 55
121 38 40
122 52 00
123 31 00
123 15 00
123 22 00
124 06 00
124 23 00
125 33 57
124 52 00
123 33 57
122 52 00
121 46 00
120 14 30
126 22 00
127 19 00
128 01 00
129 00 00
128 28 00
129 29 00
130 17 44
131 23 30
131 55 00
131 34 00
134 31 00
134 40 00
132 54 00
131 58 00
131 47 00
131 50 00
131 25 23
129 53 18
127 06 18
128 07 04
128 10 00
122 20 00
126 21 19
126 01 00
127 18 00
129 55 48
130 12 00
Rawean Island: Sangkapura flagstaff
Great Solombo Island • N W pt
Arentes Island* S pt
Bali Island: Buleleng lighthouse.
Peak, 11,326 ft
Badong Bay, Kotta village. .
Lombok Island : Peak, 12,379 ft
10 50
4 38
8.7
3.0
Ampenam light
7 50
1 37
5.8
2.0
Sumbawa I. : Sumbawa village
Tambora Volcano, summit
E. side of crater
Bima flagstaff
0 00
6 12
5.7
2.0
Postilion Islands: N. island
Maria Reigersbergen I.
Ardassier Islands* S id
Brill Reef- Lighthouse
Hegadis Island
Token Bessi I. : Wangi-Wingi, NW. pt . . .
Binongko, S. pt
Gunong Api: Volcano
Lucipari Islands: N. islet
Flores Island : Reo village
Ende village
Flores Head, extreme. . . .
Komba Island: Peak, S. part
Adenaf a Island : Summit, Mount Woka
Lombata Island : Mount Lamararap
Pan tar Island: S. peak of saddle on S. pt.
Ornbay Island : Dololo anchorage
Timor Island: Deli, customhouse
0 45
6 58
5.7
2.0
Atapopa
Koupang, Fort Concordia. .
Rotti Island : W. pt
10 50
4 37
8.5
2.9
Saru Island: Seba Bay, on NW. side
Sandalwood Island: Nangamessie
11 20
5 07
16.5
5.6
Wetta Island* Ilwaki road
M olukka Islands.
Roma Island: W pt
Moa Island: Buffalo Peak 4 100 ft
Senna ta Island: NE pt
Damma Island: Kulewatta Harbor, N. pt.
Nila Island : Center
Mano or Bird Island: NW. extremity.
Timor Laut Island: Olilet, on E. coast
Vordate Island : S. pt
Mulu Island : N. pt
Aru Islands: S. island
N pt
Great Ki Island * S pt
Tello Islands' S island summit
Tehor Island * NE pt
Matabella Islands: Kukur
Goram Islands* Goram Mosque
Banda Island : Mole
1 45
1 20
7 57
7 32
9.0
4.2
6.6
3.1
Bouro Island Kajeli: Fort Defense
Ceram Island : Kawa
Amboina Island : Lighthouse
2 20
8 32
7.5
5.5
Sula Islands, Taliabo Island: NW. pt
Mandela Island* E pt
Besi Island* E pt
Obi Major Island * W pt
Popa Island * Outer Extremity Bay
Mysole Island* Efbe Harbor
APPENDIX IV. [Page 333
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
I
P
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Molukka Islands.
Gebey Island* "N"W pt
0 02 02
0 11 00
1 26 00
2 12 00
0 24 00
0 47 13
Lat. S.
0 38 03
Lat. N.
2 05 15
1 43 50
1 33 55
2 45 20
2 36 15
5 02 00
5 15 25
5 50 24
5 16 30
1 01 12
Lat. S.
0 45 00
4 05 42
4 10 40
3 18 55
3 16 00
2 54 00
1 14 00
0 40 00
5 36 00
5 08 09
0 57 00
Lat.N.
1 20 00
0 29 41
1 31 00
2 07 00
2 22 00
2 44 00
3 21 00
3 49 00
0 27 00
Lat. S.
0 46 00
3 58 00
4 23 30
5 15 00
5 29 15
5 35 00
5 47 00
6 26 00
Lat. N.
7 49 25
8 20 25
9 22 30
9 43 43
10 50 00
129 17 30
128 52 00
128 37 00
128 03 30
127 21 00
127 22 39
127 28 21
109 39 07
110 30 30
109 20 40
111 21 20
113 58 57
115 03 00
115 16 05
118 07 12
119 16 00
119 00 00
117 37 00
116 01 40
114 42 18
114 34 56
113 08 00
111 24 00
109 58 00
109 16 00
119 26 00
119 23 55
119 47 30
120 43 30
123 03 08
124 50 00
125 22 00
125 24 30
125 26 00
125 39 00
127 02 30
124 26 00
123 27 00
123 00 00
123 04 00
123 16 00
122 36 41
120 29 00
120 30 00
120 28 30
117 00 00
117 09 35
118 17 30
118 43 03
119 31 10
ft. 77J.
ft. TO.
A
ft.
Halmahera I., Cape Tabo: E. extreme. . .
(Gillolo I.) Cape Salawag: N. E. pt..
Derrick Point: N. ex
treme
Makkian or Makjan I.: Fort Reeburgh. . .
Ternate Inland' Residency flagstaff
5 00
11 10
3.9
2.9
Batian Island : Church
Tanjong Datu
Borneo.
Sardwak River* Po Pt light
4 00
5 20
10 12
11 35
9.0
14.1
3.9
6.1
Sarawak' Fort
Capo Sirik * Lighthouse .
Tanjon°* Barram .
Bruni River: Lighthouse
Labuan I., Victoria Hbr. : Lighthouse. . .
Sandakan Harbor* Flagstaff
9 35
12 00
3 23
5 50
5.5
6.8
2.4
Ito4
Unsang* Anchorage
Tanjong Mangkalihat E. pt. of Borneo
Pamaroong I. : E. pt. delta River Koetei . .
Pulo Laut* S pt Koeno-it Islet. . .
[745]
[1 33]
[7.0]
.....
Selatan Point: Extreme of Sita Pt
Bandjermasin: Residency flagstaff
Sampit Bay: Bandaran Pt
Kottarin°rin Bav: Samadra I
Succadana : Town
Padang Tikar: Point.
7 00
0 47
7.2
3.1
Port Laykan : SW. pt. of Celebes
Celebes Island.
Maka^^ar* Fort li^ht
4 40
10 55
3.9
2.9
Palos Bay Village at head
Cape Rivers: XE. Cape, Slime Islet
Gorontalo : Lighthouse
Alanado Bav Lighthouse
6 00
12 15
4.3
3.1
Bajuren Island* Summit
Ta°"ulanda Island: Peak
Seao Island: Conical peak
Sauguir Island: S. pt. Cape Palumbatu.. .
Taluat Island: Kabruang L, SE. pt
Cape Flesko: Extreme
Cape Talabo: E. end
Wowoni Island: N. pt
Bouton Island : N. pt
E. pt..
Fort
Cape Lassa* Extreme
Salavar Island: N. pt
S. pt
Balabac Island, Cape Melville: Light
house
'. Philippine Is.
Palawan Island, Cape Buliluyan: S. ex
treme
Victoria Peak, 5.680 ft. .
Port Royalist: Tide Pole
Pt Light
[11 30]
[520]
[6.5]
Tavtay Fort
Page 334] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
1
a
Place.
Lat. N".
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Philippine Islands.
Palawan Island, Port Barton: BuboiiPt.
Kabul! I.: Summit, N. •
extreme
o r n
10 29 19
11 26 25
10 51 26
11 09 09
11 25 47
11 53 53
12 02 09
12 39 46
11 54 28
12 06 45
12.20 03
12 50 15
13 28 40
13 31 35
13 06 05
12 17 15
13 49 30
13 45 22
13 56 17
14 12 20
14 21 48
14 22 27
14 29 57
14 35 49
]4 35 31
14 52 36
14 55 33
15 19 30
15 34 48
15 45 43
16 04 06
16 27 15
16 37 15
17 11 43
17 16 55
17 33 56
17 47 17
18 01 09
18 31 08
18 39 02
18 21 43
18 28 32
18 32 02
18 50 26
18 52 54
19 03 03
19 22 00
19 30 00
19 58 30
20 28 30
20 48 00
21 04 56
17 20 17
119 05 36
119 29 55
121 00 25
120 56 26
120 45 38
120 00 48
120 12 56
120 27 18
121 30 24
121 20 10
121 03 33
120 44 42
120 22 33
120 59 17
121 29 20
121 01 53
120 09 58
121 02 56
120 43 37
120 38 10
120 36 40
120 33 48
120 54 43
120 57 19
120 58 06
120 13 52
120 00 15
119 57 11
119 54 16
119 54 00
120 06 01
119 56 10
120 18 25
120 26 14
120 25 07
120 22 51
120 25 04
120 28 44
120 35 35
120 50 53
121 37 27
122 04 14
122 05 49
121 48 26
121 15 42
121 11 28
121 32 00
121 52 00
122 14 00
122 01 20
121 52 30
121 58 24
122 19 20
Ji. m.
ft> m.
ft.
ft.
Cuyo Island* Obs spot
Agutaya Islet: Summit of Mt. Aguade.. ..
Quiniluban Islet: Summit
Culion Islan^ : Fort
Busuanga Island: Mt. Tundalara
Apo Islet: Summit
Caluya Island: Summit
Semerara Island* N extremity
Mindoro Island: Mangarin Pt., SE. ex
tremity
Sablayan Pt., Vantay. . .
Monte Calavite
Escarceo Pt
Pt Dumaly
Ylin Island
Lubang Island, Port
Tulio-
Luzon Island, Batangas: Ast. station. —
Balavan* Plaza Rizal. . . .
[11 07]
[450]
[4.9]
Loro Peak: Summit, 3,985
feet ....
Caballo I. : Lighthouse
Corregidor Island: Light
house
[10 22]
[3 56]
[4.4]
Cavite: Sangley Pt. light..
Manila: Pasig lighthouse. .
Manila* Cathedral
10 44
[410]
[4- 6]
Subic: Town
[942]
[4 33]
[3.8]
Capones Islet: Lighthouse.
Iba* Ast station
Port Masinloc: Bani Pt. . .
Santa Cruz: Plaza
Sual: Army Hospital...
[10 20]
[10 21]
[940]
[3 33]
[3 44J
[3 29]
[2.4]
[2.3]
[2.6]
Silaqui Islet: Summit
Port San Fernando: Main
street
Candon: Ast station
Port Santiago: Remarkable
tree S of port
Vigan: Race track
Salomague Island: Port
Salomague flagstaff
Currimao * Town
Cape Bojeador: Light
house
Mairaira Pt. : Semaphore. . .
Aparri: Plaza.. .
5 43
-0 02
3.2
1.9
Port San Vicente: San
Vicente Islet
Cape Engano: Rona Islet..
Camiguin I . : Summit
6 00
-0 12
5.0
2.7
Fuga Island: W. summit. .
Dalupiri Island: Peak. . . .
Calavan Island* NE pt
Babavan Claro Island * \V pt
Balingtang Islands
Batan Island * Mount Irada
Ibavst Island" Mount Santa Rosa
Yami Island * Islet off SW part
Luzon Island, Port Dimasalasan: En
trance
APPENDIX IV. [Page 335
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
jj
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L. w.
Spg.
Neap.
1 Philippine Islands.
Luzon Island, Polillo I: Port Polillo....
Tabaco: Church belfry . . .
Catanduanes Islands :"N.
islet ...
ft. m.
ft. m.
ft.
ft.
14 51 00
13 21 33
14 09 00
13 28 30
12 31 20
12 52 20
12 22 10
12 36 00
12 10 03
11 56 09
13 07 40
13 18 10
12 54 03
12 56 56
12 38 42
12 33 44
12 03 15
12 36 00
12 35 33
12 24 55
11 01 30
11 46 44
11 47 30
11 15 08
11 00 17
11 02 37
10 07 39
10 03 22
10 17 30
9 15 17
9 03 37
9 18 25
10 24 35
10 40 21
10 26 38
10 41 27
10 44 08
11 16 47
11 28 20
11 45 30
11 35 40
11 35 06
10 11 26
9 53 00
9 41 34
9 47 53
6 14 30
7 01 22
5 22 30
6 28 50
7 21 15
6 52 15
6 54 03
121 54 48
123 43 53
124 06 48
124 04 48
124 04 18
123 49 22
123 35 58
123 14 36
123 12 47
123 07 34
123 02 45
121 54 33
121 43 08
122 04 48
122 08 38
121 58 32
121 53 53
122 17 08
122 16 26
122 33 23
125 43 14
124 51 37
124 18 15
124 59 56
124 36 20
124 22 07
124 50 15
124 32 35
123 54 18
123 34 26
123 06 09
123 18 43
123 07 05
122 55 42
122 40 20
122 34 26
121 54 27
122 09 09
121 52 36
121 58 59
122 28 50
122 45 03
126 02 53
125 31 17
125 58 22
125 28 30
125 47 48
125 34 35
125 13 48
123 57 37
124 11 42
122 04 00
122 04 52
6 08
0 00
5.2
2.8
Catanduanes Islands: S.
extreme
Point Calaan: S. extreme.
Port Sorsogon, Tinacos
Islet
Masbate Island, Palanog: Pier
Bugui Pt. lighthouse
Camasusu I. : Summit. . .
Tintolo Point: Extreme.
Burias Island * Busainga
[430]
[10 20]
[5.5]
Marinduque I. : Summit of Mount Catala. .
Maestro de Campo Island, Port Concep-
cion: Point Fernandez
Ban ton Island : Ban ton Mountain
Tablas Island : Tablas Head
Sanguilan Pt
Carabao Island : W. pt
Romblon Island: Sabang Pt. light
Summit over port
Sibuyan Island : Summit
Samar Island, Guiuan: Pier
Catbalogan : Fort
Maripipi Island : Summit
Leyte Tacloban
6 53
1 25
1.5
1.1
Ormoc : Ast. station
Palompon : Church
Maafdn . .....
11 47
4 50
2.8
2.0
Cebu Island Cebu* Plaza
Siquijor Island, PortCanoan: S. pt. of
entrance
Negros Island, Port Bunbonon; E. pt. of
entrance
Dumaguete : Town
Volcano of Malaspina,
8 192 ft
Bacalod : Town
Guimaras I., Inampulugan I., SW. pt
Panay Island Iloilo' Fort
11 06
5 22
4.2
1.9
San Jos6
Pan de Azucar
Batbatan Island: Summit.
Pucio Point: Extreme
Port Batan: Village
Capiz* Town
Siargao Island, Port Sapao: Semaphore. . .
Gibdo Island* Semaphore
i Bucas Island' E pt of Port Sibanga . ..
Mindanao Island ' Suri°"3.o
[11 40]
[6 15]
[6.5;
Cape St Augustin
Davao • Mole
6 00
-0 13
6.9
5.1
Saranguni Islets: W.
islet
Basianang Bay: N. pt.
of Donauanc" I
PoUoc: Small hill back
of town
Santa Cruz Islands:
SE islet
Zamboan^a: Fort
6 50
0 42
3.8
2.8
Page 336] APPENDIX IV. 1
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued. I
l
Place.
I
Lat. N.
Long. E.
Lun. Int.
Range. {
H.W.
L.W.
Spg.
Neap. I
Philippine Islands.
Mindanao Islands Sibuco Bay: Hill S. of
beach . .
n. m.
ft. m.
ft.
ft. j
7 18 05
7 45 41
8 40 15
8 08 29
9 10 19
10 43 00
10 27 00
9 35 30
7 43 00
7 00 38
4 54 10
4 49 30
4 55 30
5 50 00
5 00 30
5 13 00
5 25 15
5 27 10
5 32 35
5 41 30
5 44 30
5 54 45
6 02 30
6 03 30
5 52 30
6 15 15
6 42 43
3 17 00
4 53 00
5 21 40
5 44 21
6 13 25
6 57 01
7 13 54
8 24 47
13 44 32
12 31 00
12 27 43
12 01 55
11 33 00
11 06 25
10 13 45
9 18 14
8 25 20
10 46 47
10 21 16
10 19 51
11 21 00
12 53 40
13 45 23
15 23 34
15 57 10
16 07 00
19 22 14
20 25 30
20 40 03
20 51 44
20 56 29
21 01 57
122 03 18
122 04 58
123 23 13
123 50 44
124 42 50
121 33 00
121 03 00
121 23 30
118 27 00
118 26 06
119 22 45
119 48 00
119 46 45
118 11 00
119 44 15
120 40 45
120 35 00
120 11 30
120 48 51
120 49 45
120 55 00
121 00 40
121 18 20
120 59 52
119 55 55
120 29 30
121 56 50
103 40 00
103 38 00
103 08 00
103 01 45
102 10 30
101 17 39
100 36 12
100 45 27
100 29 29
100 57 30
102 04 19
102 15 47
102 57 14
102 47 49
102 52 45
103 27 14
104 48 30
106 42 12
106 20 38
107 04 55
108 58 00
109 23 42
109 14 52
109 05 35
108 32 47
108 11 30
105 55 22
106 08 41
106 47 10
106 40 54
106 17 56
105 48 40
Port Sta. Maria: Fort.
Dapitan* Village
[10 48]
[450]
[5.11
Misamis* Fort
Camiguin Island • Mount Camiguin
Sombrero Rock' Center
Piedra Blanca' Center
!
Cagayanes Islands: Rocky islet between
two larger islands
|
San Miguel Isles: E.pt.of Manuk Manukan .
Cagayan Jolo Island: Middle of W. coast.
Omapui Island • NW. extreme
'
i
Sibutu Island* Hill on E coast
Simonor Island' NW pt
!
Bahal tolls Island • Sandakan Harbor
Bongao Island* S pt
j
Keenapoussan Island* Center
!
Bubuan Island • Lagoon entrance
1
Cuad Basang Island : SW. pt
•
Siassi: Town, center of old fort
5 54
-0 18
8.6
6.4
Bulipongpon01 Island* Center hill
Tapul Island * Center hill 1 676 ft
"*:::
Jolo Islands: Maimbun Anchorage, dry
bank . .
Dalrymple Harbor, Tulyan
Islet
!
Jolo lighthouse
[938]
[310]
[5.0]
....
Doc Can Islet* W extreme
Pangituran Island* SW pt
Basilan Island* La Isabela
PuloVarella* Center
Gulf of Slam.
Pulo Brala: Center
Tringano River: N pt
8 00
1 48
5.8
2.5
Great Redang Harbor: Bukit Mara
KelantanR.: Lighthouse
:::::
Tanjong Patani* NE pt
Singora (Sungkla): SW. pt. of Koh Ngu. .
Koh Krah Islet* SE pt
8 20
2 08
2.8
1.2
Bangkok* Wat Chen°-
8 00
2 00
7.3
3.1
Cape Liant* Koh Chuen Lighthouse
Chentabun River: Entrance Bar I
10 00
3 50
4.5
2.1
Cochin China.
Koh Chang: Obsy I. on W side
Koh Kong R.: S. pt. of entrance
:::::
Kusrovie Rock* Center
Koh Tan«- Rocks- Veer Islet
..
Panjano- Island* West Pt
Obi Islands: Lighthouse
-
i
Saigon: Observatory
5 00
11 20
9.8
4.2
Mitho: S. gate of citadel
Cape St James* Lighthouse
".:
Cape Padaran* Extreme
"
Cape Varella* Extreme
:
Quin Hon: Battery flagstaff
Canton Pulo: Lighthouse
..
--
Cham-Callao Islet: Watering place
...
Tourane Bay * Lighthouse
Hon-Me* Summit,
--
Nam-Dinh * Citadel tower
Hon Dau Island * Lighthouse
9 00
2 48
4.3
2.1
I
Haifong: Observation pagoda
Haiduong * Citadel tower
.. . I
Hanoi * Citadel tower
i
APPENDIX IV. [Page 337
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP ASIA— Continued.
j
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W. j L.W.
Spg.
Neap.
Clllna
Sea.
Condore Islands : Lighthouse
h. TO.
h. m.
ft.
ft.
8 40 06
9 58 23
10 32 36
2 02 55
3 00 00
21 29 00
18 09 00
18 11 30
20 01 15
15 46 30
16 36 00
16 40 07
16 49 55
20 42 03
21 22 30
21 24 15
21 31 00
21 34 00
21 28 00
22 11 40
22 11 24
23 06 35
22 02 00
106 41 42
109 06 00
108 56 27
109 06 10
107 48 00
109 06 00
109 35 00
109 41 30
110 16 10
111 14 30
111 40 30
112 43 32
112 20 44
116 43 07
111 10 30
111 15 25
111 38 30
111 46 43
112 21 30
113 34 00
113 33 25
113 16 30
113 47 00
113 56 20
114 09 31
114 10 02
114 19 25
114 22 07
114 36 45
114 39 12
114 50 00
115 01 00
115 06 54
115 47 56
116 04 26
116 29 44
116 47 00
116 40 22
117 17 04
117 42 00
117 36 48
118 13 30
118 10 00
118 30 11
118 41 00
118 58 00
119 27 07
119 10 36
119 35 00
119 45 00
119 56 07
119 59 02
119 27 16
119 37 35
120 24 06
120 29 40
120 10 00
120 11 12
120 22 42
120 32 33
120 42 34
120 25 50
120 32 42
Safatu Island • Summit
Ceicer de Mer Island: SW. hill..
Natuna Islands: Murundum I., SE. pt...
Low I
Pakhoi: Customhouse flagstaff
5 00
11 12
14.0
6.6
J China.
Hainan Island : Cape Bastion, extreme. . .
Gaalong Bay, E. Brother.
Lighthouse
Paracel Islands: Triton I
Observation bank .
Lincoln I
Woody I
Pratas Island: NE. part.
Ty-fung-kvoh Island: Center
Tien-pak Harbor: Pauk Pvah Islet..
11 50
5 37
8.2
3.8
Song-yui Point: Extreme."
Hui-lang-san Harbor: Mamechow Islet. . .
Mandarins Cap : Summet, 200 ft
Macao : Fort Guia light
9 50
3 38
6.3
3.0
Fort San Francisco
Canton: Dutch Folly light. . .
2 00
8 00
5.1
2.4
Raleigh Rock' Center
Gap Rock: Lighthouse
21 48 50
22 16 52
22 16 23
22 03 40
22 15 45
22 27 06
22 24 06
22 30 42
22 32 54
22 18 30
22 48 14
22 48 07
22 56 24
23 14 00
23 20 43
23 15 43
23 32 30
23 47 15
24 09 49
24 23 16
24 25 44
24 49 13
24 52 12
24 59 36
25 02 18
25 12 00
25 16 30
25 26 10
25 58 10
25 59 00
26 08 26
26 09 29
26 22 37
26 30 00
26 36 06
26 42 30
26 51 25
26 58 52
27 09 20
27 09 42
Hongkong: Cathedral..
Wellington Battery
9 20
2 52
4.4
2.0
Lema Island : Lema Head
Nine-pin Rock : Center
Tnni-ang Island : Summit
Single Island: E summit
Mendoza Island : Summit
Pank Piah Rock: Summit
Pedra Blanca Rock: Summit, 130 ft
Chino Bav : Obs. spot
Cupchi Point: Hill
Breaker Point: Lighthouse
Cape of Good Hope: Lighthouse
Swatow: British consulate
2 50
9 00
7.5
3.5
Lamock Island : Lighthouse.
Brothers Islets: SE. Islet
Tong-sang Harbor : Fall Peak
11 20
5 08
12.0
7.6
Chapel Inland* Lighthouse
Amov: Taitan I li^ht
0 05
6 13
15.5
9.9
Dodd Island : Lighthouse
Chinchin Harbor* Pisai Islet
Pyramid Point* Extreme
Ockseu Island * Lighthouse
Sorrel Rock' Summit
Lamyit Island : Hi^h Cone Peak
Hun^wha Channel' Sentry I
Turnabout Island' Lighthouse
East Dog Island • Lighthouse
Min River: Pagoda Losing I
0 30
9 45
7 00
3 33
19.3
19.0
12.2
12.0
Temple Pt
Alligator Island • Summit
Tung-yung Islands' Peak N end
Coney Island • Summit
Double Peak Island * Highest peak
Pih-seans" Island * Town I
Dangerous Rock - Summit
Tae Islands* Summit
Nam-quan Harbor* Bate I
9 50
3 38
17.2
10.9
Ping-fons" Island ' Summit
Page 338] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
J
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
China.
Pih-quan Peak: Summit
ft. m.
ft. m.
ft.
ft.
27 19 18
27 26 18
27 37 36
28 05 07
28 43 45
29 22 45
29 34 20
29 51 53
29 57 08
29 59 21
30 04 30
30 08 04
30 20 50
30 36 00
30 48 37
30 51 41
30 44 07
31 14 41
31 23 18
31 25 27
35 39 00
36 02 50
36 45 29
37 24 00
37 27 41
37 34 10
37 32 51
38 23 37
38 58 16
39 09 00
38 56 00
40 35 00
39 30 46
39 16 00
38 43 17
38 47 50
38 52 38
38 40 00
39 04 00
23 32 53
23 32 54
21 55 00
22 36 14
24 46 00
25 10 24
25 09 12
24 35 28
22 01 40
24 26 00
24 21 30
24 25 00
24 48 18
25 55 00
25 58 30
25 47 07
120 27 14
121 06 36
121 12 09
121 30 04
121 55 21
122 13 16
121 43 15
122 35 24
121 43 06
121 45 22
122 03 47
122 45 48
121 51 25
121 03 00
122 10 12
122 40 17
123 08 27
121 28 55
121 29 36
122 14 12
119 51 30
120 17 30
122 16 48
122 42 00
122 15 05
121 31 09
121 21 27
120 55 00
117 42 48
117 11 44
118 31 00
122 00 00
121 18 03
121 35 59
121 08 26
121 15 54
121 51 59
122 11 30
123 10 34
119 28 05
119 30 12
120 51 00
120 15 54
120 55 00
121 25 00
121 44 28
121 49 20
121 39 45
122 56 00
124 17 40
124 06 40
125 17 57
124 35 00
123 40 00
123 30 31
Port Namki : E. horn
Pih-ki-shan Island : Summit
Pe-shan Islands* Summit SW end
Tung-chub. Island : Summit .
Kweshan Islands: Patahecock
Nimrod Sound : Middle islet
Tong-ting Islet: Summit
Chin-hai: Citadel
Ning-po* Square I light
I 00
7 12
8.8
4.6
Chusan Islands* Ting-hai Harbor
Video Island : Summit
West Volcano Island : Lighthouse .... .
Chapu : Battery
Gutzlaff Island : Lighthouse
Saddle Islands: N. Saddle light
West Barren Island : Summit
Shanghai: Eng. consulate flagstaff
Woosung: Lighthouse
0 12
8 06
9.1
4.8
Shaweishan Island : Lighthouse ... .
Wang-kia-tia Bay: Langwang temple
Kiaochow Bay: Yunui San light
4 50
11 03
11.4
6.0
Staunton Island: Landing place, N. side..
Shantung Promontory : Lighthouse
4 00
9 20
10 25
10 12
3 08
4 13
6.8
9.0
8.1
5.0
6.6
6.0
Weihaiwei: Light, S. side harbor
Chifoo: Lighthouse
Fort flagstaff
Miautao Island • Peak of N. Island
Pei Ho: S. TakuFort, S Cavalier
Tientsin: Shore opp. NE. angle of wall. . .
Shaluitien Island: Lighthouse. .
6 50
1 00
4.5
3.3
Newchwang: Lightship. ....
4 30
10 50
11.7
8.7
Hulu-shan Bay: N. side.
Port, A dams: Entry
Liao-ti-shan Promontory: SW. pt. light..
Ryojun Ko (P. Arthur): Obs. spot . .
10 05
3 53
7.5
5.5
Dairen Wan: Isthmus on S. Sanshan I
Round Island: Summit
Thornton Haven, Hai-yun-tan Island:
Beach opposite Temple Point . .
Pescadores Islands' Fisher I light
Second pt. on N. side
Makung Harbor. . . .
South Cape: Lighthouse
Taiwan
(Formosa) .
Takau : Saracen Head. . .
9 45
3 32
4.0
1.7
Port Heon°'san
Tamsui Harbor: White Fort
10 00
10 15
6 00
3 47
4 03
12 13
8.0
3.0
5.8
3.4
1.3
2.5
Kiirun Ko (Kelung Hbr.): Lighthouse . . .
Soo (Sauo) Bay: Beach near village
Botel Tobago Sima* S extreme
Sakishima Gunto, Kumi I.: N. beach
(Meiaco Sima Is.) Broughton Bay: Land
ing place
IS. W. Islands
of Japan.
Port Haddington:
Hamilton pt
Tai-pin-san: Hirara,
Karimata Anch
7 27
1 14
4.9
2.1
Raleigh Rock* Summit 270 ft
APPENDIX IV. [Page 339
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
i
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
S.W.lsls. of Japan.
Nansei Shoto, Great Xansei: Nafa-Kiang.
Yori-sima 413 ft
ft. m.
6 30
ft. m.
0 15
t*
ft.
2.5
26 12 25
27 02 00
27 21 00
27 44 00
27 53 00
28 31 40
28 18 00
30 51 00
30 50 00
30 47 00
30 17 00
30 05 00
29 59 00
29 54 00
29 52 00
29 38 00
29 08 00
28 47 30
38 27 00
37 58 00
37 27 40
36 26 45
36 24 30
36 07 00
35 48 08
35 21 00
34 42 00
34 42 30
34 06 00
34 17 20
34 01 23
33 57 00
33 59 00
33 29 40
34 39 00
34 33 00
34 48 00
35 07 15
36 05 45
36 36 00
37 09 30
37 30 00
39 19 12
34 18 55
33 44 30
33 52 10
33 53 50
33 41 30
33 32 30
33 23 31
32 36 45
32 13 12
32 03 00
32 43 21
32 43 15
,32 36 05
127 40 10
128 25 24
128 33 10
128 59 00
128 14 30
129 42 30
129 59 00
129 28 00
129 55 30
130 18 00
130 32 00
130 03 00
129 56 00
129 33 00
129 52 30
129 42 00
129 13 30
129 01 30
124 34 40
124 34 30
126 36 27
126 28 00
126 24 00
126 01 09
126 31 00
125 58 00
126 19 45
125 16 00
125 07 00
126 35 28
127 18 34
126 18 00
126 55 00
126 58 25
128 14 00
128 40 00
128 44 00
129 02 10
129 33 30
129 20 00
131 55 00
130 53 00
127 32 48
129 13 06
129 42 30
130 02 00
130 25 20
129 58 50
129 52 43
129 33 21
128 36 10
128 04 39
128 25 00
129 52 25
129 49 55
130 13 40
Yerabu-sima peak, 687 ft..
Kakirouma: Summit,
2 207 ft
Iwo-sima: Volcano,
541 ft
Oho-sima: N. extreme
Kikai-jima: Summit,
867ft
Kusakaki Jima: Ingersoll Rocks, 530 ft
Euro Sima: 2,160ft
3C
M
«
E
8$
A
Iwo Shima' Peak 2 469 ft
Yakuno Shima: Mount Matomi, 6,252 ft. .
Firase Rocks' Highest 92ft
•
Kuchino Shima • Summit 2 230 ft
Guaja Shima' Summit, 1,687ft
Naka no Shima' Peak, 3,400ft
Suwanose Jima: Volcano, 2,706 ft
Tokara Jima: Summit, 860ft
Yoko Shima: Summit, 1,700 ft
Choda Island* S pt
Chosen (Korea).
Sir James Hall Islands* N island
Chemulpo* So Wolmi
4 19
10 31
28.8
11.6
Marjoribanks Harbor : Manzoc Islet .
Tasde foin Islet: Center. . .
Guerin Island : Summit,, 969 ft
Kokoun-tan Islands* Camp Islet
Barren Island • Center 600 ft
Sea Rock1 Center 160ft
Mod este Island- N peak. 1,228 ft .
Ross Island : Peak , 1 , 920 f t . . .
Kuper Harbor: NE. extreme of Josling I. .
Port Hamilton: \V. pt. of Obs. Island
Bate Islands: Summit Thornton Islet. . . .
Montravel Island • Center 1041 feet
9 05
2 52
10.5
4.2
Quelpart Island: Beaufort I., middle of
W side
Observation Island: Point of \V. arm
Sentinel Island : Summit, 400 feet
Broughton Head * Extreme
Tsau-ling-hai Harbor: Lighthouse
7 35
1 23
7.0
3.0
Cape Clonard * Extreme
Pin°r-hai Harbor
Liancourt Rocks: Summit, 410 ft
Matu Sima' Peak 4 000 ft
Port Lazaref : S. 1J miles from the S. end
of Bontenef I
Tsu Sima' Observation rock
8 56
2 44
6.7
2.4
fl
s
*»
Iki fiima • Summit S fnd of island
Oro \oSima' Summit 277ft
Kosime No Osima' Summit Wilson I.
Yeboshi Sima * Lighthouse
Yobuko Harbor: Bluff opposite Nicoya —
Hirado No Seto * Taske li<*ht
9 23
3 10
6.4
2.5
Goto Island * Ose Saki li^ht
Pallas Rocks' S rock
Meiaco Sima. * Ears Peak
Nagasaki: U. S. Transit Venus Station
NezumiJima* Obs spot
7 54
8 14
1 41
8.4
11.2
3.5
7.2
Kuchinotsu * Lighthouse
Page 340] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
I
Place.
Lat. N.
Long. E.
Luiu Int.
Range.
H.W.
L.W.
Spg.
Neap.
d
e3
ft
Kagoshima: Breakwater light
h. m.
6 40
h. m.
1 00
ft.
10.5
ft.
4.4
31 35 39
31 20 00
31 12 00
31 12 43
30 59 30
33 57 46
33 58 53
33 59 11
33 23 19
34 22 37
34 35 58
34 37 27
34 38 05
34 39 20
34 41 18
34 39 45
34 35 12
34 07 42
33 57 34
33 41 14
33 28 15
33 33 37
34 06 10
34 13 52
34 21 57
34 35 52
35 00 51
34 34 25
34 39 49
35 17 30
35 26 41
35 39 18
34 54 17
34 43 30
34 13 15
34 05 00
33 56 50
33 52 00
33 39 00
33 04 24
32 29 00
32 00 40
31 27 00
30 28 26
29 46 28
35 42 13
38 16 57
39 16 30
39 27 17
41 25 58
41 33 34
40 50 00
41 16 17
40 31 00
39 12 02
38 29 23
38 19 55
36 47 47
37 31 45
37 55 14
37 35 00
37 02 37
35 40 24
130 33 49
129 46 20
129 29 00
130 37 00
130 39 30
130 57 50
130 52 07
130 47 36
133 17 00
133 23 23
133 59 24
134 09 21
135 01 51
135 10 56
135 11 34
135 26 00
135 27 44
135 08 19
135 07 21
135 23 04
135 51 59
135 54 25
136 14 35
136 48 51
136 54 09
138 13 49
138 31 19
138 56 30
138 57 30
139 39 43
139 39 00
139 44 30
139 53 24
139 23 00
139 08 00
139 31 00
138 48 15
139 34 00
139 17 45
139 50 24
139 43 31
140 00 00
140 02 00
140 14 02
140 19 40
140 52 22
141 35 33
141 52 50
141 59 00
141 27 32
140 56 36
140 44 40
140 22 37
139 31 00
139 32 58
139 15 31
138 27 09
337 03 15
137 19 00
139 03 01
136 54 00
136 58 24
136 01 22
Tsukarase Rocks: Summit, 96 ft
UjiShima: High Peak, 1,097ft
Yamagawa Harbor : Spit N . of town . .
7 20
1 08
9.5
3.9
Sataiio Misaki: Lighthouse
Shimonoseki Strait: Meji Zaki, extreme. .
Rokuren Island ' Lighthouse
8 30
2 20
6.7
2.4
Shirasu Reef : Lighthouse
Susaki: SW battery
5 55
11 16
12 08
5 04
5.0
10.2
2.0
4.5
Tomo Roads' Tamatsu Sima
Port Okayama: Take Sima temple
Wusimado Pt. : Wusimado Peak, 548 ft. . .
Akashi-no-seto * Maico Fort.
Hiogo ' Wada Misaki light
Kobe1 Lighthouse
Osaka* Fort Temposan light
7 30
1 25
4.7
2.0
Sakai: Pier-head light
Osaki Bay : Tree Islet, S. pt
Yura No Uchi: Pier
Tanabe Bay : Fossil pt *
Oo-sima Hbr.: Kashmosaki light, E. pt..
Uragami Harbor* Village pt
Owashi Bay ' Hikimoto
Mura Harbor* Osima Islet
6 23
5 52
0 10
12 04
4.7
4.3
2.0
1.7
Matoya Harbor* Anori-saki light
Omoi Saki* Lighthouse
Shimizu Bay* Mound on pt.
5 52
12 04
3.9
1.6
Mikomoto Island * Light house . ...
Simoda Harbor: Center I
Yokosuka Harbor: Eyi Yama pt
Yokohama : Time-ball station
5 25
11 30
4.9
1.9
Tokio * University Observatory
No Sima Saki* Lighthouse
5 04
11 17
3.7
1.4
Vries Island (O Sima) Volcano: Summit,
2 512 ft
Kozu Shima Volcano: Summit, 2,000 ft. .
Mikake Jima * Summit 2 690 ft
Redfield Rocks * S rock
Mikura Jima* Summit
Brou°liton Rock* Summit 60 ft
Fatsizio Island * Observation spot
Ao°"a Shima * Center
Bayonnaise Island* Summit 26 ft
Smith Island * Summit 250 ft
Ponafidin Island * Summit 1 328 ft
Lots Wife Rock* Summit 300 ft
Inaboye Saki* Lighthouse
Kinkwosan Island* Lighthouse
Kamaishi Harbor: SE. end of village. . . .
Yamada Harbor: Ko Sima, 90 ft
4 30
10 45
3.4
1.3
Siriya Saki* Lighthouse
Toriwi Saki* Center of Low Islet off
Aomori: Lighthouse. ..
Tatsupi Saki* N side
Bittern Rocks* SW rock
Tobi Shima* Takamori Yama
Awa Sima* NE extreme
Sado Island * Ya Saki
Fushiki Harbor* Lighthouse
Cape Rokugo* Extreme
Niigata* Buddhist temple
Mana Sima* Summit 200 ft
Manao Harbor* Sorenjo Pt
Tsuru^a* Town
2 30
8 42
0.6
0.4
APPENDIX IV. [Page 341
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
o
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L. w.
Spg.
Neap.
Japan.
Oki Islands* N pt
0 / H
36 30 00
34 40 00
34 32 00
34 48 00
34 21 12
41 47 36
42 19 54
42 56 52
43 22 56
43 20 22
43 33 11
45 26 30
45 11 00
44 20 00
45 38 30
45 37 00
46 42 30
47 02 50
47 17 30
48 06 00
48 52 00
49 08 00
49 19 00
49 51 00
50 15 36
50 46 00
45 53 10
46 01 20
54 24 30
42 14 30
42 38 05
42 33 40
43 05 13
42 41 00
43 22 00
43 53 40
44 30 00
44 43 45
44 46 15
45 05 00
45 19 30
45 41 30
47 20 00
48 59 30
51 28 00
53 08 05
55 11 00
56 25 28
•56 22 30
59 19 45
51 02 00
52 52 37
53 04 30
54 56 00
54 32 24
56 10 00
58 26 00
59 55 00
62 14 30
Of*
133 23 00
131 36 00
131 18 00
131 09 00
130 50 29
140 41 49
140 59 33
144 52 38
145 49 10
145 34 40
145 18 00
141 38 40
141 19 00
146 15 00
149 14 00
149 34 00
150 28 30
151 52 50
152 24 00
153 12 30
154 08 00
154 39 00
154 44 00
154 32 00
156 15 20
156 26 00
142 04 51
143 26 30
142 46 30
137 17 00
130 48 45
131 10 00
131 52 46
133 02 00
135 15 00
135 27 19
136 02 00
136 22 30
136 27 15
136 44 00
137 10 15
137 38 15
138 58 00
140 23 40
140 48 00
140 42 58
137 40 00
138 25 50
143 15 45
143 07 14
156 46 00
158 46 42
160 04 00
166 43 00
168 09 00
163 24 00
163 34 00
170 22 00
179 04 30
ft. m.
h. m.
ft.
ft.
Taka Yama (Cape Louisa): Extreme. . . .
Ai Sima* Summit 300 ft
11 41
5 28
1.1
0.5
Alino Sima* Summit 492ft
Kado Sima* T^uno Shima light
Hakodate* Lightship
3 40
3 32
3 41
3 48
3 33
4 50
10 00
9 45
9 53
10 00
9 46
11 05
3.0
3.5
3.0
3.1
2.1
3.7
1.2
1.5
1.4
1.4
0.5
1.8
Endermo Harbor* Bluff on E side
Okishi Bay* Lighthouse
Noshiaf Saki: Lighthouse
Nemuro: Benten Sima light
Not^uke Anchorage* Village
Noshiaf Misaki* Lighthouse
Risiri Islet* Peak, 5 713 ft
Kunashir Island: St. Anthonys Peak. . . .
Iturup Island: NE pt
*
1
S
-
*ac
t
3
H
L rup Island : Cape Vanderlind
Broughton Island : Summit
Simusir Island* Prevost Peak
Ketoy Island* S pt
Matana Island: Peak
Shiash-Xotan Island : Center
Kharim-Kotan Island: Peak
Oune-Kotan Island * SW pt
Moukon rushi Island* Center
Pore musir Island: Fool's Peak
Soumshu Island: Center. .
Karafuto (S. Sakhalin):
C. Nortoro (Nishi Notoro Mi
saki) Light
C. Shiretoko (Nata Shiretoko
Misaki)
Sakhalin I , Cape Elizabeth: N pt
11 20
5 08
4.2
1.7
j Siberia.
Wawoda Rock : Summit, 12 ft
Expedition Bay : Lighthouse
Port N o vogoroa : Lighthouse
Vladivostok: Cape Goldobin light
2 45
9 00
1.9
0.8
Cape Povorotnyi: Lighthouse
Port Olga: Lignthouse ...
St. Vladimir Bay : Orekhera Pt
Shelter Bay
Sybillo Bay
Pique Bay
Bullock Bay .
Luke Point: Extreme
Cape Disappointment* Extreme
Cape Suffren: Extreme
Cape St. Nikolaia: Lighthouse
9 50
10 45
3 40
4 40
2.7
6.3
1.1
2.6
De Kastri: Lighthouse ..
Nikolaevsk: Cathedral
Great Shan tar Island* N pt
Port Aian : Cape Vneshni
0 10
7 30
8.4
3.4
St. Jona Island: Summit, 1,200 ft
Okhotsk* Battery
Cape Lopatka* Extreme
3 55
3 30
10 08
9 45
4.6
5.1
1.9
2.1
Petropavlovsk : Rakof light
Cape Shipunski: Extreme .
Bering Island* Cape Khitroff
Mednoi, or Copper Island: SE. extreme.
Cape Kamchatka: Extreme
Karajinski Island* S pt
Cape Oliutorski* Extreme 2 480 ft
6 00
12 15
4.5
1.8
Cape Navarin* Extreme 2 512 ft
Page 342] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
o
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L. W.
Spg.
Neap.
Siberia.
St. Matthew Island: Cape Upright, SE. pt.
St. Lawrence Island: N. pt
60 18 00
63 12 00
64 16 00
64 25 55
64 24.30
64 46 00
64 50 00
65 00 30
66 02 00
172 04 00
159 50 00
173 10 00
173 07 15
172 12 30
172 07 00
Long. E.
178 40 00
Long. W.
175 54 00
169 32 30
A. m.
h. m.
ft.
ft.
Cape Tchoukotskio : Extreme
Port Providence: Emma Harbor
Cape Indian : Extreme
Arakam Island: Cape Kiguinin
Anadir River: Mouth
Cape Bering* Extreme
East Cape : Extreme
ISLANDS OF THE PACIFIC.
Malpelo Island: Summit, 1,200 ft
4 03 00
5 32 57
0 13 30
0 20 00
0 18 50
0 34 25
1 22 55
0 59 00
0 31 00
0 15 20
0 25 00
0 36 30
0 33 25
0 50 30
1 19 00
1 25 00
0 44 15
1 57 17
3 51 26
4 41 10
5 52 15
0 13 30
0 49 00
Lat. S.
2 40 54
2 35 00
1 50 00
1 29 14
1 23 42
1 17 14
0 36 00
Lat. N.
0 11 10
0 20 54
0 51 30
1 38 45
1 44 15
2 03 00
3 01 30
81 36 00
86 59 17
91 03 00
89 58 43
90 30 08
90 44 23
91 49 43
91 29 12
91 36 00
90 52 53
90 43 30
90 41 00
90 33 58
90 06 13
90 28 13
89 40 08
89 16 58
157 27 45
159 21 50
160 24 30
162 05 00
176 32 39
176 43 09
Long. E.
177 01 13
176 07 00
175 39 00
175 12 20
176 31 33
175 57 09
174 24 00
173 32 40
173 51 14
173 03 30
173 03 00
173 07 00
173 25 30
172 45 40
Cocos Island: Head of Chatham Bay
Redondo Rock: Summit, 85 ft
Galapagos Islands.
Towers Island' W cliff
Bindloe Island" S summit
Abingdon Island' Summit 1 950 ft
Wenman Island' Summit 550 ft
Albemarle Island: Iguana Cove
2 00
8 13
6.2
3.1
Marlboro ugh Island : Cape Hammond
James Island: Sugarloaf, 1,200 ft
2 45
8 58
5.2
2.6
Jervis Island : Summit
Indefatigable Island: NW. bay
2 00
8 13
6.2
3.1
Barrin°rton Island' W summit 900ft
Charles Island : Summit, 1,780 ft
2 10
8 23
6.0
3.0
Fatu Huku or Hood Island: E. summit,
640 ft
Chatham Island' Mount Pitt 800 ft
2 20
4 25
6 00
8 33
10 38
12 15
6.5
2.4
2.4
3.3
1.4
1.4
Christmas Island: N. pt. of Cook Islet —
Fanning Island: Flagstaff, entrance to
English Hbr
\Vashington Island
Palmyra Island
5 25
11 40
1.5
0.9
Baker Islet* Center
Ho wland Islands : Center island
7 10
1 00
6.2
3.6
Gilbert Islands.
Arorai or Hurds Island* S pt
Tamana Island* Center
Onoatoa Island' Center
Taputeuea or Drummond Island: SE.pt..
Nukunau or Bvron Island* SE pt
Peru or Francis Island: NW pt
Nonuti or Sydenham Island
Aranuka or Henderville Island: W. pt.
of "W island
Apamama or Hoppers Island: Entrance
islet
4 30
10 45
4.7
2.7
Maiana Island* S pt
Tarawa Island* NE pt
Apaiang Island : S pt
4 45
11 00
4.7
2.7
Maraki Island * N pt
Taritari Island * S pt
APPENDIX IV. [Page 343
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
o
Place.
Lat. X.
Long. E.
Lun. Int.
Range.
H.W.
L.w.
Spg.
Neap.
j Caroline Islands. Marshall Islands.
Ebon Atoll: Rube Pt
h. m.
4 45
ft. m.
11 00
ft.
4.7
ft.
2.7
4 35 25
5 55 07
6 14 00
7 05 30
7 09 17
7 15 00
8 14 00
8 27 00
8 19 00
8 54 21
9 28 09
10 03 40
10 17 25
11 48 00
11 19 21
11 24 00
11 07 00
11 40 00
10 05 00
11 40 00
9 39 00
1 04 00
8 18 30
9 29 00
9 52 30
10 06 00
9 46 00
8 06 00
6 40 00
7 21 45
7 15 00
8 35 00
8 03 00
7 43 30
7 29 30
7 22 00
8 09 00
6 40 00
7 38 00
8 59 45
8 25 30
7 18 30
5 55 00
5 29 18
3 51 00
7 39 00
5 48 00
7 00 35
6 41 45
6 14 00
5 20 06
168 41 31
169 39 31
171 46 00
171 24 30
171 55 51
168 46 00
168 03 00
168 26 00
171 09 00
170 49 00
170 16 05
169 01 57
169 59 20
170 07 00
167 24 57
167 35 00
166 35 00
166 24 25
166 04 00
162 15 00
161 08 30
154 47 55
137 33 30
138 04 00
139 42 00
139 46 00
140 35 00
140 52 00
143 11 00
143 57 30
144 31 00
144 36 00
146 50 00
145 55 45
146 24 30
147 06 48
147 42 00
149 21 00
149 27 30
150 14 30
151 49 15
151 56 30
153 13 30
153 58 00
155 00 54
155 05 00
157 31 30
158 17 35
159 50 00
160 38 43
163 00 45
Jaluit or Bonham Islands: Jarbor Pier
Burrh Island: Port Rhin, N. pt. of en
trance
5 00
11 15
5.0
2.8
Majuro or Arrowsmith Islands: Anchor
age Djarrit I
Arno Atoll: NE. pt
Odia Islands: S. islet
Namu Island ' S pt . ]
Jabwat Island ' Center.
Aurh or Ibbetson Island: NE. end, an-
chora°re .
Maloclab Islands: NW. end Karen Islet. .
Wotje or Romanzov Islands: Christmas
Harbor
Litkieh Island • N W pt
Ailuk Islands* Capeniur Islet
4 50
11 00
6.2
3.6
Bi^ar Islet' Center
Kongelab or Pescadores Islands: Center
of group
Rongerik or Radakala Islands: Observa
tion spot
Ailin^inae Island • Easternmost Islet
Bikini or Eschholtz Islands: W. ex
treme
Wottho or Schanz Island : Center
Eniwetok Islands: North or Engibi I. ...
Ujelang or Providence Island: Center of
atoll
Greenwich Island: Northern islet
Matelotas group: Easternmost of the S.
islands
Yap Island • Li^ht in Tomil Bay
7 15
1 00
3.4
1.9
Eau Island' Center
Uluthi or Mackenzie Islands: Mogmog
Islet
Feys or Tromelin Island: E. extreme.
Sorol or Philip Island : Center
Eauripik or Kama Islands • E islet
Oleai group * Raur Islet N pt
Ifalik or Wilson Islets: N end
Faraulep Island* S end.
W Faiu Islet: Center
Olimarao Islet : Center
Toass Island' Center
Sata\val Island' Center
Coquille or Pikelot Island' Center
Suk or Polusuk Island : S end
Los Martires: Ollap Islet, N. pt
Namonuito Island^' Ma^ur Islet
Hall Island' Namuine Islet
Hogolu (Hogulu) Group: N. end of Tsis
Islet ..
Namoluk Islands * N^*V islet
Mortlock Islands: Lukanor, Port Cha-
misso
Nukuor or Monteverde Islands: E. pt
Oraluk or Bordelai^e Island' Center
Ngatik or Valientes Islands: E. extreme..
Ponapi Island * Ponapi Harbor
4 00
10 15
4.3
2.4
Mokil or Duperrey Islands: Aoura, NE. pt.
Pingelasp or MacAskill Islands: E. end
of island
Ualan or Strong Island : Chabrol Harbor. .
6 00
12 15
3.5
2.0
Page 344] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
1
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Pelew Islands.
Angaur Island • SW pt
ft. TO.
h. m.
ft.
ft.
6 53 55
7 02 00
7 08 00
7 19 00
7 40 30
,8 08 00
4 20 00
3 02 00
5 20 00
13 26 22
14 07 30
14 59 22
15 08 30
15 17 10
16 20 00
16 41 00
17 17 00
17 36 00
18 04 00
18 46 20
19 45 00
20 00 00
20 32 54
19 15 00
14 41 00
16 44 48
10 17 00
19 46 14
20 03 00
19 28 00
19 38 26
20 33 39
20 36 00
20 52 00
21 06 17
21 18 16
21 15 08
21 17 57
21 17 55
22 12 51
21 57 17
23 05 50
23 35 18
23 46 00
25 00 40
25 31 00
25 48 00
26 00 00
27 56 30
28 13 15
28 24 45
24 14 00
134 05 24
133 18 03
134 27 00
134 32 30
134 39 30
134 17 00
132 21 00
131 11 00
132 16 00
144 39 42
145 13 04
145 36 20
145 43 55
145 42 50
145 39 00
145 47 00
145 57 00
145 55 00
145 52 00
145 41 45
145 30 00
145 21 00
144 54 00
166 31 30
168 54 28
Long. W.
169 32 24
109 13 00
155 05 31
155 48 00
155 55 00
156 00 15
156 35 04
156 26 00
156 35 00
157 18 32
157 39 07
157 48 44
157 51 34
157 51 54
159 30 47
159 40 08
161 58 17
164 40 47
166 17 57
168 00 52
170 39 20
171 44 00
173 57 00
175 46 00
177 21 30
178 27 45
Long. E.
154 00 00
Pililu Island : S pt .
Earakong or Akamokan Islands: Center..
Korro Islands: Korror Harbor, Malakal
pier
Baubeltaub Island: Cape Artingal
Kyangle Islets: Center of largest
Warren Hastings Island : Center
Nevil or Lord North Island: Center
Sonserol Island: Approx.
Guam: Fort Sta. Cruz, Harbor of ,Apra. . .
Rota Island : Summit
7 20
I 20
2.6
1.5
Marianas (Lad rune Is.)*
Tinian Island: Sunharon village
Saipan Island: Magic ienne Bay, landing.
Tanapag Hbr., Garapag...
Anataxan Island: Center
7 00
0 50
2.0
1.1
Sariguan Island: Center
Guguan Island: Center
Alamaguan Island: Center
Pagan Island* SW pt
A.grigan Island* SE pt
Asuncion Island* Crater 2 600 ft
Urracas Islands* Largest islet
Farralon de Pajaros* S end
Wake Island* Obs spot
Gaspar Rico Reef: N. clump of rocks ....
Johnston or Cornwallis Islands: Flagstaff
on W island
Clipperton Island: Center
Hawaii Island: Hilo, Kanaha Pt. light
Kawaihae light
3 09
9 06
2.3
1.3
Hawaiian Islands.
Kealakeakua Bay light.
Kailua, stone church...
Kahoolawe Island* Summit
2 20
8 10
1.6
0.9
Maui Island* Kanahena Pt light
Lahaina light
3 32
2 38
9 58
8 56
2.2
2.1
1.2
1.1
Molokai Island* Lighthouse
Oahu Island: E. pt. Makapuu station ....
Diamond Head
Honolulu, Tr. of V. Obs. . . .
Honolulu, Reef light
3 46
9 59
1.5
0.8
Kauai Island: Hanalei, Black Head
Waimea, stone church ....
Bird Island: Center
4 00
10 20
2.0
1.1
Necker Island: Center
French Frigate Shoal: Islet (120 ft )
Gardiner Island: Center
Maro Reef: NW. pt
Laysan Island* Lighthouse
Lisiansky Island: Lighthouse . .
Pearl and Hermes Reef: NE. extreme
Midway Islands: Lighthouse, Sand I
3 30
9 45
1.1
0.6
Ocean Island : Sand Islet . .
Marcus Island * Center
APPENDIX IV. [Page 345
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
I
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H.W. !
L. W.
Spg.
Neap.
Ogasawara Is. (Benin Is.), Parrys Group:
N. rock . .
0 / *
27 45 00
27 31 00
27 05 37
25 14 00
24 48 00
24 14 00
27 15 32
20 30 00
25 59 38
25 52 45
24 27 00
Lat. S.
10 32 00
10 01 40
9 56 00
9 45 00
9 27 30
9 29 30
8 55 13
8 03 30
8 44 00
8 54 00
7 55 00
10 00 01
10 06 00
11 25 23
4 03 00
5 37 00
8 55 15
0 22 33
10 02 00
10 20 30
9 23 02
9 13 06
8 39 40
2 44 25
3 08 30
3 42 28
3 34 15
4 37 42
3 35 10
4 30 95
9 18 00
8 25 19
8 04 02
7 32 00
7 15 45
6 12 00
6 06 00
5 39 00
o / n
142 06 53
142 11 53
142 11 23
141 11 00
141 13 00
141 20 00
140 50 28
136 10 00
131 19 30
131 12 17
131 01 50
Long.W.
138 39 20
138 48 30
139 09 00
138 47 40
138 55 10
140 04 45
140 04 00
140 44 00
140 38 30
139 33 30
140 34 40
150 14 30
152 23 00
151 48 34
155 01 00
155 56 00
158 07 00
159 54 11
161 05 30
161 01 12
171 14 46
171 44 40
172 28 10
171 45 29
171 10 00
170 42 37
171 32 07
174 40 18
174 17 26
172 13 28
Long. E.
179 50 00
179 07 25
178 28 51
178 41 01
177 16 50
176 16 30
177 20 01
176 06 15
ft. 771.
h. m.
A.
ft.
Kater Island:
N. rock
Peel Island:
Port Lloyd,
observatory.
Volcano Is., San Alessandro or North Is
land" Center
6 10
0 00
2.4
1.4
Sulphur Inland
San Augustine Island: Center
Rosario Island* Center 148 ft
Douglass Rocks* Center
Borodino Islands: Center of N. island
Center of S. island.
Rasa Island : Center
Fatu Hiva Island- S pt ...
Marquesas Islands.
Motane Island • SSE pt
Tahuata Island: Port Resolution, water
ing place
2 30
8 45
3.1
1.9
Hiva-Oa Island: C. Balguerie
Fatu Huku Island : Center
Roa Poua Island: Obelisk Islet
Nuka-Hiva Island: Port Tai-o-hae light. .
Hiaou Island' S pt
3 50
10 05
3.5
2.1
Motu-ili Island: Summit, 130 ft
Ua-Huka or Ua-TJna Island: N. pt. .
Fetouhouhou Island: NE. pt
Caroline Islands: Solar Eclipse Transit
Pier
4 00
10 14
1.1
0.7
Vostok Island' Center
Flint Island' S extremity
Maiden Island: Flagstaff, W side
Starbuck Island: Flagstaff, W side
Penrhyn or Tongarewa Island: NNW. pt.
Jarvie Island: Center
6 00
12 15
1.5
0.9
Reirson Island : Church
Humphrey Island: N. pt
Union or Tokelau Islands: Spot N. of
Fakaofu or Bowditch Islet
6 00
12 13
2.4
1.4
Union or Tokelau Islands: Nuku-nono,
or SE island Duke of Clarence I
Union or Tokelau Islands: Clump on S.
island, Oatafu or Duke of York I
Canton or Mary Island ' N pt
/
M
M
i
Enderbury Island : W. pt
5 00
11 15
4.6
2.7
Phoenix Island N pt
Birneys Island' S pt
Gardners Island • Center . .
McKean Island : Center
Hulls Island: W. pt
Mukulaelae or Mitchells Island: S. pt
Funafuti or Ellice Island' E pt
Elllce Islands.
Nukufetau or De Peysters Island: S. pt. .
Vaitupu Island : S end . . ....
Nui or Netherland Island: S. pt
Nauomaga Island' Center
Niutao Island: Church
Nanomea Island: Center . . .
Page 346] APPENDIX IV. j
MARITIME POSITIONS AND TIDAL DATA. [
ISLANDS OF THE PACIFIC— Continued. j
l
Place.
Lat. S.
Long. E.
Lun. Int.
Range. ;
H.W.
L.W.
Spg.
Neap.
Ocean or Paanopa ^sland: Center (appx.).
Pleasant Island : Center
0 52 00
0 25 00
12 50 15
11 52 15
11 33 45
10 17 32
9 41 47
9 01 30
9 30 00
8 23 00
8 30 50
8 05 40
6 42 40
7 24 30
6 35 00
5 00 00
5 38 00
5 18 00
5 18 00
4 14 12
4 06 25
4 41 26
3 11 00
2 47 30
2 33 43
2 26 30
1 35 00
1 55 10
2 25 40
2 22 00
0 45 00
0 53 15
1 28 00
2 51 00
1 25 40
2 44 00
3 47 00
8 22 00
8 41 00
9 25 30
10 14 30
10 43 35
10 37 00
6 43 00
169 35 00
167 05 00
160 26 00
160 40 15
159 55 00
161 33 30
159 39 30
160 27 20
161 27 40
162 58 15
159 38 20
156 50 15
156 23 16
155 34 00
155 05 00
154 35 00
159 21 00
159 34 00
159 17 00
152 11 35
152 06 15
152 42 25
151 35 30
150 57 35
150 04 33
149 55 36
149 37 00
146 40 56
147 28 35
147 55 00
145 17 00
145 33 04
145 08 00
146 15 00
135 28 12
132 04 00
134 06 00
137 40 00
143 36 04
147 07 04
148 30 30
150 14 20
150 40 34
147 53 20
h. m.
ft. TO.
ft.
ft. \
•
Indispensable Reefs: S. pt. of S. reef
Rennel Island : SE. extreme
W. end
i
SanCristoval Island: Point Wangalaha. ..
Guadalcanal Island: Wanderer Bay,
mouth of Boyd Creek
6 45
0 33
3.3
2.0
Solomon Islands
Florida Island: Mboli Harbor, Tree Islet.
Malaita Island: Village, Mary I., Port
Adam
!
i
Stewart Islands: Largest islet
i
Isabel Island: N. side of Cockatoo Islet. . .
Gizo or Shark Island: N. point village
Choiseul Island: Choiseul Bay entrance.
Treasury Islands: Observation Islet.
5 00
11 15
3.5
2.1
i
i
Bougainville Island: Husker Pt., Gazelle
Harbor
12 00
5 47
2.7
1.6
Buka Island : Cape North
Lord Howe Group: Center, small SW.
islet
!
Center, small NE.
islet
NW. pt. of Ham
mond I
i
Neu Pommern (New Britain), Blanche
Bay: Matupi I. N. pt
9 00
2 45
2.1
1.3
Duke of York Island: Makada Harbor,
Spit Pt
Neu Mecklenburg (New Ireland): Car-
teret Harbor, Cocoa-
nut I. . .
Katharine Haven
Holz Haven, E. side. .
New Hanover Island: Water Haven,
creek mouth ....
North Haven an
chorage .
2 50
9 03
2.4
1.4
2 30
8 43
2.4
1.4
St. Matthias Island: SW. extreme.
Admiralty Island: Nares Harbor, obs.
islet
Admiralty Is.
St. Andrew Island: Violet Islet 60ft
Jesus Maria Island : SE. pt. .
Commerson Island : Center of largest islet .
Anchorite Island: N. pt
!
Hermit or Loaf Island : Pem6 Islet
i
Purdy Island : Mole Islet
Point d'Urville: extreme
!
; New Guinea Island.
Drei Cap Peninsula: Wass Islet
...
Triton Bay: Fort Dubus, Dubus Haven. . .
Cape Walsche: Extreme
0 55
7 08
7.3
4.3
Fly River: Free Islet, S. pt »
:::
Port Moresby: N. end of Jane I
Cape Rodney: Extreme
8 50
2 38
8.0
4.8
South Cape: S. pt. Su Au I
9 15
8 25
3 00
2 12
8.1
5.8
4.8
3.4
TTayter Island: W. end
Cape Cretin i Cretin Islets
1
APPENDIX IV. [Page 347
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
i
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
•
\\
r
Trobriand Islands: NE. pt. Cape Denis. . .
Woodlark Islands: N. pt
0 / H
8 24 00
9 03 30
9 38 00
9 41 00
9 43 53
10 42 00
10 52 40
11 23 25
11 29 10
16 50 00
16 55 50
17 43 00
17 07 20
17 24 39
19 08 00
19 14 00
22 10 30
23 15 02
9 48 00
10 21 00
10 23 30
10 40 00
11 17 30
11 40 24
13 15 00
13 48 00
14 11 00
14 58 00
16 26 00
17 44 58
18 47 30
19 31 17
19 31 20
20 15 17
22 20 12
22 24 02
22 38 07
11 55 00
12 30 10
18 38 15
19 07 09
19 05 30
18 36 00
17 40 45
or*
151 01 24
152 47 00
150 30 00
150 58 00
150 44 43
152 42 04
152 47 12
154 08 00
154 25 14
149 58 00
149 11 54
150 42 04
152 06 20
155 52 24
158 40 00
159 00 00
155 28 24
155 33 04
166 53 15
166 17 15
165 47 30
166 00 30
166 32 14
166 57 45
166 33 00
167 30 31
167 30 00
168 02 00
167 47 15
168 18 50
168 58 00
169 27 30
170 11 15
169 44 45
171 20 30
172 05 15
168 56 45
170 10 00
177 07 15
178 32 15
177 57 09
178 10 24
177 38 00
178 49 00
ft. m.
4 45
7 05
ft. m.
10 58
0 53
£o
4.2
ft
2.5
D'Entrecasteaux Is. : Ferguson I., SW.
extreme
Well Island, E.pt..
Normanby I., obe.
islet
St Aignan Island* Summit
Renard Inlands* W pt
Rossel Island' E pt
Adele Island* S extreme
Coringa Islands: Chilcott Islet
IVew Hebrides Inlands. 1 Stt£iandis,UZ 1 Coral Sea Arch.
Herald Cays: NE. Cay
Tregosse Islands* S islet
Lhou Reef* Observation Cay
Melliflh Reef* Cay beacon
Bampton Island
Renard Island: Center ...
Wreck Reef: Bird Islet
Cato Island: Center
Duff or Wilson Group* N island
Matema or Swallow Group: Nimanu Islet .
Tinakula Island: Summit, 2 200 ft
Nitendi Island: NE. pt., Cape Byron
Tapua Island: Basilisk Harbor, S. pt. of
entrance
Vanikoro* Ocili villas
4 50
11 05
3.8
2.3
Torres or Ababa island: Hayter Bay,
Middle I
Vanua Lava Island: Port Patterson,
Nusa Pt
6 40
0 30
3.8
2.3
Santa Maria Island: Lasolara Anchorage. .
Aurora Island* Laka-rere
Mallicollo Island: Port Sandwich, pt. on
E side
4 38
5 15
10 50
11 27
3.8
3.0
1.9
L8
Vate or Sandwich Island: Havannah
Harbor Matapou Bay flagstaff
Erromango Island: Dillon Bay, Pt. Wil
liams
Tanna Island: Port Resolution, Mission. .
Erronan or Futuna Island: NW. pt
Aneitviim Island: Port Anatom, Sand
Islet
5 10
11 23
3.1
1.9
Matthew Island* Peak 465 feet
Hunter Island* Peak 974 feet
Walpole Island* S pt
Mitre Island* Center
Rotumah Island* Epipigi Peak ....
6 15
0 00
4.2
2.5
Kandavu Island: N. rock Astrolabe Reef
li^ht
FIJI Islands.
Mt. Washington, N.
peak
Ngaloa Harbor, outer
beacon
6 40
0 25
4.0
2.4
Vatu Lele Island* S pt
Ovalau Inland" Levuka lighthouse
Page 348] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
l
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H.W.
h. m.
L. W.
Spg-
Neap.
FIJI Islands.
Viti Levu Island: Summit of Malolo Islet.
Suva Harbor, low light .
Mbega or Mbengha Island: Swan Harbor,
Leaven Pt
0 / //
17 44 45
18 06 50
18 22 00
19 09 38
18 32 49
17 59 32
17 37 11
17 27 14
17 15 21
16 42 01
16 57 53
16 49 19
16 08 00
16 46 00
15 44 45
17 03 00
17 25 33
17 17 20
17 10 00
17 25 26
17 44 12
17 39 33
17 59 00
18 14 10
18 25 46
18 38 56
18 46 00
18 56 15
18 58 57
19 03 00
19 04 00
19 49 11
20 39 10
21 00 09
21 01 39
14 14 20
13 23 35
15 34 00
15 52 00
15 58 00
13 45 00
13 48 56
14 18 06
14 19 00
14 32 00
19 10 00
10 52 47
13 14 30
18 05 50
16 28 00
15 48 00
16 52 00
a t n
177 09 00
178 24 40
178 06 53
179 44 27
179 56 25
179 14 08
178 59 29
178 57 46
179 20 44
178 54 15
178 48 32
179 16 08
Long. W.
179 58 46
179 51 00
179 54 26
179 17 00
179 32 17
179 10 00
179 05 45
179 10 33
179 19 49
178 50 27
179 04 00
178 52 00
178 27 04
178 30 54
178 44 00
178 59 05
179 52 58
178 47 25
178 33 25
178 13 38
178 43 27
178 44 03
178 49 47
178 06 45
176 11 47
175 40 40
173 52 00
173 52 00
172 17 00
171 44 56
170 42 14
169 32 00
168 09 00
169 50 00
165 51 30
163 04 10
163 10 00
154 30 00
154 31 00
154 00 00
h. m.
ft-
ft.
6 30
0 15
3.6
2.2
Matuku Island: N. side of Matuku en
trance
Moala Island: Rocks off N pt
Ngau Island : Herald Bay, E side
Wakaya Island : Rocky Peak
Makongai Island : Dilliendreti Peak
Goro Island • NW pt
Vanua Le-vu Island • Mount Dana
Nandi, observation
islet
Savu Savu Pt., ex
treme
6 00
12 13
4.3
2.6
NE Pt
Taoiuni Island: Somu-Somu town
Thikombia Island • E hummock .
Naitamba Island: Center
Vatu Vara Island: N end, summit .
Kanathea Island : S pt
Vanua Mbalavu Island : NW. pt
Mango Island : Pier end
6 10
0 00
3.1
1.9
Thithia Island : Highest peak
Tuvutha Island : Peak
Naian Island : Summit, 580 ft
Lakemba Island : Kendi Pt
Oneata Island: Summit of Loa I
Mothe Island : Summit
Mamuka Island: Center, 260 feet
Kambara Island : Highest peak
Totoya Island: Black Rock Bay, W. side.
Fulanga Island • W bluff
6 35
0 20
3.5
2,1
Ongea Levu Island • Center
Vatoa or Turtle Island : Hummock ....
6 10
0 00
3.1
1.9
Ono Islands* Peak
Michaeloff Island' Center
Simonoff Island' Center
Fatuna or Home Island: Mt. Schouten. . .
Uea or Wallis Island: Fenua-fu Islet. . . .
Niua-fu or Good Hope Island: NW. ex
treme
6 40
0 28
4.4
2.7
Keppel Island: Center
Boscawen Island : Center
Savaii Island* Paluale village
Samoa Is.
Upulo Is.: Apia Harbor, obs. spot..
6 25
7 00
6 00
0 13
0 45
12 13
3.1
2.7
4.6
1.9
1.6
2.7
Tutuila Island: Pago-Pago, obs. pt
Manua Island: Village, NW. side. .
Rose Island* Center
Niue or Savage Island: S. pt
Danger, or Bernardo, 'Is. : Middle rock...
Suwarrow or Souwaroff Island: Cocoanut
Islet. .
3 10
9 23
2.4
1.4
Palmerston Islands' W islet
Scilly Islands' E islet
Bellingshausen Island* Center
Mopelia (Lord Howe) Island: Center. . . .
APPENDIX IV. [Page 349
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
I
Place.
Lat. S.
Long. W.
Lun. Int.
Range.
H. W.
Lr.W.
Spg-
Neap.
Society Islands.
Maitea Island' Summit
0 / »
17 53 00
17 29 10
17 36 39
17 29 23
16 42 30
16 50 00
16 35 00
16 31 35
16 11 00
16 26 00
24 40 20
25 03 50
24 21 20
24 01 20
23 07 36
21 31 30
22 01 00
21 20 00
23 07 50
20 46 20
21 50 00
21 38 00
20 43 00
19 53 17
20 46 07
19 16 30
18 00 29
18 16 00
18 43 30
19 37 00
19 25 00
17 19 30
18 05 20
19 08 45
18 18 30
17 49 35
17 35 28
17 20 30
14 49 00
14 12 00
15 50 00
15 44 20
16 39 10
16 44 29
17 20 20
16 47 49
17 28 41
16 26 09
16 31 00
15 43 15
15 30 00
15 50 00
14 43 00
14 29 10
15 14 30
15 50 30
14 53 00
0 / H
148 05 00
149 29 00
150 36 56
149 50 30
151 01 28
151 27 21
151 35 00
151 46 00
151 48 00
152 12 00
124 48 00
130 08 30
128 19 00
130 41 00
134 57 54
135 33 05
136 10 15
136 38 53
137 06 15
138 27 45
138 56 30
140 38 45
143 03 15
144 57 00
139 08 45
138 48 30
136 26 30
137 03 30
138 53 15
140 15 45
138 40 45
138 26 26
140 59 30
141 41 10
142 11 31
143 05 23
142 35 16
141 29 43
138 46 45
141 15 37
140 53 35
142 08 40
144 14 45
142 53 34
145 30 54
144 17 18
143 31 17
143 57 59
145 22 45
144 38 34
145 24 45
146 02 45
145 11 00
146 20 00
147 11 00
148 15 00
148 39 45
ft. m.
ft. m.
ft.
^
Tahiti Island * Lighthouse ....
12 00
5 48
1.0
0.6
Tubuai-Manu or Maia-iti I. : NW. pass. . .
Eimeo Island: Talu Hbr., Vincennes Ft..
Huaheine Inland' Lighthouse
Ulietea Island • Recent Pt
Tahoa Island: Center
Bola-Bola Island : Otea-Vanua village
Tubai or Motu-iti Island: N. pt. of reef. .
Mania or Maupili Island : Center. . ,
12 10
6 00
1.4
0.8
Ducie Island* NE entrance
Tuamotu Arcblpelago.
Pitcairn Island* Village
Henderson or Elizabeth Island: Center. .
Oeno Island: N. pt
Mangareva or Gambier Island: Flagstaff..
Marutea or Lord Hood Island: Center
Maria or Moerenhout Island * Center
1 50
8 03
2.4
1.4
Vahanga Island* W. pt
Morane or Cadmus Island* Center
Tureia or Carysfort Island: E. pt
Mururoa or Osnabrug Island: Obs. spot. .
Tematangi or Bligh Island: N. pt
Nukutipipi* SW pt
Hereheretue or St. Paul Island: Center...
Vanavana or Barrow Island* Center
Nukutavake or Queen Charlotte I. : X. pt.
Reao or Clermont Tonnere Island: NW.
point
Puka-ruha or Series Island: NW. pt
Vahitahi Island* W pt
Ahunui or Byam Martin Island: NW. pt.
Pinaki or \\ nitsunday Island: E pt
Tatakoto or Clerke Island: Flagstaff on
western coast
Hao or La Harpe Island* NW pass
2 40
8 55
2.4
1.4
Paraoa or Gloucester Island * Center
Ravahere Island* S pt
Reitoru or Bird Island: N beach . ..
Hikueru or Melville Island: E. pt
Tauere Island : NWT. pt
Puka-puka Island : E*. pt
Napuka Island * W pt
Angatau or Araktcheff Island: W. pt. . . .
Tukume or Wolkonsky Island: NW. pt. .
Tuanske Island : NW pt
Nihiru Island (Tuanake): SW. pt
Anaa Island* Islet in N pass
Tepoto Island * N pt
Haraiki or Crocker Island : SW pt
Makemo or Phillips Island: W. pass
Fakarana or Wittgenstein Island: SE.
pass
Taiaro or Kings I. : Middle of W. shore. . .
Aratika Island : E pt
Toau or Elizabeth Island: Amyot Bay. . .
Takapoto Island * S pt
Aheu Island * Lagoon Entrance
Rangiroa Island * E pt
4 30
.
10 43
2.1
1.3
Makatea Island * \V pt
Matahi va Island * W pt
Page 350] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA,
ISLANDS OF THE PACIFIC— Continued.
i
Place.
Lat. S.
Long.W.
Lun. Int.
Kange.
H.W.
L. W.
Spg.
Neap.
Juan Fernandez Island: Fort S. Juan
Batista
h. m.
ft. m.
/*.
ft-
33 37 36
33 46 00
26 18 07
26 16 00
26 27 41
27 10 00
27 35 46
27 55 30
23 55 00
23 21 45
22 29 00
22 45 00
21 47 00
21 49 00
21 11 35
20 17 00
20 01 00
20 04 00
19 18 00
18 54 00
18 39 02
19 41 35
19 45 00
21 08 00
23 37 06
23 55 00
29 15 30
30 15 00
30 35 00
21 44 45
20 27 06
20 46 00
21 42 00
21 29 12
22 00 10
22 16 22
22 28 44
22 42 30
29 03 45
29 56 00
31 31 38
31 45 10
54 19 00
50 32 15
52 33 26
49 42 00
47 43 00
43 57 24
43 49 03
78 50 02
80 46 00
79 54 56
80 06 56
105 28 00
109 26 00
144 17 20
143 28 21
147 48 00
149 35 35
151 23 41
152 55 00
154 51 00
157 56 00
159 47 00
157 23 00
157 34 00
158 08 00
158 54 00
159 32 00
174 01 00
174 59 50
175 03 00
175 12 00
178 55 45
179 07 45
177 55 40
178 31 45
178 37 00
Long. E.
174 37 45
166 35 25
167 02 30
168 00 00
165 58 50
166 03 30
166 25 52
166 28 51
167 27 55
167 58 06
159 04 30
159 05 58
159 16 10
158 56 00
166 13 20
169 08 41
178 43 05
179 00 27
Long. W.
176 32 15
176 42 00
Mas Afuera Island* Summit 4 000 ft
St Ambrose Island * N part creek
St Felix Island- Center
Salay Gomez- NW pt
4 00
0 40
0 10
10 15
6 53
6 25
3.3
2.8
2.4
2.0
1.7
1.4
Easter Island - Cooks Bay mission
Rapa or Oparo Island - Tauna Islet
Bass Islets (Morotiri): SE. islet, 344 ft. . .
Tubuai or Austral Is., Vavitoal.: Center.
Tubuai I.: Flag
staff, N. side
Rurutu I.: N. pt-.
Rimitara I. : Center.
Hull Island- NW pt
3 00
9 13
2.4
1.4
Cook Islands.
Mangaia Island: Center
Rarotonga Island: NW. pt
6 00
12 15
2.7
1.7
Mauki or Parry Island: Center
Mitiero Island* Center
Vatiu or Atiu Island* Center
Hervey Islets* Center
Aitutaki Island* Center
Vavau Island: Port Valdes, Sandy Pt. . . .
Kao Island* Summit 5 000 ft
6 20
0 10
3.8
2.3
l>
Tofua Island: Summit, 2,800 ft
Tongatabu Island: Lighthouse
6 20
7 50
0 10
1 35
3.8
5.5
2.3
3.3
Minerva Reefs, N. Minerva: NE. side
S. Minerva: S. side of en
trance
Kermadec Is., Raoul or Sunday I.: Den-
ham B flagstaff
6 00
12 13
3.3
2.7
Macauley I * Center
Curtis I.: Center
Conway Reef* Center
Loyalty Is. , Uvea or Halgan I. : Uvea
Church
Lifu I.: Wreck Bay, NW.
shore
6 30
0 18
4.2
2.5
Mare or Britannia I. : S. pt. . .
Port Kanala* Observatory
New Cale
donia.
St. Vincent Bay: Marceau I
5 40
8 25
11 52
2 13
3.3
3.1
2.0
1.9
Noumea* Lighthouse
Balari Pass: Amedee I li^ht
Port Alcmeme: Alcmene I
7 55
7 30
1 45
1 17
3.6
4.7
2.2
3.9
Norfolk Island: Inner end of jetty
Elizabeth Reef* Center
Lord Howe Island : S . end of middle beach
Balls Pyramid* Summit 1 816 ft
8 20
2 08
5.4
3.3
Macquarie Island: N pt
Auckland Is. : Port Ross, Terror Cove
Campbell Island: S. harbor, Shoal Pt
Antipodes Island: Summit, 600 ft
11 50
11 45
3 20
5 38
5 33
9 30
3.2
3.5
5.3
2.6
2.9
4.3
Bounty Islands: Anchorage N. I., West
Group
Chatham Island, Whare-Kauri Island:
Port Waitan0"! Pt Hanson
Chatham Island, Whare-Kauri Island:
Port Hutt, Gordon Pt
5 22
0 23
2.5
2.1
APPENDIX IV. [Page 351
MARITIME POSITIONS AND TIDAL DATA.
AUSTRALIA.
_j
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
North Australia.
Groate Eylandt' SE pt
ft. TO.
ft. m.
A
ft.
14 16 00
13 45 00
12 14 00
11 53 00
10 59 00
11 36 00
11 57 00
11 54 00
10 57 00
11 22 02
11 08 00
11 51 00
12 13 20
12 23 20
12 30 58
13 59 00
14 25 50
15 13 45
14 42 00
13 44 DO
13 52 00
13 57 07
14 15 00
13 55 00
14 14 00
14 23 00
14 51 00
15 16 36
15 06 00
14 59 20
15 13 15
15 46 00
15 52 00
15 39 25
17 24 25
16 23 00
16 50 00
17 09 00
18 29 00
19 54 00
20 36 00
20 19 00
20 27 00
20 35 00
20 16 45
20 40 40
21 46 41
24 00 00
25 29 19
28 18 05
28 12 00
31 18 00
32 00 20
32 03 12
31 57 09
32 27 00
33 31 45
34 21 55
34 52 00
35 05 00
35 09 00
35 11 54
35 02 20
136 58 00
136 15 00
137 00 00
136 34 00
136 46 00
i36 07 00
134 45 00
134 12 00
132 36 30
132 09 18
130 19 00
129 58 00
131 16 30
130 37 00
130 27 00
129 37 00
129 20 42
129 48 14
128 ]0 00
126 57 00
126 12 00
125 38 45
125 39 00
124 55 00
125 12 00
125 00 00
124 42 00
125 07 00
125 01 00
124 32 11
124 14 00
124 04 00
123 45 00
123 36 27
123 39 47
122 55 45
122 05 30
122 15 00
121 54 00
118 48 00
117 11 00
116 45 00
116 30 00
116 23 00
115 22 00
115 27 45
114 10 08
113 21 00
112 57 09
113 35 33
114 14 30
115 30 00
115 30 12
115 43 48
115 50 26
115 44 00
115 00 15
115 08 00
116 01 00
116 38 00
117 40 00
117 53 45
117 54 04
Bickerton Island* Summit
Cape Arnheinr Extreme
Cape Wilberforce* E extreme
8 00
1 48
9.8
5.8
Cape Wessel * Extreme
Dale Point' Extreme
Cape Stewart* Extreme
Liverpool River* W pt entrance
6 17
0 05
12.0
7.1
Cape Croker* Extreme
Port Essinarton* Government house
Melville Island: Cape Van Diemen
Bathurst Island: Cape Fourcroy
Adelaide River* E entrance pt
5 15
4 57
3 50
5 45
6 45
11 27
11 18
10 00
11 58
0 27
16.8
17.0
16.7
21.9
23.0
9.9
10.0
9.9
12.9
13.6
Port Darwin' Charles Pt. light
Port Patterson* Quail Islet ..
Port Keats* Tree Pt
Pearce Point* Extreme..
Victoria River: Water Valley
Cape Dussejour: Rock off cape
I Western Australia.
Cape Londonderry : Extreme
Cape Bougainville * Extreme.
Cassini Island ' S pt. .
Cape Voltaire- Flat Hill
Barker Islets* Center
Montalivet Islands: W. islet
Maret Islets: N . islet
Colbert Islet: Center
Prince Regent River: Mount Trafalgar..
Port Nelson' Careening beach ..
De Frevcinet Islets: Beacon on summit. . .
Red Islet- Center
Cockell Islet: W. pt
MacLeay Islets: Rock off N. end
Port Usborne: S. pt
Fitz Roy River: Escape Pt
Cape L'Eve'que" Extreme ...
Lacepede Island* NW. islet.
Cape Baskerville* Extreme
Cape Latouche Treville: Extreme
Turtle Isles: Center of N. isle
Cape Lambert" Extreme
11 30
5 10
17.6
10.4
Legendre Island: NW. extreme
Rosemary Island: W. summit
Enderby Island : Rocky Head
Monte bello Island * N extreme of reef
Barrow Island * N pt
Northwest Cape * Extreme
Cape Cuvier: Extreme
Cape Inscription: Extreme
Houtman Rocks: N . islet
Port Gregory
Cape Leschenault* Extreme .
Rottnest Island * Lighthouse
Perth (Fremantle) : Arthur Head light
State Observatory
Peel* Robert Pt - -
[10 16]
[3 43]
[2.1]
I
Cape Naturaliste • Extreme . .
Cape Leeuwin* Lighthouse
D'Entrecasteaux Point* Extreme
Nuyts Point* Extreme
West Cape Howe* Extreme .
Eclipse Islets: Summit of largest
King George Sound: Commissariat house
near Albany jetty
[10 53]
[4 40]
[2.6]
Page 352] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
AUSTRALIA— Continued.
i
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Western
Australia.
Bald Isle: Center
h, TO.
h. m.
ft.
ft.
34 55 00
34 24 00
34 30 00
32 57 00
32 34 00
32 01 30
32 48 00
34 29 29
35 00 15
35 20 15
34 43 22
33 44 08
32 29 42
34 28 25
35 18 21
35 07 31
34 12 00
34 50 25
34 55 38
35 36 45
35 45 30
35 51 00
35 34 06
36 57 00
38 04 18
38 26 00
38 24 39
38 23 47
38 51 45
39 35 38
38 18 00
38 08 52
37 49 53
38 29 42
38 29 15
39 08 00
39 25 45
40 11 45
40 18 40
40 43 40
38 45 06
37 34 15
37 30 10
37 15 40
37 04 18
36 18 30
36 14 30
35 43 58
35 21 41
35 09 15
34 40 25
34 25 30
33 51 41
33 51 30
33 35 00
32 55 15
32 45 10
32 26 20
31 25 30
30 12 00
29 25 30
118 27 00
119 34 00
121 58 00
124 39 00
125 30 00
132 33 00
134 13 40
135 24 56
135 56 09
136 06 24
135 51 03
136 57 22
137 45 24
137 22 21
136 53 30
137 49 39
138 09 00
138 26 58
138 35 05
138 05 29
136 34 39
138 07 45
138 37 09
139 39 39
140 39 40
141 32 39
141 40 02
142 14 37
143 30 39
143 57 03
144 37 00
144 21 47
144 58 35
144 52 51
145 01 34
146 25 16
147 18 39
148 04 00
147 47 39
148 07 24
146 37 43
149 55 10
149 58 39
150 03 04
149 54 45
150 01 34
150 13 34
150 12 34
150 29 29
150 46 26
150 52 19
150 55 14
151 12 23
151 18 15
151 20 30
151 48 19
152 13 20
152 33 40
152 55 19
153 17 00
153 23 10
Hood Point: Doubtful Isles
Recherche Archipelago: Termination
Isle
Culver Point: Extreme
Dover Point: Extreme
Fowler Point' Extreme
11 50
9 35
5.1
0.3
South Australia.
Streaker Bay: Port Blanche
Coffin Bay Mount Dutton
0 35
6 55
5.5
0.3
Cape Catastrophe: W. pt.
Neptune Isles: SE. islet
Port Lincoln: English Church
Franklin Harbor: Observation spot
Port Augusta: Flagstaff
8 20
2 15
11.4
0.7
Port Victoria: Wardang Island hut
Cape Spencer: S. pt
Investigator Strait: Troubridge light
Port Wakefield' Lighthouse
4 31
4 04
10 45
10 22
10.2
6.3
0.6
0.9
Port Adelaide : Wonga Shoal light
Observatory
Cape Jervis: Lighthouse
Cape Borda: Lighthouse
Cape Willoughby : Lighthouse ....
4 00
10 15
5.8
0.3
Port Victor: Flagstaff
Cape Jaffa: Margaret Brock lighthouse. . .
Cape Northumberland: Lighthouse.
11 52
5 40
4.2
0.2
Cape Nelson: S. extreme
Victoria.
Portland Bay: Lawrence Rock. . . .
0 20
6 35
2.7
2.1
Port Fairy: Griffith Island summit
Cape Otway : Lighthouse
King Island : Cape Wickham light
Port Phillip: Point Lonsdale light
10 43
2 02
2 19
4 30
8 20-
8 41
2.5
3.0
1.9
1.9
2.3
1.5
Geelong: Customhouse
Melbourne: Observatory
Cape Schanck : Lighthouse
Port Western: Extreme of W. head
Wilson Promontory: Light, SE. pt
Kent Island: Deal Island light
Flinders Is.: Strzelecki Peaks, SE. peak.
Goose Island: Lighten S. end..
10 38
4 25
8.1
6.2
Banks Strait: Swan Island light
Port Albert : Lighthouse
Gabo Island : Lighthouse
8 40
2 27
4.5
3.4
Cape Howe : East extreme
Cape Green: SE. pt
Twofold Bay: Lookout Pt light
j New South Wales.
8 05
1 52
5.2
3.1
Dromedary Mountain: Summit
Montagu Island: Lighthouse...
8 20
2 07
5.3
3.2
Bateman Bay: Observation head
Ulladulla: Inner end of pier
8 20
2 07
5.4
3.3
Jervis Bay : Lighthouse
Kiama Harbor: Outer extreme of S. head.
Wollongong: Summit of head
Sydney: Observatory
8 40
2 27
4.2
2.5
Port Jackson: Outer S. Head light
Broken Bay: Baranjo Head light. .
Newcastle : Nobby Head light
8 35
8 15
2 23
2 00
4.7
5.8
2.8
3,6
Port Stephens' Lighthouse
Sugar Loaf Point: Lighthouse.
Port Maccjuarie : Entrance
9 00
2 46
4.1
2.4
Solitary Islands: S. Isle light
Clarence River: S. Head light
8 15
2 00
4.0
2.4
APPENDIX IV. [Page 353
MARITIME POSITIONS AND TIDAL DATA.
AUSTRALIA— Continued.
l
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H.W.
L. w.
Spg.
Neap.
Queensland.
Richmond River* N Head liaht
ft. m.
h. m.
ft.
ft.
28 51 30
27 23 22
27 28 00
27 26 20
27 02 10
25 56 00
25 00 15
24 43 20
24 45 00
24 07 00
24 01 20
24 01 20
23 53 00
23 29 30
22 31 40
21 39 00
21 19 15
21 32 00
20 32 20
20 18 50
20 15 30
20 00 50
19 57 30
19 41 50
19 19 20
19 11 25
18 45 30
18 09 30
17 40 40
17 09 45
16 04 20
15 45 00
15 29 45
15 16 30
14 37 15
14 10 00
14 07 45
14 00 30
13 24 45
12 51 00
11 58 15
11 55 00
11 46 30
11 36 30
10 41 30
10 37 45
10 22 00
10 46 00
10 36 05
17 36 40
17 35 10
17 06 50
153 35 55
153 10 31
153 01 36
153 33 50
153 28 04
153 13 00
153 23 00
153 13 40
152 25 00
152 45 15
151 41 04
151 37 15
151 23 50
151 14 04
150 45 44
150 14 00
149 43 30
149 31 04
148 58 00
148 53 15
149 00 00
148 16 54
148 27 34
148 23 00
147 27 40
147 01 10
146 42 50
146 11 04
146 11 00
146 02 30
145 29 34
145 28 30
145 17 30
145 23 15
144 57 30
144 32 34
144 15 19
143 42 15
143 36 19
143 34 00
143 15 15
143 29 00
143 06 00
142 56 19
142 32 24
142 39 20
142 21 19
142 10 50
141 53 49
140 37 06
139 45 56
139 38 36
Brisbane: Signal station, Fisherman Is...
Observatory
10 45
4 30
6.4
3.9
Lookout Point' Extreme .
Cape More ton * Lighthouse .
Double Island Point* Licrhthou<*e
Indian Head* Extreme
Sandy Cape* Lighthouse
Burnett River* S Head light
Lady Elliot Islet* Lighthouse
Bustard Head* Lighthouse
Rodd Bay Spit end
Port Curtis: Gatcombe Head light
Cape Capricorn: Lighthouse. . .
Port Bo wen: Observation rock
Percy Isles: Pine I. light
Northumberland Isles: Summit of Prud-
hoe I
Cape Palmerston: N. extreme
Cape Conwav: SE. pt *
Port Molle* S side of entrance
Cumberland Island: Whitsunday I., sum
mit, rm W- fiidp
Port Denison: Obs. pt., W. side of Stone
Isle .
10 05
3 53
9.0
5.4
Gloucester Island: Summit near N. end..
Holborne Islet: Center
Cape Bowling Green: Lighthouse
Cape Cleveland: Lighthouse
Palm Islands: SE. point of SE. island. . .
Rockingham Bay: Peak of Goold Isle
Barnard Island: Lighthouse
Frankland Island: High islet
Cape Tribulation: Extreme
Hope Island: S. islet
Cook Mountain: Summit
8 55
2 43
7.5
4.5
Cape Bedford: SE. extreme
Murdock Point: Extreme
Cape Melville: NE. extreme
Flinders Island: N. extreme of N. island.
Claremont Point: Extreme
Cape Sidmouth* Extreme
9 00
2 47
9.6
5.8
Cape Direction: NE. extreme
Cape Grenville: Extreme
Sir Charles Hardy Island: N. extreme of
SE. isle .
Bird Island: NW. isle
Hannibal Isles: E. isle
Cape York: Sextant Rock
1 00
7 10
8.0
4.7
Mount Adolphus: Summit.
Travers Isles: Center
Prince of Wales Island: Cape Cornwall,
extreme .
Booby Island : Center ...
4 20
10 30
7.8
4.7
Flinders River: Entrance
Albert River: Kangaroo Pt
Sweers Island : Inscription Pt
Page 364] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
TASMANIA.
i
Place.
Lat. S.
Long. E.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
Cape Portland: NW pt
A. m.
A. m.
ft.
ft.
40 44 15
41 03 25
41 07 05
41 10 00
41 08 30
41 02 50
40 23 40
40 40 10
40 22 00
41 04 00
41 41 00
42 11 37
42 11 00
43 19 00
43 33 30
43 44 30
43 29 40
43 21 00
42 53 25
43 14 00
42 52 00
42 13 00
41 34 00
40 59 40
147 56 09
146 47 54
146 33 30
146 24 30
146 12 00
145 56 39
144 47 45
144 39 44
144 39 19
144 44 00
144 57 00
145 12 34
145 10 30
145 53 00
146 01 04
146 22 04
147 08 49
147 23 40
147 20 07
148 02 00
148 00 00
148 18 04
148 19 30
148 20 50
Port Dalrymple: Low Head light .
11 10
5 00
9.0
6.9
Port Sorrell: NW. entrance head ...
Port Frederick: Entrance.
Leven River: W. entrance head
Emu Bay: Blackman Pt
Hunter Island: N. pt
Cape Grim: Outer Doughboy Islet
Albatross Islet: N. pt. .". ".
Arthur River: Entrance
Pieman River: Rocks close to entrance. .
Macquarie Harbor* Entrance Islet
7 20
1 07
2.7
2.1
Cape Sorrell : Lighthouse
Port Davey : Pollard Head
Southwest Cape: Extreme pt
Mewstone Rock: Center
Cape Bruny: Lighthouse
Bruny Island: Penguin Islet ....
Hobart Town: Transit of Venus station. . .
Cape Pillar: Tasman Islet
8 05
1 52
4.2
3.2
Cape Frederik Hendrik : Extreme
Freycinet Peninsula: Summit
St. Patrick Head: N. pt
Eddystone Point: Extreme
NEW ZEALAND.
1 North Island.
Three Kings Islands: NE. extreme of NE.
island
34 06 20
34 25 07
34 31 00
35 00 20
35 01 44
35 17 00
35 23 48
35 51 09
36 01 15
36 50 06
36 48 35
36 28 20
36 26 20
37 36 25
37 30 00
37 30 45
37 40 00
38 20 50
39 18 00
39 28 30
39 38 00
41 36 45
41 21 40
41 17 17
41 17 04
40 27 10
39 57 00
39 18 00
39 03 35
38 04 50
172 08 49
173 03 34
173 00 54
173 32 39
173 45 48
174 06 06
174 21 24
174 31 14
175 25 34
174 51 00
175 24 34
175 21 04
175 49 00
176 10 14
177 10 49
177 59 34
178 35 09
178 20 14
177 53 15
176 54 14
177 06 44
175 18 45
174 51 04
174 47 25
174 46 04
175 14 40
174 59 44
174 03 59
174 04 35
174 48 04
North Cape: Cape Islet
Parenga-renga Harbor* Kohan Pt
Mauivanui Harbor* \Vhite Pt
Wangaroa Harbor: Peach Islet
7 40
7 26
7 15
7 05
1 30
1 55
1 05
0 55
6.4
5.9
6.5
6.7
4.5
4.2
4.6
4.8
Bav of Islands: Motu Mea Islet
Wangflriini TTarhor: (rrovfi Pt.
Wangari Harbor : Loot Pt
Great Barrier Island* Needles Pt
Auckland Harbor : Lighthouse
7 20
7 05
1 10
0 55
10.8
10.7
7.7
7.6
Coromandel Harbor : Tuhnia I
Cape Colville* N pt
Cuvier Island* Lighthouse
Tauranga Harbor: Mount Maunganui,
860ft
7 05
0 55
6.1
4.4
White Island* Summit 863 ft
Cape Runaway: Extreme
8 10
8 00
2 00
1 50
6.6
6.8
4.7
5.8
East Cape: Islet, 420 ft
Tolasra Bav" Matu-heka Islet
Mahia Peninsula: S. extreme of Port
land I
Ahuriri Harbor * Lighthouse
6 05
12 15
3.5
3.0
Kidnappers Cape* Extreme
Cape Palliser* Lighthouse
4 40
10 50
5.7
49
Port Nicholson: Pencarrow light
Wellington* Queens Wharf light
4 52
10 54
3.6
3.1
New Observatory
Mana-watu River: Lighthouse
9 40
3 30
6.3
5.4
"WaTifraTmi "River* N head
New Plymouth: Flagstaff
9 15
9 10
3 05
3 00
11.6
11.9
8.2
8.5
Kawhia Harbor* S head
APPENDIX IV. [Page 355
MARITIME POSITIONS AND TIDAL DATA.
NEW ZEALAND— Continued.
^
Place.
Lat. S.
l
Long. E.
Lun. Int.
Range.
H.W.
L. w.
Spg.
Neap.
£«
»i
c~
* m
^w
Aotea Harbor* S head
/». TO.
ft. TO.
ft.
ft.
37 59 35
37 46 22
37 03 00
36 23 00
35 32 05
41 44 00
43 46 40
43 54 00
44 04 50
44 54 50
45 46 55
46 24 05
46 27 10
46 37 00
46 20 40
46 36 00
46 10 00
45 54 50
45 02 07
44 40 20
44 00 30
42 26 20
42 42 20
41 45 40
40 29 50
41 16 05
40 46 35
41 01 55
41 20 28
46 50 30
46 58 30
47 03 52
47 11 40
46 45 45
48 06 43
174 50 04
174 52 19
174 31 14
174 08 00
173 21 59
174 17 14
172 44 17
173 00 20
171 48 34
171 11 14
170 44 02
169 47 53
169 50 04
168 23 00
167 42 19
166 54 04
166 38 15
166 25 49
168 40 06
167 54 45
168 21 34
171 11 54
170 59 30
171 27 44
172 41 04
173 17 30
173 54 04
174 11 22
174 08 24
168 05 34
168 09 54
168 10 57
167 40 51
167 36 49
166 27 44
WTiaingaroa Harbor* S entrance pt
9 08
9 05
9 00
8 40
4 45
3 45
2 55
2 50
2 50
2 30
11 00
10 00
12.3
12.6
10.0
9.2
7.5
7.4
8.7
9.0
7.1
6.5
6.5
5.8
Manukau Harbor* Paratutai flagstaff
Kaipara Harbor* Lighthouse . - -
Hokianga River: Flagstaff at entrance
Cape Campbell ' Lighthouse
South Island.
Port Cooper * Lyttleton customhouse
Akaroa Island * Lighthouse
Ashburton River* N entrance pt
Waitangi River* N entrance head . .
Otago Harbor: Taivoa Head light
Molyneux Bay* Landing place
3 31
9 39
5.6
4.4
Nu°*get Point* Lighthouse
Bluff Harbor* Lighthouse
1 05
7 15
7.8
6.2
Tewaewae Bay* Pahia Pt
Solander Islands* Summit, 1,100 ft
Preservation Inlet: Lighthouse
11 10
5 00
7.5
5.9
West Cape: Extreme
Queenstown: U. S. Tr. of Venus station. . .
Milford Sound : Freshwater Basin
Cascade Point* N extreme
Grey River* Entrance
10 10
10 20
4 00
4 10
9.8
9.5
7.7
7.5
Hokitika* Entrance light
Cape Foulwind* Lighthouse
Cape Farewell* Extreme
j
Nelson* Bowlder Bank light
9 55
9 45
3 45
3 35
12.0
11.6
9.4
9.2
D'Urville Island : Port Hardy
Port Gore* Head of Melville Cove
Port Underwood* Flag Pt
6 00
12 15
7.6
6.6
Port William* Ho well's house.
M
E
I
•
Paterson Inlet* Glory Cove
1 00
9 15
7.8
6.2
Port Adventure: White Beach, S. end
Port Pegasus: Cove abreast Anchorage I. .
Codfish Island* NW extreme
11 45
5 40
7.9
6.2
Snares Islands* SW. islet . . .
THE ARCTIC REGIONS.
Cape Walsingham* Extreme
Lat, N.
66 00 00
64 04 00
62 33 00
63 42 00
69 21 00
70 09 17
70 38 14
70 05 00
73 09 13
73 13 39
73 13 00
73 50 05
76 49 00
81 04 40
82 27 00
82 40 00
82 54 00
83 07 00
74 47 10
68 55 00
Long. W.
69 28 00
77 50 00
91 06 00
87 15 00
81 31 00
91 30 33
92 10 56
96 47 00
89 00 54
88 54 48
91 08 00
90 12 00
73 10 00
64 45 00
61 18 00
63 38 00
64 45 00
70 20 00
110 48 15
Long. E.
179 57 00
Mile Island* N pt
Marble Island: E end . .
4 00
10 15
12.0
5.1
Cape Kendall: Extreme
Iglooik Island* E pt
6 50
0 40
8.0
4.2
Victoria Harbor* N shore
Elizabeth Harbor* Entrance
Magnetic Pole 1831
Port Neill* N pt of entrance
Port Bowen* N cove
J
Batty Bay* S pt of entrance
Port Leopold* Whaler Pt
11 38
5 29
5.5
2.9
Careys Islands
Discovery Harbor
i
Alert's \Vinter Quarters
10 35
4 20
2.6
1.0
Cape Joseph Henry* N extreme
Cape Hecla* N extreme
Cape Columbia* Extreme
Melville Island* Winter Harbor
1 20
7 40
3.8
1.9
North Cape
Page 356] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
THE ARCTIC REGIONS— Continued.
^j
Place.
Lat. N.
Long. E.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
Liakhov Islands: E. pt. of New Siberia
Cape Tscheljuskin: E. pt
o / n
75 10 00
77 41 00
70 25 00
70 55 00
76 58 00
79 55 00
65 50 18
66 45 50
64 32 06
65 32 17
63 53 36
65 07 00
68 08 51
74 30 00
76 35 00
79 50 00
79 42 00
Lat. N.
83 39 00
81 38 00
75 55 00
72 47 48
72 20 42
70 40 00
69 14 04
69 13 12
69 07 30
68 49 06
68 42 30
68 58 30
66 55 54
65 48 42
65 24 30
64 10 36
63 29 12
63 05 12
62 50 00
62 42 36
61 59 36
61 28 20
61 10 24
61 09 42
61 12 12
60 47 30
60 48 36
60 43 07
60 08 12
60 00 00
59 49 00
60 09 00
61 25 00
62 01 00
63 14 00
64 30 00
65 18 00
66 19 02
69 00 12
74 40 00
74 55 00
76 47 00
0 / It
150 30 00
104 01 00
59 10 00
53 01 50
65 40 00
58 45 00
44 17 00
42 30 00
40 33 30
36 51 30
38 08 30
35 37 00
39 48 54
20 00 00
17 23 00
11 40 30
11 07 00
Long. W.
30 40 00
61 44 00
65 30 00
55 53 42
55 20 00
51 59 00
53 24 07
50 56 30
50 55 30
51 00 00
52 46 00
53 27 00
53 40 18
53 23 00
52 54 00
51 45 48
51 10 48
50 43 36
48 57 00
50 20 48
49 44 00
48 51 00
48 26 00
48 30 42
48 10 30
47 52 00
47 46 48
46 01 00
45 16 00
44 40 00
44 01 42
42 55 00
42 15 00
42 00 00
40 50 00
39 30 00
38 30 00
35 11 00
26 10 24
18 17 00
17 33 00
18 40 00
ft. m.
ft. TO.
ft-
ft.
Nova Zembla: Vaigats I.. N. pt
Cape Costin (Kostina)
NE. pt., Cape Desire
10 00
3 50
7.0
4.0
Franz Josef Land : Wilczek I
Mezen: Epiphany Church
Morjovetz Island: Lighthouse
Archangel* Trinity Church
7 18
5 05
9 02
2 00
11 30
3 10
2.2
3.8
9.1
1.3
2.1
5.2
Jighinsk Island' Lighthouse
Onega: St. Michael's Church
Salovetski: Lighthouse
Cape Sviatoi Nos: Lighthouse
9 05
2 55
13.9
7.8
Bear Island .
Spitzbergen Island : S. cape
Cloven Cliff
Danes I., Robbe Bay
Cape Morris Jesup
0 14
(approx)
6 25
5.3
3.0
i Greenland.
Thank God Harbor
5 58
5.4
2.0
Cape York: Extreme.
Upernivik: Flagstaff ...
10 50
4 38
8.0
3.0
Proven : Village ...
Omenak Island : Village
Godhavn : Village
Jacobshavn: Village
Claushavn: Village.
Christianshaab : Village
Egedesmunde: Village
\\halefish Island: Boat Inlet
8 05
6 20
1 52
0 07
7.5
10.0
3.6
4.8
Holsteinberg: Village
Kan°pamint
Ny Sukkertop : Village
Godthaab- Flagstaff
6 40
0 27
12.5
6.0
Sermelik Fjord' Kasuk Peak
Fiskernaes' Village
Jensen Nunatak: Peak
1
Ravn Storo: Peak
1
Frederikshaab : Church
6 12
0 00 9. 0
3.6
Kangarssuk Havn: Village
Arsuk: Pingo Beacon . . .
6 15
0 03 12. 0
4.8
Kajartalik Island: Summit. .
Ivigtuk' House
i
Bangs Havn* Anchorage
Aurora Harbor
Julianshaab: Village
4 56
5 33
2 55
4 00
11 09
11 46
9 10
10 13
7.0
8.6
9.4
7.5
2.8
3.4
3.8
3.0
Neunortalik: Village
Frederiksthal : Village
Cape Farewell: Staten Huk
Aleuk Islands* Center
Cape Tordenskjold" Extreme
Cape Bille: Extreme
Cape Juul : Extreme
Cape Lowenorn: Extreme
Dannesbrog Island * Beacon
Ingolsfjeld
Rio'ny Mount' Summit
Pendulum Islands
11 05
11 10
4 53
4 58
6.7
3.7
3.9
2.1
Cape Philipp Broke
Cape Bismarck: Extreme.
APPENDIX IV. [Page 357
MARITIME POSITIONS AND TIDAL DATA.
THE ARCTIC REGIONS— Continued.
i
Place.
Lat. N.
Long. W.
Liin. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Jan Mayen Island: Mt. Beerenberg, 6,870
ft
h. m.
h. m.
*
ft.
71 04 00
71 08 00
71 00 00
66 22 45
66 32 40
66 33 42
66 07 30
66 27 29
66 26 30
65 30 15
64 48 04
64 08 40
64 04 09
63 48 06
63 48 19
64 35 42
64 55 27
65 16 14
65 45 00
7 36 00
7 26 00
8 28 00
14 30 46
16 10 24
17 57 36
20 05 26
22 23 04
23 08 00
24 31 26
23 45 08
21 55 00
22 39 04
22 39 00
16 36 13
14 08 31
13 41 10
13 32 22
14 23 35
Youngs Foreland, or
Cape Northeast
Mary Muss Bay. . . .
11 21
5 06
3.8
2.2
Langanaes Point...
) Iceland.
Rissnaes Point ....
Grimsey Norddranger: Tr. Station
Skagataas Point
North Cape* Kalfatindr
Straumness Point
Fugle or Staabierg Huk' Point
Snaefells Yokul- Tr Station
Reykiavik* Observatory
5 10
11 25
14.5
8.4
Cape Ska^i* Lighthouse
Reykianaes: Lighthouse
In^olfshofde* Tr Station
Papey Island* Tr Station
Revthur Fjeld' Tr Station
Balatangi* Lighthouse
Dia Fjeld* Tr Station
Page 358]
INDEX TO APPENDIX IV.
REGIONS AND COASTS.
Page.
Admiralty Islands 346
Adriatic Sea 315-321
Africa, east coast 323-325
north coast 320, 321
west coast 321-323
Alabama 284
Alaska 287,288
Albania 318
Aleutian Islands 287
Algeria 321
Arabia 327
Arctic regions 355-357
Argentina 298
Asia, east coast. 331-342
south coast 327-330
Atlantic Ocean, islands 302-304
Australia 351-353
Austria 317, 318
Azores Islands 302
Bahama Islands 292
Balearic Islands 316
Baluchistan 328
Banka Strait 331
Belgium 313
Belize 285,286
Bermuda Islands 303
Black Sea 315-321
Borneo 333
Brazil 295, 297
British Columbia 288,289
Burma 329
California 289
Canary Islands 303
Cape Breton Island 281
Verde Islands 303
Caroline Islands 343
Celebes Island 333
Central America, east
coast 285-287
west coast 291
Ceylon 329
Chile 298-301
China 337,338
Sea 337
Entrance 331
Chosen 339
Cochin China 336
Colombia, north coast. . 295, 302
west coast.
Connecticut 282, 283
Cook Islands 350
Coral Sea Archipelago 347
Corsica 316
Costa Rica 286
Crozet Islands 327
Cuba 292,293
Cyprus 320
Delaware 283
Denmark . 312
East Indian Is., smaller
Dutch 332
Ecuador 302
Egypt 320
Ellice Islands 345
Europe, Atlantic coast. 304-315
Falkland Islands 304
Fiji Islands 347, 348
Florida 284
Formosa Island 338
France, north and west
coasts 313,314
France, south coast 316
Galapagos Islands 342
Caspar Strait 331
Georgia 283
Germany 310-312
Gilbert Islands 342
Great Britain 304-307
Greece 319
Greenland 356
Guatemala 286
Guiana 296
Haiti, island of 293, 294
Hawaiian Islands 344
Holland 313
Honduras 286
Iceland. . . 357
India 328,329
Indian Ocean, islands.. 325-327
Italy 316,317
Jamaica 293
Japan 339-341
Java 331
Kerguelen Islands 327
Korea 339
Kuril Islands 341
Labrador 279, 280
Laccadive Islands 325
Ladrone Islands 344
Louisiade Archipelago 347
Louisiana 284
Lower California 290
326
Madeira Islands 303
Magdalen Islands 280
Maine 281,282
Malaysia 329,330
Maldive Islands 325
Mariana Islands 344
Marquesas Islands 345
Marshall Islands 343
Maryland 283
Massachusetts 282
Mauritius Island. . . 325
Mediterranean Sea 315-321
Mexico, east coast 285
west coast 290, 291
Mississippi 284
Molukka Islands 332, 333
Morocco 321
Mosquito Coast 286
New Brunswick 280, 281
Caledonia 350
Newfoundland 279, 280
New Guinea Island 346
Hampshire 282
Hebrides Islands 347
Jersey 283
South Wales 352
York 282, 283
Zealand 354, 355
Nicaragua 286
North America, east coast 279-287
west coast. . . . 287-291
Australia 351
Carolina 283
Island,NewZealand 354, 355
Norway 307, 308
Nova Scotia 281
Oregon 289
Pacific Ocean, islands. . 342-350
Panama. 287
Pelew Islands 344
Pennsylvania 283
Persia 328
Peru 301,302
Philippine Islands 333-336
Phoanix Islands 345
Porto Rico 294
Portugal 314, 315
Prince Edward Island 280
Queen Charlotte Islands 288
Queensland 353
Red Sea 324,325
Rhode Island 282
Russia, south coast 320
west coast 309, 310
St. Lawrence, River and
Gulf 280
Samoan Islands 348
Santa Cruz Islands 347
Sardinia 316
Siam, Gulf 336
Siberia 341, 342
Society Islands 349
Solomon Islands 346
South America, north and
east coasts 295-298
South America, W. coast 298-302
Australia 352
Carolina . .283
INDEX TO APPENDIX IV.
[Page 359
Page.
South Island, New Zealand 355
S. W. Is. of Japan 338, 339
Spain, north and west
coasts 314,315
south and east coasts. . 315
Stewart Island 355
Sumatra 330
Sweden 308,300
Taiwan (Formosa).
338
Aalborg 312
Aarhus 312
Ababa Island 347
Abaco Island 292
A bang Besar Island 330
Abbeville 313
Abd-al-Kuri Island 324
Aberdeen 305
Abervrach 313
Aberyetwith 304
Abingdon Island 342
Abo 309
AboukirBay 320
Abreojos Point 290
Abrolhos Island 297
Absecon Inlet 283
Acajutla 291
Acapulco 291
Accra 322
AcheenHead 330
Aconcagua Mountain 300
Acre 320
Adakh Island 287
Adalia 320
Adams, Port 338
Addu Atoll 325
Adelaide, Port 352
River 351
Adele Island 347
Aden 327
Adenara Island 332
Admiralty Head 289
Islands 346
Adolphus Mountain 353
Adventure, Port 355
uEgina 319
Aero Island 312
^rstenen 308
Africa Rock 316
Agalegas Island 326
Agdenes 307
Agiabampo 291
Agrigan Island 344
AguadillaBay 294
Aguja Point 302
Agulhas, Cape 323
Agutaya Islet 334
Aheu Island 349
Ahunui Island 349
Ahuriri 354
Ai Sima 341
Aian 341
Aignan, St., Island 347
Aigues Mortee 316
Ailinginae Islands 343
Aillick Harbor 279
Ailly Point 313
REGIONS AND COASTS — continued.
Page.
Tasmania 354
Texas 284
Tokara Islands 339
Tonga Islands 350
Trinidad 296
Tuamotu Archipelago 349
Tunis 321
Turkey 320
Uruguay 298
PLACES.
Ailuk Islands 343
Aitutaki Island 350
Aix Island -t 314
Ajaccio 316
Ajano 320
Akamokan Island 344
Akaroa Island 355
Akashi-no-seto 340
Akpatok Island 279
Akyab 329
Alacran Reef 285
Alamaguan Island 344
Aland Island 309
Alargate Reef 286
Albany 283
Albatross Islet 354
Albemarle Island 342
Albert, Port 352
River.., . 353
Alboran Island 321
Albuquerque Bank 286
Alcatrazes Island 297
Alcmene 350
Alcobaca 297
Aldabra Island 327
Alden 308
Alderney Harbor 307
Alegranza Island 303
Alegre, Porto 297
Alert Js Winter Quarters 355
Alessandro, San, Island 345
Aleuk Islands 356
Alexander, Port 322
Vancouver 288
Alexandretta 320
Alexandria 320
Alfaques, Port 315
Alfred, Port 323
Algeciras 315
Algiers 321
Ali-Agha, Port 320
Alicante 315
Alijos Rocks 290
Alipee 328
Alligator Island 337
— Reef 284
Almadie Point 321
Almeria 315
Almirante Bay 287
Alphonse Island 325
AltaVela 294
Altata 291
Altea 315
Altona 311
Alvarado 285
Ama^er Island 312
Amber, Cape 326
Page.
Vancouver Island 288
Venezuela 295, 296
Victoria 352
Virginia 283
Washington 289
Western Australia 351, 352
West India Islands 292-295
Yucatan .. 285
Amboina Island 332
Ambrose, St., Island 350
Amchitka Island 287
Amelia Island 284
Ameni Islet 325
Amherst Harbor 280
Amirante Islands 325
Amour Point 280
Amoy 337
Amsterdam 313
Island 327
Ana, Sta., Lagoon 285
Anaa Island 349
Anacapa Island 289
Anadir River 342
Analaboe 330
Anamba Islands 331
Anataxan Island 344
Anchorite Island 346
Ancona 317
Ancud 300
Andaman Islands 329
Andenes 307
AndravaBay 326
Andrea, St., Rock 318
Andrew, St 281
Cape 326
Island 346
Andrews, St., Island 286
Andros Island, Bahamas. . . 292
Grecian Arch • 319
Anegada 294
Aneityum Island 347
Angatau 349
Angaur Island 344
Angeles Bay 290
Los 289
Port, Mexico 291
, Washington 289
AnghrisHead 306
Angosto, Port 299
Angoxa Island 323
Angra dos Reis 297
Pequena 322
Anguilla 294
Anhatomirim 297
Anholt Island 312
Animas, Las 290
Anjer 331
Anjoe, Cape 331
Ann, Cape 282
St., Bay 293
Anna, Sta., Island, N. Brazil 297
S.Brazil.... 296
Annapolis, Maryland 283
Nova Scotia 281
Anne, St., Island 299
Page 360]
INDEX TO APPENDIX IV.
Page.
Annisquam 282
Anno Bon Island 322
Anns, St., C. Breton 1 281
England 304
Anowik Island 288
Antareh, Has 324
Antibes 316
Anticosti Island 280
Antigua 294
Antipodes Island 350
Antivari 318
Antofagasta 301
Antonina 297
Antonio, Port 293
San, Cape, Argentina. . 298
Cuba 293
Mt. and Island. . . 303
Port, Argentina. . 298
Chile 300
Sierra
Antwerp 313
AogaShima 340
Aomori 340
Aor, Pulo 331
Aotea 355
Apaiang Island. 342
Apalachicola 284
Apamama 342
Aparri 334
Apenrade 311
Apo Islet 334
Apostle-Rocks 299
Arago Cape 289
Araish, El 321
Arakam Island 342
Araktcheff Island 349
Aran Island 306
Aransas Pass 284
Aranuka Island 342
Aratika Island 349
Arcadins Islands 294
Areas Cays 285
Archangel 356
Ardassier Islands 332
Ardrossan 305
Arena de la Ventana 290
Point, California 289
L. California 290
Arenas Cay 285
Arendal Inlet 308
Arentes Island 332
Argentina 298
Argostoli, Port 319
Arica 301
Arichat Harbor 281
Arkona 311
Armeghon 329
Arnheim, Cape 351
Arno Atoll 343
Arorai Island 342
Arran Island 306
Arrowsmith Islands 343
Arsuk 356
ArtakiBay 320
Arthur River 354
Port 338
Am Islands 332
Arvoredo Island 297
Ascension Bay 285
Island.. . 303
PLACES — continued.
Page.
Ashburton River .......... 355
Ashrafi Island .............. 324
Asia Rock ................ 301
Assateague Island .......... 283
Assens ..................... 312
Assumption Island ........ 326
Astoria ................... 289
Asuncion Island, Ladroues. 344
-- L.California ..... 290
Atalaia Point .............. 296
Athens ................... 319
Atico ..................... 301
Atiu Island ............... 350
Atka Island ................ 287
Atkinson Point ............ 289
Attu Island ................ 287
Auckland .................. 354
- Islands ................ 350
Audierne .................. 314
Angusta .................. 282
- Port, Australia ........ 352
Sicily ........... 317
Augustenberg ............. 311
Augustin, St., Cape, Brazil. 296
-- . -- Philippines. 335
Augustine, San, Island ..... 345
- St., Bay .............. 326
-- Harbor ........... 284
Aurh Island .............. 343
Aurora Harbor ............ 356
- Island ............... 347
Austral Islands ............. 350
Aux Cayes ................ 294
Avarena Point ............ 294
Aves Island ................ 295
Aviles ..................... 314
Avlona .................... 318
AximBay ................. 322
AwaSima ......... , ........ 340
Ayamonte ................ 315
AyerBangis ............... 330
Ayr ...................... 305
Baago Island 312
Babayan Claro Island 334
Baccalieu Island 279
Bagamoyo 324
Bahaltolis Island 336
Bahama Island 292
Bahia, Brazil 296
Colombia 295
de Cadiz Cay 293
Honda, C. America 291
Honda 293,295
Bahrein Harbor 327
Baitiqueri, Port 293
Bajo Nuevo 285
Bajuren Island 333
Baker Islet 342
Bakers Island 281
Baklar 320
Balabac Island 333
Balaklava Bay 320
Balari Pass 350
Balasor River 329
Balatangi 357
Balayan 334
Bald Isle. . . 352
Page.
Balfour Rock 327
Bali Island 332
Balingtang Islands 334
Ballena Bay 291
Balls Pyramid 350
Ballum 311
Ballycottin 307
Balstrum 312
Balta Island 305
Baltic Port 310
Baltimore 283
Bampton Island 347
Banda Island 332
Banderburum 327
Bandjermasin 333
Bangkaru Islands 330
Bangkok 336
Bangor 281
Bangs Havn 356
Banjuwangi 331
Banka Island 331
Strait 331
Bankot 328
Banks Strait 352
Bantal 330
Bantam 331
Bantenan 331
Banton Island 335
Bantry Bay 306
Baracoa 292
Barataria Bay 284
Baratoube Bay 326
Barbados Island 295
Barbara, Santa, California. . 289
Island 289
Mexico 291
Port 299
Barbe, St., Island .' . . 331
Barbuda 294
BarceloBay 299
Barcelona, Spain 315
Venezuela 295
Bardsey Island 304
Barfleur, Cape 313
Bari 317
Barker Islets 351
Barnard Island 353
Barnegat Inlet 283
Barneveldt Islands 298
Barnstable 282
Barra Head 305
SaoJoiio 297
Barren Island 339
West 338
Barrier, Great, Island 354
Barrington Island 342
Barrow Island, Australia. . . 351
TuamotuArch... 349
Point 287
Bartholomew, St 294
Cape 298
Bartolome', San 290
Barton, Port 334
Baru, Point 330
Barung Island 331
Bas, De, Island 313
Basdorf 311
Basianang Bay 335
Basidu 328
Basilan Island.. . 336
INDEX TO APPENDIX IV.
[Page 361
Baskerville, Cape.
Basrah
Bass Islets
Bassa, Grand
Bassas Rocks
da India
Bassein, Burma. . .
India
River
Basseterre
Bastia
Bastion, Cape
Basto
Batabano
Batalden Island . .
Batan Island
Port...
Batavia.
Batbatan Island
Bate Islands
Bateman Bay
Bath
Bathurst
Island
Batian Island
Batoe Islands
Batoe Toetong
Batoum
Batticaloa
Battle Islands
Batty Bay
Baubeltaub Island
Bauld Cape
Baxo Nuevo
Bay of Islands
Baynes Sound
Bayonnaise Island
Bayonne
Bazaruto Island
Beachy Head
Beale Cape
Bear Island
Cape
Beata Island
Beaufort, N. Carolina.
S. Carolina
Port
Beaver Harbor
Beaver- tail Light
Bee du Raz
Beda'a, Al
Bedford, Cape
Bees, St
Beeves Rocks
Beirut
Bel Air
Belfast
Bay
Belgrano
Belize
Bell Island
Rock, Scotland. .
Bellavista Cape
Belle Isle, France
Belle Isle, Labrador. . .
Bellingshausen Island.
Bellone, Cape
Ben Ghazi
Benbane Head . .
Page.
. 351
. 327
. 350
. 322
. 329
. 326
. 329
. 328
. 329
. 294
. 316
. 337
. 308
. 293
. 308
. 334
. 335
. 334
. 331
. 335
. 339
. 352
. 282
. 321
. 351
. 333
. 330
. 330
. 320
. 329
. 279
. 355
. 344
. 279
. 293
. 354
. 288
. 340
. 314
. 323
. 304
. 298
. 356
. 316
. 294
. 283
. 283
. 323
. 288
. 282
. 314
. 327
. 353
. 305
. 306
. 320
. 326
. 281
. 306
. 298
. 286
. 279
. 305
. 316
. 314
. 279
. 348
. 326
. 321
. 306
PLACES — continued.
Page.
Bender Erekli 320
Benedicto, San, Island 291
Benevente 297
Benguela 322
Benicia 289
Benidonne 315
Benin River 322
Benito, San, Island 290
Benkulen 330
Bento, San, River 322
Benzert 321
Bequia Island 295
Berbera 324
Berdiansk 320
Bergen, Germany 311
Norway 308
Berikat 331
Bering, Cape 342
Island 341
Berlanga Island 315
Berlin :.. 311
Bermeja Head 298
Bermudas 303
BernalChico 285
Bernardo Islands 348
Berwick 305
Besuki 331
Betrapar Islet 325
Beverly 282
Beyt 328
Bhaunagar 328
Bianche Point 318
Biarritz 314
Bickerton Island 351
Bideford 304
Bidstone 305
Bierneborg 309
Bigar Islet 343
Bikini Islands 343
Bilbao 314
Bille, Cape 356
Billiton Island 331
Bindloe Island 342
Bintang Hill 330
Bintoean 330
Bird Island, Australia 353
Bahamas 292
BandaSea 332
N. Pacific 344
Seychelle Islands. 325
Tuamotu Arch. . . 349
W. Africa 321
Islands 323
Birneys Island 345
Bismarck, Cape 356
Bittern Rocks 340
Bjuroklubb 309
Blaabjerg 312
BlackHead 279
Point Bay 322
Stairs Mountain 307
Blackness 305
Blacksod Point 306
Blair, Port
Blaize, St 323
Blanco Cape, N., Africa 321
Oregon 289
Peru 302
Africa 321
Peak... . 287
Page.
Blankenberghe 313
Bias, San, Argentina 298
Cape, Florida. ... 284
Mexico 291
Blasket Islands 306
Bligh Island 349
BlighsCape 327
Blimbing Bay 330
Blinyu 331
Block Island 282
Bloody Foreland 306
Bluefields 286
Bluff Harbor 355
Boar Islands 280
Boavista Island 303
Bobara Rock 318
BocaadelToro 287
Bodie Island 283
Bogense 312
Bogsher 309
Bohol Island 335
Bojador, Cape 321
Bojeador, Cape 334
Bola-Bola Island 349
Bom Abrigo Islet 297
Bombay 328
Bon, Cape 321
Point 330
Bona 321
Bonacca Island 286
Bonaire Island 295
Bona venture Head 279
Island 280
Bonavista Cape 279
Bongao Island 336
Bonham Islands 343
Bonifacio 316
Bonin Islands 345
Boobjerg 312
Booby Island, Leeward Is. . 294
Queensland 353
Boompjeo Island 331
Boon Island 282
Borda, Cape 352
Bordeaux. 314
Bordelaise Island 343
BorjaBay 299
Bornholm 312
Borodino Islands 345
Boscawen Island 348
"Bosphorus 320
Boston 282
Botel Tobago Sima 338
Bougainville, Cape 351
Island 346
Bougaroni, Cape 321
Boulogne 313
Bounty Islands 350
Bourbon,, Cape 327
Bouro Island 332
Bouton Island 333
Bouvets Island 304
Bowditch Islet 345
Bowen, Port, Australia 353
BaffinsBay 355
Bowling Green, Cape 353
BoyannaBay 326
BradoreBay 280
Brala, Pulo 336
Bras, Pulo 330
Page 362]
INDEX TO APPENDIX IV.
Page.
Brass River 322
Brava Island, C. Verde Is. . 303
E. Africa 324
Brazos Santiago 284
Bray Head 307
Breaker Point 337
Bremerhaven 311
Bremerton 289
Brest 314
Brewers Lagoon 286
Bridgeport 283
Brielle 313
Brill Reef 332
Brindisi 317
Brisbane 353
Bristol, England 304
Rhode Island 282
Britannia Island 350
Broadhaven 306
Broken Bay 352
Bronnosund 307
Brothers Island, Red Sea. . 324
Islets, China 337
Broughton Bay 338
Head 339
Island 341
Rock 340
Brunet Island 280
Bnini River 333
Brunswick, Georgia 283
Maine 282
Bruny, Cape 354
Island 354
Brussels 313
Brusterort 310
Bryer Island 281
Bubuan Island 336
Bucas Island 335
Buchanness 305
Buddonness 305
Budrum 320
Buliluyan, Cape 333
Budua 318
Buenaventura 302
San 289
Buenos Ayres 298
Bugui Point 335
Buitenzorg 331
Buka Island 346
Bulipongpong Island 336
Bulk...?. 311
Bull Harbor 288
Rock 306
Bullock Bay 341
Burg 311
Burghaz 320
Burias Island 335
Burin Harbor 279
Burnett River 353
Burntcoat Head 281
Burrh Island 343
Busios 297
Islets 297
Bustard Head 353
Busuanga Island 334
Biisum 311
Butt of Lewis 305
Button Islands 279
Byam Marti n Island 349
Byron Island 342
PLACES — continued.
Page.
Caballo Island 334
Cabeceira, Cape 323
CabezadeVaca 300
Cabrera Island 316
Cabron Cape 293
Cabrut Islet 325
Cadaques 315
Cadiz 315
Cadmus Island 349
Caen 313
Cagayan Jolo Island 336
Cagayanes Islands 336
Cagliari 316
Caicara 296
Caicos Island 292
West, Cay 292
Calaan, Point 335
Calais, France 313
Maine 281
Calavite, Monte 334
Calayan Island 334
Calbuco 300
Calcasieu Pass 284
Calcutta 329
Caldera 300
Caldy Island 304
Calebar River, New 322
Old 322
Caledonia Harbor 287
CalfofMan 305
Calicut 328
Calimere Point 329
Callao 301
Calpe 315
Caluya Island 334
Calvi 316
Camamu 296
Camaron Cape 286
Camasusu Island 335
Cambay 328
Cambria 297
Cambridge, England 304
United States 282
Camiguin Island, Luzon.... 334
; — Mindanao 336
Cammin 310
Campbell, Cape 355
Island 350
Campeche 285
Campobello Island 281
Canaria, Gran, Island 303
Canaveral Cape 284
Cancun Island 285
Candia Island 319
Candon 334
Cannes 316
Cannonier Point 325
Canoas Point 290
Canso, Cape 281
North 281
Canton 337
Island 345
Pulo 336
Can tyre 305
CapeHaitien 293
Cape Town 323
Cape Verde Islands 303
Capel Island 307
Caped'Istria 317
Capones Islet 334
Page.
Capraia Island 316
Caprera Island 316
Capri Island 317
Capricorn, Cape 353
Car Nicobar 330
Carabane 321
Carabao Island 335
Caraques Bay 302
Carataska Lagoon 286
Caravellas 297
Carbon, Cape 321
Carbonera Cape 316
Cardamum Islet. 325
Cardenas 293
Cardiff 304
Careys Islands 355
Cargados Carajos 325
Caribana Point 295
Carimare Mountain 296
Carimata Island 331
Carlingf ord Lough 307
Carlobago 318
Carloforte 316
Carlos, San £00
Point 290
Carmen Island 285
Caroline Islands, N. Pacific. 343
S. Pacific 345
Carousel Island 280
Carreta Mountain 301
Point 287
Carreto, Port 287
Carrizal, Port 300
Cartagena, Colombia 295
Spain 315
Cartago Mountain 286
CarteretCape 313
Harbor 346
Cartwright Harbor 279
Carupano 295
Carysfort Island 349
Reef 284
Cascade Point 355
Casilda 293
Casquets Rocks 313
Cassini Island 351
Castillos 298
Castle Island 292
Castlehaven 306
Castro 300
Urdiales 314
Cat Island 284
Catalina Harbor 279
Sta., Island 289
Catanduanes Islands 335
Catania 317
Catastrophe, Cape 352
Catbalogan 335
Catharine Point 299
St 304
Catherina, Sta. , Island 297
Cato Island 347
CatocheCape 285
Cattaro 318>
Cavite 334
Caxones 286
Cayenne 290
Cayeux 313
Caymans 293
Cazza Island 318
INDEX TO APPENDIX IV.
[Page 363
Page.
Ceara 296
Cebu Island 335
Cedar Keys 284
Cedeira 314
Ceicer de Mer Island 337
Celebes 333
Centinela Islet 295
Ceram Island 332
Cerros Island 290
Cestos 322
Cette 316
Ceuta 321
Ceylon 329
Chacachacare Island 296
Chacopata 295
ChagosArch 325
Chagres 287
Chahbar Bay 328
Chala Point. 301
Chaleur Bay 280
Challenger, Cape 327
ChamaBay 322
Cham-Callao Island 336
Chame, Point 291
Chamisso Island 287
Champerico 291
ChanaralBay 330
Island/ 300
Chandeleur Islands 284
Chao Islet 301
Chapel Island 337
Chapu 338
Charles Cape 283
Island, Chile 299
Galapagos Group. 342
Hudson Strait 279
Charleston 283
Charlottetown 280
Chateau Bay 280
Chatham Harbor 282
Island, Galapagos
Group 342
S. Pacific 350
ChatteCape 280
Chaume, La 314
Chausey Islands 313
Chedubah Island 329
Chemulpo 339
Chentabun River 336
Chepillo Island 291
Cherbourg 313
Cheribon 331
Cherso 317
Chicarene Point 291
Chidleigh Cape 279
Chifoo 338
Chignecto Cape 281
Chignik Bay 288
Chilca Point 301
Chimba Bay 301
Chimbote 301
Chincha Islands 301
Chinchin Harbor 337
Chinchorro Bank 285
Chin-hai 338
ChinoBay 337
Chirambiri Point 302
Chirikof Island 288
Chiriqui Lagoon 287
Chirivico... . 293
PLACES — continued.
Page.
Chitlac Islet 325
Chittagong River 329
Choda Island 339
Choiseul Island 346
Port 326
Chores Islands 300
Christiana Islands 319
Christiania 308
Christianshaab 356
Christianso Island 372
Christianssand 308
Christiansund 307
Christmas Cove 299
Harbor 327
I., Indian Ocean 327
N. Pacific 342
Christopher, St 294
Chuapa River 300
Chuluwan Island 323
Chupat River 298
Churruca, Port 299
Chusan Islands 338
Claris Island 291
Cica, Mount 318
Cienfuegos 293
Ciotat 316
Cispata, Port 295
Citta Nuova 317
Civita Vecchia 316
Clara, Sta 289
Clare Island 306
Claremont Point 353
Clarence Harbor, Bahamas. 292
Port, Alaska 287
River 352
Clarion Island 291
Claushavn 356
Clear Cape 306
Clearwater Point 280
Clerke Island 349
Clermont Tonnere Island. . . 349
Cleveland, Cape 353
Clew Bay 306
ClifdenBay 306
Clipperton Island, Mexico. . 291
N. Pacific... . 344
Clonard, Cape 339
Coast Castle, Cape 322
Cobija 301
CobreBay 301
Cochin 328
Cockell Islet 351
Cockscomb Mountain 286
Coconada 329
Cocos Island, C. America. . . 291
N. Pacific £42
Cod, Cape 282
CoderaCape 295
Codfish Island 355
Codroy Island 280
Caetivy Island 326
Coffin Bay 352
Island, Madagascar 326
Nova Scotia 281
Cofre de Perote Mt 285
Coiba Island 291
Coimbra 315
Colberg 310
Colbert Islet 351
Coles Point 301
Page.
Colina Redonda 301
Colnett Bay 290
Colombo 329
Colon 287
Colonia 298
Colonna, Cape, Greece. . . 319
Italy 317
Columbia, Cape 355
Columbretes Islands 315
Columbus Island 287
Colville, Cape 354
Comau Inlet 300
Comandatuba 297
Commerson Isiand 346
Comorin, Cape 328
Comoro Island 326
Conceicao 297
Conception Island 292
Point.. . 289
Conde 296
Condor Cove 300
Condore Islands 337
Conducia 323
Conejo, El, Point 290
Coney Island 337
ConfitesCay 292
Congo River 322
Congrehoy Peak 286
Connetable Islet 296
Constantinople 320
Constitution Cove 301
Contas 296
Conte, Port 316
Contoy Island 285
Conway, Cape 353
Reef 350
Cook Cape 288
Mountain 353
Cooper, Port 355
Copenhagen 312
Copiapo 300
Copper Island 341
Coquet Island 305
Coquille Island 343
Coquimbo 300
Coral Island 297
Islet 297
Corcovado Volcano 300
Cordouan, Point 314
Corfu 319
Coringa Islands 347
Corinto 291
Cork, Ireland 307
Port, Staten Island. . . 298
Cormorant Island 288
Corn Islands 286
Cornwallis Islands 344
Port 329
Coro, Velade 295
Coromandel Harbor 354
Coronation Island 304
Corregidor Island 334
Corrientes, Cape, Argentina. 298
Colombia 302
Mexico 291
S. Africa 323
CorsariosBay 295
Corseulles, Port 313
Corso, Cape. 316
Mountain 299
Page 364]
INDEX TO APPENDIX IV.
Page.
Corti 316
Coruna 314
Corvo Island 302
Coelin 310
Cosmoledo Island 327
Cotinguiba 296
Cotrone 317
Coubre, Point de la 314
Courtown Cays 286
Coutances 313
Cove Rock 323
Cow Head 280
Coy Inlet 298
Cozumel Island 285
Cracker Bay 298
Crassok Point 331
Crawl Cay 287
Crescent City 289
Cretin, Cape 346
Creux, Cape 315
Cristoval, San, Island 346
Crocker Island 349
Croisic 314
Croix, St 294
Croker, Cape 351
Crooked Island 292
Crozet Islands 327
CnizCape 293
Sta., Brazil 297
California 289
Island 289
Islands, Philip
pines 335
S. Pacific.... 347
Luzon 334
Port 298
Cuad Basang Island 336
Cuba
Culebra 291
Culebrita Island 294
Culion Island 334
Cullera,Cape 315
Culver Point 352
Cumana 295
Cumberland Island 353
Cumshewa Harbor 288
Cupchi Point 337
Cupica Bay 302
Curacao Island 295
Little 295
Currimao 334
Currituck Beach 283
Curtis Island 353
Port 353
Curzola Island 318
Cuttyhunk Light 282
Cuvier, Cape 351
Island 354
Cuxhaven. 311
Cuyo Island 334
Cyprus 320
Daedalus Shoal 324
Dago Island 310
Dairen Wan 338
Dakar, Port 321
Dalcahue 300
Dale Point 351
Dairy mple Harbor 336
Port... . 354
PLACE s — con tinued .
Page.
Dalupiri Island 334
Dame Marie, Cape 294
Damghot S27
Damma Island 332
Danger Islands 348
Dangerous Rock 337
Dannesbrog Island 356
Danube River 320
Dantzig 310
Dapitan 336
Dardanelles 320
Dar el Beida, Cape 321
Dar-es-Salaam 324
Darien Harbor 291
Georgia, U. S 283
Darsserort 311
Darwin, Port 351
Dato Island 331
Datu, Point 330
Dauphin, Fort 326
Davao 335
Davey, Port 354
Davids, St., Island 303
De Freycinet Islets 351
DeKastri 341
De Peysters Island 345
Deadman Rock 280
Deception Island 304
Deimaniyeh 327
Delagoa Bay 323
Delgada Point 299
Delgado, Cape 324
Point 298
Demerara 296
Denia 315
Denis, St 326
Denison, Port 353
D'Entrecasteaux Islands... 347
Point 351
D'Urville Island 355
Point 346
Deseado, Cape 299
Desert, ML, Rock 281
Desertas 303
Desirade 294
Desire, Port 298
Desolation, Cape 298
DiaFjeld 357
Diamond Harbor 329
Point 330
Diedrichshagen 311
Diego Garcia 325
Ramirez Island 298
San 289
Cape 298
Dieppe 313
Digges Islands 279
Dimas 293
Dimasalasan, Port 334
Dinding Channel 329
Dingle Bay 306
Diomede Island 287
Direction, Cape 353
Island 331
Disappointment, Cape, Sib. 341
— Washington. 289
Discovery Harbor 355
Diseilsland 324
DiuHead 328
DixCove.. ... 322
Djabon, Point 330
Djambi 330
Djursten 309
Dnieper Bay 320
Doc Can Islet 336
Dodd Island 337
Dog Island 294
Domar, Pulo 331
Demesnes 310
Domingo, San, Point 290
St., Cay 292
Dominica 295
Donaghadee 306
Dondra Head 329
Donegal Bay 306
Double Island 329
Point 353
Peak Island 337
Douglass Rocks 345
Dounpatrick Head 306
Douvres Rocks 313
Dover Point 352
Drei Cap Peninsula 346
Drepano, Port 319
Drobak 308
Drogheda 307
Dromedary Mountain 352
Drummond Island 342
Dublin 307
Ducie Island 349
Duff Islands 347
Duke of Clarence Island 345
York I.,N. Britain. 346
S.Pac.. 346
Dulce Gulf 286
River 286
Dulcigno 318
Dumaguete 335
Dumaly Point 334
Dumford Point 323
Duncan Island 342
Dundee, Rock of 299
DundrumBay 307
Dungarvan 307
Dungeness 304
New 289
Point 299
Dunkerque. . 313
Dunnet Head , 305
Duperrey Islands 343
Duppel 311
Durazzo 318
Durnfprd, Port 324
Dussejour, Cape 351
Dwarka 328
Eagle Island 306
Earakong Island 344
East Cape, Madagascar 326
New Zealand 354
_ Siberia 342
Dog Island 337
Island, Crozet Is 327
Magdalen Is 280
Easter Island 350
Eastport 281
Eau Island 343
Eauripik Islands 343
Ebon Atoll 343
INDEX TO APPENDIX IV.
[Page 365
Eckemforde
Eclipse Harbor
Islands
Eddystone
'Point
Eden Harbor
Edenshaw Cape
Edenton.
Edinburgh
Eeragh Island
Egedesmunde
Eggegrund Islet
Egmont Mountain
Port
Eimeo Island
Ekholm Islet
Elba Island
Elbing
Elena, St., Port
Sta., Point
Elephant Bay
Eleuthera Island
Elias, St., Mount
Elizabeth Bay
Cape
City
Harbor
Island, Chile
Tuamotu Arch
Port...
Elizabeth Reef
Ellice Islands
Emden
Emu Bay
Enanger
Endelave Island
Enderbury Island
Enderby Island
Endermo
Enfant Perdu Island.
Engano, Cape
Engano, Cape
Engano Island
Engelholm
English Cay
Eniwetok Islands. . . .
Enrage", Cape
Ensenada
Entry Island
Erromango Island
Erronan Island
Escarceo Point, Phil.
, Venezuela
Eschholtz Islands
Escondido, Port. ^
Escudo de Veragua
Escumenac Point
Esdu Island
Esmeralda Islet
River
Espada Point, Colombia.
Espenberg, Cape
Esperanza Inlet
Espiritu Santo Bay
Cape
Esquimalt
Essington, Port
Estaca Point
Estangues Point
Estevan Point
Etches, Port
Is...
Page.
311
279
351
304
354
299
288
283
305
306
356
309
354
303
349
310
316
310
298
302
322
292
288
322
282
283
355
299
349
323
350
345
312
354
309
312
345
351
341
296
293
334
330
308
285
343
281
290
280
347
347
334
295
343
293
287
280
325
296
302
295
287
288
297
299
288
351
314
295
288
288
PLACE s — continued .
Page.
EtenHead 302
Eu, Pulo 331
Eureka 289
Euripo Strait 319
Europa Island 326
Eustatius, St 294
Evangelistas Island 209
Evaristo, San 290
Expedition Bay 341
Exuma, Great, Island 292
Faero Islands 302
Fair Isle Skroo 305
Fairy, Port 352
Faiu, W., Islet 343
Fakaofu Islet 345
Fakarana Island 349
Falkenberg 308
Falkland Islands 304
Falmouth, England 304
Jamaica 293
False, Cape 294
False Cape Horn 298
Point 329
Falster Island 312
Falsterbo 308
Famagusta 320
Famine, Port 299
Fanad Point 306
Fanning Island 342
Fano Island, Adriatic 319
Denmark 312
Farallon Islet 289
Faraulep Island 343
Farewell, Cape, Greenland. 356
New Zealand 355
Farina, Cape 321
Farisan Island 325
Farn Island 305
Faro Island, Sweden 309
of Messina 317
Farquhar Islands 326
FarrallRock 286
Farralon de Pajaros 344
Fartak, Ras 327
Fastnet Rock 306
Father Point 280
Fateizio Island 340
Fatu Hiva Island 345
Huku Island, Galapagos 342
Marquesas . . 345
Fatuna Island 348
Fayal Channel 302
Island 302
Fecamp 313
Felipe, San, Cays 293
Point 290
Felix, St., Island, Chile.... 300
-S. Pacific.... 350
Fenerive Point 326
Fermin Point 289
Fernandina 284
Fernando Noronha 303
Po Island 322
San, Cuba 292
River 285
Port, P. 1 334
Trinidad 296
Fe"rolle Pena., New 280
Ferro Island 303
Ferrol . 314
Page.
Fetouhouhou Island 345
Feys Island 343
Fidonisi Island 320
Figari Cape 316
Filzand Island 310
Finisterre, Cape 314
Firase Rocks 339
Fire Island 283
Firmin, San 290
Fischausen 310
Fish, Great, Bay 322
Little, Bay 322
Fiskernaes 356
Fitz Roy River 351
Fiume 317
Five Fathom Bank 283
Flamborough 305
Flamenco 300
Island 291
Rat Island 325
Flattery, Cape 289
Flensberg 311
Flesko, Cape 333
Flinders Island 352
Islands 353
River 353
Flint Island 345
Florence 316
Flores Island, Azores 302
Indian Arch 332
Uruguay 298
Florida Island 346
Flower Cove 280
Flushing 313
Fly River 346
Foerder Islet 308
Fo^o Island 303
Fohr 311
Foreland, North 304
South... . 304
Formicas Islands 302
Shoal 293
Formosa Island 338
Fornses 312
Forsmark 309
Forsyth Point 288
Forth Mountain 307
Fortune Island 292
Foulwind, Cape 355
Four, Le, Rock 314
Fowey Rocks 284
Fowler Point 352
Frances, Cayo 292
Francis Island 342
St., Cape, C. Colony... 323
Newf 'dl 'd. . . 279
Francisco, San 289
Cape 302
Head.. .. 301
River 296
Sao 297
Frankland Island 353
Franklin Harbor 352
Franz Josef Land 356
Fraser River 289
FraileRock 294
Frayles Point 301
Frederick, Port 354
Frederik Hendrik, Cape. . . 354
Frederikshaab 356
Frederiksthal. . 356
Page 366]
INDEX TO APPENDIX IV.
Page.
Frederiksvaern 308
Fredriksten 308
FreelsCape 279
Frehel, Cape 313
Freikallen 307
Fremantle 351
French Cay 292
Frigate Shoal 344
Freycinet, De, Islets 351
Peninsula 354
Frio, Cape, Brazil 297
W.Africa 322
Port 297
Froward Cape. 299
Fruholm 307
Frying Pan Shoals 283
Fuenterrabia 314
Fuerta Ventura Island 303
Fuerte Island 295
Fuga Island 334
Fugle Huk 357
Fulanga Island 348
Fulehuk 308
Funafuti Island 345
Funk Island 279
Funkenhagen 310
Furen Islet 308
Fushiki 340
Futuna Island 347
GaalongBay... . 337
Gabo Island 352
Gabriel Mountain 306
Gaeta 316
Gafor Island 325
Galapagos Islands 342
Galera Point, Ecuador 302
Trinidad 206
Galgenberg 311
GaliolaRock 318
Galita Island 321
Gallant, Port 299
Galle, Point de 329
Gallegos River 298
Galley Head 307
Gallinas River 322
Gallipoli, Italy 317
Turkey 320
Galloway, Mull of 305
Galveston 284
Galway 306
Gambler Island 349
Gange 309
Gannet, Outer, Island 279
Rock 281
Gap Rock 337
Garcia d'Avila 296
Gardiner Island 344
Gardners I., Long Island... 232
S. Pacific 3-15
Garras, Little 330
Gaspar, Island and Strait. . 331
Rico Reef 344
Gasparilla Island 284
Gaspe Cape 280
Gata, Cape, Cyprus 320
de, Spain 315
Gaujam 329
Gay Head 282
Gebey Islands 333
PLACES — continued.
Page.
Geelong 352
Gene 309
Genoa 316
George, Fort, Cay 292
St., Cape, Florida 234
NewfdPd... 280
Nova Scotia. 281
Island, Alaska. . . 287
Azores 302
Georges Island 290
St., Cay 285
Georgetown 283
Georgia, South, Island 304
Geronimo, San, Island 290
Geyser Reef 326
Gharib, Ras 324
Ghir, Cape 321
Gibara 292
Gibdo Island 335
Gibraltar 315
Giglio Island 316
Gijon 314
Gilbert Islands 342
Gillolo Island 333
Ginger Cay 292
Girgenti 317
Gizau 325
Gizo Island 346
Glas Island 305
Glasgow 305
Glashedy Island 306
Glenan Islands 314
Glorioso Islands 326
Gloucester Island, Aus 353
Tuamotu Arch. . . 349
Massachusetts 282
Glover Reef 285
Gnarp 309
Goa 328
Gobernadora 293
Godhavn 356
Godthaab 356
Goedereede 313
GolamHead 306
Gomenitza 319
Gomera Island 303
Gonaives 294
Gonave Island 294
Good Hope, Cape, Africa... 323
China 337
Island 348
Success Bay 208
Goose Island 352
Gopalpur 329
Goram Islands 332
GordaCay 236
Point 331
Gore, Port 335
Goree Island 321
Road 298
Gorgona Island 302
Goro Island 348
Gorontalo 333
Goto Island 339
Gottenburg 308
Gotfcland Island 309
Gough Island 303
Gozier Islet 294
Gozo Island 317
Gracias a Dios, Cape 286
Graciosa Island 302
Grado 317
Grand Manan Island 281
Port 325
Riband Island 316
Grande Point 301
Granitz 311
Granville 313
Grappler, Port 299
Grave, Point de 314
Gravelines 313
Gready Harbor 279
Great Bird Rock 280
Rock Head 286
Green, Cape 352
Island, Labrador 279
Newfoundland... 280
Nova Scotia. .... 281
Greenly Island 280
Greenspond Island 279
Greenwich 304
Island 343
Gregory, Cape 299
Port 351
Grenada 295
Grenville, Cape 353
Grey River 355
Greytown 286
Griefswald 311
Griefswalder Oie 311
Grim, Cape 354
Grimsey Norddranger 357
Grip 307
GrisNezCape 313
Groate Eylandt 351
Groix, Island de 314
Gross-Horst 310
Grouin du Cou, Point de. . . 314
Gruizza Rock 318
Gryto 307
Guadalcanal Island 346
Guadeloupe, L. California.. 290
West Indies 294
Guafo 1 300
Guaineco Islands 299
Guaira, La 295
Guaja Shima 339
Guam Island 344
Guana, Little, Cay 292
Guanape Islands 301
Guanica 294
Guantanamo 293
Guarapiri Islets 297
Guaratiba, Cape 297
Guardafui, Cape 324
Guascama Point 302
Guatulco, Port 291
Guayaquil 302
Guaymas 290
Guerande 314
Guerin Island 339
Guguan Island 344
Guimaras Island 335
Guiuan 335
Guldager 312
Gull Island, Little 282
Gullan, San, Island 301
Gun Cay 292
Gunong Api Island 332
Gutzlaff Island.. ... 338
INDEX TO APPENDIX IV.
[Page 367
Page.
GwadarBay 328
Gwatar Bay 328
Habana 293
Habibas Island 321
Hacha, Rio de la 295
Haddington, Port 338
Haedic Island 314
Haiun, Has 324
Hagenmeister Island 287
Hague, Cape la 313
• The 313
Haiduong 336
Haifong 336
Haifa 320
Hainan Island 337
Hai-yun-tan Island 338
Hakodate 341
Half Port Bay 299
Halfmoon Cay, Belize 285
Nicaragua 286
Halgan Island 350
Halifax 281
Halisuen, Port 314
Hall Island.... 343
Islands, Sir James. . . . 339
Halmahera 1 333
Halmstad 308
Hals 312
Halt Bay 299
Halten Island 307
Hamberg 308
Hamburg 311
Hamilton Island 303
Mountain 289
Port 339
Hammamet Bay 321
Hammerfest 307
Hampton 282
Hamrange 309
Hanalei 344
Hanfelah Bay 324
Hangklip, Cape 323
Hanjam Islet 328
Hannibal Isles 353
Hano Island 309
Hanoi 336
Hao Island 349
Haradsskar Islet 309
Haraiki Island 349
Harbor Grace 279
Harburg 311
Hardy, Sir C., Island 353
Harpe, La, Island 349
Harrison Cape 279
Hartlepool 305
Harvey, Port 288
Harwich 305
HatterasCape 283
Haustholm 312
Haute Island 281
Have, Cape la 281
Havre 313
Hawaii 344
Hayter Island 346
Heard Island 327
Hearts Content 279
HeaudeBrehat 313
Heawandu Island 325
Hecate Bay 288
PLACES — continued.
Page.
Hecate Cove 288
Hecla, Cape 355
Hed, Rasal 327
Hee-tah-doo Island 325
Hegadis Island 332
Heiligen Creutz 310
Hekkingen 307
Hela 310
Helena, St., Island 303
Helgoland 311
Heliers, St 307
Hellevoetsluis 313
Helliso 308
Hellyer Rocks 299
Helsinborg 308
Helsingfors 309
Helvick Head 307
Hendaye 314
Henderson Island 349
Henderville Island 342
Henlopen Cape 283
Henry Cape 283
Port 299
Heongsan, Port 338
Herald Cays 347
Hereheretue Island 349
Hermes, Cape 323
Hermit Island 346
Hermite Island 298
Herradura de Carrizal 300
Hervey Islets 350
Hesquiat Harbor 288
Hesselo Island 312
Hessenstein 311
Hestskjaer 308
Heve, Cape La 313
Hiaou Island 345
Hikueru Island 349
Hillswickness 305
Hilo... 344
Himmittee Island 325
Hinawar 328
Hiogo 340
Hirado No Seto 339
Hirtehals 312
Hiva-Oa Island 345
Hjelm Islet 312
Hjertholm 307
Hjoerringa Mountain 307
Hoa-pin-su Island 338
Hobart Town 354
Hodeidah Road 325
Hog Island, Indian Ocean. . 327
Virginia 283
Islands 286
Hogland Island 309
Hogolu Islands 343
Hogsty Reef 292
Hogufu Islands 343
HoheWeg 311
Hohenschonberg 311
Hokianga River 355
Hokitika 355
Holborne Islet 353
Hole-in-the-Wall 323
Hollo Island 308
Holmestrand 308
Holmogadd 309
Holsteinberg 356
Holvhead . 304
Page.
HonDau Island 336
HondeklipBay 323
Honfleur 313
Hongkong 337
Hon-M6 336
Honolulu 344
Hood Island 342
Lord, Island 349
Point, Australia 352
Port, Cape Breton I... 281
Hope Island 353
Hopedale Harbor 279
Hopes Advance, Cape 279
Hoppers Island 342
Horn, Cape 298
False Cape 298
Head 306
Island 284
Home Island 348
Hornelen Mountain 308
Horsens 312
Horten 308
Hospital Bight 286
Hougue, Cape La 313
Houtman Rocks 351
Howaiyuh 327
Howe, Cape, East 352
West 351
Lord, Island 348, 350
Islands 346
Sound 288
Howland Islands 342
Howth Peninsula 307
Huaheine Island 349
Huanchaco Point 301
Huarmey 301
Huasco 300
Hudiksvalls 309
Huelva 315
Hiigeberg 311
Hui-lang-san 337
Hull Island 350
Hulls Island 345
Hulu-shan Bay 338
Humber River 305
Humboldt 289
Humphrey Island 345
Hungwha Channel 337
Hunter Island, N. Hebrides 347
Tasmania 354
Hurds Island 342
Hurst Castle 304
Husum 311
Hvidingso 308
Iba 334
Ibayat Island 334
Ibbetson Island 343
Ibiza, Port 316
Icacos Point, Belize 286
Trinidad 296
Ichabo Island 322
Icy Cape 287
leraka 319
Ifalik Islands 343
Iglooik Island 355
Ignacio, San, Point 290
Iguape 297
Iki Sima 339
Ildefonso Islands. . . 298
61828°—
Page 368]
INDEX TO APPENDIX IV.
Page.
liha Grande 297
Ilheos 297
Ilo 301
Iloilo 335
Inaboye Saki 340
Inaccessible Island 303
Inagua Islands 292
Inch Keith Rocks 305
Indefatigable Island 342
Indian, Cape 342
Harbor 279
Head 353
— — Tickle 279
Indianola 284
Indio Point 298
Indispensable Reefs 346
Indrapura Point 330
Ingolfshofde 357
Ingolsf jeld 356
Inishboffia 306
Inishowen Head 306
Inishrahull 306
Inishturk Island 306
Iniue Island
Innamban Bay 323
Inscription, Cape 351
Investigator Strait 352
Ipswich 282
Iquape 297
Iquique 301
Ireland Island 303
Isaac, Great, Cay 291
Isabel, Cape 299
Island 346
Point 284
Isabella de Sagua 293
Isene 320
Isidro, San, Cape 299
Isla Grande 291
Island Harbor 288
May 301
Isle of Man 305
Isola 317
Isolette, Cape 327
Istria, Cape d' 317
Itacolomi Islet 297
Point 296
Itapacaroya Point 297
Itaparica 296
Itapemirim 297
Iturup Island 341
Ivigtuk 356
Iwo Shima 339
Iwo-sima. . . . 339
Jabwat Island 343
Jackson, Port 352
Jacksonville 284
Jacmel 294
Jacobshavn 356
Jaffa, Cape 352
Jago, St., Island 303
Jaguaribe River 296
Jaluit Island 343
Jamaica 293
James Island 342
St., Cape, C. China.... 336
Vancouver 1 . 288
Jan Mayen Island 357
JaraHead.. . 301
PLACES — continued.
Page.
Jarea ..................... 315
Jarvis Island .............. 345
JaskBay .................. 328
Java ...................... 331
- Head ................. 331
Jean, St., de Luz ........... 314
Jebel Zukur Island ......... 325
Jelaka, Pulo ................ 331
Jelalil ..................... 324
Jensen Nunatak ........... 356
Jeremie ................... 294
Jershoft ................... 310
Jervis Bay ................. 352
- Cape ......... t ....... 352
- Island ................. 342
Jesus Maria Island ......... 346
Jiddah ..................... 324
Jighinsk Island ........... . . 356
Johanna Island ............ 326
John, St., Cape, Newf'dPd. 279
--- Staten Island 298
-- Island ........... 294
Johns, St., Island, Red Sea. 324
-- New Brunswick. . 281
-- Newfoundland... 279
-- River ............ 284
Johnston Islands .......... 344
Jolo Islands ............... 336
Jomfruland ................. 308
Jona, St., Island ........... 341
Jos<§, San, California ........ 289
-- de Guatemala ____ 291
-- delCabo ......... 290
Joseph Henry, Cape ....... 355
Juan Fernandez Island ---- 350
- San ................... 294
-- Cape ............. 294
-- delSur ........... 291
-- Point ............ 285
-- Port, Peru ...... 301
--- Vancouver I. 288
- St., Bay .............. 295
Juanico, San, Point ....... 290
Juby, Cape ................. 321
Jucaro .................... 293
Judith Point ............... 282
Juggernath ................ 329
Jinst ...................... 312
Julian, San, Port ........... 298
- St., Island ............. 331
Julianshaab ............... 356
Juneau .................... 288
Jupiter Inlet .............. 284
Jura Island ................. 319
Juul, Cape ................ 356
Kabenda Bay 322
Kabul! Island 334
Kado Sima 341
Kagoshima 340
Kahoolawe Island 344
Kahrig Islet 328
Kaipara Harbor 355
Kais Islet 328
Kajartalik Islan d 356
Kakirouma 339
Kal Farun Islet 324
Kalboden Island 309
Kalibia.. . 321
Kalingapatam
Kallundborg
Kalpeni Islet
Kama Islands
Kamaishi
Kamaran Bay
Kambangan Island
Kambara Island
Kamchatka, Cape
Kanala, Port
Kanathea Island
Kandavu
Kandeliusa Island
Kangamint
Kangarssuk Havn
Kannanur
Kao Island
Kappeln
Kara Burnu, Cape
Karachi
Karafuto
Karajinski Island
Karimon Djawa Island.
Karlshamn
Karlskrona
Kaske
Kasm
Katakolo Bay
Kater Island
Katiagam
Katie Rock
Kauai Island
Kawhia Harbor
Keats, Port
Kee-lah Island
Keeling Islands
Keenapoussan Island . .
Keitum
Kelantan River
Kendall, Cape
Kent Island
Keppel Island
Kermadec Islands
Kertch
Ketoy Island
Key West
Kharig Islet
Kharim-Kotan Island..
Kheli
Khor Nohud
Nowarat
Fakan Bay
Ki Islands
Kiaochow Bay
Kiama Harbor
Kidnappers Cape
Kiefali, Cape
Kiel
Kiirun Ko
Kikai-jima
Kiliman :
KillineyHill
Killybegs
Kilwa Kisiwani
Kimbeedso Island
King George Sound
Island, Australia. .
Kings Island
Kingston
Kingstown
Kinkwosan Island . .
Page.
. 329
- 312
. 325
. 343
. 340
. 325
. 331
. 341
. 350
.. 348
. 347
. 319
. 356
. 356
. 328
. 350
. 311
. 320
. 328
. 341
.. 341
. 332
. 309
. 309
. 309
. 328
. 319
. 345
. 330
. 318
. 344
. 354
. 351
. 325
. 327
. 336
. 311
. 336
. 355
. 352
. 348
. 350
. 320
. 341
. 284
. 328
. 341
. 319
. 324
. 324
. 327
. 332
. 338
. 352
.''.354
338
339
323
307
306
323
325
351
352
349
293
307
340
INDEX TO APPENDIX IV.
[Page 369
Page.
Kinnsund 308
Kino Point 290
Kinsale 307
Kirkwall 305
Kisimayu Bay 324
Kiska Island 287
Kistna 329
Kiswere 324
Kittan Islet 325
Kjorge 312
Knocklane 306
Knockmealdown Mountain. 307
Knocknarea 306
KnoxBay 288
Cape 288
Knyena 323
Kobe 340
Kodiak Island 288
Koh Chang 336
Kong River 336
Krah Islet 336
Tang Rocks 336
Kokoun-tan Islands 339
Koksher 310
Kolding 312
Komba Island... 332
Kompas Mountain 308
Kongelab Islands 343
Komgsberg 310
Koniushi Island 287
Koppem 307
Koroni Anchorage 319
Korror Islands 344
Kos 320
Kosair, Arabia 327
-Red Sea.. 324
Kosime No Osima 339
Koster 308
Kottaringin Bay 333
Kovra Rythi Point 326
Kozu Shuna Mountain 340
Krakatoa Island 331
Krishna Shoal 329
Kroe 330
Kronberg 312
Kronstadt 310
Krusenstern Cape 287
Kub Kalat 328
Kuchino Shima 339
Kuchinotsu 339
Kuino 310
Kullen Point 308
Kumi Island 338
Kumpta 328
Kunashir Island 341
Kundapur 328
Kunfidah 324
Kuper Harbor 339
Port 288
Kuria Maria Islands 327
Kuro Sima 339
Kusakaki Jima 339
Kusrovie Rock 336
Kusterjeh 320
Kutpur 328
Kuweit 327
Kweshan Islands 338
Kyangle Islets 344
Kyuquot Sound 288
PLACES — continued.
Page.
Labuan Island 333
Labyrinth Head 298
La Caloma 293
Laccadive Islands 325
Lacepede Island 351
Lady Elliot Island 353
Frances, Port 326
Lagartos 285
Laghi, Cape 318
Lagoon Head 290
315
River 322
Lagosta Island 318
Lagostini Island 318
Lakemba Island 348
Lamaka 320
Lambayeque 302
Lambert, Cape 351
Lamo Bay 324
Lamock Island 337
Lampedusa Island 317
Lampong Bay 330
Lamyit Island 337
Landfall Island 299
Lands End 304
Landskrona 308
Landsort 309
Langanaes Point 357
Langeland Island 312
Langeoog 312
Langesund 308
Langford, Port 288
Langkuas Island 331
Langotangen 308
Langwarden 311
Lanzarote Island 303
La Paz 290
La Plata 298
Laruehuapi Cove 300
Lassa, Cape 333
Lassau 311
Latakia 320
Latouche Treville, Cape.... 351
Laun 279
Laurie Island 304
Laut, Pulo 333
Lavaca 284
Lavata 301
Lawrence, St., Island,
Alaska 287
Siberia 342
Laykan, Port 333
Laysan Island 344
Lazaref, Port 339
Lazaro, San, Cape 290
Leander Shoal 280
Leba 310
Lebu River 300
Leeuwin, Cape 351
Legendre Island 351
Leghorn 316
Lema Island 337
Lemnos Island 319
Lengua de Vaca Point 300
Lennox Cove 298
Leones Island 298
Leopold, Port 355
Lepar, Pulo 331
Le Pilier Island 314
Page.
L^preau Cape 281
Lerma 285
Lei-wick 305
Leschenault, Cape 351
Lesina Island 318
L'Etang Harbor 281
Leven Island 326
Port 326
River 354
L'Eye-que, Cape 351
Lewis, St., Cape 279
Leyden 312
Leyte Island 335
Lhou Reef 347
Liakhov Islands 356
Liancourt Rocks 339
Liant, Cape 336
Liao-ti-shan 338
Libau 310
Libertad, C. America 291
Mexico 290
Lifu Island 350
Lighthouse Rocks 288
Limerick 306
Limon, Port 286
Lincoln Island 337
Port 352
Lindesnes 308
Lindi River 324
Lindo, Port 320
Linga Island 330
Linguelta, Cape 318
Linosa Island. 317
Lipari Island 317
Lisbon 315
Lisburne Cape 287
Lisiansky Island 344
Lissa Island 318
List 311
Lister 308
Lith 324
Litkieh Island 343
Little Hope Island 281
Lituya Bay 288
Liverpool 305
Port 326
River 351
Livorno 316
Lizard Point ; . . . 304
Llico 300
Loa River 301
Loaf Island 346
Loango Bay 322
Lobito Point 322
Lobos Cay, Bahamas 292
Mexico 285
de Afuera Island 302
Tierra... 302
Island, Canaries 303
Uruguay 298
Point, N. Chile 301
S.Chile 301
Lodingen 307
Lofoten Island 307
Loggerhead Key 284
Loheiyah 325
Loma 'Point 289
Lomas Point 301
Lombata Island 332
Page 370]
INDEX TO APPENDIX IV.
Page.
Lombok Island 332
London, East 323
Londonderry 306
Cape 351
Long Island, Bahamas 292
United States 282
Looke", Port 326
Lookout Cape, N . Carolina . . 283
Point, Australia: 353
Maryland 283
Lopatka, Cape 341
Lopez, Cape 322
Lorenzo, San, Cape 302
Island 301
Loreto 290
Lorient 314
Loro, Mount 334
Lorstakken Mountain 308
Los, Isles do 321
Lota 300
Lots Wife Rock. 340
Lough Lame 306
Louis, Port, Falkland Is 304
Guadeloupe 294
Mauritius Island . 325
St 321
Louisburg 281
Louisiade Archipelago 347
Loune 312
Low Island 337
Port 300
Lowenorn, Cape 356
Lowestoft 305
Loyalty Islands 350
Lubang Island 334
Lucar, San 315
Lucas, San 290
Lucia, Santa 326
St 293
Cape 323
I., C.Verde Is... 303
Windward Is. 295
Lucipara Island 332
Lucipari Islands 331
Lucrecia Point 292
Lucrietta Island 318
Luis, San, Island 290
Luke Point 341
Lund 308
Lundy Island 304
Lunenburg 281
Lungo 309
Lupona Point 290
Lurio Bay 323
Lussin Piccolo 318
Luzon Island 334
Lyo Island 312
Maasin 335
Macahe" 297
Macao * 337
MacAskill Islands 343
Macauley Island 350
Maceio 296
Machias 281
— Island 281
Machikora 326
Mackenzie Islands 343
MacLeay Islets 351
Macquarie Harbor 354
Island 350
PLACES — continued .
Page.
Macquarie, Port 352
Macquereau Point 280
Madagascar 323
• Beef, Africa 323
— — Yucatan 285
Madame Island 281
Madanas Point 298
Madeira Island 303
Madras 329
Madryn, Port 298
Madura Island 331
Maestro de Campo Island.. 335
Mafamale Island 323
Mafia Island 324
Magadoxa 324
Magdalen Cape 280
— Islands 280
Magdalena Bay 290
River 295
Magnetic Pole 355
Magoari Cape 296
Mak Kundu Island 325
Mahanuru 326
Mah£ 328
Mahia Peninsula 354
Mahon, Port 316
Maiana Island 342
Maiden Rocks 306
Mairaira Point 334
Mait Island 324
Maitea Island 349
Maitencillo Cove 300
Majamba Bay 326
Majorca 316
Majunga 326
Majuro Islands 343
Makalleh Bay 327
Makarska 318
Makassar 333
Makatea Island 349
Makaua Island 324
Makemo Island 349
Makers Ledge, South 280
Makkian Island (Makjan I. ) . 333
Makongai Island 348
Makry 320
Mala Cape 291
Malabrigo Bay 301
Malaga 315
Malaita Island 346
Malakka 330
Malamocco 317
Malaspina, Port 298
Maiden Island 345
Maldonado, Mexico 291
— Uruguay 298
Mate Island 325
MalembaBay 322
MalinHead 306
Mallicollo Island 347
Malmo 308
Malo, St 313
Maloclab Islands 343
Maloren 309
Malpelo Island, Galapagos.. 342
Panama 291
Malpeque Bay 280
Malta 317
Mamuka Island 348
Manaar 329
Mana Sima. . 340
Manado Bay 333
Manao 340
Mana-watu River 354
Manda Roads 324
Mandarins Cap 337
Mandavi 328
Manfredonia 317
Mangaia Island 350
Mangalore 328
Mangaratiba 297
Mangareva Island 349
Mangarin Point 334
Mangarol 328
Mangles Point 302
Mango Island 348
Manila 334
Mano Island, Asia 332
— — • — — -Denmark 312
Manoel, Cape 321
Manroux 1 294
Manta Bay 302
Manua Island 348
Manukau Harbor 355
Manvers, Port 279
Manzanillo, Cuba 293
Manzanillo Bay, Mexico 291
— - Point, Haiti 293
Maracaibo 295
Maraki Island 342
Marambaya Island 297
Maranhao Island 296
Marble Island 355
Marblehead 282
Marcial, San, Point 290
Marcos, San, Island 290
Marcus Island 344
Mare Harbor 304
— - Island, California 289
S. Pacific 350
Maret Islets 351
Margaret Bay 281
Margate Head 322
Maria Island 349
Madre Island 291
— Port 293
— Sta., Cape, Portugal.. . 315
__ _ Uruguay ... 298
— Cove
— — • di Leuca, Cape. .
— — • Island, Azores...
— — Chile
— — S. Pacific.. .
, , Port
290
317
302
300
347
335
Marianas ". — . 344
Maricas Islands 297
Marie Galante 294
Marienleuchte 311
Mariguana Island 292
Marinduque Island 335
Marion Island 327
Maripipi Island 335
Maritime Island 317
Marjes Islets 295
Marjoribanks 339
Marks,St 284
Marlborough Island 342
Marmora Island 320
Marmorice 320
MaroReef 344
MaroniRiver 296
INDEX TO APPENDIX IV.
[Page 371
Page.
Marsala 317
Marseilles 316
Marshall 322
• Islands 343
Marstenen Islet 308
Marta, Sta 295
Martha, St., Cape 297
Martin de la Arena, San .... 314
Garcia Island 298
San, Island, L. Cal. . . . 290
St., I., Leeward Is 294
Vaz Rocks 303
Martinique 294
Martires, Los 343
Mania Island 349
Marutea Island 349
Mary Island 345
St., Bay 322
Cape, Madagascar. 326
Newfound
land.... 279
Nova Scotia. 281
• Reefs 280
Marys, St., Island 326
MarzoCape I. 302
Mas Afuera Island 350
Masbate Island 335
Masinloc 334
Masirah Island 327
Maskat 327
Massaua Harbor 324
Masset Harbor 288
Masulipatam 329
Matabella Islands 332
Matacong Island 321
Matagorda 284
Matahiva Island 349
Matamoras Cove- 300
Matana Island 341
Matanzas Peak 293
Matatane 326
Matelotas Islands 343
Matema Islands 347
Maternillos Point 292
Matinicus Rock 281
Matoya 340
Matthew Island 347
St., Island, Alaska ... 287
Burma 329
Siberia 342
Matthias, St., Island 346
Matu Sima 339
Matuku Island 348
Manger Cay 285
Maui Island 344
Mauki Island 350
Maunganui Harbo: . 354
Maupili Island 349
Mauritius 325
May, Cape 283
Island 305
Mayaguez 294
May 6 Mountain 296
Mayne Harbor 299
Mountain 300
Mayo Island 303
Mayotta Island 326
Maysi Cape 292
MayumbaBay 322
Mazarron . 315
PLACES — continued .
Page.
Mazatlan 291
Mazemba River 323
Mbega Island 348
Mchmga Bay 324
McKean Island 345
Mecate Mountain 285
Mednoi Island 341
Mega Island 330
Megalo Kaetron 319
Mehediah 321
MeiacoSima 338
Meiaco-sima Islands 339
Mejia Island 290
i Mekattina Islands 280
I Mel, Ilhado 297
Melbourne ". . . . 352
Meleda Island 318
Melinda 324
Melle, Cape 316
MsllishReef 347
MelmoreHead 306
Melo, Port 298
Melville, Cape, Balabac I . . 333
Queensland 353
Island, Australia 351
Barrows Strait. . . 355
Tuamotu Arch... 349
Memel 310
Memory Rock 292
Menali Island 330
Menchikof Cape 287
Mendocino Cape 289
Mendoza Island 337
Merbat 327
Mercy Harbor 299
Mergui 329
Mesa de Dona Maria 301
Messina 317
Mesurado, Cape 322
Meurka 323
Mew Islands 306
Mewstone Rock 354
Mexican Boundary 289
Mexico, City of 285
Mexillon Bay 301
Mexillones Mountain 301
Mezen 356
Miautao Island 338
Michael, St., Fort 287
Island 302
Michaeloff Island 348
Middleton Island 288
Midway Islands 344
Miguel, San, Island 289
Islands 336
Mikake Jima 340
Mikindini 324
Mikomoto Island 340
Mikura Jima 340
Milagro Cove 300
Milazzo 317
Mile Island. .. 355
Milford Sound 355
Milo Island 319
Min River 337
MinaBay, El 322
Minchinmadiva Mountain . . 300
Mindanao Island 335
Mindoro Island 334
Mine Head 307
Page.
Minerva Reefs 350
Minikoi Island 325
Mino Sima 341
Minorca 316
Minota Ledge 282
Minow 326
Minsener Sand 311
Mintok 331
Miramichi Bay 280
Misamis 336
Miscou Island 280
Miskito Cays 286
Mississippi River, mouth. . . 284
City 284
Misteriosa Bank 286
Mita Point 291
Mitchells Island 345
Mitho 336
Mitiero Island 350
Mitre Island 347
Mity leni Island 319
MizenHill 306
Moa Cayo, Port. 292
Island 332
Moala Island 348
Mobile 284
Mocha Island 300
Mocomoco Point 296
Modeste Island 339
Moeara Kompehi 330
Moen Island 312
Moerenhout Island 349
Mogador 321
Mohilla Island 326
Mojanga
Mokambo, Port 323
Mokatein 327
Mokha 325
Mokil Islands 343
Molle, Port 353
Mollendo, Port 301
Moller Port 287
Molloy 327
Molokai Islands 344
Molonta Peninsula 318
Moluk Island 325
Molukka Islands 333
Molyneux Bay 355
Sound 290
Mombasa 324
Mona Island 294
Monastir 321
Mondego, Cape 315
Monfalcone 317
Monhegan Island 281
Monomoy Point 282
Monrovia 322
Montagu Island 352
Montalivet Islands 351
Montauk Point 282
Monte Christo Islet 316
Monte Cristi 293
Montebello Island 351
Montego Bay 293
Montepio 285
Monterey 289
Monteverde Islands 343
Montevideo 298
Montravel Island 339
Montreal 280
Monte, Point de 280
Page 372]
INDEX TO APPE1TOIX IV.
Montserrat
Montt, Port
Monze, Cape
Mopelia Island
Morane Island
Morant Cays
Point
Morayva
Morecambe Bay
Moreno Mountain
Moresby, Port
Moreton, Cape
Morgan, Cape
Morjovetz Island
Morlaix
Morotiri Islands
Morris Jesup, Cape..
Morro Ayuca
de Sao Paulo
Petatlan
Solar
Mortlock Islands
Mota, Point
Motane Island
Mothe Island
Mothoni
Motu-ili Island
Motu-iti Island
Moudros
Moukon rushi Island.
Moulmein
River
Mount, Cape
Mourondava
Moville
Mozambique
Msimbati
Mugan Mwania
Mugeres Island ,
Muilcalpue Cove
Mukulaelae Island...
Muleje
Mulu Island
Mura Harbor
MuratHill
Murderers Bay
Murdock Point
Murundum Island
Mururoa Island
Muscat
Musendum, Ras
Mussel Bay
Mysole Island
Nachvack Bay.
Nafa-Kiang
Nagai Island...
Naian Island
Nain
Nairn Cay
Naitamba Island...
Naka no Shima
Nakkehooed
Nam-Dinh
Namki, Port
Namoluk Islands...
Namonuito Islands.
Nam-quan
Page.
. 249
. 300
. 328
. 348
. 349
. 293
. 293
. 315
. 305
. 301
. 346
. 353
. 323
. 356
. 313
. 350
. 356
. 291
. 296
. 291
. 301
. 343
. 293
. 345
. 348
. 319
. 345
. 349
. 319
. 341
. 329
. 329
. 322
. 326
. 306
. 323
. 324
. 324
. 285
. 300
. 345
. 290
. 332
. 340
. 324
. 326
. 353
. 337
. 349
. 327
. 327
. 299
. 332
. 279
. 339
. 287
. 339
. 348
. 279
. 292
. 348
. 339
. 312
. 336
. 338
. 343
. 343
. 337
PLACE s — continued.
Page.
Namu Island 343
Nanaimo 288
Nancowry Harbor 330
Nanka Island 331
Nanomea Island 345
Nanoose Harbor 288
Nansei Shoto 339
Nantes 314
Nantucket Island 282
Shoals 282
Naples 317
Napuka Island 349
Nar Foree Island 325
Naranjo, Port 292
Narendri Bay 326
Nargenlsland 310
Narva 310
Nasca Point 301
Nasparti Inlet 288
Nassau 292
Natal, Brazil 296
Port, Africa 323
Sumatra 330
Natashquan Point 280
Natuna Islands 331, 337
Naturaliste, Cape 351
Nauomaga Island 345
Navachista 291
Navalo, Port 314
Navarin 319
Cape 341
Navassa Island 294
Navesink Highlands 283
NavidadBank 292
Bay 291
Navire Bay 327
Naxos Island 319
Nazaire, St., Port 314
Necker Island 344
Needles Rocks 304
Negapatam 329
Negrais, Cape 329
Negro, Rio 298
Negros Island 335
Neill, Port 355
Nelson 355
Cape 352
Port 351
Nemuro 341
Neptune Isles 352
Nera Point 317
Netherland Island 345
Neunortalik 356
Neuwerk 311
Nevil Island 344
Neville, Port 288
Nevis 294
New Bank 285
Bedford 282
Britain 346
Caledonia 350
Guinea 346
Hanover 346
Haven 282
Hebrides 347
Ireland 346
London 282
Mecklenburg 346
Orleans... ... 284
Plymouth 354
Page.
NewPommern 346
South Orkneys 304
Shetland 304
Westminster 289
York 283
Newbern 283
Newburyport 282
Newcastle 352
Newchwang 338
Newfoundland 279
Newport, Ireland 306
-Rhode Island.. . 282
Newton Head, Great 307
Nezumi Jima 339
Ngatik Islands 343
Ngau Island 348
Nias Island 330
Nice 316
Nicholas, St., Island 303
Nicholson, Port 354
Nickerie River 296
Nicobar, Great, Island 330
Islands 330
San, Island 289
Nidingen Islet 308
Nieuport 313
Niewe Diep 313
Nihiru Island 349
Niigata 340
Nikalao, St., Island 319
Nikolaevsk 341
Nikolaia, St., Cape 341
Nikolaieff 320
Nikolo, St., Port 319
Nila Island 332
Nile River 320
Nimrod Sound 338
Nine-pin Rock 337
Ning-po 338
Nipe Bay 292
Niquero 293
Nitendi Island 347
Niua-fu 348
Niue Island 348
Niutao Island 345
No Sima Saki 340
Noir Island. . . ^ 299
Noir Moutier Island 314
Nolloth, Port 323
Nome Cape 287
Nonuti Island 342
Nootka Sound 288
Nord Koster Islands 308
Norderney 312
Norfolk 283
Island . . .350
Norman Cape 280
Norrkopings Inlopp 309
Norrsher Islet 309
Norrtelge 309
North Cape, Arctic Amer. . 355
Brazil 296
C. Breton 1 281
Iceland 357
New Zealand 354
Norway 307
Harbor 288
Island, Vancouver 288
Volcano Islands. . 345
Lord, Island 344
INDEX TO APPENDIX IV.
[Page 373
North Standing Creek . . .
Northumberland, Cape . .
Isles
Northwest Cape
Norwalk Island
Noshiaf Misaki
Said
NosiBe
Nossa Senhora do Deserto.
Notch Cape
Notsuke
Nottingham Island
Noumea
Noun, Cape
Nouvelle, Port
Nova Zembla
Novogorod, Port
Nuevitas, Port
Nuevo, Port
Nugget Point
Nui Island
Nuistad.
Nuka-Hivi
Nukufetau Island
Nukunau Island
Nuku-nono
Nukuor Islands
Nukutavake Island
Nukutipipi Island
Numba Island
Nunez River
Nunivak Island
Nurse Channel Cay. .
Nuyts Point
Ny Sukkertop
Nyborg
Nykjobing
Page.
. 286
. 352
. 353
. 351
. 283
. 341
. 341
. 326
. 297
. 299
. 341
. 279
. 350
. 321
. 316
. 356
. 341
. 292
. 291
. 355
. 345
. 309
. 345
. 345
. 342
. 345
. 343
349
. 349
. 323
. 321
. 287
. 292
. 351
. 356
. 312
. 312
Oahu
Oataf u Island
Oban
Obi Islands
Obi Major Island
Obispo Shoal
Obristadbroekke
Observation Island
Occasional Harbor
Ocean Island, N. Pacific.
S. Pacific
Ockseu Island
Ocracoke
Oddensby
Odenskholm
Odessa
Odia Islands
Oeno Island
Offer Wadham
Ogasawara Islands
Oho-sima
Okay ama, Port
Okhotsk
Oki Islands
Okishi Bay
Okso
Oland Island
Old Fort Island
Point Comfort
Providence
Oloai Islands
Oleron Island . . .
. 344
. 345
. 305
. 336
. 332
. 285
. 308
. 339
. 279
. 344
. 346
. 337
. 283
. 312
. 310
. 320
. 343
. 349
. 279
. 345
. 339
. 340
. 341
. 341
. 341
308
. 308
. 280
. 283
. 286
. 343
. 314
PLACE s — continued .
Page.
Olga, Port 341
Olimarao Islet 343
Olinda 296
OlipaRock 318
Oliutorski, Cape 341
Olivenca 297
Omapui Island 336
Omenak Island 356
Omo Island 312
Omoa 286
Omoi Saki 340
One Fathom Bank 329
Oneata Island 348
Onega 356
Ongea Levu Island 348
Ono Islands 348
Onoatoa Islands 342
06-Sima Harbor 340
Oparo Island 350
Opobo River 322
Oporto 314
Oraluk Island 343
Oran 321
Orange Cape, Brazil 296
Magellan Strait. . 299
Oranienbaum 310
Orchila Island 295
Oregrund 309
Orfordness 305
Orizaba Mountain 285
Orkney Islands 305
Ormarah 328
Ormoc 335
Ornbay Island 332
Oro No Sima 339
Oropesa Cape 315
OrskarRock 309
Oruba Island 295
Osaka 340
OsakiBay 340
Oscarsberg 308
Osnabrug 349
Ostend 313
Osthammar 309
Ostro Point 318
Otago Harbor 355
Otranto, Cape and Port 317
Ottawa 280
Otway, Cape 352
Port 299
Oune-Kotan Island 341
Ouro River 321
Ovalau Island 347
Owashi Bay 340
Oxford 304
Oxhoft 310
Paanopa Island 346
Pabellon de Pica 301
Pacasmayo 301
Padang 330
Tikar 333
Padaran, Cape 336
Padre, Port 292
Pagan Island 344
Pagonia, Port 319
Paimboeuf 314
Paix, Port 294
Pajaros Islets 300
Pak Chan River 329
Page.
Pakhoi 337
Pakonj idol Rock 318
PalamosBay 315
Palanog 335
Palawan Island 333
Palembang 330
Palerdta 291
Palermo 317
Port 318
Pali, Cape 318
Pallas Rocks 339
Palliser, Cape 354
Palm Islands 353
Palma Island 303
PalmasBay 297
Cape 322
Point 285
Palmerston, Cape 353
Islands 348
Palmyra Island 342
Palompon 335
PaloeBay 333
Pamaroong Island 333
Pamban Pass 328
Pampatar Island 295
Pan de Azucar Island 300
Panama 291
Panay Island 335
Pangituran 336
Panjang Island 336
PankPiahRock 337
Pantar Island 332
Papey Island 357
Paposo Road 301
Para 296
Paraca Bay 301
Paracel Islands 337
Parahiba River and Port. . . 296
Paramaribo. 296
Paranagua 297
Paranahiba River 296
Paraoa Island 349
Parati 297
Paredon Grande Cay 292
Parenga-renga 354
Parenzo 317
Parga. 319
Parida 291
Parinaa Point 302
Paris 313
Parker Cape 299
Pares Island 319
Parry Island 350
Panys Group 345
Pasado Cape 302
Pasages, Port 314
Pascagoula, East 284
Pasni 328
Passaro, Cape 317
Pasuruan 331
Patache Point 301
Patani, Tanjong 336
Paternoster Rocks 308
Paterson Inlet 355
Pato Island 296
Patuca River 286
Patos Island 290
Patras 319
Patrick, St. , Head 354
Patterson, Port 351
Page 374]
INDEX TO APPENDIX IV.
Page.
Paul, St., de Loando 322
Island, N. Amer. 281
Tuamotu 349
Reunion Island.. 326
Bocks 303
Pauls, St., Island 327
Paxo Island 319
Pay po ton Mountain 285
Pearce Point 351
Pearl and Hermes Reef 344
Cays 286
Pedra Blanca Bock 337
Branca 330
deGalha 321
Pedro Bank 293
San 290
Point 301
Port 300
Peel.:..;; 351
Island 345
Pegasus, Port 355
PeiHo.. 338
Pekalongan 331
yPelado Island 301
PelagosaBock 318
Peloro, Cape 317
PembaBay 323
| Pembroke Cape 304
Pena Point 296
Penang, Pulo 329
Penas Anchorage 291
Pendulum Islands 356
I Penguin Islands 327
Penha Grande 321
Peniche 315
Penmarch Bocks 314
Penrhyn Island 345
Pensacola 284
Pentland Skerries 305
Percy Isles 353
Perim Island, Africa 324
India 328
Pernambuco 296
Pernau 310
Peros Banhoa Islands 325
Perth 351
Peru Island 342
PerulaBay 291
Pescadores Islands, Asia, E.
coast 338
N. Pacific 343
Peru 301
Point 301
Pe-shan Islands 338
Petali Island 319
PetalidiBay 319
Peter, St., Port 313
Peterhof 310
Petersburg, St 310
Petersdorf 311
Petit Manan Island 281
Petite Terre 294
Petropavlovsk 341
Petropolis 297
Pha-li-du Island 325
Philadelphia 283
Philip Island 343
Philipp Broke, Cape 356
Philips Point 290
Phillip, Port 352
PLACES — continued .
Page.
Phillips Island 349
Phoenix Island 345
Pi 316
Pianosa Island 316
Pichidanqui 300
Pichilinque Bay 290
Pico Island 302
Pictou Harbor 281
Piedra Blanca 336
Piedras Blancas 289
Cay, Cuba, N. coast. . . 293
S. coast 293
Point 298
Pieman Biver 354
Pierre, St., Newf 'dl'd 280
B6unionl 326
Bock 331
Pietro di Nembo, St., Island 318
Pigeon Point 289
Pih-ki-shan Island 338
Pih-quan Peak 338
Pih-seang Island 337
Pikelot Island 343
Pililu Island 344
Pillau 310
Pillar, Cape, Chile 299
Tasmania 354
Pinaki Island 349
Pine, Cape 279
Pingelasp Islands 343
Ping-fong Island 337
Ping-hai Harbor 339
Pinnacle Islet 287
Pinos, Isla de 293
Pinos Point 289
Pique Bay 341
Piraeus 319
Pirano 317
Pisagua 301
Pisang 330
Pisco 301
Pitcairn Island 349
Pitea 309
Pitong Island 330
Pitre Point 294
Placentia Harbor 279
Point 286
Pladda Island 305
PlanaCay 292
PlanierBock 316
Plata, Isle 302
Platte Island 325
Playa Colorado 291
Maria, La 290
PardaCove 299
Pleasant Island 346
Plettenburg Bay 323
Plum Island 282
Plymouth, England 304
U.S 282
Poile, La, Bay 280
Pola 317
Sta., Bay 315
Polillo Island 335
Pollard Cove 299
Polloc 335
Polusuk Island 343
Pomo Bock 318
Ponafidin Island 340
Ponapi Island 343
Pond Mountain
Pondicherri
Ponga Biver
Ponza Islet
Poolbeg
Popa Island
Popof Island
Porcos Grande Islet. .
Porbandar
Ponnan
Poro musir Island
Poros Island
Port au Prince
- Montt
- of Spain
- Plata
- Boyal, Jamaica.
-- S. Carolina.
- Said
Portendik
Porthcurnow
Portland, Bay
- Cape
- England
- Maine
Porto Bello
- Bico ............
- Santo ............
- Seguro ...........
- Vecchio ..........
Portsmouth, England.
- U.S .............
Possession, Cape .......
- Island ............
Postilion Islands ......
Povorotnyi, Cape .....
Prado ................
Pratas Island ..........
Premeira Islands .....
Preservation Inlet ____
Prestenizza Point .....
Prevesa ..............
Pribilof Islands .......
Prince Edward Island.
- Edwards Islands .
Prince of Wales Cape .
--- Island .
- Begent Biver . . .
- Bupert Hbr .....
Princes Island ........
Proeste ..............
Progreso .............
Promontore Point . ___
Proti Passage ..........
Proven ...............
Providence ..........
- Island ............
- Port .............
Psara Island .........
Pucio Point ...........
Puerto Cabello .......
- Mexico .........
- Santo Bay ........
Puka-puka Island ____
Puka-ruha Island ....
Pulicat ..............
Pulkowa ..............
Pulpito Point ........
Page.
. 299
. 329
. 321
. 317
. 307
. 332
. 287
. 297
. 328
. 315
. 341
. 319
. 294
. 300
. 296
. 293
. 293
. 283
. 320
. 321
. 304
. 352
. 354
. 304
. 282
. 287
. 317
. 294
. 303
. 297
. 316
. 304
. 282
. 299
. 327
. 332
. 341
. 297
. 337
. 323
. 355
. 317
. 319
. 287
. 280
. 327
. 287
.. 353
. 279
. 351
. 288
. 322
. 312
. 285
. 317
. 319
. 356
. 282
. 343
. 342
. 319
. 335
. 295
. 285
. 295
. 349
. 349
. 329
. 310
. 290
INDEX TO APPENDIX IV.
[Page 375
Page.
Puna 302
Purdy Island 346
Putziger Heisternest 310
Pyramid Point 337
Pyramidal Rocks 331
Quaco, Cape 281
Quaebo River 322
Quebec 280
Queen Charlotte Island .... 349
Queenstown, Ireland 307
N.Zealand 355
Quelpart Island 339
Quemada Grande Island . . . 297
Quentin, San, Port 290
Querimba Islands 323
QueuleBay 300
Quilan, Cape 300
Quilca 301
Quilon 328
Quin Hon 336
Quiniluban Islet 334
Quintero Point 300
Quita Sueno Bank 286
Quod, Cape 299
QuoddyHead 281
Quoin Great, Island 327
Point 323
Race, Cape 279
Island 288
Rachado, Cape 330
Radakala Islands 343
Radama Islands 326
Port 326
Ragged Island 292
Ragusa Rocks, Pettini di. . . 318
Rakkin, Has. 327
Raleigh Rock, China 337
Formosa 338
Ramas, Cape 328
RameHead 323
Ramree Island 329
Rangiroa Island 349
Rangoon 329
River 329
Ranu Cove 300
Raoul Island
Rapa Island 350
RaperCape 299
Raphti, Port 319
Rarotonga Island 350
Rasa Island 345
Rathlin Island 306
O'Birne Island 306
Ratnagherry 328
Ravahere Island 349
Ravn Storo 356
Rawean Island 332
Ray Cape 280
Raza Island, Brazil 297
C. Verde Is 303
L. California 290
Razzoli Island 316
Re Island 314
Real River 296
Reao Island 349
Recherche Archipelago 352
Recife Cape 323
Red Islet. ....... .351
PLACES — continued.
I Page.
Redan?, Great, Harbor 336
Redfield Rocks 340
Redonda Islet 294
Redondo Rock 342
Reirson Island 345
Reitoru 349
Rembang 331
Remedies Bay 290
Renard Island 347
Islands 347
Rennel Island 346
Rensher 309
Repon, Pulo 331
Resolution Island 279
Reunion Island 326
Revel 310
Rey Island 291
Reyes Head 301
Point.. . 289
Reykianaes 357
Reykiavik 357
ReythurFjeld 357
Rhio 330
Rhodes, Port 320
Rhynns of Islay 305
Ribnitz 311
Rich Point 280
Richmond 283
River 353
Riga 310
Rigny Mount 356
Rimitara Island 350
Ringkjobin 312
Rio Grande del Norte 284
do Norte 296
Sul 297
Janeiro 297
Riofrio, Port 299
Risiri Islet 341
Rissnaes Point 357
Rivadeo 314
Rivadesella 314
Rivers, Cape 333
Rixhoft 310
Roa Poua Island 345
Roatan 286
Roberts Point 289
Roca, Cape 315
Partida, Mexico, E.
coast 285
W. coast 291
Rocas Reef 303
Rochefort 314
Rochelle 314
RockabiU 307
Rockall Islet 302
Rockingham Bay 353
Rockland 281
RoddBay 353
Rodkallen 309
Rodney, Cape 346
Rodoni, Cape 318
Rodriguez Island 325
Rodsher Island 309
Roeskilde 312
Rogosnizza 318
Rokugo, Cape 340
Rokuren Island 340
Roma Island 332
Remain, Cape 283
Page,
Roman, San, Cape 295
Romanzof Cape 287
Romanzov Islands 343
Romblon Island 335
! Rome 316
Ronaldsay, North 305
Roncador Cay 286
Rongerik Islands 343
Roodewal Bay 323
Roque, St., Cape 296
Roques Islands 295
Rosa, Sta. , Island 289
Rosalia, Sta., Bay 290
Rosalind Bank 286
Rosario Island 345
Rose Island 348
Spit Point 288
Rosemary Island 351
Rosier Cape 280
Ross Island 339
Rossel Island 347
Rostock 311
Rota Island 344
Rotterdam 313
Rotti Island 332
Rottnest Island 351
Rotumah Island 347
Round Island 338
Roundhill Island 279
Rovigno 317
RoxoCape 285
Royallsland 292
Royalist, Port 333
Ruad Island 320
Rugen\valde 310
Rum Cay 292
Runaway, Cape 354
Runo Island 310
Rupert Island 299
Rurutu Island 350
Ryvingen Island 308
Ryojun Ko 338
Saba 294
Sabine Pass 284
Sabioncello Peninsula 318
Sablayan Point 334
Sable Cape 281
Island 281
Sacatula River 291
Sacrificios Island 285
Point 291
Saddle Group 338
Island 279
Sado Island 340
Safajah Island 324
Safatu Island 337
Sagua, Isabello de
Saida 320
Saigon 336
Saintes Islands 294
Saipan Island 344
Sakai 340
Sakhalin Island 341
Sakishima Gun to 338
Sakonnet Point 282
SalCav 293
Island 303
Sala y Gomez 350
SaladoBay 300
Page 376]
INDEX TO APPENDIX IV.
Page.
Salayar Island 333
Saldanha Bay 323
Salem 282
Sail 321
Salina Cruz 291
Salinas Bay, C. America — 291
L. California 290
Point 294
Salisbury Island 279
Salomague Island 334
Salonika 319
Salovetski 356
Saltee, Great 307
Salut Islands 296
Salvador, San 292
Salvage Islands 303
Salvore Point 317
Sama, Port and Peak 292
Samana 293
Cay 292
Samanco Bay 301
Samar Island 335
Samarang 331
Sambro Island 281
Samoa Islands
Samos Island 320
Sampit Bay 333
Samso Island 312
Samsoe Island 312
San Bias, Gulf 287
Sand Island 284
Key 284
Sandakan Harbor 333
Sandalo, Cape 316
Sandalwood Island 332
Sandfly Cay 286
Sandhammaren 309
Sandwich Island 347
Islands 304
Sandy Cape 353
Hook 283
Point 299
SangwinRiver 322
Sanibel Island 284
Sankaty Head 282
Sannakh Island 287
Santa Cruz del Sur 293
Santander 314
River 285
Santiago Cape 299
de Chile 300
Cuba 293
Port 334
Santo Domingo City 294
Santona 314
Santos 297
Sao Joao da Barra 297
Saona Island 294
Sapelo Island 283
Saranguni Islands 335
Sarawak 333
River 333
Sariguan Island 344
Sarstoon River 286
Saru Island 332
Saseno Island 319
Satano Misaki 340
Satawal Island 343
Saugor Island 329
Sauguir Island 333
PLACE s — continued .
Page.
Sauh, Pulo 330
Saukhoum 320
Saunders, Port 280
SauoBay 338
Savage Island 348
Savaii Island. . 348
Savanilla 295
Savannah 283
Savanna-la-Mar 293
Saybrook 282
Scalp Mountain 306
Scarcies River 321
Scatari Island 281
Schama Mountain 301
Schanck, Cape 352
Schanz Island 343
Scharhorn 311
Scheveningen 313
Schillighorn 311
Schleimunde 311
Schleswig 311
Schonberg 311
Scilly Islands, England 304
S. Pacific 348
Scott Cape 288
Scutari 320
Sea Bear Bay 298
Rock 339
Seal Cays 286
• Island 281
Seao Island 333
Seattle 289
Sebastian, San, Cape,M'g'sc'r 326
Spain 314
St., Cape, S. Africa. ... 323
Island 297
Sebastopol 320
Sebenico 319
Sedano, Cape 331
Sedashigar Bay 328
Seguin Island 281
Sem, I. de 314
Sejro Island 312
Selatan Point. 333
Seldom-come-by Harbor 279
Semeny River 318
Semerara Island 334
SemiamooBay 289
Semione Island 331
Sentinel Island 339
Series Island 349
Sermata Island 332
Sermelik Fjord 356
Sermo Island 319
SerranaBank 286
Serranilla Bank 286
Seskar Islet 310
Setubal 315
SeuheliPar 325
Seven Heads 307
Seychelles 325
Sfax 321
Shag Rocks 304
Shahah 327
Shahr, Abu 328
Shaikh Shu'aib Islet 328
Shaluitien Island 308
Shanghai 338
Shannon River 306
Shantar Islands ... 341
Shantung
Sharjah
Shark Island
Shannon
Shaweishan Island...
Shelburne Harbor. . .
Shelter Bay
Shepherd Island
Sherbedat, Ras
Sherbro Island
River
Shenn Hassey
Joobbah
Rabegh
Wej
Yahar
Shetland Islands
Shiash-Kotan Island.
Shields, North
Shimizu Bay
Shimonoseki Strait. .
Shinnecock Bay
Ship Island
Shoal
Shipunski, Cape
ShirasuReef
Shoals, Isles of
Shoal water Cape
Island
Siargao Island
Siassi
Siberoet Island
Siboga
Sibuco Bay
Sibutu Island
Sibuyan Island
Sidmouth, Cape
Sierra Leone
Sighajik
Sigri, Port
Sihuatanejo Point...
Sihut
Silan
Silaqui Islet
Silver Bank
Simaloe Island
Simeonof Island
Simoda
Simon, St., Island...
Simonoff Island
Simonor Island
Simons Bay
Simpson, Port
Simusir Island
Singapore
Singkel Island
Singkep Island
Single Island
Singora (Sungkla) —
Sinon
Sinope
Siphano Island
Siquijor Island
Sink, Cape
Siriya Saki
Sisal
Sitka
Sittee Point
Skagataas Point ,
Skagi, Cape
Page.
. 338
. 327
. 346
. 327
. 338
. 281
. 341
. 287
. 327
. 322
. 322
. 324
. 324
. 324
. 324
. 324
. 305
. 341
. 305
. 340
. 340
. 283
. 284
. 284
. 341
. 340
. 282
. 289
. 331
. 335
. 336
. 330
. 330
. 335
. 336
. 335
. 353
.. 322
. 320
. 319
. 291
. 327
. 285
. 334
. 292
. 330
. 287
. 340
.. 283
. 348
. 336
. 323
. 288
. 341
. 330
. 330
. 330
. 337
. 336
. 322
. 320
. 319
,. 335
. 333
. 340
. 285
. 288
. 286
. 357
. 357
INDEX TO APPENDIX IV.
[Page 377
Page.
SkagsHead 309
Skaw, Cape 312
Skelligs Rocks 306
Skerries Rocks 305
Skerryvore Rocks 305
Skiathos Island 319
SkidegateBay 288
Skoorgaarde 311
Skumbi River 318
Skyring Mountain 298
Sligo Bay 306
SlyneHead 306
Smalls Rocks 304
Smerwick 306
Smith Island, Japan 340
Washington 289
Smyrna 320
Snaefells Yokul 357
Snares Islands 355
Socorro Island, Chile 300
Mexico 291
SoderSkars 309
Soderarm 309
Soderhamm 309
Sofala 323
Sohar 327
Sokotra Island 324
Sola Island 295
Solander Islands 355
Solitary Islands 352
Solombo, Great, Island 332
Solomon Islands 346
Solta Island 318
Sombrero 294
Key 284
Rock 336
Sommer Island 310
Song-yui Point 337
Sonserol Island 344
SooBay 338
Sorelle Rocks 318
Sorol Island 343
Sorrel Rock 337
Sorrell, Cape 354
Port 354
Sorsogon, Port 335
Soumsbu Island 341
Souwaroff Island 348
South Cape, Formosa 338
N. Guinea 346
Rock 306
Water Cay 286
Southampton 304
Southsea Castle 304
Southwest Cape 354
Reef 284
Spalato Passage 318
Port 318
Sparo Vestervik 309
Spartel, Cape 321
Spartivento Cape, Italy 317
Sardinia 316
Spencer, Cape 352
Spezzia 316
Spikeroog 312
Spiridione, St., Port 319
Spitzbergen 356
Spodsbjerg 312
Spurn Head 305
Square Handherchief Bank. 292
PLACES — continued.
Page.
StaabiergHuk 357
Stack, South 304
Stade 311
Stag Rocks 307
Stamp Harbor 288
Stampali Island 319
Stanley, Port 304
Starbuck Island 345
Start Point 304
Startpoint 305
Staten Island 298
Staunton Island 338
Stavanger 308
Steilacoom 289
Steinkirchen. 311
Stemshesten 308
StensherRock 310
Stephens, Port 352
Stettin 310
Stewart, Cape 351
Stewart Islands 346
Stirrup Cays 292
Stirsudden 310
Stockholm 309
Stonington 282
Stopelmiinde 310
Stora 321
Stornoway 305
Stot 307
Stralsund 311
Strati Island 319
Straumness Point 357
Streaker Bay 352
Streckelsberg 311
Strogonof Cape 288
Stromstad 308
Stromtangen 308
Strong Island 343
Strovathi Island 319
Stuart Island 287
Suakin 324
Sual 334
Subic 334
Succadana 333
Suda, Port 319
Sueik 327
Suez 324
Suffren, Cape 341
Sugar Loaf Point 352
Sughrah 327
Suk Island 343
Sula Islands 332
Sulphur Island 345
Sumbawa Island 332
Sumburgh Head 305
Sunda Strait 331
Sunday Island 350
Sunderland 305
Sundsvall 309
Sunmiyani 328
Supe 301
Sur 320
Surabaya 331
Surat 328
River -328
Surigao 335
Surop 310
Susaki : 340
SuwanoseJima 339
Suwarro w Island 348
Page.
Svalferort Tzerel 310
Svartklubben 309
Svendborg. 312
Svenor 308
Sviatoi Nos 356
Svinoen 308
Swallow Bay 299
Islands 347
Swan Islands 286
Swansea 304
Swatow 337
Sweers Island 353
Swinemunde 310
SybilloBay 341
Sydenham Island 342
Sydney, Australia 352
Harbor, C. Breton I. . . 281
Synesvarde Mountain 308
Syra 319
Syracuse 317
Tabaco 335
Tabasco River. 285
Tabertness 305
Tablas Island 335
Point 300
Table Bay 323
Head 279
Island 329
Taboga Island 291
Tabou River 322
Tacloban 335
Tacoma 289
Tacorady Bay 322
Tae Islands 337
Tagulanda Island 333
Tahiti 349
Tahoa Island 349
Tahuata Island 345
Taiaro Island 349
Tai-pin-san 338
Tajer, Port 318
Taka Yama 341
Takapoto Island 349
Takau 338
Takhkona Point 310
Talabo, Cape 333
Talcahuano 300
Talinay Mountain 300
Taltal, Port 301
Taluat Island 333
Tamana Island 342
Tamandare 296
TamarPort 299
Tamatave 326
Tambelan Island 331
Tampa Bay 284
Tampat Toewon Point 330
Tampico 285
Tamsui Harbor 338
Tanabe Bay 340
Tancook Island 281
TangaBay 324
Tangier 321
Tanjong Ban-am 333
Datu 333
Mangkalihat 333
Pandan 331
Patani 336
Tanna Island 347
Page 378]
INDEX TO APPENDIX IV.
Page.
Tantang, Port 326
Taoiunu 348
Taormina Cape 317
Tapua Island 347
Tapul Island 336
Taputeuea 342
TaraHill 307
Taranto 317
Tarawa Island 342
Tarbertness 305
Tarifa 315
Taritari Island 342
Tarpaulin Cove 282
Tarragona 315
Tas de Foin Islet 339
Tatakoto 349
TatsupiSaki 340
Tauere Island 349
Tauranga Harbor 354
Tauzon, Cape 326
Tavolara Cape 316
Tavoy River 329
TaytaoCape 300
TaytayFort 333
Tchesme" 320
Tchoukotskoi, Cape 342
Tegal 331
Tenor Island 332
Tellicherri 328
Tello Islands 332
Tematangi Island 349
Tenasserim 329
Tenedos Island 320
Teneriff e Island 303
Tenez, Cape 321
TepocaCape 290
Tepoto Island 349
Tequepa 291
Terceira Island 302
Teresa, Sta., Bay 290
Terkolei 330
Terminos Lagoon 285
Ternate Island 333
Terstenik Rock 318
Testa, Cape 316
Testigos Islets 295
Tewaewae Bay 355
Thabi, Abu 327
Thank God Harbor 356
Thermia Island 319
Thikombia Island 348
Thithia Island 348
Thomas, St., I., B. of Biafra 322
West Indies. 294
Thome", St., Cape 297
Thorton Haven 338
Three Kings Islands 354
Points Cape, Africa. . . 322
Argentina... 298
Honduras... 286
Ti-ao-usu Island 338
Tiburon Island 290
Tiegenort 310
Tien-pak 337
Tientsin 338
Tilly Bay 299
Timbalier Island 284
Timor Island 332
Laut Island.. . 332
Tinakula Island 347
Tinian Island .344
PLACE s — continued .
Page.
Tintolo Point 335
Tirby Point 287
Tiruchendore 328
Toass Island 343
Toau 349
Tobago 295
Tobi Shima 340
TobolAli 331
Tocopilla 301
Todos Santos 290
To-du Island 325
Tofua Island 350
Tokara Jima 339
Tokelau Islands 345
Token Bessi Island 332
Tokio 340
Tolaga Bay 354
Tolkemit 310
Tomas, San 290
Tomo Roads 340
Tongarewa Island 345
Tonga tabu Island 350
Tongka Harbor 329
Tongoi 300
Tong-sang Harbor 337
Tong-ting Islet 338
Tonning 311
Topolobampo 291
Tor 324
Torbjornskjaer 308
Tordenskjold, Cape 356
Torgauten -308
ToriwiSaki 340
Tornea 309
Toro Point 287
Torres Island 347
Point 297
Port 316
Tortola 294
Tortosa, Cape 315
Tortugas Island 295
Tory Hill 307
Island 306
Tosco Cape 290
Totoya Island 348
Toulinguet Islands 279
Toulon 316
TouraneBay 336
Towers Island 342
Townsend, Port 289
Traenen 307
Trafalgar, Cape 315
TraleeBay 306
Trani 318
Trapani 317
Travemunde 311
Travers Islands 353
Treasury Islands 346
Trebizond 320
Tregosse Islands 347
Trelleborg 309
Tremiti Islands 317
Trepassey Harbor 279
Tres Montes Cape 299
— - Puntas Cape, Chile.... 299
Venezuela. . . 296
Trevose Head 304
Triangles 285
Tribulation, Cape 353
Trieste 317
Trincomali.. . 329
Tringano River 336
Trinidad Head 289
Island 303
Tripoli, Africa 321
Turkey 320
Tristan da Cunha 303
Triton Bay 346
Island . 337
Triunfo Cape 286
Trivandrum 328
Trobriand Islands 347
Tromelin Island, Caroline Is. 343
Indian Ocean 326
Tromso 307
Trondheim 307
Troon 305
Truxillo 286
Tsau-liang-hai 339
Techeljuskin, Cape 356
Tsmano 326
TsuSima 339
Tsukarase Rocks 340
Teuruga 340
Tuanske Island 349
Tubai Island 349
Tubuai Islands 350
Tubuai-Manu Island 349
Tucacas Island 295
Tuckers Beach 283
Tukume Island 349
Tully Mountain 306
Tumaco 302
Tumbez 302
Tung-chuh Island 338
Tung-yung Islands 337
Tuni-ang Island 337
Tunis 321
Tuno Island 312
Tupilco River 285
Tureia Island 349
Turk Island 292
Turnabout Island 337
Turo Island 312
Turtle Island 348
Isles 351
Tuskar Rock 307
Tuticorin 328
Tutoya 296
Tutuila Island 348
Tuvutha Island 348
Tuxpam Reefs 285
Tuxtla Volcano 285
Twelve Islands 327
Twofold Bay 352
Tybee Island 283
Ty-fung-kyoh Island 337
Tynemouth 305
Ua-Huka Island 345
Ualan Island 343
Ubatuba 297
Uea Island 348
Ujelang Island 343
Uii Shima.. . 340
Uj
Ul
eaborg 309
Ulietea Island 349
Ulko Kalla Rock 309
Ulladulla 352
Ulsire 308
Uluthi Islands 343
Umea 309
INDEX TO APPENDIX IV.
[Page 379
PLACES — continued.
Una
Unalaska Island. .
Unare Bay
Underut Islet
Underwood, Port.
Unga Island
Unie Island
Union Bay
Islands
• Port de la...
Unsang
Upernivik
Upright Port
Upsala
Upulo Islands
Uragami
Urracas Islands..
Urup Island ,
Usborne, Port
Usedom ,
Ushant
Ustica Island
Ute Islet
Utilla Island
Utrecht
Uvea Island..
Page.
. 297
. 287
. 296
. 325
. 355
. 287
. 318
. 298
. 345
. 291
. 333
. 356
. 299
. 309
. 348
. 340
. 344
. 341
. 351
. 311
. 313
. 317
. 309
. 286
. 313
. 350
Verd Cay, Bahamas
Cuba
Vicente, San, Cape.
Port
Page.
. 292
. 292
. 299
. 334
Vadso
Vahanga Island
Vahitahi Island
Vaitupu Island
Valdes Island
Valdivia
Valencia
Valentia
Valentine Harbor. . .
St., Cape
Valery en Caux, St. .
Valiente Peak
Valientes Islands
Valparaiso
Vanavana Island
Vancouver
Vanikoro
Vannes
Vanua Lava Island. .
Levu Island
Mbalavu Island
Vardo
Varella Cape
Pulo
Varna Bay
Vat6 Island
Vathi, Port
Vatiu Island
Vatoa Island
Vatu Lele Island
Vara Island
Vavau Island
Vavitoa Island
Vaza Barris River. . .
Veglia
Veiro Island
Vela, La, Cape
Venangue Be Bay. . .
Vendres, Port
Venice
Ver, Point de
Vera Cruz
Verde Cape
307
349
349
345
288
300
315
306
299
299
313
287
343
300
349
289
347
314
347
348
348
307
336
336
320
347
31d
350
348
347
348
350
350
296
317
312
295
326
316
317
313
285
321
Victor, Port 352
Victoria 288
Harbor 355
Port, Australia 352
Seychelle Islands. 325
River 351
Victory Cape 299
Island 331
Vidal, Cape 323
Video Island 338
VieborgBay 310
Vieques Island 294
Vieste 317
Vigan 334
Vigo 314
Villa 307
Nova da Princessa. . . . 297
Villajoyose 315
Villefranche 316
Vinaroz 315
Vincent. San, de la Barquera 314
St. Cape, Chili 299
Madagascar . 326
Portugal 315
I., C.Verde Is... 303
' Windward Is. 295
Bay, S. Pacific ... 350
Vineyard Haven 282
Vingorla 328
Rocks 328
Virgin Gorda 294
Virgins, Cape 298
VitiLevu 348
Vizagapatam 329
Viziadrug 328
Vladimir, St., Bay 341
Vladivostok 341
Vliko, Port 319
Vohemar 326
Vojazza River 318
Volcano Island, West 338
Islands 345
Volta River 322
Voltaire, Cape 351
Vordate Island 332
Vordingborg 312
Vostok Island 345
Vourlah 320
Vries Island 340
Wadero Island 308
Wads worth, Fort 283
Wahdu Island 325
Waimea 344
Waitangi River 355
Wakaya Island 348
Wake Island 344
Wakefield, Port 352
WalfischBay 322
WalkerCay 292
Wallis Island 348
Walpole Island 347
Walsche, Cape 346
Walsingham, Cape 355
Wanganui River 354
i Wangari Harbor 354
Page.
Wangaroa Harbor 354
Wangaruru 354
Wangeroog 312
Wang-kia-tia Bay 338
Warberg 308
Warnemunde 311
Warren Hastings Island 344
Washington 283
Island 342
Watch Hill Point 282
Watcher, North, Island 331
Waterfall Bluff 323
Waterford 307
Waterloo Bay 323
Watliugs Island 292
WawodaRock 341
Wedge Island 281
WTe£gs Cape 279
Weichselmunde 310
Weihaiwei 338
Wellington 354
Wenman Island 342
Wessel, Cape 351
West Cape 355
Western, Port 352
Westminster Hall Islet 299
Wetta Island 332
Wexford 307
Whaingaroa Harbor 355
WhaleBack 282
Whalefish Island 3,56
Whare-Kauri 350
White Haven 305
Head Island 281
Island 354
Rock
Whitsunday Island 349
Whittle Cape 280
Wicklow 307
Wilberforce, Cape 351
Wilhelmshaven 312
Willemstadt 313
William, Port 355
Willoughby, Cape 352
Wilmington 283
Wilson Islands 347
Islets 343
Promontory 352
Windau ". 310
Winter Harbor 355
Wismar 311
Wittgenstein Island 349
Wolgast 311
Wolkonsky Island 349
Wollaston Island 298
Wollin 310
Wollongong 352
Wood Island, Labrador 280
Maine 282
Woodlark Islands 347
Woody Island 337
Woosung 338
Wostenholme Cape 279
Wotje Islands 343
Wottho Island 343
Wowoni Island 333
Wrangell 288
WTrath, Cape 305
Wreck Reef • 347
Wusimado Point 340
Wustrow 311
Page 380]
INDEX TO APPENDIX IV.
Yakuno Shima.
Page.
339
PLACES — continued
Yobuko
Page.
339
Zaf arana .
Page.
324
Yakutat Bay
288
Yolco Sbimq.-
339
Zafarin Islands
321
Yamada
340
Yokohama
340
Zambesi River
323
Yamagawa
340
Yokosuka
. 340
Zamboanga
335
Yarni Tpland m:.
. . ..334
Yori-gima
.. 339
Zante
.. 319
Yanez
300
York, Cape, Greenland. .
Queensland .
.. 356
.. 353
Zanzibar
... 324
Yap Island
343
Zapotitlan Point
... 285
Yaquina Head
289
Minister Rock
298
Zara
318
Yarmouth
281
Youghal
307
Vecchia
318
Yeboshi Sima
339
Ystad
309
Zempoala Point
285
Yemb6
324
Ytapere Bay
326
Zenersr
318
Yerabu-sima
339
Point
326
Zeyla
.. 324
Yeu Island de
314
Yuiada Road
320
Zirona Grande Island. .
.. 318
Ylin Island
334
Yura No Uchi
340
INDEX TO PART T.
Subject.
Art.
Page.
Subject.
Art.
Page.
Abbreviations
7
Apparent time relation to mean
288
109
Account (See Dead reckoning )
Arctic Current
530
235
Adjustments horizon mirror
246
93
Arie^, first point of, definition
226
89
index mirror
245
93
Arming of lead
19
13
plane table
413
192
Artificial horizon description
256
97
sextant
244
93
method of use
257
98
permanent
248
94
should be tested
258
98
theodolite or transit
410
190
Ascension right (See Right ascen
Afternoon sights
389
171
sion )
Agulhas Current
544
237
Astronomical base
441
200
Airy's method for great circle sailing
194
82
bearing
359
148
Alidade plane table
412
192
time. . _T_
?77
103
Almanac, Nautical. (See Nautical Al
transit instruments
427
196
manac )
work of survey
445
201
Altitude anrj A7imiith
235
90
Atlantic Ocean, currents
523
233
time azimuth
356
147
storms
489
224
azimuth
353
147
Attraction, local
76
36
calculated method of
371
155
Australia Current . .
540
236
circle, definition. .
217
88
Axis of rotation, definition
6
9
circum-meridian
326
129
Azimuth, altitude
353
147
forms for
257
and altitude
235
90
corn pu ted method of
371
155
circle
34
18
definition
220
88
definition
223
88
ex-meridian
326
129
from Sumner line
370
153
forms for
257
how determined
345
144
meridian , ponstarvt
325
128
named .
344
144
form for
257
of body determines use.
395
174
forms for.
256
terrestrial object
359
148
latitude by
321
126
time and altitude
356
147
observation of
322
126
determination
349
145
reduction to
326
129
diagram
351
145
forms .
257
for compass errors
89
40
observed, how corrected
294
115
in great circle sailing. . .
191
82
of Polaris for latitude
333
136
tables
351
145
single, for chronometer error
316
123
Barometer, aneroid
56
27
latitude. . .
332
134
comparisons
57
27
longitude ashore
340
141
definition
48
24
at sea
341
142
effect of on tides
496
226
true definition
294
115
mprnirial
49
24
Altitudes, double forchro error
320
125
sea..
51
25
Amplitude, definition
224
89
standard
51
25
determination of
347
144
temperature correction.
55
26
Anchorage, position to be plotted
166
71
to determine h^ifht,
58
28
Angle danger (See Danger an^le )
vernier
52
25
hour (See Hour an^le )
Base, astronomical
441
200
to repeat
411
191
line, desrription
434
198
Angles, between three known objects
152
62
Beam compass, description.
430
197
horizon, for findin01 distance
139
58
Bearing and angle, position by.
143
59
round of
411
191
distance, position by . .
138
57
sextant and theodolite in hy
daneer
157
64
drography
45?,
202
method of observing and plot-
vertical terrestrial to measure
139
58
tine
134
56
26£°-45° on bow
147
60
of terrestrial object
359
148
Anticyclonic regions, features of
476
214
Bearings, bow and beam.
146
60
Apparent day, definition
273
102
cross
134
56
variation in length
273
102
sun for compass error
89
40
noon definition
273
102
two of object with run be
time, conversion to mean
292
110
tween
144
59
definition
273
102
Beaufort's scale for wind
68
33
ineaualitv of...
273
102
Bench mark, definition..
511
230
381
382
INDEX TO PART I.
Subject.
Art.
Page.
Subject.
Art.
Page.
Binnacles, description. . ....
35
18
Comparison, barometer.
57
27
Bottom, quality of, on chart
46
23
chronometer, method
263
99
Boxing the compass
?,7
14
record . .
264
99
Brazil Current
532
235
Compass beam description
430
197
Buoys
162
66
boxing
27
14
C— W, definition
268
100
compensation (See Devia
Calculated Altitude Method
371
155
tion )
Cape Horn Current
541
236
declination
75
36
Celestial coordinates
234
90
definition
25
14
equator, definition
215
88
deviation. (See Deviation.)
horizon, definition
213
87
divisions on card
26
14
latitude and longitude
238
90
dry
30
17
definition
229
89
error (See Error, compass )
meridian, definition
216
88
local attraction
76
36
sphere or concave, definition.
210
87
Lord Kelvin
32
17
Celo-Navigation, definition
4
9
Navy service, 7J-inch.
31
17
Chart. (See also Projection.)
variation
75
36
as record of piloting
166
71
wet
30
17
employment in piloting
165
68
Compasses (drawing)
7
11
general features
37
20
Compensation compass (See Devia
great circle
189
80
tion )
for composite sailing
197
83
Composite sailing, computation
198
83
isobaric
460
270
definition
184
79
measures of depth on
47
24
graphic approxima
Mercator, to construct
41
21
tion
199
83
quality of bottom on
46
23
shortest course for
196
83
standard meridians on
45
23
terrestrial globe
200
83
Chilean Current
541
236
Computed altitude method
371
155
Chronometer advantage of more than
Concave, celestial, definition
210
87
one
265
100
Constant deviation (See Deviation )
C— \V, definition
268
100
for meridian altitude
325
128
care on shipboard
260
98
form
257
comparison . .
263
99
Conversion of time, apparent to mean
292
110
record
264
99
definition
286
108
correction. (See Chro
nometer error.)
description
259
98
mean to apparent .
sidereal. . .
sidereal to mean
292
290
291
110
110
110
error, by double alts .. .
320
125
Coordinates, celestial
234
90
single altitude .
316
123
definition ...
230
89
time sight
316
123
Correction, chro. (See Chronometer.)
signals
314
121
index, sextant
250
95
transits
315
122
of observed altitude
294
115
definition
261
98
Course, definition
6
10
differs from corr
312
121
to lay . .
132
56
from rate
311
121
Culmination, definition
271
102
hack, use of . .
268
100
Current, Agulhas..
544
237
max. and min. ther
allowance for
206
86
mometer
262
99
Arctic
530
235
minus watch, definition .
268
100
Australia
540
236
second difference
265
100
Brazil
532
235
sight (See Time sio-ht )
Cape Horn
541
236
temperature curve
266
100
Chilean
541
236
transportation of
260
98
determined at noon
388
171
winding .
262
99
effect in piloting
164
67
Circle, declination, definition.
216
88
equatorial, Atlantic .
523
233
hour, definition
216
88
Indian
543
237
of altitude, definition
217
88
Pacific
535
235
equal altitude
363
150
Guinea .
529
235
illumination
363
150
Gulf Stream
526
233
vertical definition
217
88
Humboldt
541
236
Circum-meridian altitude...
326
129
Japan Stream
536
235
forms .
257
Kamchatka
537
236
Civil time
277
103
Kuroshiwo
536
235
Clouds, description and symbols
71
34
Labrador
530
235
Coefficients, constant
111
48
ocean, Atlantic
523
233
quadrantal .
107
47
cause of
517
232
semicircular. .
103
46
definition
516
232
value and relation . . .
114
48
determination of
519
232
Collimation, line of, definition
410
190
drift, definition
516
232
Comparing watch, use of. .
268
100
of Atlantic...
523
233
INDEX TO PART I.
383
Subject.
Art.
|
Page. ! Subject.
Art.
Page.
CuiT6Dt ocean Indian
542
535
516
518
538
541
531
540
533
490
500
506
207
266
475
476
477
486
487
478
481
155
156
157
237
235
232
232 :
236 ;
236
235
236
235
225
227
230
86
100
213
214
214
221
222
214
218
64
64
64
277
169
169
84
254
84
84
266
90
90
88
88
36
192
87
10
10
169
84
24
14
44
45
49
48
48
37
53
49
41
47
47
54
46
45
40
43
37
39
145
116
117
115
117
117
Distance and Dearin°p. .
138
139
6
139
219
91
498
498
7
431
465
145
527
6
248
225
214
275
288
215
6
6
215
226
74
78
83
250
398
492
326
57
58
9
58
88
40
227
227
11
197
209
60
234
10
94
89
87
103
109
88
9
10
88
89
36
37
39
95
176
226
129
257
117
223
89
103
47
54
66
254
265
176
266
231
189
268
269
9
17
98
83
82
94
80
83
10
80
82
81
79
82
Pacific
by horizon ar>glf»
stream definition
definition
submarine
of objects of known height. . .
polar, definition
Oyashiwo
Peruvian . . ...
zenith. (See Zenith distance.)
Distant object for compass error
Rennells ....
Rossel
Diurnal inequality of tide
Southern connecting
tvpe of tide
tidal definitions
Dividers description
description of
prcfportional, description
Doldrums.
observation of ....
to find
Doublin^ angle on bow .
Curve temperature chronometer
Drift currents, Atlantic
Cyclones and cyclonic circulations
Earth definitions relating to
Cyclonic regions features of
Eccentricity sextant
storms description
Ecliptic definition
maneuvering in
Elevated pole
summary of rules
Ephemeris. (See Nautical Almanac.)
Equation of time, definition
tropical
character. . . .
Danger angle horizontal
in conversion of time
Equator celestial, definition
vertical
earth's
bearing
Equatorial currents. (See Current.)
Equiangular spiral
Data useful miscellaneous
Day's work routine ....
383
382
202
Equinoctial definition
Dead reckonin01 always kept
Equinox definition
definition
vernal. (See First point of
Aries.)
Error, chro. (See Chronometer.)
compass causes
form for
method of working
value of
205
203
Decimal fractions
to apply
Declination and hour an°le . .
236
237
216
218
75
412
209
1
6
382
204
47
23
99
100
119
112
111
77
125
116
94
107
106
128
103
101
92
96
78
84
351
300
303
294
301
302
find
right ascension
heeling. {See Deviation.)
index sextant, description. .. .
circle definition
definition
probable, of position, how
of compass
Declinatoire plane table
sextant. (See Sextant.)
Establishment tidal definitions
Definitions nautical astronomy
navigation . .
Ex-meridian altitudes
Departure definition
forms . .
on beginning voyage
Extraordinary refraction near horizon. .
Extra-tropical cyclonic storms
301
488
226
276
105
127
163
. to take
Depth measures of on charts
Fir^t point of Aries definition
recorder, sounding machine
Deviation causes of
hour angle is si-
rjprpal tirnp
classes of
Flinders bar definition
compensation of
to place
constant coefficient . ...
Fc^s and fo01 si°Tials
definition
Forms for sights etc
definition
notes on
heeling error, compensation
definition
use recommended.
Fractions decimal
399
Napier diagram for
1 Gauges tide description
513
408
quadrantal coefficients
Geodetic surveying
definition .
; Geometry
recompensation
formulae derived from
semicircular, coefficients
definition
table
Geo- Navigation, definition. .
4
28
259
200
193
248
189
197
6
186
194
190
183
192
i Gimbals, compass
chronometer
theory of
Glasses, shade. (See Shade glasses.)
Globe, terrestrial, for comp. sailing. . .
gt. circle sailing.
Graduation sextant error
to apply. .
find
Diagram, time azimuth
Difference, second. (See Second dif
ference.)
Dip of horizon, definition
Great circle charts
for comp. sailing . . .
course . .
how applied
8HilinGr ad van tft^p-s
none with artificial
horizon
Airy's method
computation
variation in
definition
when land intervenes..
graphic approx. . . .
61828°— 16 25
384
INDEX TO PART I.
Subject.
Art. ! Page.
Subject.
Great circle sailing methods
terrestrial globe. . .
time azimuth
methods
Greenwich adopted as prime meridian.
time, to find
Guinea Current
Gulf Stream, description
extraordinary dip in . . . .
Gyro-compass
Hack chronometer, use of
Heading, magnetic, determination of. .
Heeling error. (See Deviation . )
Height, determination by barometer. . .
Heliograph, use in surveying
Heliotrope, use in surveying
Horizon angle, distance by
artificial, description
method of use
no dip with
should be tested
celestial, definition
dip of, definition
how applied
none with artificial
horizon
variation in
when land intervenes. .
mirror, adjustment
description
prismatic
visible or sea, definition
Horse latitudes
Hour angle and declination
time, conversion
definition
how measured
circle, definition
Humboldt Current
Hydrographic survey, method of
surveying, definition
Hydrography in survey, description. . .
to plot
Ice and its movements in the North
Atlantic Ocean
Identification of unknown bodies
Index correction, sextant, to find
error, sextant, description
minor, adjustment
description
prismatic
Indian Ocean, currents
Induction, magnetic
Instruments, astronomical transit
nautical astronomy
navigation
surveying
Interpolation, Nautical Almanac
Intersection, Sumner. (£ee Sumner.)
Intervals, lunitidal, definitions
list of
mean and sidereal time
Iron, hard and soft.
Isobars, chart showing
Japan Stream
Kamchatka Current
Knot, length of
Kuroshiwo Current
Labrador Current
Lagging of tide
Land and sea breezes
188
193
191
336
280
529
526
301
33
268
122
58
426
426
139
256
257
294
258
213
300
303
294
301
302
246
240
248
213
466
236
293
222
278
216
541
432
408
451
452
392
250
249
245
240
248
542
97
427
239
7
409
283
492
289
97
460
436
537
6
536
530
497
469
80
82
82
140
104
235
233
117
18
100
50
28
195
195
58
97
98
115
98
87
116
117
115
117
117
93
91
95
87
209
90
111
88
103
88
236
197
189
202
202
238
172
95
95
93
91
94
237
44
196
91
11
189
106
226
279
109
44
270
235
236
10
235
235
227
211
Latitude, by meridian altitude
forms . .
Polaris
reduction to meridian
reduction to meridian,
forms
single altitude
forms
q/ q/f method
forms
celestial, definition
definition
difference, of definition
horse
Lead, arming.
description
line, marking of
Level of bench mark .
surveying, use of
description
Lights, employment in piloting
Line, base, description of
of collimation, definition
position . ( See S umner line . )
sight, definition
Sumner. (-Sea Sumner line.)
Local attraction
time, to find
Log book
chip
ground
patent
electric registers
revolutions as substitute . . .
Logarithms, explanation
Longitude, by single altitude ashore. .
at sea. . .
time sights, forms
transit observations
celestial, definition
definition
difference of
of secondary meridians
tertiary meridians
Loxodromic Curve
Lubber's line
Lunitidal intervals, definitions
list of
Magnetic observations in survey
Magnetism, acquired in building vessel.
features of earth's
subpermanent
transient
Main triangulation
Maneuvering, cyclonic storms
summary of rules
Marine surveying
Mean day, definition
directive force
noon, definition
sun, definition
Mean time, conversion to apparent . —
sidereal
definition
intervals, relation to side
real
time, relation to apparent
sidereal
Mercator projection, description
to construct
sailing
INDEX TO PART I.
385
Subject.
Art.
Page.
Subject.
Art.
Page.
Meridian altitude constant
235
128
Plane table, to improvise. . .
416
193
forms for
256
use of
413
193
latitude by
321
126
Planet, correction of observed altitude
294
115
observation of
322
126
form for latitude sights
258
reduction to
326
129
meridian altitude
256
celestial definition
216
88
time sight
255
of earth definition
6
9
identification of unknown.
392
172
passage definition
271
102
Planets, stars, and moon, use of
391
172
prime Greenwich adopted
336
140
Polar distance definition
219
88
secondary definition
336
140
Polaris latitude by
333
136
determination of
337
140
Pole elevated
214
87
standard on charts
45
23
star latitude by
333
136
tertiary definition
336
140
Poles of earth
6
9
determination of
339
141
Portable transit
427
196
Meridional parts
40
20
Position by angles between 3 objects. .
15?
62
Method of Saint Hilaire or of the com
puted altitudes
371
155
26*CM5° on bow . . .
bearing and angle
147
143
60
59
Middle latitude sailing
175
75
distance
138
57
correction
178
77
bow and beam bearings
146
60
Mile, nautical or sea length of ...
6
10
cross bearings
134
56
Mirror, horizon, (See Horizon mirror. ) .
index. (See Index mirror.)
doubling angle on bow
two bearings and run
145
144
60
59
sextant resilverin°r
254
96
methods of fixing
133
56
Monsoon winds
468
210
of anchorage to be plotted
166
71
Moon, correction of observed altitude.,
form for latitude sights
294
115
259
body determines its use
soundings in survey
395
452
174
202
meridian altitude
257
probable error of by Sumner
time sight
256
lines, how shown ....
398
176
planets, and stars, use of
391
172
Pressure, effect in wind
460
207
value of observations of
394
174
progressive areas of
474
212
Morninor sights, ,
384
169
seasonal variations in ... .
461
207
Nadir definition
212
87
variation of atmospheric
471
212
Napier diagram .
94
41
Prime meridian Greenwich adopted
336
140
Nautical Almanac, description
282
105
vertical definition
217
88
for 1915, extracts
248
Priming of tide
497
227
gives horizontal
Projection, gnomonic ......
44
23
parallax
305
118
Mercator ..... .. ..
39
20
interpolation
283
106
polyconic . ....
43
22
reduction of ele
systems in use .
38
20
ments
283
106
Proportional dividers description
431
197
second differences.
285
108
Prosection method, plane table
414
192
Astronomy, definitions
209
87
Protractor, ordinary
9
11
instruments. . .
239
91
three armed description
428
196
mile, length of
6
10
substitute.
429
196
Navigation, definitions
1
9
use of .
152
62
instruments and accessories
Neap tides
7
494
11
226
Quadrantal deviation. (See Deviation.)
Quintant description
255
97
Noon sights
386
170
Ran^e of tide at various places
279
Notes on forms for sights etc
265
definitions
493
226
Occupying a station
411
190
Ranges for finding compass error
90
40
Ocean current. (See Current, ocean )
in piloting....
158
65
Octant, description
255
97
Rate, chronometer. (See Chronometer
Optical principal of sextant
242
92
rate )
Orient, to, a plane table
414
192
Reciprocal bearings for compass error
88
39
Oyashiwo current. .
538
236
Reckoning dead (See Dead reckon
Parallax, definition
304
118
ing )
horizontal, in Nautical Al
Record of astronomical work
399
176
manac
305
118
chronometer comparison^
263
99
how applied
306
119
piloting . .
166
70
of planet or star
294
115
tidal
507
230
Parallel of latitude definition
6
9
Red Sea extraordinary dip in
301
117
rulers, description. . .
8
11
Reduction to meridian
326
129
sailing, description
173
75
forms for
257
Passage, meridian, definition
271
102
Reference, planes of, tidal
509
230
Pelorus, description
36
19
Refraction correction for
298
116
Peruvian Current
541
236
definition
296
115
Piloting, definition
130
56
effect on dip
301
117
requisites
131
56
extraordinary near horizon
301
117
Plane of reference tidal
509
230
how applied
299
116
sailing
169
72
Relative humiditv
63
30
table, adjustments
413
192
Rennells Current
531
235
description..
412
191
Repeat, to. an ansrle...
411
191
386
INDEX TO PAKT I.
Subject.
Resection method, plane table
Residual deviation
Rhumb line, definition
not shortes^ course
Right ascension and declination
definition
Roaring forties
Rossel Current
Round of angles
Run, calculation of
determined at noon
Running survey, description
Sailing, composite. (See Composite.)
great circle. (-See Great circle.)
Mercator
middle latitude
correction
parallel
plane .
spherical
traverse
Sailings, definition
kinds of
Saint Hilaire's method
Sargasso sea
Sea and land breezes
mile, length of
symbols for state of
water temperature
Second difference, chronometer
Nautical Almanac . .
Secondary meridian, definition
determination of .
triangulation
Seconds, employment in naut. sights. . .
Semicircles, storm
Semicircular deviation. (See Devia
tion. )
Semidiameter, definition
how applied
measured
of planet or star
Semidiurnal type of tide
Sextant adjustments
permanent
angles for plotting soundings. . .
choice of
definition
description
eccentricity
graduation errors
index correction, to find
error, description
method of use
optical principle
prismatic mirrors
shade glasses
resilvering mirrors
surveying
vernier
Shade glasses, for artificial horizon
sextant, description. . . .
prismatic
Sidereal day, definition
noon, definition
time, conversion to mean
definition
intervals, relation to
mean
relation to mean
Sight, chronometer. (See Time sight.)
latitude. (See Latitude.)
Art.
414
123
6
185
237
237
467
540
411
208
388
457
186
179
175
178
173
169
168
172
167
168
371
528
469
6
73
64
265
285
336
337
444
397
485
307
308
251
294
498
244
248
452
253
239
240
248
248
250
249
252
242
248
248
254
423
241
256
240
248
276
276
291
276
289
287
Page.
192
52
10
80
90
90
210
236
191
86
171
204
80
78
75
77
75
72
72
74
72
72
155
235
211
10
35
30
100
108
140
140
201
179
221
119
120
96
115
227
93
94
202
96
91
91
94
94
95
95
96
92
94
94
96
195
92
97
91
94
103
103
110
103
109
108
Subject.
Sight, line of, definition
longitude. (See Longitude.)
time. (See Time sight.)
Sights, afternoon
employment of various
morning
noon....
Signals, surveying, description
time, for chronometer error
Silvering sextant mirrors
Solar time. (See Apparent time.)
Solstice, definition
Sound, velocity of
Sounding machine, barometric corr
depth recorder ....
description
tubes
Soundings, surveying, how plotted
use in piloting
Southern connecting current
Sphere, celestial, definition
Spherical sailing *
Spring tides
Stadia. (See Telemeter.)
Star, correction of observed altitude . . .
form for latitude sights
meridian altitude
time sight
identification
observations in surveying
Stars, planets, and moon, use of
Station pointer. (See Protractor, three
armed.)
Storm center, motion of
rate of progress
to avoid
fix bearing
distance
semicircles
tables
Storms, along transatlantic routes
cyclonic . (See Cyclonic storms . )
Submarine ocean currents
Sumner line, always recommended
applications of
choice of bodies
description
determination. .
uses
lines, intersection, computation
graphically,
when run in
tervenes..
Sun, correction of observed altitude . . .
form for latitude sights
meridian altitude
time sight
mean, definition
observations in surveying
Survey, astronomical work of
hydrographic, method of
running, description
to plot soundings in
Surveying, hydrographic, definition...
instruments
marine, definition
topographic, definition
transit, description
Symbols for clouds
sea
weather
Table, plane. (See Plane table.)
INDEX TO PART I.
387
Subject.
Art.
Page.
Subject.
Art.
Page.
Table tide . .
501
228
Time of transit, how found
323
127
time azimuth
351
145
sidereal. (See Sidereal time.)
Telemeter description
417
194
signals for chronometer error
314
121
substitute for
422
195
eight for chronometer error
316
123
use of . -
417
194
longitude ashore
340
141
Telescope direct and reversed
411
191
at sea
341
142
sextant adjustment
247
94
forms for . .
254
description
zenith
240
4?,7
91
196
solar. (See Apparent time.)
Topographic surveving, definition
408
189
Temperature curve, chronometer
?66
100
Topographv in hydroeraphic survev . .
450
202
Terrestrial object true bearin^ of
359
148
Tracing paper to plot soundings
160
65
Tertiary meridian definition
336
140
3-point problem
429
196
determination of
339
141
Trade wind
464
209
Theodolite adjustments
410
190
Transit, astronomical
427
196
ancles for plotting sound
definition
?,71
102
ings . . . .
451
203
observations for chronometer
description
409
189
error
315
122
method of use
411
190
longitude . . .
338
140
Thermometer classes of
59
28
portable . .
427
196
§ description
59
28
surveying. (See Theodolite.)
dry and wet bulb
61
28
time of how found
323
127
max and ruin chro
262
99
Traverse sailing
17?,
74
Three-armed protractor (Sec Pro
tables, use of
170
73
tractor )
Trian°Tilation, main
443
201
point problem, conditions
153
63
secondary
444
201
explanation
152
62
Trigonometric functions
270
Tidal current (See Current tidal )
lo°rarithms
271
day, definition
497
227
Tropic tide
498
227
establishment definitions
492
226
Tropical cyclonic storms
478
214
observations in survey
503
229
character
481
218
instructions for
503
229
Tubes sounding machine
?,1
13
record
507
230
Unknown bodies identification of
39?
172
Tide, bench mark, definition
511
230
Useful data miscellaneous
277
cause of
491
225
Variation of compass, definition
75
36
definitions relating to
490
2-25
to applv
78
37
diurnal inequality
498
227
find
83
39
type
498
227
Variations, atmospheric
471
212
effect of, in piloting
164
67
nonperiodic . . .
473
212
wind and barometer on
496
226
periodic
472
212
gauges description
513
231
Vernier barometer . .
52
25
observation of
504
229
sextant '
?41
92
planes of reference of . . .
509
230
theodolite.. .. .
409
189
priming and lagging of
497
227
Vertical angles, terreetial, to measure
139
58
range of, at various places..
279
circle, definition
?,17
88
definitions
493
226
prime
?17
88
semidiurnal type
498
227
Visible horizon, definition
?13
87
spring and neap
494
226
Watch comparing use of
268
100
tables
501
228
Weather symbols
70
34
timp of high and !<~>w
501
228
Wind Beaufort's scale
68
33
form for
259
causes of
459
206
tropic
498
227
definition
458
206
types of
498
227
doldrums
465
209
Time and altitude azimuth. . .
356
147
effect of, on tides
496
226
hour angle, conversion of ...
293
111
land and sea breezes
469
211
apparent. (See Apparent time.)
monsoon
468
210
astronomical
277
103
normal pressure
460
207
at different meridians
279
103
prevailing
462
207
azimuth. (See Azimuth, time )
westerly
467
210
civil
277
103
"Roaring forties"
467
210
conversion of. (See Conversion.)
equation of. (See Equation of
storms. (See Cyclonic storms.)
Trade
464
209
time.)
true direction and force
69
33
Greenwich, to find
280
104
wire drag . ...
454
203
local, to find
279
103
Zenith, definition
?,!?,
87
mean. (See Mean time.)
distance definition
?,?,!
88
of high and low water
501
228
how named
321
126
form for
259
telescope
4?,7
196
II.
TABLES.
501
PREFACE.
The following tables comprise Part II of the AMERICAN PRACTICAL NAVIGATOR, by the late Nathaniel
Bowditch, LL. D., as revised in 1880 and in 1903, and again in 1914, under the direction of the Bureau
of Navigation, Navy Department.
In the oresent edition, former tables 28A, 28B, 28C and 28D, Latitude by Polaris; 37, Logarithms for
Equal Altitude Sights; 37 A, Equation of Equal Altitudes near Noon, have been omitted, but the former
assignment of table numbers and page numbers has not been disturbed, the pages on which these
tables were printed being simply dropped from the book and the tables and pages not renumbered
consecutively.
This edition has been extended by incorporating Table 45, Logarithmic and Natural Haversines;
Table 46, Consolidated Altitude Corrections; Table 47, Longitude Factor, and Table 48, Latitude Factor.
HYDROGRAPHIC OFFICE,
Washington, D. C., 1916.
503
NOTE ON REPRINT OF 1916. — This reprint is the same as the 1914 edition, except that a new table
Has been added — Table 49, corrections to be applied in order to find the true altitude of the moon from
the observed altitude above the horizon.
504
CONTENTS OF PART II.
Page.
Explanation of the Tables 507
Table 1. Traverse Table, Quarter Points 515
2. Traverse Table, Degrees 531
3. Meridional Parts 621
4. Length of Degrees of Latitude and Longitude 629
5A. Distance of an Object by Two Bearings, Quarter Points 631
5B. Distance of an Object by Two Bearings, Degrees 634
6. Distance of Visibility of Objects of different Heights 640
7. Conversion of Arc and Time 641
8. Conversion of Sidereal into Mean Solar Time 642
9. Conversion of Mean Solar into Sidereal Time 645
10. Local mean time of Sun's visible Rising and Setting 648
11. Reduction of Moon's Meridian Passage for Longitude 672
12. Reduction of Quantities from Nautical Almanac 673
13. Change of Sun's Right Ascension 683
14. Dip of Sea Horizon 685
15. Dip at Distances short of Horizon 685
16. Parallax of Sun 685
17. Parallax of Planet .- 686
18. Augmentation of Moon's Semidiameter 687
19. Augmentation of Moon's Horizontal Parallax 687
20A. Mean Refraction 688
20B. Mean Refraction and Parallax of Sun . . .. 689
21 . Correction of Refraction for Barometer 690
22. Correction of Refraction for Thermometer 691
23. Mean Refraction and Mean Parallax of Moon 693
24. Mean Refraction and Parallax of Moon 693
25. Variation of Altitude due to change of Declination 702
26. ATariation of Altitude in one minute from Meridian 704
27. Variation of Altitude in given time from Meridian 714
28A.
28B.
<
Omitted.
28C. ,
28D. J
29. Nautical and Statute Miles 725
30. Conversion of Metric and English Linear Measure V26
31. Fahrenheit, Centigrade, and Reaumur Temperatures 727
32. True Force and Direction of Wind 728
33. Distance by Vertical Angle 729
34. Distance by Horizon Angle 731
35. Speed Table for Measured Mile 732
36. Local Mean and Standard Meridian Times 733
3?A. }°mitted.
38. Error in Longitude produced by Error in Latitude 739
39. Amplitudes 740
40. Correction for Amplitude observed in Apparent Horizon 745
41. Natural Sines and Cosines 746
42. Logarithms of Numbers 755
43. Logarithms of Trigonometric Functions, Quarter Points 771
44. Logarithms of Trigonometric Functions, Degrees 772
45. Logarithmic and Natural Haversines 817
46. Consolidated table of Altitude Corrections 922
47. The Longitude Factor 938
48. The Latitude Factor 941
49. Corrections to be applied to observed altitude of the moon 946
505
EXPLANATION OF THE TABLES.
TABLES 1, 2: TRAVERSE TABLES.
Tables 1 and 2 were originally calculated by the natural sines taken from the fourth edition of
Sherwin's Logarithms, which were previously examined, by differences; when the proof sheets of the
first edition were examined the numbers were again calculated by the natural sines in the second edition
of Button's Logarithms; and if any difference was found, the numbers were calculated a third time by
Taylor's Logarithms.
The first table contains the difference of latitude and departure corresponding to distances not
exceeding 300 miles, and for courses to every quarter point of the compass. Table 2 is of the same
nature, but for courses consisting of whole degrees; it was originally of the same extent as Table 1, but
has been extended to include distances up to 600 miles. The manner of using these tables is particularly
explained under the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V.
The tables may be employed in the solution of any right triangle.
TABLE 3: MERIDIONAL PARTS.
Thie table contains the meridional parts, or increased latitudes, for every degree and minute to 80°,
calculated by the following formula :
m
in which
=jj|- log tan ^45° — ^J — a (e1 sin L -f £ e<> sin* L-f- \ e6 sin5 L -f . . . . ),
108007
the Equatorial radius a = — — = 3437'.74677 (log 3.5362739);
M, the modulus of common logarithms = 0.4342945;
^= 2.3025851 (log 0.3622157);
C, the comprex*ion or meridional eccentricity of the earth
according to Clarke (1880) = 293*465 = 0.003407562 (log 7.5324437) ;
e=x/ 2(7-0*= 0.0824846 (log 8.9163666);
from which
= 7915^7044558 (log 3.8984895) ;
a* = 23^.38871 (log 1.3690072);
lae*= 0'.053042 (log 8.7246192);
icu*= 0'.000216523 (log 6.3355038).
The results are tabulated to one decimal place, which is sufficient for the ordinary problems of
navigation.
The practical application of this table is illustrated in Chapters II and V, in articles treating of the
Mercator Chart and Mercator Sailing.
TABLE 4: LENGTH OF DEGREES OF LATITUDE AND LONGITUDE.
This table gives the length of a degree in both latitude and longitude at each parallel of latitude on
the earth's surface, in nautical and statute miles and in meters, based upon Clarke's value (1866) of the
earth's compression, ;>OQ ^ -• In the case of latitude, the length relates to an arc of which the given
degree is the center.
TABLES 5 A, 5B: DISTANCE BY TWO BEARINGS.
These tables have been calculated to facilitate the operation of finding the distance from an object by
two bearings from a given distance run and course. In Table 5A the arguments are given in points,
in Table 5B in degrees; the first column contains the multiplier of the distance run to give the distance
of observed object at second bearing; the second, at time of passing abeam.
The method is explained in article 143, Chapter IV.
507
508
EXPLANATION OF THE TABLES.
TABLE 6: DISTANCE OF VISIBILITY OF OBJECTS.
This table contains the distances, in nautical and statute miles, at which any object is risible at sea.
It is calculated by the formulae:
d = 1. 15 v/X and d' = 1.32 vX
in which d is the distance in nautical miles, d' the distance in statute miles, and x the height of the eye
or the object in feet.
To find the distance of visibility of an object, the distance given by the table corresponding to its
height should be added to that corresponding to the height of the observer's eye.
EXAMPLE: Required the distance of visibility of an object 420 feet high, the observer being at an
elevation of 15 feet.
Dist. corresponding to 420 feet, 23.5 naut. miles.
Dist. corresponding to 15 feet, 4.4 naut. miles.
Dist. of visibility,
27.9 naut. miles.
TABLE 7: CONVERSION OF ARC AND TIME.
In the first column of each pair in this table are contained angular measures expressed in arc
(degrees, minutes, or seconds), and in the second column the corresponding angles expressed in time
(hours, minutes, or seconds). As will be seen from the headings of columns, the time corresponding
to degrees (°) is given in hours and minutes; to minutes of arc ('), in minutes and seconds of time;
and to seconds of arc ("), in seconds and sixtieths of a second of time.
The table will be especially convenient in dealing with longitude and hour angle. The method of
its employment is best illustrated by examples.
EXAMPLE I.
Required the time corresponding to 50° 31' 21".
50° 00' 00" = 3h 20m 00s
31 00 = 2 04
21 - If*
50 31 21 =3 22 05.4
EXAMPLE II.
Required the arc corresponding to 6h 33m 26s. 5.
6n 32m 00s _ 98o 00/ 00//
1 24 = 21 00
030 Q7 K
&TnR — o/. O
6 33 26.5 =
21 37.5
TABLES 8 AND 9: SIDEREAL AND MEAN SOLAR TIMES.
These tables give, respectively, the reductions necessary to convert intervals of sidereal time into
those of mean solar time, and intervals of mean solar into those of sidereal time. The reduction for any
interval is found by entering with the number of hours at the top and the number of minutes at the side,
adding the reduction for seconds as given in the margin.
The relations between mean solar and sidereal time intervals, and the methods of conversion of
these times, are given in articles 289-291, Chapter IX. •
TABLE 10: SUN'S RISING AND SETTING.
This table gives the local mean time of the sun's visible rising and setting — that is, of the appearance
and disappearance of the sun's upper limb in the unobstructed horizon of a person whose eye is 15 feet
above the level of the earth's surface, the atmospheric conditions being normal.
The local apparent times of rising and setting were determined from the formula for a time sight,
the altitude employed being — 0° 56' 08","1 made up of the following terms: Refraction, — 36' 29"; semi-
diameter, — 16' 00"; dip, — 3' 48"; and parallax, -f 9".
To ascertain the time of rising or setting for any given date and place, enter the table with the
latitude and declination, interpolating if the degrees are not even. In the line R will be found the time
of rising; in the line S, the time of setting. Be careful to choose the page in which the latitude is of
the correct name, and in which the "approximate date" corresponds, nearly or exactly, with the
given date.
This table is computed with the intention that, if accuracy is desired, it will be entered with the
decimation as an argument — not the date — as it is impossible to construct any table based upon dates
whose application shall be general to all years. But as a given degree of declination will, in the
majority of years, fall upon the date given in the table as the ''approximate date," and as, when it
does not do so, it can never be more than one day removed therefrom, it will answer, where a slight
inaccuracy may be admitted, to enter the table with the date as an argument, thus avoiding the neces
sity of ascertaining the declination.
EXAMPLE: Find the local mean time of sunset at Rio de Janeiro, Brazil (lat. 22° 54' S., long.
43° 10' W.), on January 1, 1903 (dec. 23° 04' S.).
Exact method.
Lat. 22° \
Dec.23°J
Corr. for + 54' lat .
Corr. for 4- 04' dec.
6h 48"
+ 02
00
Approximate method.
Lat. 22°..) 6h 4gl
January 2 / "
Corr. for -f 54' lat +02
Corr. for 1 dav.. . - 01
L. M. T. sunset . . 6 50
L. M. T. simset 6 49
EXPLANATION OF THE TABLES. 509
TABLE 11: REDUCTION FOB, MOON'S TRANSIT.
This table was calculated by proportioning the daily variation of the time of the moon's passing the
meridian.
The numbers taken from the table are to be added to the Greenwich time of moon's transit in weet
longitude, but subtracted in east longitude.
TABLE 12: REDUCTIONS FOR NAUTICAL ALMANAC.
This is a table of proportional parts for finding the variation of the sun' s right ascension or declination,
or of the equation of time, in any number of minutes of time, the horary motion being given at the top of
the page in seconds, and the number of minutes of time in the side column; also for finding the variation
of the moon's declination or right ascension hi any number of seconds of time, the motion in one minute
being given at the top, and the numbers in the side column being taken for seconds.
TABLE 13: CHANGE OF SUN'S RIGHT ASCENSION.
This is a table that may be employed for finding the change of the sun's right ascension for any
given number of hours, the hourly change, as taken from the Nautical Almanac, being given in the
marginal columns.
TABLE 14: DIP OF SEA HORIZON.
This table contains the dip of the sea horizon, calculated by the formula:
D = 58//.8Vf,
in which F = height of the eye above the level of the sea in feet.
It is explained in article 300, Chapter X.
TABLE 15: DIP SHORT OF HORIZON.
This table contains the dip for various distances and heights, calculated by the formula:
D = %d _|_ 0.56514 X -„
7 a
in which D represents the dip in miles or minutes, d, the distance of the land in sea miles, and h, the
height of the eye of the observer in feet.
TABLE 16: PARALLAX OF SUN.
This table contains the sun's parallax in altitude calculated by the formula:
par. = sin z X 8*. 75,
in which 2 = apparent zenith distance, the sun's horizontal parallax being 8". 75.
It is explained in article 304, Chapter X.
TABLE 17: PARALLAX OF PLANET.
Parallax in altitude of a planet is found by entering at the top with the planet's horizontal parallax,
and at the side with the altitude.
TABLE 18: AUGMENTATION OF MOON'S SEMLDIAMETER.
This table gives the augmentation of the moon's semidiameter calculated by the formula:
x = c s2 sin h -f £ c2 s3 sin2 h 4- £ c1 s8,
where h = moon's apparent altitude;
8 = moon's horizontal semidiameter;
x = augmentation of semidiameter for altitude h; and
log c = 5.25021.
TABLE 19: AUGMENTATION OF MOON'S HORIZONTAL PARALLAX.
This table contains the augmentation of the moon's horizontal parallax, or the correction to reduce
the moon's equatorial horizontal parallax to that point of the earth's axis which lies in the vertical of
the observer in any given latitude; it is computed by the formulae:
where n = equatorial horizontal parallax;
L= latitude;
e = eccentricity of the meridian; log & = 7.81602; and
A * = augmentation of the horizontal parallax for the latitude L.
510 EXPLANATION OF THE TABLES.
TABLE 20 A: MEAN REFRACTION.
This table gives the refraction, reduced from Bessel's tables, for a mean atmospheric condition in
which the barometer is 30.00 inches, and thermometer 50° Fahr.
TABLE SOB: MEAN REFRACTION AND PARALLAX OF SUN.
This table contains the correction to be applied to the sun's apparent altitude for mean refraction
and parallax, being a combination of the quantities for the altitudes given in Tables 16 and 20A.
TABLES 21, 22: CORRECTIONS OF REFRACTION FOR BAROMETER AND
THERMOMETER.
These are deduced from BessePs tables. The method of their employment will be evident.
TABLE 23: MEAN REFRACTION AND MEAN PARALLAX OF MOON.
This table contains the correction of the moon's altitude for refraction and parallax corresponding
to the mean refraction (Table 20A), and a horizontal parallax of the mean value of 57' 30".
TABLE 24: MEAN REFRACTION AND PARALLAX OF MOON.
This table contains the correction to be applied to the moon's apparent altitude for each minute of
horizontal parallax, and for every 10' of altitude from 5°, with height of barometer 30.00 inches, and
thermometer 50° Fahr.
For seconds of parallax, enter the table abreast the approximate correction and find the seconds of
horizontal parallax, the tens of seconds at the side and the units at the top. Under the latter and
opposite the former will be the seconds to add to the correction.
For minutes of altitude, take the seconds from the extreme right of the page, and apply them as
there directed.
TABLE 25: CHANGE OF ALTITUDE DUE TO CHANGE OF DECLINATION.
This table gives the variation of the altitude of any heavenly body arising from a change of 100" in
the declination. It is useful for finding the equation of equal altitudes by the approximate method
explained in article 324, Chapter XI, and for other purposes.
If the change move the body toward the elevated pole, apply the correction to the altitude with the
signs in the table; otherwise change the signs.
TABLE 26: CHANGE OF ALTITUDE IN ONE MINUTE FROM MERIDIAN.
This table gives the variation of the altitude of any heavenly body, for one minute of time from
meridian passage, for latitudes up to 60°, declinations to 63°, and altitudes between 6° and 86°. It is
based upon the method set forth in article 328, Chapter XII, and the values may be- computed by the
formula: i.vtsS
_lx/.9635 cos L cos d
O — • J T^ •» \ " ' '
sin (L — d)
where a = variation of altitude in one minute from meridian,
L = latitude, and
d = declination — positive for same name and negative for opposite name to latitude at upper
transit, and negative for same name at lower transit.
The limits of the table take in all values of latitude, declination, and altitude which are likely to
be required. In its employment, care must be taken to enter the table at a place where the declination
is appropriately named (of the same or opposite name to the latitude) ; it should also be noted that at
the bottom of the last three pages values are given for the variation of a body at lower transit, which can
only be observed when the declination and latitude are of the same name, and in which case the reduc
tion to the meridian is subtract! ve; che limitations in this case are stated at the foot of the page, and
apply to all values below the heavy rules.
TABLE 27: CHANGE OF ALTITUDE IN GIVEN TIME FROM MERIDIAN.
This table gives the product of the variation in altitude in one minute of a heavenly body near the
meridian, by the square of the number of minutes. Values are given for every half minute between
0™ 30s and 26ra 0s, and for all variations likely to be employed in the method of "reduction to the
meridian."
The formula for computing is:
Red. = a X <*,
where a = variation in one minute (Table 26) , and
t = number of minutes (in units and tenths) from time of meridian passage.
The table is entered in the column of the nearest interval of time from meridian, and the value
taken out corresponding to the value of a found from Table 26. The units and tenths are picked out
separately and combined, each being corrected by interpolation for intermediate intervals of time.
The result is the amount to be applied to the observed altitude to reduce it to the meridian altitude,
which is always to be added for upper transits and subtracted for lower.
EXPLANATION OF THE TABLES. 511
TABLE 28, A, B, C, D: LATITUDE BY POLARIS,
[OMITTED.]
TABLES 29, 30, 31: CONVERSION TABLES.
These are self-explanatory.
TABLE 32: TRUE FORCE AND DIRECTION OF WIND.
This table enables an observer on board of a moving vessel to determine the true force and direction
of the wind from its apparent force and direction. Enter the table with the apparent direction of the
wind (number of points on the bow) and force (Beaufort scale) as arguments, and pick out the direc
tion relatively to the ship's head and the force corresponding to the known speed of the ship.
EXAMPLE: A vessel steaming SE. at a speed of 15 knots appears to have a wind blowing from three
points on the starboard bow with a force of 6, Beaufort scale. What is the true direction and force?
In the column headed 3 (meaning three points on bow, apparent direction) and in the line 6
(apparent force, Beaufort scale), we find abreast 15 (knots, speed of vessel) that the true direction is 5
points on starboard bow, i. e. , S. by W*. , and true force 4.
TABLE 33: VERTICAL ANGLES.
This table gives the distance of an object of known height by the vertical angle that it subtends at
the position of the observer. It was computed by the formula:
tan<r = jj,
where a = the vertical angle;
h = the height of the observed object in feet; and
d = the distance of the object, also converted into feet.
The employment of this method of finding distance is explained in article 139, chapter IV.
TABLE 34: HORIZON ANGLES.
This shows the distance in yards corresponding to any observed angle between an object and the
sea horizon beyond, the observer being at a known height.'
The method of use is explained in article 139, chapter IV.
TABLE 35: SPEED TABLE.
This table shows the rate of speed, in nautical miles per hour, of a vessel which traverses a measured
mile in any given number of minutes and seconds. It is entered with the number of minutes at the top
and the number of seconds at the side; under one and abreast the other is the number of knots of speed.
61828°— 16 26
512 EXPLANATION OF THE TABLES.
TABLE 36: LOCAL AND STANDARD TIMES.
This table contains the reduction to be applied to the local time to obtain the corresponding time
at any other meridian whose time is adopted as a standard. The results are given to the nearest minute
of time only; being intended for the reduction of such approximate quantities as the time of high water
or time of sunset. More exact reductions, when required, may be made by Table 7.
TABLE 37: LOGARITHMS FOR EQUAL ALTITUDE SIGHTS.
[OMITTED.]
TABLE 37 A: EQUATION OF EQUAL ALTITUDES NEAR NOON.
[OMITTED.]
TABLE 38: EFFECT UPON LONGITUDE OF ERROR IN LATITUDE.
Table 38 shows, approximately, the error in longitude in miles and tenths of a mile, occasioned by
an error of one mile in the latitude.
Thus, when the sun's altitude is 30°, the latitude 30°, and the polar distance 100°, the error is
eight-tenths of a mile.
The effect of an increase of latitude is as follows:
In West longitude, /East \ of meridian, the ("decreased! except where marked ("increased )
the body being \WestJ longitude is \increased J ' by *, when it is (.decreased/'
In East longitude, /East \ of meridian, the /increased 1 except where marked /decreased!
the body being (West/ longitude is (.decreased/' by *, when it is \ increased/'
A decrease of latitude has the contrary effect.
The direction of error may readily be seen by drawing the Sumner line in a direction at right angles
to the approximate bearing of the body.
TABLE 39: AMPLITUDES.
This table contains amplitudes of heavenly bodies, at rising and setting, for various latitudes and
declinations, computed by the formula:
sin amp.=sec. Lat.Xsin dec.
It is entered with the declination at the top and the latitude at the side.
Its use is explained in article 358, Chapter XIV.
EXPLANATION OF THE TABLES.
TABLE 40: CORRECTION FOR AMPLITUDES.
This table gives a correction to be applied to the observed amplitude to counteract the vertical
displacement due to refraction, parallax, and dip, when the body is observed with its center in the
visible horizon.
The correction is to be applied for the sun, a planet, or a star, as follows:
to the
to the left-
For the moon, apply half the correction in the contrary manner.
TABLE 41: NATURAL SINES AND COSINES.
This table contains the natural sine and cosine for every minute of the quadrant, and is to be
entered at the top or bottom with the degrees, ami at the side marked M., with the minutes; the
corresponding numbers will be the natural sine and cosine, respectively, observing that if the degrees
are found at the top, the name sine, cosine, and M. must also be found at the top, and the contrary if
the degrees are found at the bottom. It should be understood that all numbers given in the table
should be divided by 100,000— that is, pointed off to contain five decimal places. Thus, .43366 is the
natural sine of 25° 42X, or the cosine of 64G IS'.
In the outer columns of the margin are given tables of proportional parts, for the purpose of finding,
approximately, by inspection, the proportional part corresponding to any number of seconds in the
proposed angle, the seconds being found in the marginal column marked M., and the correction in
the adjoining column. Thus, if we suppose that it were required to find the natural sine corresponding
to 25° 42' 19", the difference of the sines of 25° 42' and 25° 43' is 26, being the same as at the top of the
left-hand column of the table; and in this column, and opposite 19 in the column M., is the correc
tion 8. Adding this to the above number .43366, because the numbers are increasing, we get .43374 for
the sine of 25° 42' 19". In like manner, we find the cosine of the same angle to be .90108— 4=. 90104,
using the right-hand columns, and subtracting because the numbers are decreasing; observing, however,
that the number 14 at the top of this column varies 1 from the difference between the cosines of 25° 42/
and 25° 43', which is only 13; so that the table may give in some cases a unit too much between the
angles 25° 42' and 25° 43'; but this is, in general, of but little importance, and when accuracy is required,
the usual method of proportional parts is to be resorted to, using the actual tabular difference.
TABLE 42: LOGARITHMS OF NUMBERS.
This table, containing the common logarithms of numbers, was compared with Sherwin's, Button's,
and Taylor's logarithms; its use is explained in an article on Logarithms in Appendix III.
TABLE 43: LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, QUARTER POINTS.
This table contains the logarithms of the sines, tangents, etc. , corresponding to points and quarter
points of the compass. This was compared with Sherwin's, Mutton's, and Taylor's logarithms.
TABLE 44: LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, DEGREES.
This table contains the common logarithms of the sines, tangents, secants, etc. It was compared
with Sherwin's, Button's, and Taylor's tables. Two additional columns are given in this table, which
are very convenient in finding the* time from an altitude of the sun: also, three columns of proportional
parts for seconds of space, and a small table at the bottom of each page for finding the proportional parts
for seconds of time. The degrees are marked to 180°, which saves the trouble of subtracting the given
angle from 180° when it exceeds 90°.
The use of this table is fully explained in Appendix III in an article on Logarithms.
TABLE 45: LOGARITHMIC AND NATURAL HAVERSINES.
The haversine is defined by the following relation:
hav. A=£ vers. A=£(l— cos A)=sin2 JA.
It is a trigonometric function which simplifies the solution of many problems in nautical astronomy
as well as in plane trigonometry. To afford the maximum facility in carrying out the processes of
solution, the values of the natural haversine and its logarithm are set down together in a single table
for all values of angle ranging from 0° to 360°, expressed both in arc and in time.
514 EXPLANATION OF THE' TABLES.
TABLE 46: CORRECTIONS TO BE APPLIED IN ORDER TO FIND THE TRUE ALTI
TUDE OF A STAR AND ALSO OF THE SUN FROM THE OBSERVED ALTITUDE
ABOVE THE HORIZON.
This is a consolidated table in which the tabulated correction for an observed altitude of a star
combines the mean refraction and the dip, and that for an observed altitude of the sun's lower limb
combines the mean refraction, the dip, the parallax, and the mean semidiameter, which is taken as
16'. A supplementary table at the foot of the main table takes account of the variation of the sun's
semidiameter in the different months of the year.
TABLE 47: THE LONGITUDE FACTOR.
The change in longitude due to a change of V in latitude, called the longitude factor, F, is given in
this table at suitable intervals of latitude and azimuth. The quantities tabulated are computed from
the formula —
F=sec. LatXcot. A/.
When a time sight is solved with a dead-reckoning latitude, the resulting longitude is only true
if the latitude be correct. This table, by setting forth the number of minutes of longitude due to each
minute of error in latitude, gives the means of finding the correction to the longitude for any error that
may subsequently be disclosed in the latitude used in the calculation.
Regarding the azimuth of the observed celestial body as less than 90° and as measured from either
the North or the South point of the horizon towards East or West, the rule for determining whether the
correction in longitude is to be applied to the eastward or to the westward will be as follows: If the
change in latitude is of the same name as the first letter of the bearing, the change in longitude is of the
contrary name to that of the second letter, and vice versa.
Thus, if the body bears S. 45° E. and the change in latitude is to the southward, the change in
longitude will be to the westward; and, if the change in latitude is to the northward, the change in
longitude will be to the eastward.
The convenient application of the longitude factor in finding the intersection of Sumner lines is
explained in article 389.
TABLE 48: THE LATITUDE FACTOR.
The change in latitude due to a change of 1' in the longitude, called the latitude factor, f, is given
in this table at suitable intervals of latitude and azimuth. The quantities tabulated, being the reciprocals
of the values of the longitude factor, are computed fron? the formula —
f=4=sec. LatXcot. Az.=CO8' Lat Xtan- Az'
When an ex-meridian sight is solved with a longitude afterwards found to be in error, this table, by
setting forth the number of minutes of latitude due to each V of error in longitude, gives the means
of finding the correction in the latitude for the amount of error in the longitude used in the calculation.
Regarding the azimuth of the observed celestial body as less than 90° and as measured from either
the North or the South point of the horizon towards East or West, the rule for determining whether the
correction in latitude is to be applied to the northward or to the southward is as follows: If the change
in longitude is of the same name as the second letter of the bearing, the change in latitude is of the
contrary name to the first letter, and vice versa. Thus, if the body bears S. 14° E. and the change in
longitude is to the westward, the change in latitude will be to the southward, and, if the change in
longitude is to the eastward, the change in latitude will be to the northward.
The convenient application of the latitude factor in finding the intersection of Sumner lines is
explained in article 390.
TABLE 49: CORRECTIONS TO BE APPLIED IN ORDER TO FIND THE TRUE
ALTITUDE OF THE MOON FROM THE OBSERVED ALTITUDE ABOVE THE
HORIZON.
In this table, which is to be entered with the observed altitude in the side column and from the
top with the horizontal parallax as obtained from the Nautical Almanac for the time of observation,
there are set down the corrections to be applied to the observed altitude of the moon's upper limb above
the horizon, and also of the lower limb, giving the combined effect of the dip of the horizon for a height
of the eye of the observer of 35 feet above the level of the sea, of the astronomical refraction for the mean
state of the atmosphere, and of the parallax and semidiameter of the moon.
A supplementary table, following the main table, takes account of heights of the eye of the observer
differing from 35 feet.
TABLE 1. [Page 515
Difference of Latitude and Departure for £ Point.
N. i E. N. J W. S. i E. S. i W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
1
1.0
0.0
61
60.9
3.0
121
120.9
5.9
181
180.8
8.9
241
240.7
11.8
2
2.0
0.1
62
61.9
3.0
22
121.9
6.0
82
181.8
8.9
42
241.7
11.9
3
3.0
0.1
63
62.9
3.1
23
122.9
6.0
83
182.8
9.0
43
242.7
H.9
4
4.0
0.2
64
63.9
3.1
24
123.9
6.1
84
183.8
9.0
44
243.7
12.0
5
5.0
0.2
65
64.9
3.2
25
124. 8 6. 1
85
184.8
9.1
45
244.7
12.0
6
6.0
0.3
66
65.9
3.2
26
125. 8 6. 2
86
185.8
9.1
46
245. 7
12.1
7
7. 0 0. 3
67
66.9
3.3
27
126. 8 6. 2
87 186. 8
9.2
47
246.7 12.1
8
8.0 i 0.4
68
67.9
3.3
28
127. 8 6. 3
88 187.8
9.2
48
247.7
12.2
9
9.0 0.4
69
68.9
3.4
29
128. 8 6. 3
89 188.8
9.3
49
248.7
12.2
10
10. 0 0. 5
70
69. 9 3. 4
30
129. 8 6. 4
90 189. 8
9.3
50
249.7
12.3
11
11.0 0.5
71
70.9
3.5
131
130. 8 6. 4
191 190.8
9.4
251
250.7
12.3
12
12.0
0.6
72
71.9
3.5
32
131.8 6.5
92 . 191.8
9.4
52
251.7
12.4
13
13.0
0.6
73
72.9 $.6
33
132.8 6.5
93 192. 8
9.5
53
252.7
12.4
14
14.0
0.7
74 73. 9
3.6
34
133. 8 6. 6
94
193.8
9.5
54
253.7
12.5
15
15.0
0.7
75 74. 9
3.7
35
134. 8 6. 6
95
194.8
9.6
55
254.7
12.5
16
16.0
0.8
76 75. 9
3.7
36
135. 8 6. 7
96
195.8
9.6
56
255. 7
12.6
17
17.0
0.8
77 76. 9
3.8
37
136. 8 6. 7
97
196.8
9.7
57
256. 7
12.6
18
18.0
0.9
78 j 77.9
3.8
38 137. 8 6. 8
98
197.8
9.7
58
257.7
12.7
19
19.0
0.9
79 78. 9
3.9
39 1 138.8 6.8
99
198.8
9.8
59 258. 7
12.7
20
20.0
1.0
80 ! 79.9 3.9
40 1 139.8
6.9
200 199. 8
9.8
60 259. 7
12.8
21
21.0
1.0
81 80. 9
4.0
141
140.8
6.9
201 200. 8
9.9
261 260. 7
12.8
22
22.0
1.1
82 81. 9
4.0
42
141.8
7.0
02 201. 8
9.9
62 261.7
12.9
23
23.0
1.1
83 i 82.9
4.1
43
142.8
7.0
03 202. 8
10.0
63 262. 7
12.9
24
24.0
1.2
84 ; 83.9
4.1
44
143.8
7.1
04 203. 8
10.0
64 263. 7
13.0
25
25.0
1.2
85 i 84.9 4.2
45
144.8
7.1
05 204. 8
10.1
65
264.7
13.0
26
26.0
1.3
86 i 85.9
4.2
46
145.8 7.2
06 205. 8
10.1
66
265.7
13.1
27
27.0
1.3
87 i 86.9
4.3
47 146. 8 7. 2
07 206. 8
10.2
67
266.7
13.1
28
28.0
1.4
88 1 87. 9 4. 3
48 147. 8 ! 7. 3
08 207. 7
10.2
68
267.7
13.2
29
29.0
1.4
89 88. 9
4.4
49 148. 8 t 7. 3
09 208. 7
10.3
69
268.7
13.2
30
30.0
1.5
90 89.9
4.4
50 149.8 i 7.4
10 209. 7
10.3
70
269.7
13.2
31
31.0
1.5
91 ! 90.9 | 4.5
151 150. 8 7. 4
211 210. 7
10.4
271
270. 7
13.3
32
32.0
1.6
92 91. 9
4.5
52 151. 8 7. 5
12 211. 7
10.4
72
271.7
13.3
33
33.0
1.6
93 92. 9
4.6
53 152. 8
7.5
13 1 212. 7
10.5
73
272.7
13.4
34
34.0 ! 1.7
94 93. 9
4.6
54 153.8 i 7.6
14 | 213. 7
10.5
74
273.7
13.4
35
35.0
1. 7
95 ! 94.9
4.7
55 154.8 7.6
15
214.7
10.5
75
274.7
13.5
36
36.0
1.8
96 I 95.9
4.7
56 155. 8 ! 7. 7
16
215.7
10.6
76
275.7
13.5
37
37.0
1.8
97 96. 9
4.8
57 156. 8 7. 7
17
216.7
10.6
77
276.7
13.6
38
38.0
1.9
98 97. 9
4.8
58 157.8 I 7.8
18
217.7
10.7
78
277.7
13.6
39
39.0
1.9
99 ! 98. 9
4.9
59 158.8 i 7.8
19
218.7
10.7
79
278.7
13.7
40
40.0
2.0
100 99.9
4.9
60 159. 8 7. 9
20 219. 7
10.8
80
279.7
13.7
41
41.0
2.0
101 i 100.9
5.0
161
160.8 1 7.9
221 220. 7
10.8
281
280.7
13.8
42
41.9
2.1
02
101.9
5.0
62
161.8 i 7.9
22 221.7
10.9
82
281.7
13.8
43
42.9
2.1
03
102.9
5.1
63
162.8 j 8.0
23
222.7
10.9
83
282. 7
13.9
44
43.9
2.2
04
103.9
5.1
64
163.8 8.0
24
223.7
11.0
84
283.7
13.9
45
44.9
2.2
05
104.9
5.2
65
164. 8 8. 1
25
224.7
11.0
85
284.7
14.0
46
45.9
2.3
06
105.9
5.2
66
165. 8 8. 1
26
225.7
11.1
86
285.7
14.0
47
46.9
2.3
07
106.9
5.3
67
166.8
8.2
27
226.7
11.1
87
286.7
14.1
48
47.9
2.4
08
107.9
5.3
68
167.8
8.2
28
227.7
11.2
88
287.7
14.1
49
48.9
2.4
09 108. 9
5.3
69 168. 8 8. 3
29
228.7
11.2
89
288.7
14.2
50
49.9
2.5
10 j 109.9
5.4
70 169.8 1 8.3
30
229.7
11.3
90
289.7
14.2
51
50.9
2.5
111 110.9
5.4
171 170. 8
8.4
231
230.7
11.3
291
290.6
14.3
52
51.9
2.6
12
111.9
5.5
72 1 171.8
8.4
32
231.7
11.4
92
291.6
14.3
53
52.9
2.6
13
112.9
5. 5
73 172. 8
8.5
33
232.7
11.4
93
292.6
14.4
54
53.9
2.6
14
113.9
5.6
74 ! 173. 8
8.5
34
233.7
11.5
94
293.6
14.4
55
54.9
2.7
15
114.9
5.6
75 174. 8
8.6
35
234.7
11.5
95
294.6
14.5
56
55.9
2.7
16
115.9
5.7
76 175. 8
8.6
36
235.7
11.6
96
295.6
14.5
57
56.9
2.8
17
116.9
5.7
77 176. 8
8.7
37
236.7
11.6
97
296.6
14.6
58
57.9
2.8
18
117.9
5.8
78 ! 177. 8
8.7
38
237.7
11.7
98
297.6
14.6
59
58.9
2.9
19
118.9
5.8
79 178. 8
8.8
39
238.7
11.7
99 298. 6
14.7
60
59.9
2.9
20
119.9
5.9
80
179.8
8.8
40
239.7
11.8
300 299. 6
14.7
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
E. i N. E. i S. W. i N. W. i S. [For 7f Points.
Page 516] TABLE 1.
Difference of Latitude and Departure for \ Point.
N. \ E. N. \ W. S. \ E. S. \ W.
DM,
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.7
6.0
121
120.4
11.9
181
180.1
17.7
241
239.8
23.6
2
2.0
0.2
62
61.7
6.1
22
121.4
12.0
82
181.1
17.8
42
240.8
23.7
3
3.0
0.3
63
62.7
6.2
23
122. 4
12,1
83
182.1
17.9
43
241.8
23.8
4
4.0
0.4
64
63.7
6.3
24
123.4
12.2
84
183.1
18.0
44
242.8
23.9
5
5.0
0.5
65
64.7
6.4
25
124.4
12.3
85
184.1
18.1
45
243.8
24.0
6
6.0
0.6
66
65.7
6.5
26
125.4
12.4
86
185.1
18.2
46
244.8
24.1
7
7.0
0.7
67
66.7
6.6
27
126.4
12.4
87
186.1
18.3
47
245.8
24.2
8
8.0
0.8
68
67.7
6.7
28
127.4
12.5
88
187.1
18.4
48
246.8
24.3
9
9.0
0.9
69
68.7
6.8
29
128.4
12.6
89
188.1
18.5
49
247.8
24.4
10
10.0
1.0
70
69.7
6.9
30
129.4
12.7
90
189.1
18.6
50
248.8
24.5
11
10.9
1.1
71
70.7
7.0
131
130.4
12.8
191
190.1
18.7
251
249.8
24.6
12
11.9
1.2
72
71.7
7.1
32
131.4
12.9
92
191.1
18.8
52
250.8
24.7
13
12.9
1.3
73
72.6
7.2
33
132.4
13.0
93
192.1
18.9
53
251. 8
24.8
14
13.9
.4
74
73.6
7.3
34
133.4
13.1
94
193.1
19.0
54
252.8
24.9
15
14.9
.5
75
74.6
7.4
35
134.3
13.2
95
194.1
19.1
55
253.8
25.0
16
15.9
.6
76
75.6
7.4
36
135.3
13.3
96
195.1
19.2
56
254.8
25.1
17
16.9
.7
77
76.6
7.5
37
136.3
13.4
97
196.1
19.3
57
255.8
25.2
18
17.9
.8
78
77.6
7.6
38
137.3
13.5
98
197.0
19.4
58
256.8
25.3
19
18.9
.9
79
78.6
7.7
39
138.3
13.6
99
198.0
19.5
59
257.8
25.4
20
19.9
2.0
80
79.6
7.8
40
139. 3
13.7
200
199.0
19.6
60
258.7
25.5
21
20.9
2.1
81
80.6
7.9
141
140.3
13.8
201
200.0
19.7
261
259.7
25.6
22
21.9
2.2
82
81.6
8.0
42
141.3
13.9
02
201.0
19.8
62
260.7
25.7
23
22.9
2.3
83
82.6
8.1
43
142.3
14.0
03
202.0
19.9
63
261.7
25.8
24
23.9
2.4
84
83.6
8.2
44
143.3
14.1
04
203. 0
20.0
64
262.7
25.9
25
24.9
2.5
85
84.6
8.3
45
144. 3
14.2
05
204.0
20.1
65
263.7
26.0
26
25.9
2.5
86
85.6
8.4
46
145.3
14.3
06
205.0
20.2
66
264.7
26.1
27
26.9
2.6
87
86.6
8.5
47
146.3
14.4
07
206.0
20.3
67
265.7
26.2
28
27.9
2.7
88
87.6
8.6
48
147.3
14.5
08
207.0
20.4
68
266.7
26.3
29
28.9
2.8
89
88.6
8.7
49
148. 3
14.6
09
208.0
20.5
69
267.7
26.4
30
29.9
2.9
90
89.6
8.8
50
149.3
14.7
10
209.0
20.6
70
268.7
26.5
31
30.9
3.0
91
90.6
8.9
151
150.3
14.8
211
210.0
20.7
271
269.7
26.6
32
31.8
3.1
92
91.6
9.0
52
151.3
14.9
12
211.0
20.8
72
270.7
26.7
33
32.8
3.2
93
92.6
9.1
53
152.3
15.0.
13
212.0
20.9
73
271.7
26.8
34
33.8
3.3
94
93.5
9.2
54
153.3
15.1
14
213.0
21.0
74
272.7
26.9
35
34.8
3.4
95
94.5
9.3
55
154.3
15.2
15
214.0
21.1
75
273.7
27.0
36
35.8
3.5
96
95.5
9.4
56
155.2
15.3
16
215.0
21.2
76
274.7
27.1
37
36.8
3.6
97
96.5
9.5
57
156.2
15.4
17
216.0
21.3
77
275.7
27.2
38
37.8
3.7
98
97.5
9.6
58
157.2
15.5
18
217.0
21.4
78
276.7
27.2
39
38.8
3.8
99
98.5
9.7
59
158.2
15.6
19
217.9
21.5
79
277.7
27.3
40
39.8
3.9
100
99.5
9.8
60
159.2
15.7
20
218.9
21.6
80
278.7
27.4
41
40.8
4.0
101
100.5
9.9
161
160.2
15.8
221
219.9
21.7
281
279.6
27.5
42
41.8
4.1
02
101.5
10.0
62
161.2
15.9
22
220.9
21.8
82
280.6
27.6
43
42.8
4.2
03
102.5
10.1
63
162.2
16.0
23
221.9
21.9
83
281.6
27.7
44
43.8
4.3
04
103.5
10.2
64
163.2
16.1
24
222.9
22.0
84
282.6
27.8
45
44.8
4.4
05
104.5
10.3
65
164.2
16.2
25
223.9
22.1
85
283.6
27.9
46
45.8
4.5
06
105.5
10.4
66
165. 2
16.3
26
224.9
22.2
86
284.6
28.0
47
46.8
4.6
07
106.5
10.5
67
166.2
16.4
27
225.9
22.2
87
285.6
28.1
48
47.8
4.7
08
107.5
10.6
68
167.2
16.5
28
226.9
22.3
88
286.6
28.2
49
48.8
4.8
09
108.5
10.7
69
168.2
16.6
29
227.9
22.4
89
287.6
28.3
50
49.8
4.9
10
109.5
10.8
70
169.2
16.7
30
228.9
22.5
90
288.6
28.4
51
50.8
5.0
111
110.5
10.9
171
170.2
16.8
231
229.9
22.6
291
289.6
28.5
52
51.7
5.1
12
111.5
11.0
72
171.2
16.9
32
230.9
22.7
92
290.6
28.6
53
52.7
5.2
13
112.5
.11.1
73
172.2
17.0
33
231.9
22.8
93
291.6
28.7
54
53.7
5.3
14
113.5
11.2
74
173.2
17.1
34
232.9
22.9
94
292.6
28.8
55
54.7
5.4
15
114.4
11.3
75
174.2
17.2
35
233.9
23.0
95
293.6
28.9
56
55.7
5.5
16
115.4
11.4
76
175.2
17.3
36
234.9
23.1
96
294.6
29.0
57
56.7
5.6
17
116.4
11.5
77
176.1
17.3
37
235.9
23.2
97
295.6
29.1
58
57.7
5.7
18
117.4
11.6
78
177.1
17.4
38
236.9
23.3
98
296.6
29.2
59
58.7
5.8
19
118.4
11.7
79
178.1
17.5
39
237.8
23.4
99
297.6
29.3
60
59.7
5.9
20
119.4
11.8
80
179.1
17.6
40
238.8
23.5
300
298.6
29.4
1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
E. i N. E. \ S. W. * N. W J 8. [For 7 \ Points.
TABLE 1. [Page 517
Difference of Latitude and Departure for £ Point
N. IE. N. fw. s. IE. s. fw.
Dist.
Lat. Dep.
Dist
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat
Dep.
1
1.0
0.1
61
60.3
9.0
121
119.7
17.8
181
179.0
26.6
241
238.4
35.4
2
2.0
0.3
62
61.3
9.1
22
120.7
17.9
82
180.0
26.7
42
239.4
35.5
3
3.0
0.4
63
62.3
9.2
23
121.7
18.0
83
181.0
26.9
43
240.4
35.7
4
4.0
0.6
64
63.3
9.4
24
122.7
18.2
84
182.0
27.0
44
241.4
35.8
5
4.9
0.7
65
64.3
9.5
25
123.6
18.3
85
183.0
27.1
45
242.3
35.9
6
5.9
0.9
66
65.3
9.7
26
124.6
18.5
86
184.0
27.3
46
243.3
36.1
7
6.9
1.0
67
66.3
9.8
27
125.6
18.6
87
185.0
27.4
47
244.3
36.2
8
7.9
1.2
68
67.3
10.0
28
126.6
18.8
88
186.0
27.6
48
245.3
36.4
9
8.9
1.3
69
68.3
10.1
29
127.6
18.9
89
187.0
27.7
49
246.3
36.5
10
9.9
1.5
70
69.2 10.3
30
128.6
19.1
90
187.9
27.9
50
247.3
36.7
11
10.9
1.6
71
70.2 10.4
131
129.6
19.2
191
188.9
28.0
251
248.3
36.8
12
11.9
1.8
72
71.2 ! 10.6
32
130.6
19.4
92
189.9
28.2
52
249.3
37.0
13
12.9
IT9
73
72. 2 ! 10. 7
33
131.6
19.5
93
190.9
28.3
53
250.3
37.1
14
13.8
2.1
74
73.2 i 10.9
34
132.5
19.7
94
191.9
28.5
54
251.3
37.3
15
14.8
2.2
75
74.2 1 11.0
35
133.5
19.8
95
192.9
28.6
55
252.2
37.4
16
15.8
2.3
76
75.2 11.2
36
134.5
20.0
96
193.9
28.8
56
253.2
37.6
17
16.8
2.5
77
76.2 1 11.3
37
135.5
20.1
97
194.9
28.9
57
254.2
37.7
18
17.8
2.6
78
77.2 11.4
38
136.5
20.2
98
195.9
29.1
58
255.2
37.9
19
18.8
2.8
79
78.1 11.6
39
137.5
20.4
99
196.8
29.2
59
256.2
38.0
20
19.8
2.9
80
79. 1 11. 7
40
138.5
20.5
200
197.8
29.3
60
257. 2
38.1
21
20.8
3.1
81
80.1 11.9
141
139.5
20.7
201
198.8
29.5
261
258.2
38.3
22
21.8
3.2
82
81.1 12.0
42
140.5
20.8
02
199.8
29.6
62
259.2
38.4
23
22.8
3.4
83
82.1
12.2
43
141.5
21.0
03
200.8
29.8
63
260.2
38.6
24
23.7
3.5
84
83.1
12.3
44
142.4
21.1
04
201.8
29.9
64
261.1
38.7
25
24.7
3.7
85
84.1
12.5
45
143.4
21.3
05
202.8
30.1
65
262.1
38.9
26
25.7
3.8
86
85.1
12.6
46
144.4
21.4
06
203.8
30.2
66
263.1
39.0
27
26.7
4.0
87
86.1
12.8
47
145. 4
21.6
07
204.8
30.4
67
264.1
39.2
28
27.7
4.1
88
87.0
12.9
48
146.4
21.7
08
205.7
30.5
68
265.1
39.3
29
28.7
4.3
89
88.0
13.1
49
147.4
21.9
09
206.7
30.7
69
266.1
39.5
30
29.7
4.4
90
89.0
13.2
50
148.4
22.0
10
207.7
30.8
70
267.1
39.6
31
30.7
4.5
91
90.0
13.4
151
149.4
22.2
211
208.7
31.0
2/1
268.1
39.8
32
31.7
4.7
92
91.0 i 13.5
52
150.4
22.3
12
209."
31.1
72
269.1
39.9
33
32.6
4.8
93
92.0
13.6
53
151.3
22.4
13
210."
31.3
73
270.0
40.1
34
33.6
5.0
94
93.0
13.8
54
152.3
22.6
14
211."
31.4
74
271.0
40.2
35
34.6
5.1
95
94.0
13.9
55
153.3
22.7
15
212.7
31.5
75
272.0
40.4
36
35.6
5.3
96
95.0 ! 14.1
56
154.3
22.9
16
213.-
31.7
76
273.0
40.5
37
36.6
5.4
97
96.0
14.2
57
155.3
23.0
17
214.7
31.8
77
274.0
40.6
38
37.6
5.6
98
96.9
14.4
58
156.3
23.2
18
215.6
32.0
78
275.0
40.8
39
38.6
5.7
99
97.9
14.5
59
157.3
23.3
19
216.6
32.1
79
276.0
40.9
40
39.6
5.9
100
98.9
14.7
60
158.3
23.5
20
217.6
32.3
80
277.0
41.1
41
40.6
6.0
101
99.9
14.8
161
159.3
23.6
221
218.6
32.4
281
278.0
41.2
42
41.5
6.2
02
100.9
15.0
62
160.2
23.8
22
219.6
32.6
82
278.9
41.4
43
42.5
6.3
03
101.9
15.1
63
161.2
23.9
23
220.6
32.7
83
279.9
41.5
44
43.5
6.5
04
102.9
15.3
64
162.2
24.1
24
221.6
32.9
84
280.9
41.7
45
44.5
6.6
05
103.9
15.4
65
163.2
24.2
25
222.6
33.0
85
281.9
41.8
46
45.5
6.7
06
104.9
15.6
66
164.2
24.4
26
223.6
33.2
86
282.9
42.0
47
46.5
6.9
07
105.8
15.7
67
165.2
24.5
27
224.5
33.3
87
283.9
42.1
48
47.5
7.0
08
106.8
15.8
68
166.2
24.7
28
225.5
33.5
88
284.9
42.3
49
48.5
7.2
09
107.8
16.0
69
167.2
24.8
29
226.5
33.6
89
285.9
42.4
50
49.5
7.3
10
108.8
16.1
70
168.2
24.9
30
227.5 ! 33.7
90
286.9
42.6
51
50.4
7.5
111
109.8
16.3
171
169.1
25.1
231
228.5
33,9
291
287.9
42.7
52
51.4
7.6
12
110.8
16.4
72
170.1
25.2
32
229.5
34.0
92
288.8
42.8
53
52.4
7.8
13
111.8
16.6
73
171.1
25.4
33
230.5
34.2
93
289.8
43.0
54
53.4
7.9
14
112.8
16.7
74
172.1
25.5
34
231.5
34.3
94
290.8
43.1
55
54.4
8.1
15
113.8
16.9
75
173.1
25.7
35
232.5
34.5
95
291.8
43.3
56
55.4
8.2
16
114.7
17.0
76
174.1
25.8
36
233.4
34.6
96
292.8
43.4
57
56.4
8.4
17
115.7
17.2
77
175.1
26.0
37
234.4
34.8
97
293.8
43.6
58
57.4
8.5
18
116.7
17.3
78
176.1
26.1
38
235.4
34.9
98
294.8
43.7
59
58.4
8.7
19
117.7
17.5
79
177.1
26.3
39
236.4
35.1
99
295.8
43.9
60
59.4
8.8
20
118.7
17.6
80
178.1
26.4
40
237.4
35.2
300
296.8
44.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. | Lat.
Dist.
Dep.
Lat.
E. |N. E. | S. W. f N. W. f S. [For 7J Points.
Page 518] TABLE 1.
Difference of Latitude and Departure for 1 Point.
N. by E. N. by W. S. by E. S. by W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.8
11.9
121
118.7
23.6
181
177.5
35.3
241
236.4
47.0
2
2.0
0.4
62
60.8
12.1
22
119.7
23.8
82
178.5
35.5
42
237.4
47.2
3
2.9
0.6
63
61.8
12.3
23
120.6
24.0
83
179.5
35.7
43
238.3
47.4
4
3.9
0.8
64
62.8
12.5
24
121.6
24.2
84
180.5
35.9
44
239.3
47.6
5
4.9
1.0
65
63.8
12.7
25
122.6
24.4
85
181.4
36.1
45
240.3
47.8
6
5.9
1.2
66
64.7
12.9
26
123.6
24.6
86
182.4
36.3
46
241.3
48.0
7
6.9
1.4
67
65.7
13.1
27
124.6
24.8
87
183.4
36.5
47
242.3
48.2
8
7.8
1.6
68
66.7
13.3
28
125.5
25.0
88
184.4
36.7
48
243.2
48.4
9
8.8
1.8
69
67.7
13.5
29
126.5
25.2
89
185.4
36.9
49
244.2
48.6
10
9.8
2.0
70
68.7
13.7
30
127.5
25.4
90
186.3
37.1
50
245. 2
48.8
11
10.8
2.1
71
69.6
13.9
131
128.5
25.6
191
187.3
37.3
251
246.2
49.0
12
11.8
2.3
72
70.6
14.0
32
129.5
25.8
92
188.3
37.5
52
247.2
49.2
13
12.8
2.5
73
71.6
14.2
33
130.4
25.9
93
189.3
37.7
53
248.1
49.4
14
13.7
2.7
74
72.6
14.4
34
131.4
26.1
94
190.3
37.8
54
249.1
49.6
15
14.7
2.9
75
73.6
14.6
35
132.4
26.3
95
191.3
38.0
55
250.1
49.7
16
15.7
3.1
76
74.5
14.8
36
133.4
26.5
96
192.2
38.2
56
251.1
49.9
17
16.7
3.3
77
75.5
15.0
37
134.4
26.7
97
193.2
38.4
57
252.1
50.1
18
17.7
3.5
78
76.5
15.2
38
135.3
26.9
98
194.2
38.6
58
253.0
50.3
19
18.6
3.7
79
77.5
15.4
39
136.3
27.1
99
195.2
38.8
59
254.0
50.5
20
19.6
3.9
80
78.5
15.8
40
137.3
27.3
200
196.2
39.0
60
255.0
50.7
21
20.6
4.1
81
79.4
15.8
141
138.3
27.5
201
197.1
39.2
261
256.0
50.9
22
21.6
4.3
82
80.4
16.0
42
139.3
27.7
02
198.1
39.4
62
257.0
51. 1
23
22.6
4.5
83
81.4
16.2
43
140.3
27.9
03
199.1
39.6
63
257.9
51.3
24
23.5
4.7
84
82.4
16.4
44
141.2
28.1
04
200.1
39.8
64
258.9
51.5
25
24.5
4.9
85
83.4
16.6
45
142.2
28.3
05
201.1
40.0
65
259.9
51.7
26
25.5
5.1
86
84.3
16.8
46
143.2
28.5
06
202.0
40.2
66
260.9
51.9
27
26.5
5.3
87
85.3
17.0
47
144.2
28.7
07
203.0
40.4
67
261.9
52.1
28
27.5
5.5
.88
86.3
17.2
48
145.2
28.9
08
204.0
40.6
68
262.9
52.3
29
28.4
5.7
89
87.3
17.4
49
146.1
29.1
09
205.0
40.8
69
263.8
52.5
30
29.4
5.9
90
88.3
17.6
50
147.1
29.3
10
206.0
41.0
70
264.8
52.7
31
30.4
6.0
91
89.3
17.8
151
148.1
29.5
211
206.9
41.2
271
265.8
52.9
32
31.4
6.2
92
90.2
17.9
52
149.1
29.7
12
207.9
41.4
72
266.8
53.1
33
32.4
6.4
93
91.2
18.1
53
150.1
29.8
1-8
208.9
41.6
73
267.8
53.3
34
33.3
6.6
94
92.2
18.3
54
151.0
30.0
14
209.9
41.7
74
268.7
53.5
35
34.3
6.8
95
93.2
18.5
55
152.0
30.2
15
210.9
41.9
75
269.7
53.6
36
35.3
7.0
96
94.2
18.7
56
153.0
30.4
16
211.8
42.1
76
270.7
53.8
37
36.3
7.2
97
95.1
18.9
57
154.0
30.6
17
212.8
42.3
77
271.7
54.0
38
37.3
7.4
98
96.1
19.1
58
155.0
30.8
18
213.8
42.5
78
272.7
54.2
39
38.3
7.6
99
97.1
19.3
59
155.9
31.0
19
214.8
42.7
79
273.6
54.4
40
39.2
7.8
100
98.1
19.5
60
156.9
31.2
20
215.8
42.9
80
274.6
54.6
41
40.2
8.0
101
99.1
19.7
161
157.9
31.4
221
216.8
43.1
281
275. 6
54.8
42
41.2
8.2
02
100.0
19.9
62
158.9
31.6
22
217.7
43.3
82
276.6
55.0
43
42.2
8.4
03
101.0
20.1
63
159.9
31.8
23
218.7
43.5
83
277.6
55.2
44
43.2
8.6
04
102.0
20.3
64
160.8
32.0
24
219.7
43.7
84
278.5
55.4
45
44.1
8.8
05
103.0
20.5
65
161.8
32.2
25
220.7
43.9
85
279.5
55.6
46
45.1
9.0
06
104.0
20.7
66
162.8
32.4
26
221.7
44.1
86
280.5
55.8
47
46.1
9.2
07
104.9
20.9
67
163.8
32.6
27
222.6
44.3
87
281.5
56.0
48
47.1
9.4
08
105.9
21.1
68
164.8
32.8
28
223.6
44.5
88
282.5
56.2
49
48.1
9.6
09
106.9
21.3
69
165.8
33.0
29
224.6
44.7
89
283.4
56.4
50
49.0
9.8
10
107.9
21.5
70
166.7
33.2
30
225.6
44.9
90
284.4
56.6
51
50.0
9.9
111
108.9
21.7
171
167.7
33.4
231
226.6
45.1
291
285.4
56.8
52
51.0
10.1
12
109.8
21.9
72
168.7
33.6
32
227.5
45.3
92
286.4
57.0
53
52.0
10.3
13
110.8
22.0
73
169. 7
33.8
33
228.5
45.5
93
287.4
57.2
54
53.0
10.5
14
111.8
22.2
74
170.7
33.9
34
229.5
45.7
94
288.4
57.4
55
53.9
10.7
15
112.8
22^4
75
171.6
34.1
35
230.5
45.8
95
289.3
57.6
56
54.9
10.9
16
113.8
22.6
76
172.6
34.3
36
231.5
46.0
96
290.3
57.7
57
55.9
11.1
17
114.8
22.8
77
173.6
34.5
37
232.4
46.2
97
291.3
57.9
58
56.9
11.3
18
115.7
23.0
78
174.6
34.7
38
233.4
46.4
98
292.3
58.1
59
57.9
11.5
19
116.7
23.2
79
175.6
34.9
39
234.4
46.6
99
293.3
58.3
60
58.8
11.7
20
117.7
23.4
80
176.5
35.1
40
235.4
46.8
300
294.2
58.5
Dist.
jDep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E. by N. E. by S. W. by N. W. by S. [For 7 points.
TABLE 1. [Page 519
Difference of Latitude and Departure for 1J Pointe.
N. by E. J E. X. by W. i W. S. by E. i E. S. by W. i W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.2
14.8
121
117.4
29.4
181
175.6
44.0
241
233.8
58.6
2
1.9
0.5
62
60.1
15.1
22
118.3
29.6
82
176.5
44.2
42
234.7
58.8
3
2.9
0.7
63
61.1
15.3
23
119.3
29.9
83
177.5
44.5
43
235.7
59.0
4
3.9
1.0
64
62.1
15.6
24
120.3
30.1
84
178.5
44.7
44
236.7
59.3
5
4.9
1.2
65
63.1
15.8
25
121.3
30.4
85
179.5
45.0
45
237.7
59.5
6
5.8
1.5
66
64.0
16.0
26
122.2
30.6
86
180.4
45.2
46
238. 6
59.8
7
6.8
1.7
67
65.0
16.3
27
123.2
30.9
87
181.4
45.4
47
239.6
60.0
8
7.8
1.9
68
66.0
16.5
28
124.2
31.1
88
182.4
45.7
48
240.6
60.3
9
8.7
2.2
69
66.9
16.8
29
125.1
31.3
89
183.3
45.9
49
241.5
60.5
10
9.7
2.4
70
67.9
17.0
30
126.1
31.6
90
184.3
46.2
50
242.5
60.7
11"
10.7
2.7
71
68.9
17.3
131
127.1
31.8
191
185.3
46.4
251
243.5
61.0
12
11.6
2.9
72
69.8
17.5
32
128.0
32.1
92
186.2
46.7
52
244.4
61.2
13
12.6
3.2
73
70.8
17.7
33
129.0
32.3
93
187.2
46.9
53
245.4
61.5
14
13.6
3.4
74
71.8
18.0
34
130.0
32.6
94
188.2
47.1
54
246.4
61.7
15
14.6
3.6
75
72.8
18.2
35
131.0
32.8
95
189.2
47.4
55
247.4
62.0
16
15.5
3.9
76
73.7
18.5
36
131.9
33.0
96
190.1
47.6
56
248.3
62.2
17
16.5
4.1
77
74.7
18.7
37
132.9
33.3
97
191.1
47.9
57
249.3 ! 62.4
18
17.5
4.4
78
75.7
19.0
38
133.9
33.5
98
192.1
48.1
58
250. 3 i 62. 7
19
18.4
4.6
79
76.6
19.2
39
134.8
33.8
99
193.0
48.4
59
251.2
62.9
20
19.4
4.9
80
77.6
19.4
40
135. S
34.0
200
194.0
48.6
60
252.2
63.2
21
20.4
5.1
81
78.6
19.7
141
136.8
34.3
201
195.0
48.8
261
253. 2 63. 4
22
21.3
5.3
82
79.5
19.9
42
137.7
34.5
02
195.9
49.1
62
254. 1 63. 7
23
22. 3 5. 6
83
80.5
20.2
43
138.7
34.7
03
196.9
49.3
63
255.1 63.9
24
23. 3 5. 8
84
81.5
20.4
44
139.7
35.0
04
197.9
49.6
64
256. 1 ! 64. 1
25
24. 3 6. 1
85
82.5
20.7
45
140.7
35.2
05
198.9
49.8
65
257.1
64.4
26
25.2
6.3
86
83.4
20.9
46
141.6
35.5
06
199.8
50.1
66
258.0
64.6
27
26.2
6.6
87
84.4
21.1
47
142.6
35.7
07
200.8
50.3
67
259. 0 64. 9
28
27.2
6.8
88
85.4
21.4
48 143.6
36.0
08
201.8
50.5
68
260. 0 65. 1
29
28.1
7.0
89
86.3
21.6
49
144.5
36.2
09
202. 7
50.8
69
260.9 | 65.4
30 29.1
7.3
90
87.3
21.9
50
145.5
36.4
10
203.7
51.0
70
261. 9 65. 6
31 ' 30. 1
7.5
91
88.3
22.1
151
146.5
36.7
211
204.7
51.3
271
262. 9 65. 8
32 ! 31.0
7.8
92
89.2
22. 4
52
147.4
36.9
12
205. 6
51.5
72
263. 8 66. 1
33 ; 32. 0
8.0
93
90.2
22! 6*
53
148.4
37.2
13
206.6
51.8
73
264. 8 66. 3
34 1 33.0
8.3
94
91.2
22.8
54
149.4
37.4
14
207. 6
52.0
74
265.8
66.6
35 34.0
8.5
95
92.2
23.1
55
150. 4
37.7
15
208.6
52.2
75
266.8
66.8
36
34.9
8.7
96
93.1
23.3
56
151.3
37.9
16
209.5
52.5
76
267.7
67.1
37
35.9
9.0
97
94.1
23.6
57
152.3
38.1
17
210.5
52.7
77
268.7
67.3
38
36.9
9.2
98
95.1
23.8
58
153. 3
38.4
18
211.5
53.0
78
269.7
67.5
39
37.8
9.5
99
96.0
24.1
59
154.2
38.6
19
212.4
53.2
79
270.6
67.8
40
38.8
9.7
100
97.0
24.3
60
155.2
38.9
20
213.4
53.5
80
271.6
68.0
41
39.8
10.0
101
98.0
24.5
161
156.2
39.1
221
214.4
53.7
281
272. 6
68.3
42
40.7
10.2
02
98.9
24.8
62
157.1
39.4
22
215.3
53.9
82
273.5
68.5
43
41.7
10.4
03
99.9
25.0
63
158.1
39.6
23
216.3
54.2
83
274.5
68.8
44
42.7
10.7
04
100.9
25.3
64
159.1
39.8
24
217.3
54.4
84
275.5
69.0
45
43.7
10.9
05
101.9
25.5
65
160.1
40.1
25
218.3
54.7
85
277.5
69.2
46
44.6
11.2
06
102.8
25.8
66
161.0
40.3
26
219.2
54.9
86
277.4
69.5
47
45.6
11.4
07
103.8
26.0
67
162.0
40.6
27
220.2
55.2
87
278.4
69.7
48
46.6
11.7
08
104.8
26.2
68
163.0
40.8
28
221.2
55.4
88
279.4
70.0
49
47.5
11.9
09
105.7
26.5
69
163.9
41.1
29
222.1
55.6
89
280.3
70.2
50
48.5
12.1
10
106.7
26.7
70
164.9
41.3
30
223.1
55.9
90
281.3
70.5
51
49.5
12.4
111
107.7
27.0
171
165.9
41.5
231
224.1
56.1
291
282.3
70.7
52
50.4
12.6
12
108.6
27.2
72
166.8
41.8
32
225.0
56.4
92
283.2
71.0
53
51.4
12.9
13
109.6
27.5
73
167.8
42.0
33
226.0
56.6
93
284.2
71.2
54
52.4
13.1
14
110.6
27.7
74
168.8
42.3
34
227.0
56.9
94
285. 2 •
71.4
55
53.4
13.4
15
111.6
27.9
75
169.8
42.5
35
228.0
57.1
95
286.2
71.7
56
54.3
13.6
16
112.5
28.2
76
170.7
42.8
36
228.9
57.3
96
287.1
71.9
57
55.3
13.8
17
113.5
28.4
77
171.7
43.0
37
229.9
57.6
97
288.1
72.2
58
56.3
14.1
18
114.5
28.7
78
172.7
43.3
38
230.9
57.8
98
289.1
72.4
59
57.2
14.3
19
115.4
28.9
79
173.6
43.5
39
231.8
58.1
99
290.9
72.7
60
58.2
14.6
20
116.4
29.2
80
174.6
43.7
40
232.8
58.3
300
291.0
72.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
ENE. | E. ESE. | E. WNW. f W. WSW. f W. [For 6| Points.
Page 520] TABLE 1.
Difference of Latitude and Departure for 1£ Points.
N. by E. } E. N. by W. } W. S. by E. $ E. S. by W. J W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.4
17.7
121
115.8
35.1
181
173.2
52.5
241
230.6
70.0
2
1.9
0.6
62
59.3
18.0
22
116.7
35.4
82
174.2
52.8
42
231.6
70.2
3
2.9
0.9
63
60.3
18.3
23
117.7
35.7
83
175.1
53.1
43
232.5
70.5
4
3.8
1.2
64
61.2
18.6
24
118.7
36.0
84
176.1
53.4
44
233.5
70.8
5
4.8
1.5
65
62.2
18.9
25
119.6
36.3
85
177.0
53.7
45
234.5
71.1
6
5.7
1.7
66
63.2
19.2
26
120.6
36.6
86
178.0
54.0
46
235.4
71.4
7
6.7
2.0
67
64.1
19.4
27
121.5
36.9
87
178.9
54.3
47
236.4
71.7
8
7.7
2.3
68
65.1
19.7
28
122.5
37.2
88
179.9
54.6
48
237.3
72.0
9
8.6
2.6
69
66.0
20.0
29
123.4
37.4
89
180.9
54.9
49
238.3
72.3
10
9.6
2.9
70
67.0
20.3
30
124.4
37.7
90
181.8
55.2
50
239.2
72.6
11
10.5
3.2
71
67.9
20.6
131
125.4
38.0
191
182.8
55.4
251
240.2
72.9
12
11.5
3.5
72
68.9
20.9
32
126.3
38.3
92
183.7
55.7
52
241.1
73.2
13
12.4
3.8
73
69.9
21.2
33
127. 3
38.6
93
184.7
56.0
53
242.1
73.4
14
13.4
4.1
74
70.8
21.5
34
128.2
38.9
94
185.6
56.3
54
243.1
73.7
15
14.4
4.4
75
71.8
21.8
35
129.2
39.2
95
186.6
56.6
55
244.0
74.0
16
15.3
4.6
76
72.7
22.1
36
130.1
39.5
96
187.6
56.9
56
245.0
74.3
17
16.3
4.9
77
73.7
22.4
37
131.1
39.8
97
188.5
57.2
57
245.9
74.6
18
17.2
5.2
78
74.6
22.6
38
132.1
40.1
98
189.5
57.5
58
246.9
74.9
19
18.2
5.5
79
75.6
22.9
39
133.0
40.3
99
190.4
57.8
59
247.8
75.2
20
19.1
5.8
80
76.6
23.2
40
134.0
40.6
200
191.4
58.1
60
248.8
75.5
21
20.1
6.1
81
77.5
23.5
141
134.9
40.9
201
192.3
58.3
261
249.8
75.8
22
21.1
6.4
82
78.5
23.8
42
135.9
41.2
02
193.3
58.6
62
250.7
76.1
23
22.0
6.7
83
79.4
24.1
43 136. 8
41.5
03
194.3
58.9
63
251.7
76.3
24
23.0
7.0
84
80.4
24.4
44
137.8
41.8
04
195. 2
59.2
64
252.6
76.6
25
23.9
7.3
85
81.3
24.7
45
138.8
42.1
05
196.2
59.5
65
253.6
76.9
26
24.9
7.5
86
82.3
25.0
46
139.7
42.4
06
197.1
59.8
66
254.5
77.2
27
25.8
7.8
87
83.3
25.3
47
140.7
42.7
07
198.1
60.1
67
255.5
77.5
28
26.8
8.1
88
84.2
25.5
48
141.6
43.0
08
199.0
60.4
68
256.5
77.8
29
27.8
8.4
89
85.2
25.8
49
142.6
43.3
09
200.0
60.7
69
257.4
78.1
30
28.7
8.7
90
86.1
26.1
50
143.5
43.5
10
201.0
61.0
70
258.4
78.4
31
29.7
9.0
91
87.1
26.4
151
144.5
43.8
211
201.9
61.3
271
259.3
78.7
32
30.6
9.3
92
88.0
26.7
52
145.5
44.1
12
202.9
61.5
72
260.3
79.0
33
31.6
9.6
93
89.0
27.0
53
146.4
44.4
13
203.8
61.8
73
261.2
79.2
34
32.5
9.9
94
90.0
27.3
54
147.4
44.7
14
204.8
62.1
74
262.2
79.5
35
33.5
10.2
95
90.9
27.6
55
148.3
45.0
15
205.7
62.4
75
263.2
79.8
36
34.4
10.5
96
91.9
27.9
56
149.3
45.3
16
206.7
62.7'
76
264.1
80.1
37
35.4
10.7
97
92.8
28.2
57
150.2
45.6
17
207.7
63.0
77
265.1
80.4
38
36.4
11.0
98
93.8
28.4
58
151.2
45.9
18
208.6
63.3
78
266.0
80.7
39
37.3
11.3
99
94.7
28.7
59
152.2
46.2
19
209.6
63.6
79
267.0
81.0
40
38.3 ! 11.6
100
95.7
29.0
. 60
153. 1
46.4
20
210.5
63.9
80
267.- 9
81.3
41
39.2
11.9
101
96.7
29.3
161
154.1
46.7
221
211.5
64.2
281
268.9
81.6
42
40.2
12.2
02
97.6
29.6
62
155.0
47.0
22
212.4
64.4
82
269.9
81.9
43
41.1
12.5
03
98.6
29.9
63
156.0
47.3
23
213.4
64.7
83
270.8
82.2
44
42.1
12.8
04
99.5
30.2
64
156.9
47.6
24
214.4
65.0
84
271.8
82.4
45
43.1
13.1
05
100.5
30.5
65
157.9
47.9
25
215. 3
65.3
85
272.7
82.7
46
44.0
13.4
06
101.4
30.8
66
158.9
48.2
26
216.3
65.6
86
273.7
83.0
47
45.0
13.6
07
102.4
31.1
67
159.8
48.5
27
217.2
65.9
87
274.6
83.3
48
45.9
13.9
08
103.3
31.4
68
160.8
48.8
28
218.2
66.2
88
275.6
83.6
49
46.9
14.2
09
104.3
31.6
69
161.7
49.1
29
219.1
66.5
89
276.6
83.9
50
47.8
14.5
10
105.3
31.9
70
162.7
49.3
30
220.1
66.8
90
277.5
84.2
51
48.8
14.8
111
106.2
32.2
171
163.6
49.6
231
221.1
67.1
291
278.5
84.5
52
49.8
15.1
12
107.2
32.5
72
164.6
49.9
32
222.0
67.3
92
279.4
84.8
53
50.7
15.4
13
108.1
32.8
73
165.6
50.2
33
223.0
67.6
93
280.4
85.1
54
51.7
15.7
14
109.1
33.1
74
166.5
50.5
34
223.9
67.9
94
281.3
85.3
55
52.6
16.0
15
110.0
33.4
75
167.5
50.8
35
224.9
68.2
95
282.3
85.6
56
53.6
16.3
16
111.0
33.7
76
168.4
51.1
36
225.8
68.5
96
283.3
85.9
57
54.5
16.5
17
112.0
34.0
77
169.4
51.4
37
226.8
68.8
97
284.2
86.2
58
55.5
16.'8
18
112.9
34.3
78
170.3
51.7
38
227.8
69.1
98
285.2
86.5
59
56.5
17.1
19
113.9
34.5
79
171.3
52.0
39
228.7
69.4
99
286.1
86.8
60
57.4
17.4
20
114.8
34.8
80
172.2
52.3
40
229.7
69.7
300
287.1
87.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
ENE. J E. ESE. } E. WNW. } W. WSW. J W. [For 6* Points.
TABLE 1. [Page 521
Difference of Latitude and Departure for If Points.
N. by E. | E. N. by W. f W. S. by E. f E. S. by W. f W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat. I Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.4
20.6
121
113.9
40.8
181
170.4 i 61.0
241
226.9
81.2
2
1.9
0.7
62
58.4
20.9
22
114.9
41.1
82
171.4 61.3
42
227.9
81.5
3
2.8
1.0
63
59.3
21.2
23
115.8
41.4
83 172.3 | 61.7
43
228.8
81.9
4
3.8
1.3
64
60.3 21.6
24
116.8
41.8
84
173.2 i 62.0
44
229.7
82.2
5
4.7
1.7
65
61.2 21.9
25
117.7
42.1
85
174.2
62.3
45 230. 7
82.5
6
5.6
2.0
66
62. 1 22. 2
26
118.6
42.4
86
175.1
62.7
46 ! 231.6
82.9
7
6. 6 2. 4
67
63. 1 22. 6
27
119.6
42.8
87
176.1
63.0
47 232.6
83.2
8
7.5 2.7
68
64.0
22.9
28
120.5
43.1
88
177.0
63.3
48 233.5
83.5
9
8.5
3.0
69
65.0
23.2
29
121.5
43.5
89
178.0
63.7
49 i 234. 4
83.9
10
9.4
3.4
70
65.9
23.6
30
122.4
43.8
90
178.9
64.0
50 235.4
84.2
11
10.4
3.7
71
66. 8 23. 9
131
123.3
44.1
191
179.8
64.3
251 236. 3
84.6
12
11.3
4.0
72
67. 8 24. 3
32
124.3
44.5
92
180.8
64.7
52 j 237. 3
84.9
13
12.2
4.4
73
68.7
24.6
33
125.2
44.8
93
181.7
65.0
53 i 238.2
85.2
14
13. 2 4. 7
74
69.7
24.9
34
126.2
45.1
94
182.7
65.4
54
239.2
85.6
15
14.1
5.1
75
70.6
25.3
35
127.1
45.5
95
183.6
65.7
55
240.1
85.9
16
15.1
5.4
76
71.6
25.6
36
128.0
45.8
96
184.5
66.0
56
241.0
86.2
17
16.0
5.7
77
72.5
25.9
37
129.0
46.2
97
185. 5 66. 4
57
242.0
86.6
18
16.9
6.1
78
73.4
26.3
38
129.9
46.5
98
186.4
66.7
58
242.9
86.9
19
17.9
6.4
79
74.4
26.6
39 1 130. 9
46.8
99
187.4
67.0
59
243.9
87.3
20
18.8
6.7
80
75.3
27.0
40 : 131.8
47.2
200
188. 3 67. 4
60
244.8
87.6
21
19. 8 7. 1
81
76.3
27.3
141 ! 132.8
47.5
201
189.3
67.7
261
245.7
87.9
22
20.7
7.4
82
77.2
27.6
42
133.7
47.8
02
190.2
68.1
.62
246.7
88.3
23
21.7
T T
/. /
83
78.1
28.0
43
134.6
48.2
03
191.1
68.4
63
247.6
88.6
24
22. 6 8. 1
84
79.1
28.3
44
135.6
48.5
04
192.1
68.7
64
248.6
88.9
25
23.5 8.4
85
80.0
28.6
45
136.5
48.8
05
193.0
69.1
65
249.5
89.3
26
24. 5 8. 8
86
81.0
29.0
46
137.5
49.2
06
194.0
69.4
66
250.5
89.6
27
25. 4 9. 1
87
81.9
29.3
47
138.4
49.5
07
194.9
69.7
67
251.4
89.9
28
26. 4 9. 4
88
82.9
29.6
48
139.3
49.9
08
195.8
70.1
68
252.3
90.3
29
27.3
9.8
89
83.8
30.0
49
140.3
50.2
09
196.8
70.4
69
253.3
90.6
30
28.2
10.1
90
84.7
30.3
50
141.2
50.5
10
197.7
70.7
70
254.2
91.0
31
29. 2 10. 4
91
85.7
30.7
151
142. 2
50.9
211
198.7
71.1
271 255.2
91.3
32
30. 1 10. 8
92
86.6
31.0
52
143.1
51.2
12
199.6
71.4
72 256. 1
91.6
33
31.1 11.1
93
87.6
31.3
53
144.1
51.5
13
200.5
71.8
73
257.0
92.0
34
32. 0 11. 5
94
88.5
31.7
54
145.0
51.9
14
201.5
72.1
74
258.0
92.3
35
33. 0 11. 8
95
89.4
.32.0
55
145.9
52.2
15
202.4
72.4
75
258.9
92.6
36
33. 9 12. 1
96
90.4 32.3
56
146.9
52.6
16
203.4
72.8
76
259.9
•93.0
37
34.8 12.5
97
91.3
32.7
57
147.8
52.9
17
204.3
73.1
77
260.8
93.3
38
35.8
12.8
98
92.3
33.0
58
148.8
53.2
18
205.3
73.4
78
261.7
93.7
39
36.7
13.1
99
93.2
33.4
59
149.7
53.6
19
206.2
73.8
79
262.7
94.0
40
37. 7 13. 5
100 ! 94. 2
33.7
60 150. 6
53.9
20
207.1
74.1
80
263. 6 94. 3
41
38.6 ! 13.8
101
95.1
34.0
161
151.6
54.2
221
208.1
74.5
281 264. 6 94. 7
42
39.5 j 14.1
02
96.0
34.4
62
152.5
54.6
22
209.0
74.8
82 265. 5 95. 0
43
40. 5 14. 5
03
97.0
34.7
63
153.5
54.9
23
210.0
75.1
83
266. 5 95. 3
44
41. 4 14. 8
04
97. 9 35. 0
64
154.4
55.2
24
210.9
75.5
84
267. 4 95. 7
45
42. 4 15. 2
05
98.9
35.4
65
155.4
55.6
25
211.8
75.8
85
268. 3 96. 0
46
43. 3 15. 5
06
99.8
35.7
66
156.3
55.9
26
212.8
76.1
86
269. 3 96. 4
47
44. 3 15. 8
07
100. 7 36. 0
67
157.2
56.3
27
213.7
76.5
87
270. 2 96. 7
48
45.2
16.2
08
101.7
36.4
68
158.2
56.6
28
214.7
76.8
88
271.2 i 97.0
49
46.1
16.5
09
102.6
36.7
69
159.1
56.9
29 215. 6
77.1
89 i 272. 1
97.4
50
47.1
16.8
10
103.6
37.1
70
160.1
57.3
30
216.6
77.5
90 273. 0
97.7
51
48.0
17.2
111
104.5
37.4
171
161.0
57.6
231
217.5
77.8
291
274.0
98.0
52
49.0
17.5
12
105.5
37.7
72
161.9
57.9
32
218.4
78.2
92
274.9
98.4
53
49.9
17.9
13
106.4
38.1
73
162.9
58.3
33
219.4
78.5
93
275.9
98.7
54
50.8
18.2
14
107.3
38.4
74
163.8
58.6
34
220.3
78.8
94
276.8
99.0
55
51.8
18.5
15
108.3
38.7
75
164.8
59.0
35
221.3
79.2
95
277.8
99.4
56
52.7
18.9
16
109.2
39.1
76
165. 7
59.3
36
222.2
79.5
96
278.7
99.7
57
53.7
19.2
17
110.2
39.4
77
166.7
59.6
37
223.1
79.8
97
279.6
100.1
58
54.6
19.5
18
111.1
39.8
78
167.6
60.0
38
224.1
80.2
98
280.6
100.4
59
55.6
19.9
19
112. 0
40.1
79
168.5
60.3
39
225.0
80.5
99
281.5
100.7
60
56.5
20.2
20
113.0
40.4
80
169.5
60.6
40
226.0
80.9
300
282.5
101.1
Dist.
Dep.
Lat.
Dist.
Dep. ] Lat.
Dist.
Dep. | Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
ENE. £ E. ESE. i E. WNW. £ W. WSW. J W. [For 6£ Points.
Page 522] TABLE 1.
Differenca of Latitude and Departure for 2 Points.
NNE. NNW. SSE. SSW.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.4
23.3
121
111.8
46.3
181
167.2
69.3
241
222.7
92.2
2
1.8
0.8
62
57.3
23.7
22
112.7
46.7
82
168.1
69.6
42
223.6
92.6
3
2.8
1.1
63
58.2
24.1
23
113.6
47.1
83
169.1
70.0
43
224.5
93.0
4
3.7
1.5
64
59.1
24.5
24
114.6
47.5
84
170.0
70.4
44
225.4
93.4
5
4.6
1.9
65
60.1
24.9
25
115.5
47.8
85
170.9
70.8
45
226.4
93.8
6
5.5
2.3
66
61.0
25.3
26
116.4
48.2
86
171.8
71.2
46
227.3
94.1
7
6.5
2.7
67
61.9
25.6
27
117.3
48.6
87
172.8
71.6
47
228.2
94.5
8
7.4
3.1
68
62.8
26.0
28
118.3
49.0
88
173.7
71.9
48
229.1
94.9
9
8.3
3.4
69
63.7
26.4
29
119.2
49.4
89
174.6
72.3
49
230.0
, 95.3
10
9.2
3.8
70
64.7
26.8
30
120.1
49.7
90
175.5
72.7
50
231.0
95.7
11
10.2
4.2
71
65.6
27.2
131
121.0
50.1
191
176.5
73.1
251
231.9
96.1
12
11.1
4.6
72
66.5
27.6
32
122.0
50.5
92
177.4
73.5
52
232.8
96.4
13
12.0
5.0
73
67.4
27.9
33
122.9
50.9
93
178.3
73.9
53
233.7
96.8
14
12.9
5.4
74
68.4
28.3
34
123.8
51.3
94
179.2
74.2
54
234. 7
97.2
15
13.9
5.7
75
69.3
28.7
35
124.7
51.7
95
180.2
74.6
55
235.6
97.6
16
14.8
6.1
76
70.2
29.1
36
125.6
52.0
96
181.1
75.0
56
236.5
98.0
17
15.7
6.5
77
71.1
29.5
37
126.6
52.4
97
182.0
75.4
57
237. 4
98.3
18
16.6
6.9
78
72.1
29.8
38
127.5
52.8
98
182.9
75.8
58
238.4
98.7
19
17.6
7.3
79
73.0
30.2
39
128.4
53.2
99
183.9
76.2
59
239.3
99.1
20
18.5
7.7
80
73.9
30.6
40
129.3
53.6
200
184.8
76.5
60
240.2
99.5
21
19.4
8.0
81
74.8
31.0
141
130.3
54.0
201
185.7
76.9
261
241.1
99.9
22
20.3
8.4
82
75.8
31.4
42
131.2
54.3
02
186.6
77.3
62
242.1
100.3
23
21.2
8.8
83
76.7
31.8
43
132.1
54.7
03
187. 5
77.7
63 243. 0
100.6
24
22.2
9.2
84
77.6
32.1
44
133.0
55.1
04
188.5
78.1
64
243.9
101.0
25
23.1
9.6
85
78.5
32.5
45
134.0
55.5
05
189.4
78.5
65
244.8
101.4
26
24.0
9.9
86
79.5
32.9
46
134.9
55.9
06
190.3
78.8
66
245.8
101.8
27
24.9
10.3
87
80.4
33.3
47
135.8
56.3
07
191.2
79.2
67
246. 7 102. 2
28
25.9
10.7
88
81.3
33.7
48
136.7
56.6
08
192.2
79.6
68
247.6
102.6
29
26.8
11.1
89
82.2
34.1
49
137.7
57.0
09
193. 1
80.0
69
248.5
102.9
30
27.7
11.5
90
83.1
34.4
50
138.6
57.4
10
194.0
80.4
70
249. 4 103. 3
31
28.6
11.9
91
84.1
34.8
151
139.5
57.8
211
194.9
80.7
271
250.4
103.7
32
29.6
12.2
92
85.0
35.2
52
140.4
58.2
12
195.9
81.1
72
251.3
104.1
33
30.5
12.6
93
85.9
35.6
53
141.4
58.6
13
196.8
81.5
73
252.2
104.5
34
31.4 13.0
94
86.8
36.0
54
142.3
58.9
14
197.7
81.9
74
253.1
104.9
35
32.3
13.4
95
87.8
36.4
55
143.2
59.3
15
198.6
82.3
75
254.1
105.2
36
33.3
13.8
96
88.7
36.7
56
144.1
59.7
16
1*99. 6
82.7
76
255.0
105.6
37
34.2
14.2
97
89.6
37.1
57
145.0
60.1
17
200.5
83.0
77
255.9
106.0
38
35.1
14.5
98
90.5
37.5
58
146.0
60.5
18
201.4
83.4
78
256.8
106.4
39
36.0
14.9
99
91.5
37.9
59
146.9
60.8
19
202.3
83.8
79
257.8
106.8
40
37.0
15.3
100
92.4
38.3
60
147.8
61.2
20
203.3
84.2
80
258.7
107.2
41
37.9
15.7
101
93.3
38.7
161
148.7
61.6
221
204.2
84.6
281
259.6
107.5
42
38.8
16.1
02
94.2
39.0
62
149.7
62.0
22
205.1
85.0
82
260.5
107.9
43
39.7
16.5
03
95.2
39.4
63
150.6
62.4
23
206.0
85.3
83
261.5
108.3
44
40.7
16.8
04
96.1
39.8
64
151.5
62.8
24
206.9
85.7
84
262.4
108.7
45
41.6
17.2
05
97.0
40.2
65
152.4
63.1
25
207.9
86.1
85
263.3
109.1
46
42.5
17.6
06
97.9
40.6
66
153.4
63.5
26
208.8
86.5
86
264.2
109.4
47
43.4
18.0
07
98.9
40.9
67
154.3
63.9
27
209.7
86.9
87
265.2
109.8
48
44.3
18.4
08
99.8
41.3
68
155.2
64.3
28
210.6
87.3
88
266.1
110.2
49
45.3
18.8
09
100.7
41.7
69
156.1
64.7
29
211.6
87.6
89
267.0
110.6
50
46.2
19.1
10
101.6
42.1
70
157.1
65.1
30
212.5
88.0
90
267.9
111. 0
51
47.1
19.5
111
102.6
42.5
171
158.0
65.4
231
213.4
88.4
291
268.8
111.4
52
48.0
19.9
12
103.5
42.9
72
158.9
65.8
32
214.3
88.8
92
269.8
111.7
53
49.0
20.3
13
104.4
43.2
73
159.8
66.2
33
215.3
89.2
93
270.7
112.1
54
49.9
20.7
14
105.3
43.6
74
160.8
66.6
34
216.2
89.5
94
271.6
112.5
55
50.8
21.0
15
106.2
44.0
75
161.7
67.0
35
217.1
89.9
95
272.5
112.9
56
51.7
21.4
16
107.2
44.4
76
162.6
67.4
36
218.0
90.3
96
273.5
113.3
57
52.7
21.8
17
108.1
44.8
77
163.5
67.7
37
219.0
90.7
97
274.4
113.7
58
53.6
22.2
18
109.0
45.2
78
164.5
68.1
38
219.9
91.1
98
275.3
114.0
59
54.5
22.6
19
109.9
45.5
79
165.4
68.5
39
220.8
91.5
99
276.2
114.4
60
55.4
23.0
20
110.9
45.9
80
166.3
68.9
40
221.7
91.8
300 277. 2
114.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
ENE. ESE. WNW WSW [For 6 Points.
TABLE 1. [Page 523
Difference of Latitude and Departure for 2\ Points.
NNE. * E. NISTW. \ W. SSE. \ E. SSW. i W.
Dist
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.1
26.1
121
109.4
51.7
181
163.6
77.4
241
217.9
103.0
2
1.8
0.9
62
56.0
26.5
22
110.3
52.2
82
164.5
77.8
42
218.8
103.5
3
2.7
1.3
63
57.0
26.9
23
111.2
52.6
83
165.4
78.2
43
219.7
103.9
4
. 3.6
1.7
64
57.9
27.4
24
112.1
53.0
84
166.3
78.7
44
220.6
104.3
5
4.5
2.1
65
58.8
27.8
25
113.0
53.4
85
167.2
79.1
45
221.5
104.8
6
5.4
2.6
66 59. 7
28.2
26
113.9
53.9
86
168.1
79.5
46
222.4
105. 2
7
6.3
3.0
67
60.6
28.6
27
114.8
54.3
87
169.0
80.0
47
223.3
105.6
8
7.2
3.4
68
61.5
29.1
28
115.7
54.7
88
169.9
80.4
48
224.2
106.0
9
8.1
3.8
69
62.4
29.5
29
116.6
55.2
89
170.9
80.8
49
225.1
106.5
10
9.0
4.3
70
63.3
29.9
30
117.5
55.6
90
171.8
81.2
50
226.0
106.9
11
9.9
4.7
71
64.2
30.4
131
118.4
56.0
191
172.7
81.7
251
226.9
107.3
12
10.8
5.1
72
65.1
30.8
32
119.3
56.4
92
173.6
82.1
52
227.8
107.7
13
11.8
5.6
73
66.0
31.2
33
120.2
56.9
93
174.5
82.5
53
228.7
108.2
14
12.7
6.0
74
66.9
31.6
34
121.1
57.3
94
175.4
82.9
54
229.6
108.6
15
13.6
6.4
75
67.8
32.1
35
122.0
57.7
95
176.3
83.4
55
230.5
109.0
16
14.5
6.8
76
68.7
32.5
36
122.9
58.1
96
177.2
83.8
56
231.4
109.5
17
15.4
7.3
77
69.6
32.9
37
123.8
58.6
97
178.1
84.2
57
232.3
109.9
18
16.3
7.7
78
70.5
33.3
38 i 124.8
59.0
98
179.0
84.7
58
233.2
110.3
19
17.2
8.1
79
71.4
33.8
39 ! 125.7
59.4
99
179.9
85.1
59
234.1
110.7
20
18.1
8.6
80
72.3
34.2
40 126. 6
59.9
200
180.8 j 85.5
60
235.0
111.2
21
19.0
9.0
81
73.2
34.6
141 127. 5
60.3
201
181.7 | 85.9
261
235.9
111.6
22
19.9
9.4
82
74.1
35.1
42
128.4
60.7
02
182.6 1 86.4
62
236.8
112.0
23
20.8
9.8
83
75.0
35.5
43
129.3
61.1
03
183. 5 86. 8
63
237.7
112.4
24
21.7
10.3
84
75.9
35.9
44
130.2
61.6
04
184. 4 87. 2
64
238.7
112.9
25
22.6
10.7
85
76.8
36.3
45
131.1
62.0
05
185. 3 87. 6
65
239.6
113.3
26
23.5
11.1
86
77.7
36.8
46
132.0
62.4
06
186. 2 88. 1
66
240.5
113.7
27
24.4
11.5
87
78.6
37.2
47
132.9
62.9
07
187. 1 88. 5
67
241.4
114.2
28
25.3
12.0
88
79.6
37.6
48
133.8
63.3
08
188. 0 88. 9
68
242. 3
114.6
29
26.2
12.4
89
80.5
38.1
49
134.7
63.7
09
188.9 ! 89.4
69 I 243.2
115.0
30
27.1
12.8
90
81.4
38.5
50 j 135.6
64.1
10
189. 8 89. 8
70 ! 244.1
115.4
31
28.0
13.3
91
82.3
38.9
151 136. 5
64.6
211
190. 7 90. 2
271 ! 245.0
115.9
32
28.9
13.7
92
83.2
39.3
52
137.4
65.0
12
191.6 90.6
72 245. 9
116.3
33
29.8
14.1
93
84.1
39.8
53
138.3
65.4
13
192. 5 91. 1
73 I 246.8
116.7
34
30.7
14.5
94
85.0
40.2
54 139. 2
65.8
14
193.5
91.5
74
247.7
117.2
35
31.6
15.0
95
85.9
40.6
55 j 140.1
66.3
15
194.4
91.9
75
248.6
117.6
36
32.5
15.4
96
86.8
41.0
56 141.0
66.7
16
195.3
92.4
76
249.5
118.0
37
33.4
15.8
97
87.7
41.5
57 i 141.9
67.1
17
196.2
92.8
77
250.4
118.4
38
34.4
16.2
98
88.6 j 41.9
58 142. 8
67.6
18 197. 1
93.2
78
251.3
118.9
39
35.3
16.7
99
89.5
42.3
59 143. 7
68.0
19 j 198.0
93.6
79
252.2
119.3
40
36.2
17.1
100
90.4
42.8
60
144.6
68.4
20 198. 9
94.1
80
253.1
119.7
41
37.1
17.5
101
91.3
43.2
161
145.5
68.8
221
199.8
94.5
281 254. 0
120.1
42
38.0
18.0
02
92.2
43.6
62
146.4
69.3
22
200.7
94.9
82
254.9
120.6
43
38.9
18.4
03
93.1
44.0
63
147.4
69.7
23
201.6
95.3
83
255.8
121.0
44
39.8
18.8
04
94.0
44.5
64
148.3
70.1
24
202.5
95.8
84
256.7
121.4
45
40.7
19.2
05
94.9
44.9
65
149.2
70.5
25
203.4
96.2
85
257.6
121.9
46
41.6
19.7
06
95.8
45.3
66 150. 1
71.0
26
204.3
96.6
86
258.5 ! 122.3
47
42.5
20.1
07
96.7
45.7
67
151.0
71.4
27 205. 2
97.1
87
259. 4 122. 7
48
43.4
20.5
08
97.6
46.2
68
151.9
71.8
28 206. 1
97.5
88
260.3 123.1
49
44.3
21.0
09
98.5
46.6
69
152.8
72.3
29
207.0
97.9
89
261. 3 123. 6
50
45.2
21.4
10
99.4
47.0
70
153.7
72.7
30
207.9
98.3
90
262.2 124.0
51
46.1
21.8
111
100.3
47.5
171
154.6
73.1
231
208.8
98.8
291
263. 1 124. 4
52
47.0
22.2
12
101.2
47.9
72
155.5
73.5
32
209.7
99.2
92
264.0 , 124,8
53
47.9
22.7
13
102. 2
48.3
73
156.4
74.0
33
210.6
99.6
93
264. 9 i 125. 3
54
48.8
23.1
14
103.1
48.7
74
157.3
74.4
34
211.5
100.0
94 ; 265. 8 i 125. 7
55
49.7
23.5
15
104.0
49.2
75
158.2
74.8
35
212.4
100.5
95 j 266. 7
126.1
56
50.6
23.9
16
104.9
49.6
76
159.1
75.2
36
213.3
100.9
96 267. 6
126.6
57
51.5
24.4
17
105.8
50.0
77
160.0
75.7
37
214.2
101.3
97
268.5
127.0
58
52.4
24.8
18
106.7
50.5
78
160.9
76.1
38
215.1
101.8
98
269.4
127.4
59
53.3
25.2
19
107.6
50.9
79
161.8
76.5
39
216.1
102.2
99
270.3
127.8
60
54.2
25.7
20
108.5
51.3
80
162.7
77.0
40
217.0
102.6
300
271.2
128.3
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
Dist.
Dep.
Lat.
Dist i Dep.
Lat.
NR by E. f E. SE. by E. f E. NW. by W. f W. SW. by W. f W. [For 5| Points.
Page 524] TABLE 1.
Difference of Latitude and Departure for 2£ Points.
NNE. £ E. NNW. J W. SSE. J E. SSW. J W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.8
28.8
121
106.7
57.0
181
159.6
85.3
241
212.5
113.6
2
1.8
0.9
62
54.7
29.2
22
107.6
57.5
82
160. 5
85.8
42
213.4
114.1
3
2.6
1.4
63
55.6
29.7
23
108.5
58.0
83
161.4
86.3
43
214.3
114.5
4
3.5
1.9
64
56.4
30.2
24
109.4
58.5
84
162.3
86.7
44
215.2
115.0
5
4.4
2.4
65
57.3
30.6
25
110.2
58.9
85
163.2
87.2
45
216.1
115.5
6
5.3
2.8
66
58.2
31.1
26
111.1
59.4
86
164.0
87.7
46
217.0
116.0
7
6.2
3.3
67
59.1
31.6
27
112.0
59.9
87
164.9
88.2
47
217.8
116.4
8
7.1
3.8
68
60.0
32.1
28
112.9
60.3
88
165.8
88.6
48
218.7
116.9
9
7.9
4.2
69
60.9
32.5
29
113.8
60.8
89
166.7
89.1
49
219.6
117.4
10
8.8
4.7
70
61.7
33.0
30
114.6
61.3
90
167.6
89.6
50
220.5
117.8
11
9.7
5.2
71
62.6
33.5
131
115.5
61.8
191
168.4
90.0
251
221.4
118.3
12
10.6
5.7
72
63.5
33.9
32
116.4
62.2
92
169.3
90.5
52
222.2
118.8
13
11.5
6.1
73
64.4
34.4
33
117.3
62.7
93
170.2
91.0
53
223.1
119.3
14
12.3
6.6
74
65.3
34.9
34
118.2
63.2
94
171.1
91.5
54
224.0
119.7
15
13.2
7.1
75
66.1
35.4
35
119.1
63.6
95
172.0
91.9
55
224.9
120.2
16
14.1
7.5
76
67.0
35.8
36
119.9
64.1
96
172. 9
92.4
56
225.8
120.7
17
15.0
8.0
77
67.9
36.3
37
120.8
64.6
97
173.7
92.9
57
226. 7
121.1
18
15.9
8.5
78
68.8
36.8
38
121.7
65.1
98
174.6
93.3
58
227.5
121.6
19
16.8
9.0
79
69.7
37.2
39
122.6
65.5
99
175.5
93.8
59
228.4
122.1
20
17.6
9.4
80
70.6
37.7
40
123.5
66.0
200
176.4
94.3
60
229. 3
122.6
21
18.5
9.9
81
71.4
38.2
141
124. 4
66.5
201
177.3
94.8
261
330.2
123. 0
22
19.4
10.4
82
72.3
38.7
42
125.2
66.9
02
178.1
95.2
62
231.1
123.5
23
20.3
10.8
83
73.2
39.1
43
126.1
67.4
03
179.0
95.7
63
231.9
124.0
24
21.2
11.3
84
74.1
39.6
44
127.0
67.9
04
179.9
96.2
64
232.8
124.4
25
22.0
11.8
85
75.0
40.1
45
127.9
68.4
05
180.8
96.6
65
233.7
124.9
26
22.9
12.3
86
75.8
40.5
46
128.8
68.8
06
181.7
97.1
66
234. 6
125.4
27
23.8
12.7
87
76.7
41.0
47
129.6
69.3
07
182.6
97.6
67
235.5
125.9
28
24.7
13.2
88
77.6
41.5
48
130.5
69.8
08
183.4
98.1
68
236.4
126.3
29
25.6
13.7
89
78.5
42.0
49
131.4
70.2
09
184. 3
98.5
69
237.2
126.8
30
26.5
14.1
90
79.4
42.4
50
132.3
70.7
10
185.2
99.0
70
238.1
127.3
31
27.3
14.6
91
80.3
42.9
151
133.2
71.2
211
186.1
99.5
271
239.0
127.7
32
28.2
15.1
92
81.1
43.4
52
134.1
71.7
12
187.0
99.9
72
239.9
128.2
33
29.1
15.6
93
82.0
43.8
53
134.9
72.1
13
187.8
100.4
73
240.8
128.7
34
30.0
16.0
94
82.9
44.3
54
135.8
72.6
14
188.7
100.9
74
241.6
129.2
35
30.9
16.5
95
83.8
44.8
55
136.7
73.1
15
189.6
101.4
75
242.5
129.6
36
31.7
17.0
96
84.7
45.3
56
137.6
73.5
16
190.5
101.8
76
243.4
130. 1
37
32.6
17.4
97
85.5
45.7
57
138. 5
74.0
17
191.4
102.3
77
244.3
130.6
38
33.5
17.9
98
86.4
46.2
58
139.3
74.5
18
192.3
102.8
78
245.2
131.0
39
34.4
18.4
99
87.3
46.7
59
140.2
75.0
19
193.1
103.2
79
246.1
131.5
40
35.3
18.9
100
88.2
47.1
60
141.1
75.4
20
194.0
103.7
80
246.9
132.0
41
36.2
19.3
101
89.1
47.6
161
142.0
75.9
221
194.9
104.2
281
247.8
132.5
42
37.0
19.8
02
90.0
48.1
62
142.9
76.4
22
195.8
104.7
82
248.7
132.9
43
37.9
20.3
03
90.8
48.6
63
143.8
76.8
23
196.7
105.1
83
249.6
133.4
44
38.8
20.7
04
91.7
49.0
64
144.6
77.3
24
197.6
105.6
84
250.5
133.9
45
39.7
21.2
05
92.6
49.5
65
145.5
77.8
25
198.4
106.1
85
251.3
134.3
46
40.6
21.7
06
93.5
50.0
66
146.4
78.3
26
199.3
106.5
86
252.2
134.8
47
41.5
22.2
07
94.4
50.4
67
147.3
78.7
27
200.2
107.0
87
253.1
135.3
48
42.3
22.6
08
95.2
50.9
68
148.2
79.2
28
201.1
107.5
88
254.0
135.8
49
43.2
23.1
09
96.1
51.4
69
149.0
79.7
29
202.0
107.9
89
254.9
136.2
50
44.1
23.6
10
97.0
51.9
70
149.9
80.1
30
202.8
108.4
90
255.8
136.7
51
45.0
24.0
111
97.9
52.3
171
150.8
80.6
231
203.7
108.9
291
256.6
137.2
52
45.9
24.5
12
98.8
52.8
72
151.7
81.1
32
204.6
109.4
92
257.5
137. 6
53
46.7
25.0
13
99.7
53.3
73
152.6
81.6
33
205.5
109.8
93
258.4
138.1
54
47.6
25.5
14
100.5
53.7
74
153.5
82.0
34
206.4
110.3
94
259.3
138.6
55
48.5
25.9
15
101.4
54.2
75
154.3
82.5
35
207.3
110.8
95
260.2
139.1
56
49.4
26.4
16
102.3
54.7
76
155.2
83.0
36
208.1
111.2
96
261.0
139.5
57
50.3
26.9
17
103.2
55.2
77
156.1
83.4
37
209.0
111.7
97
261.9
140.0
58
51.2
27.3
18
104.1
55.6
78
157.0
83.9
38
209.9
112.2
98
262.8
140.5
59
52.0
27.8
19
104.9
56.1
79
157.9
84.4
39
210.8
112.7
99
263.7
140.9
60
52.9
28.3
20
105.8
56.6
80
158.7
84.9
40
211.7
113.1
300
264.6
141.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. byE. *.E. SE. by E. J E. NW. by W. J W. SW. by W. £ W. [For 5£ Points.
TABLE 1. [Page 525
Difference of Latitude and Departure for 2| Points.
NNE. | E. NNW. f W. SSE. f E. SSW. f W.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat. j Dep.
Dist. Lat. Dep.
1
0.9
0.5
61
52.3
31.4
121
103.8
62.2
181
155. 2 ! 93. 1
241 206. 7
123.9
2
1.7
1.0
62
53.2
31.9
22
104.6
62.7
82
156.1 \ 93.6
42 1 207.6
124.4
3
2.6
1.5
63
54.0
32.4
23
105.5
63.2
83
157.0 | 94.1
43 j 208. 4
124.9
4
3.4
2.1
64
54.9
32.9
24
106.4
63.7
84
157. 8 94. 6
44 i 209. 3
125.4
5
4.3
2.6
65
55.8
33.4
25
107.2
64.3
85
158.7
95.1
45 i 210.1
126.0
6
5.1
3.1
66
56.6
33.9
26
108.1
64.8
86
159.5
95.6
46
211.0
126.5
7
6.0
3.6
67
57.5
34.4
27
108.9
65.3
87
160.4
96.1
47
211.9
127.0
8
6.9
4.1
68
58.3
35.0
28
109.8
65.8
88
161.3
96.7
48
212.7
127.5
9
7.7
4.6
69
59.2
35.5
29
110.6
66.3
89
162.1
97.2
49
213.6
128.0
10
8.6
5.1
70
60.0
36.0
30
111.5
66.8
90
163.0
97.7
50
214.4
128.5
11
9.4
5.7
71
60.9
36.5
131
112.4
67.3
191
163.8
98.2
251
215.3
129.0
12
10.3
6.2
72.
61.8
37.0
32
113.2
67.9
92
164.7
98.7
52
216.1 ! 129.6
13
11.2
6.7
73
62.6
37.5
33
114.1
68.4
93
165.5
99.2
53
217. 0 i 130. 1
14
12.0
7.2
74
63.5
38.0
34
114.9
68.9
94
166.4
99.7
54
217.9
130.6
15
12.9
7. 7
75
64.3
38.6
35
115.8
69.4
95
167.3
100.3
55
218.7
131. 1
16
13.7
8.2
76
65.2
39.1
36
116.7
69.9
96
168.1
100.8
56 1 219. 6
131.6
17
14.6
8.7
77
66.0
39.6
37
117.5
70.4
97
169.0
101.3
57 220. 4
132.1
18
15.4
9.3
78
66.9
40.1
38
118.4
70.9
98
169.8
101.8
58 . 221.3
132.6
19
16.3
9.8
79
67.8
40.6
39
119.2
71.5
99
170.7
102.3
59 222.2
133.2
20
17.2
10.3
80
68.6
41.1
40
120.1
72.0
200
171.5
102.8
60 1 223.0
133.7
21
18.0
10.8
81
69.5
41.6
141
120.9
72.5
201
172.4
103.3
261 223. 9
134.2
22
18.9
11.3
82
70.3
42. 2
42
121.8
73.0
02
173.3
103.8
62
224.7
134. 7
23
19.7
11.8
83
71.2
42^7
43
122.7
73.5
03
174.1
104.4
63
225.6
135.2
24
20.6
12.3
84
72.0
43.2
44
123.5
74.0
04
175.0
104.9
64
226.4
135.7
25
21.4
12.9
85
72.9
43.7
45
124.4
74.5
05
175.8
105.4
65
227.3
136.2
26
22.3
13.4
86
73.8
44.2
46
125.2
75.1
06
176.7
105.9
66
228.2
136. 8
27
23.2
13.9
87
74.6
44.7
47
126.1
75.6
07
177.5
106.4
67
229.0
137.3
28
24.0
14.4
88
75.5
45.2
48
126.9
76.1
08
178.4
106.9
68
229.9
137.8
29
24.9
14.9
89
76.3
45.8
49
127.8
76.6
09
179.3
107.4
69
230.7
138.3
30
25.7
15.4
90
77.2
46.3
50
128.7
77.1
10
180.1
108.0
70
231.6
138.8
31
26.6
15.9
91
78.1
46.8
151 j 129.5
77.6
211
181.0
108.5
271
232.4
139.3
32 1 27.4
16.5
92
78.9
47.3
52 j 130.4
78.1
12
181.8
109.0
72
233.3
139.8
33 28. 3
17.0
93
79.8
47.8
53 131.2
78.7
13
182.7
109.5
73
234. 2 140. 4
34 29.2
17.5
94
80.6
48.3
54
132.1
79.2
14
183.6
110.0
74
235. 0 140. 9
35 30.0
18.0
95
81.5
48.8
55
132.9
79.7
15
184.4
110.5
75
235.9
141.4
36 30. 9
18.5
96
82.3
49.4
56 133. 8
80.2
16
185.3
111.0
76
236.7
141.9
37 ! 31.7
19.0
97
83.2
49.9
57 134. 7
80.7
17
186.1
111.6
77
237.6
142.4
38 32. 6
19.5
98
84.1
50.4
58 135. 5
81.2
18
187.0
112.1
78
238.4
142.9
39 33.5
20.1
99
84.9
50.9
59
136.4
81.7
19
187.8
112.6
79
239.3
143.4
40 | 34.3
20.6
100
85.8
51.4
60
137.2
82.3
20
188.7
113.]
80
240.2
143.9
41 j 35.2
21.1
101
86.6
51.9
161
138.1
82.8
221 1 189.6
113.6
281
241.0
144.5
42 ] 36.0
21.6
02
87.5
52.4
62
139.0
83.3
22 190. 4
114.1
82
241.9
145.0
43 ! - 36. 9
22.1
03
88.3
53.0
63
139.8
83.8
23 191. 3
114.6
83
242.7
145.5
44 i 37.7
22.6
04
89.2
53.5
64
140.7
84.3
24
192.1
115.2
84
243.6
146.0
45 ; 38.6
23.1
05
90.1
54.0
65
141.5
84.8
25
193.0
115.7
85
244.5
146.5
46 39.5
23.6
06
90.9
54.5
66
142.4
85.3
26
193.8
116.2
86
245.3
147.0
47 40.3
24.2
07
91.8
55.0
67
143.2
85.9
27
194.7
116.7
87
246.2
147.5
48 41.2
24.7
08
92.6
55. 5
68
144.1
86.4
28
195.6
117.2
88
247.0
148.1
49 | 42.0
25.2
09
93.5
56.0
69
145.0
86.9
29
196.4
117.7
89
247.9
148.6
50 1 42. 9
25.7
10
94.4
56.6
70
145.8
87.4
30
197.3
118.2
90
248.7
149.1
51
43.7
26.2
111
95.2
57.1
171
146. 7 87. 9
231
198.1
118.8
291
249.6
149.6
52
44.6
26.7
12-
96.1
57.6
72
147.5
88.4
32
199.0
119.3
92
250.5
150.1
53
45.5
27.2
13
96.9
58.1
73
148.4
88.9
33
199.9
119.8
93
251.3
150.6
54
46.3
27.8
14
97.8
58.6
74
149. 2 89. 5
34
200.7
120.3
94
252.2
151.1
55
47.2
28.3
15
98.6
59.1
75
150.1
90.0
35
201.6
120.8
95
253.0
151.7
56
48.0
28.8
16
99.5
59.6
76
151.0
90.5
36
202.4
121.3
96
253.9
152.2
57
48.9
29.3
17
100.4
60.2
77
151. 8 91. 0
37
203.3
121.8
97
254.7
152.7
58
49.7
29.8
18
101.2
60.7
78
152.7 91.5
38
204.1
122.4
98
255.6
153.2
59
50.6
30.3
19
102.1
61.2
79
153. 5 92. 0
39
205.0
122.9
99
256.5
153.7
60
51.5
30.8
20 102. 9
61.7
80
154.4
92.5
40
205.9
123.4
300
257.3
154.2
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
NE. by E. i E. SE. by E. i E. XW. by W. i W. SW. by \V. i W. [For 5£ Points.
Page 526] TABLE 1.
Difference of Latitude and Departure for 3 Points.
NE. by N. NW. by N. SE. by S, SW. by S.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
50.7
33.9
121
100.6
67.2
181
150.5
100.6
241
200.4
133.9
2
1.7
1.1
62
51.6
34.4
22
101.4
67.8
82
151.3
101.1
42
201.2
134.4
3
2.5
1.7
63
52.4
35.0
23
102.3
68.3
83
152.2
101.7
43
202.0
135.0
4
3.3
2.2
64
53.2
35.6
24
103.1
68.9
84
153.0
102.2
44
202.9
135.6
5
4.2
2.8
65
54.0
36.1
25
103.9
69.4
85
153.8
102.8
45
203.7
136.1
6
5.0
3.3
66
54.9
36.7
26
104.8
70.0
86
154.7
103.3
46
204.5
136.7
7
5.8
3.9
67
55.7
37.2
27
105.6
70.6
87
155.5
103.9
47
205 4
137.2
8
6.7
4.4
68
56.5
37.8
28
106.4
71.1
88
156.3
104.4
48
206.2
137.8
9
7.5
5.0
69
57.4
38.3
29
107.3
71.7
89
157.1
105.0
49
207.0
138.3
10
8.3
5.6
70
58.2
38.9
30
108.1
72.2
90
158.0
105.6
50
207.9
138.9
11
9.1
6.1
71
59.0
39.4
131
108.9
72.8
191
158.8
106.1
251
208.7
139.4
12
10.0
6.7
72
59.9
40.0
32
109.8
73.3
92
159.6
106.7
52
209.5
140.0
13
10.8
7.2
73
60.7
40.6
33
110.6
73.9
93
160.5
107.2
53
210.4
140.6
14
11.6
7.8
74
61.5
41.1
34
111.4
74.4
94
161.3
107.8
54
211.2
141.1
15
12.5
8.3
75
62.4
41.7
35
112.2
75.0
95
162.1
108.3
55
212.0
141.7
16
13.3
8.9
76
63.2
42.2
36
113.1
75.6
96
163.0
108.9
56
212.9
142.2
17
14.1
9.4
77
64.0
42.8
37
113.9
76.1
97
163.8
109.4
57
213.7
142.8
18
15.0
10.0
78
64.9
43.3
38
114.7
76.7
98
164.6
110.0
58
214.5
143.3
19
15.8
10.6
79
65.7
43.9
39
115.6
77.2
99
165.5
110.6
59
215.4
143.9
20
16.6
11.1
80
66.5
44.4
40
116.4
77.8
200
166.3
111.1
60
216.2
144.4
21
17.5
11.7
81
67.3
45.0
141
117.2
78.3
201
167.1
111.7
261
217.0
145.0
22
18.3
12.2
82
68.2
45.6
42
118.1
78.9
02
168.0
112.2
62
217.8
145.6
23
19.1
12.8
83
69.0
46.1
43
118.9
79.4
03
168.8
112.8
63
218.7
146.1
24
20.0
13.3
84
69.8
46.7
44
119.7
80.0
04
169.6
113.3
64
219.5
146.7
25
20.8
13.9
85
70.7
47.2
45
120.6
80.6
05
170.5
113.9
65
220.3
147.2
26
21.6
14.4
86
71.5
47.8
46
121.4
81.1
06
171.3
114.4
66
221.2
147.8
27
22.4
15.0
87
72.3
48.3
47
122.2
81.7
07
172.1
115.0
67
222.0
148.3
28
23.3
15.6
88
73.2
48.9
48
123.1
82.2
08
172.9
115.6
68
222.8
148.9
29
24.1
16.1
89
74.0
49.4
49
123.9
82.8
09
173.8
116.1
69
223.7
149.4
30
24.9
16.7
90
74.8
50.0
50
124.7
83.3
10
174.6
116.7
70
224.5
150.0
31
25.8
17.2
• 91
75.7
50.6
151
125.6
83.9
211
175.4
117.2
271
225.3
150.6
32
26.6
17.8
92
76.5
51.1
52
126.4
84.4
12
176.3
117.8
72
226.2
151.1
33
27.4
18.3
93
77.3
51.7
53
127.2
85.0
13
177.1
118.3
73
227.0
151.7
34
28.3
18.9
94
78.2
52.2
54
128.0
85.6
14
177.9
118.9
74
227.8
152. 2'
35
29.1
19.4
95
79.0
52.8
55
128.9
86.1
15
178.8
119.4
75
228.7
152.8
36
29.9
20.0
96
79.8
53.3
56
129.7
86.7
16
179.6
120.0
76
229.5
153.3
37
30.8
20.6
97
80.7
53.9
57
130.5
87.2
17
180.4
120.6
77
230.3
153.9
38
31.6
21.1
98
81.5
54.4
58
131.4
87.8
18
181.3
121.1
78
231.1
154.4
39
32.4
21.7
99
82.3
55.0
59
132. 2
88.3
19
182.1
121.7
79
232.0
155.0
40
33.3
22.2
100
83.1
55.6
60
133.0
88.9
20
182.9
122.2
80
232.8
155.6
41
34.1
22.8
101
84.0
56.1
161
133.9
89.4
221
183.8
122.8
281
233.6
156.1
42
34.9
23.3
02
84.8
56.7
62
134.7
90.0
22
184.6
123.3
82
234.5
156.7
43
35.8
23.9
03
85.6
57.2
63
135.5
90.6
23
185.4
123.9
83
235.3
157.2
44
36.6
24.4
04
86.5
57.8
64
136.4
91.1
24
186.2
124.4
84
236.1
157.8
45
37.4
25.0
05
87.3
58.3
65
137.2
91.7
25
187.1
125.0
85
237.0
158.3
46
38.2
25.6
06
88.1
58.9
66
138.0
92.2
26
187.9
125.6
86
237.8
158.9
47
39.1
26.1
07
89.0
59.4
67
138.9
92.8
27
188.7
126.1
87
238.6
159.4
48
39.9
26.7
08
89.8
60.0
68
139.7
93.3
28
189.6
126.7
88
239.5
160.0
49
40.7
27.2
09
90.6
60.6
69
140.5
93.9
29
190.4
127.2
89
240.3
160.6
50
41.6
27.8
10
91.5
61.1
70
141.3
94.4
30
191.2
127.8
90
241.1
161.1
51
42.4
28.3
111
92.3
61.7
171
142.2
95.0
231
192.1
128.3
291
242.0
161.7
52
43.2
28.9
12
93.1
62.2
72
143.0
95.6
32
192.9
128.9
92
242.8
162.2
53
44.1
29.4
13
94.0
62.8
73
143.8
96.1
33
193.7
129.4
93
243.6
162.8
54
44.9
30.0
14
94.8
63.3
74
144.7
96.7
34
194.6
130.0
94
244.5
163.3
55
45.7
30.6
15
95.6
63.9
75
145.5
97.2
35
195.4
130.6
95
245.3
163.9
56
46.6
31.1
16
96.5
64.4
76
146.3
97.8
36
196.2
131.1
96
246.1
164.4
57
47.4
31.7
17
97.3
65.0
77
147.2
98.3'
37
197.1
131.7
97
246.9
165.0
58
48.2
32.2
18
98.1
65.6
78
148.0
98.9
38
197.9
132.2
98
247.8
165.6
59
49.1
32.8
19
98.9
66.1
79
148.8
99.4
39
198.7
132.8
99
248.6
166.1
60
49.9
33.3
20
99.8
66.7
80
149.7
100.0
40
199.6
133.3
300
249.4
166.7
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NKbyE. SE. by E. NW. by W. SW. by W. [For 5 Points.
TABLE 1. [Page 527
Difference of Latitude and Departure for 3^ Points.
NE. | N. NW. f N. SE. f S. SW. f S.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
49.0
36.3
121
97.2
72.1
181
145.4
107.8
241
193.6
143.6
2
1.6
1.2
62
49.8
36.9
22
98.0
72.7
82
146.2
108.4
42
194.4
144.2
3
2.4
1.8
63
50.6
37.5
23
98.8
73.3
83
147.0
109.0
43
195.2
144.8
4
3.2
2.4
64
51.4
38.1
24
99.6
73.9
84
147.8
109.6
44
196.0
145.4
5
4.0
3.0
65
52.2
38.7
25
100.4
74.5
85
148.6
110.2
45
196.8
145.9
6
4.8
3.6
66
53.0
39.3
26
101.2
75.1
86
149.4
110.8
46
197.6
146.5
7
5.6
4.2
67
53.8
39.9
27
102.0
75.7
87
150.2
111.4
47
198.4
147.1
8
6.4
4^8
68
54.6
40.5
28
102.8
76.2
88
151.0
112.0
48
199.2
147.7
9
7.2
5.4
69
55.4
41.1
29
103.6
76.8
89
151.8
112.6
49
200.0
148.3
10
8.0
6.0
70
56.2
41.7
30
104.4
77.4
90
152.6
113.2
50
200.8
148.9
11
8.8
6.6
71
57. i/
42.3
131
105.2
78.0
191
153.4
113.8
251
201.6
149.5
12
9.6
7.1
72
57.8
42.9
32
106.0
78.6
92
154.2
114.4
52
202.4
150.1
13
10.4
7. 7
73
58.6
43.5
33
106.8
79.2
93
155.0
115.0
53
203.2
150.7
14
11.2
8.3
74
59.4
44.1
34
107.6
79.8
94
155.8
115.6
54
204.0
151.3
15
12.0
8.9
75
60.2
44.7
35
108.4
80.4
95
156.6
116.2
55
204.8
151.9
16
12.9
9.5
76
61.0
45.3
36
109.2
81.0
96
157.4
116.8
56
205.6
152.5
17
13.7
10.1
77
61.8
45.9
37
110.0
81.6
97
158.2
117.4
57
206.4
153.1
18
14.5
10.7
78
62.7
46.5
38
110.8
82.2
98
159.0
117.9
58
207.2
153.7
19
15.3
11.3
79
63.5
47.1
39
111.6
82.8
99
159.8
118.5
59
208.0
154.3
20
16.1
11.9
80
64.3
47.7
40
112.4
83.4
200
160.6
119.1
60
208.8
154.9
21
16.9
12.5
81
65.1
48.3
141
113.3
84.0
201
161.4
119.7
261
209.6
155.5
22
17.7
13.1
82
65.9
48.8
42
114.1
84.6
02
162.2
120.3
62
210.4
156.1
23
18.5
13.7
83
66.7
49.4
43
114.9
85.2
03
163.1
120.9
63
211.2
156.7
24
19.3
14.3
84
67.5
50.0
44
115.7
85.8
04
163.9
121,5
64
212.0
157.3
25
20.1
14.9
85
68.3
50.6
45
116.5
86.4
05
164.7
122.1
65
212.8
157.9
26
20.9
15.5
86
69.1
51.2
46
117.3
87.0
06
165.5
122.7
66
213.7
158.5
27
21.7
16.1
87
69.9
51.8
47
118.1
87.6
07
166.3
123.3
67
214.5
159.1
28
22.5
16.7
88
70.7
52.4
48
118.9
88.2
08
167.1
123.9
68
215.3
159.6
29
23.3
17.3
89
71.5
53.0
49
119.7
88.8
09
167.9
124.5
69
216.1
160.2
30
24.1
17.9
90
72.3
53.6
50
120.5
89.4
10
168.7
125.1
70
216.9
160.8
31
24.9
18.5
91
73.1
54.2
151
121.3
90.0
211
169.5
125.7
271
217.7
161.4
32
25.7
19.1
92
73.9
54.8
52
122.1
90.5
12
170.3
126.3
72
218.5
162.0
33
26.5
19.7
93
74.7
55.4
53
122.9
91.1
13
171.1
126.9
73
219.3
162.6
34
27.3
20.3
94
75.5
56.0
54
123.7
91.7
14
171.9
127.5
74
220.1
163.2
35
28.1
20.8
95
76.3
56.6
55
124.5
92.3
15
172.7
128.1
75
220.9
163.8
36
28.9
21.4
96
77.1
57.2
56
125.3
92.9
16
173.5
128.7
76
221.7
164.4
37
29.7
22.0
97
77.9
57.8
57
126.1
93.5
17
174.3
129.3
77
222.5
165.0
38
30.5
22.6
98
78.7
58.4
58
126.9
94.1
18
175.1
129.9
78
223.3
165.6
39
31.3
23.2
99
79.5
59.0
59
127.7
94.7
19
175.9
130.5
79
224.1
166.2
40
32. 1 23. 8
100
80.3
59.6
60
128.5
95.3
20
176. 7 ! 131. 1
80
224.9
166.8
41
32.9
24.4
101
81.1
60.2
161
129.3
95.9
221
177.5 .131.6
281
225.7
167.4
42
33.7
25.0
02
81.9
60.8
62
130.1
96.5
22
178.3
132.2
82
226.5
168.0
43
34.5
25.6
03
82.7
61.4
63
130.9
97.1
23
179.1
132.8
83
227.3
168.6
44
35.3
26.2
04
83.5
62.0
64
131.7
97.7
24
179.9
133.4
84
228.1
169.2
45
36.1
26.8
05
84.3
62.5
65
132.5
98.3
25
180.7
134.0
85
228.9
169.8
46
36.9
27.4
06
85.1
63.1
66
133.3
98.9
26
181.5
134.6
86
229.7
170.4
47
37.8
28.0
07
85.9
63.7
67
134.1
99.5
27
182.3
135.2
87
230.5
171.0
48
38.6
28.6
08
86.7
64.3
68
134.9
100.1
28
183.1
135.8
88
231.3
171.6
49
39.4
29.2
09
87.5
64.9
69
135.7
100.7
29
183.9
136.4
89
232.1
172.2
50
40.2
29.8
10
88.4
65.5
70
136.5
101.3
30
184.7
137.0
90
232.9
172.8
51
41.0
30.4
111
89.2
66.1
171 i 137.3
101.9
231
185.5
137.6
291
233.7
173.3
52
41.8 31.0
12
90.0
66.7
72 1 138. 2
102.5
32
186.3
138.2
92
234.5
173.9
53
42.6
31.6
13
90.8
67.3
73
139.0
103.1
33
187.1
138.8
93
235.3
174.5
54
43.4
32.2
14
91.6
67.9
74
139.8
103.7
34
188.0
139.4
94
236.1
175.1
55
44.2
32.8
15
92.4
68.5
75
140.6
104.2
35
188.8
140.0
95
236.9
175.7
56
45.0
33.4
16
93.2
69.1
76
141.4
104.8
36
189.6
140.6
96
237.7
176.3
57
45.8
34.0
17
94.0
69.7
77
142.2
105.4
37
190.4
141.2
97
238.6
176.9
58
46.6
34.6
18
94.8
70.3
78
143.0
106.0
38
191.2
141.8
98
239.4
177.5
59
47.4
35.1
19
95.6
70.9
79
143.8
106.6
39
192.0
142.4
99
240.2
178.1
60
48.2
35.7
20
96.4
71.5
80
144.6
107.2
40
192.8
143.0
300
241.0
178.7
Dist. Dep. Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist. ; Dep.
Lat
NE. f E. SE. f E. NW. f W. SW. f W. [For 4| Points.
61828°— 16 27
Page 528] TABLE 1.
Difference of Latitude and Departure for 3$ Points.
NE. J N. NW. J N. SE. J S. SW. J S.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
47.2
38.7
121
93.5
76.8
181
139.9
114.8
241
186.3
152.9
2
1.5
1.3
62
47.9
39.3
22
94.3
77.4
82
140.7
115.5
42
187. 1
153.5
3
2.3
1.9
63
48.7
40.0
23
95.1
78.0
83
141.5
116.1
43
187.8
154.2
4
3.1
2.5
64
49.5
40.6
24
95.9
78.7
84
142.2
116.7
44
188.6
154.8
5
3.9
3.2
65
50.2
41.2
25
96.6
79.3
85
143.0
117. 4
45
189.4
155.4
6
4.6
3.8
66
51.0
41.9
26
97.4
79.9
86
143.8
118.0
46
190.2
156.1
7
5.4
4.4
67
51.8
42.5
27
98.2
80.6
87
144.6
118.6
47
190.9
156.7
8
6.2
5.1
68
52.6
43.1
28
98.9
81.2
88
145.3
119.3
48
191.7
157.3
9
7.0
5.7
69
53.3
43.8
29
99.7
81.8
89
146.1
119.9
49
192.5
158.0
10
7.7
6.3
70
54.1
44.4
30
100.5
82.5
90
146.9
120.5
50
193.3
158.6
11
8.5
7.0
71
54.0
45.0
131
101.3
83.1
191
147.6
121.2
251
194.0
159.2
12
9.3
7.6
72
55.7
45.7
32
102.0
83.7
92
148.4
121.8
52
194.8
159.9
13
10.0
8.2
73
56.4
46.3
33
102.8
84.4
93
149.2
122.4
53
195.6
160.5
14
10.8
8.9
74-
57.2
46.9
34
103.6
85.0
94
150.0
123.1
54
196.3
161.1
15
11.6
9.5
75
58.0
47.6
35
104.4
85.6
95
150.7
123.7
55
197.1
161.8
16
12.4
10.2
76
58.7
48.2
36
105.1
86.3
96
151.5
124.3
56
197.9
162.4
17
13.1
10.8
77
59.5
48.8
37
105.9
86.9
97
152.3
125.0
57
198.7
163.0
18
13.9
11.4
78
60.3
49.5
38
106.7
87.5
98
153.1
125.6
58
199.4
163.7
19
14.7
12.1
79
61.1
50.1
39
107.4
88.2
99
153.8
126.2
59
200.2
164.3
20
15.5
12.7
80
61.8
50.8
40
108.2
88.8
200
154.6
126.9
60
201.0
164.9
21
16.2
13.3
81
62.6
51.4
141
109.0
89.4
201
155.4
127.5
261
201.8
165.6
•22
17.0
14.0
82
63.4
52.0
42
109.8
90.1
02
156.1
128.1
62
202.5
166.2
23
17.8
14.6
83
64.2
52.7
43
110.5
90.7
03
156.9
128.8
63
203.3
166.8
24
18.6
15.2
84
64.9
53.3
44
111.3
91.4
04
157.7
129.4
64
204.1
167.5
25
19.3
15.9
85
65.7
53.9
45
112. 1
92.0
05
158.5
130.1
65
204.8
168.1
26
20.1
16.5
86
66.5
54.6
46
112.9
92.6
06
159.2
130.7
66
205.6
168.7
27
20.9
17.1
87
67.3
55.2
47
113.6
93.3
07
160.0
131.3
67
206.4
169.4
28
21.6
17.8
88
68.0
55.8
48
114.4
93.9
08
160.8
132.0
68
207.2
170.0
29
22.4
18.4
89
68.8
56.5
49
115.2
94.5
09
161.6
132.6
69
207.9
170.7
30
23.2
19.0
90
69.6
57.1
50
116.0
95.2
10
162.3
133.2
70
208.7
171.3
31
24.0
19.7
91
70.3
57.7
151
116.7
95.8
211
163.1
133.9
271
209.5
171.9
32
24.7
20.3
92
71.1
58.4
52
117.5
96.4
12
163.9
134.5
72
210.3
172.6
33
25.5
20.9
93
71.9
59.0
53
118.3
97.1
13
164.7
135.1
73
211.0
173.2
34
26.3
21.6
94
72.7
59.6
54
119.0
97.7
14
165.4
135.8
74
211.8
173.8
35
27.1
22.2
95
73.4
60.3
55
119.8
98.3
15
166.2
136.4
75
212.6
174.5
36
27.8
22.8
96
74.2
60.9
56
120.6
99.0
16
167.0
137.0
76
213.4
175.1
37
28.6
23.5
97
75.0
61.5
57
121.4
99.6
17
167.7
137.7
77
214.1
175.7
38
29.4
24.1
98
75.8
62.2
58
122.1
100.2
18
168.5
138.3
78
214.9
176.4
39
30.1
24.7
99
76.5
62.8
59
122.9
100.9
19
169.3
138.9
79
215.7
177.0
40
30.9
25.4
100
77.3
63.4
60
123.7
101.5
20
170.1
139.6
80
216.4
177.6
41
31.7
26.0
101
78.1
64.1
161
124.5
102.1
221
170.8
140.2
281
217.2
178.3
42
32.5
26.6
02
78.8
64.7
62
125. 2
102.8
22
171.6
140.8
82
218.0
178.9
43
33.2
27.3
03
79.6
65.3
63
126.0
103.4
23
172.4
141.5
83
218.8
179.5
44
34.0
27.9
04
80.4
66.0
64
126.8
104.0
24
173.2
142.1
84
219.5
180.2
45
34.8
28.5
05
81.2
66.6
65
127.5
104.7
25
173.9
142.7
85
220.3
180.8
46
35.6
29.2
06
81.9
67.2
66
128.3
105.3
26
174.7
143.4
86
221.1
181.4
47
36.3
29.8
07
82.7
67.9
67
129.1
105.9
27
175.5
144.0
87
221.9
182.1
48
37.1
30.5
08
83.5
68.5
68
129.9
106.6
28
176.2
144.6
88
222. 6
182.7
49
37.9
31.1
09
84.3
69.1
69
130.6
107.2
29
177.0
145.3
89
223] 4
183.3
50
38.7
31.7
10
85.0
69.8
70
131.4
107.8
30
177.8
145.9
90
224.2
184.0
51
39.4
32.4
111
85.8
70.4
171
132.2
108.5
231
178.6
146.5
291
224.9
184.6
52
40.2
33.0
12
86.6
71.1
72
133.0
109.1
32
179.3
147.2
92
225.7
185.2
53
41.0
33.6
13
87.4
71.7
73
133.7
109.8
33
180.1
147.8
93
226.5
185.9
54
41.7
34.3
14
88.1
72.3
74
134.5
110.4
34
180.9
148.4
94
227.3
186.5
55
42.5
34.9
15
88.9
73.0
75
135.3
111.0
35
181.7
149.1
95
228.0
187.1
56
43.3
35.5
16
89.7
73.6
76
136.0
111.7
36
182.4
149.7
96
228.8
187.8
57
44.1
36.2
17
90.4
74.2
77
136.8
112.3
37
183.2
150.4
97
229.6
188.4
58
44.8
36.8
18
91.2
74.9
78
137.6
112.9
38
184.0
151.0
98
230.4
189.0
59
45.6
37.4
19
92.0
75.5
79
138.4
113.6
39
184.7
151.6
99
231.1
189.7
60
46.4
38.1
20
92.8
76.1
80
139.1
114.2
40
185.5
152.3
300
231.9
190.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. £ E. SE. } E. NW. * W. SW. J W. [For 4J Points.
TABLE 1. [Page 529
Difference of Latitude and Departure for 3f Pointe.
NE. i N. NW. i X. SE. 1 S. SW. J S.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
45.2
41.0
121
89.7
81.3
181
134.1
121.6
241
178.6
161.8
2
1.5
1.3
62
45.9
41.6
22
90.4
81.9
82
134.9
122.2
42
179.3
162.5
3
2.2
2.0
63
46.7
42.3
23
91.1
82.6
83
135.6
122.9
43
180.1
163.2
4
3.0
2.7
64
47.4
43.0
24
91.9
83.3
84
136.3
123.6
44
180.8
163.9
5
3.7
3.4
65
48.2
43.7
25
92.6
83.9
85
137.1
124.2
45
181.5
164.5
6
4.4
4.0
66
48.9
44.3
26
93.4
84.6
86
137.8
124.9
46
182.3
165.2
7
5.2
4.7
67
49.6
45.0
27
94.1
85.3
87
138.6
125.6
47
183.0
165.9
8
5.9
5.4
68
50.4
45.7
28
94.8
86.0
88
139.3
126.3
48
183.8
166.5
9
6.7
6.0
69
51.1
46.3
29
95.6
86.6
89
140.0
126.9
49
184.5
167.2
10
7.4
6.7
70
51.9
47.0
30
96.3
87.3
90
140.8
127.6
50
185.2
167.9
11
8.2
7.4
71
52.6
47.7
131
97.1
88.0
191
141.5
128.3
251
186.0
168.6
12
8.9
8.1
72
53.3
48.4
32
97.8
88.6
92
142.8
128.9
52
186.7
169.2
13
9.6
8.7
73
54.1
49.0
33
98.5
89.3
93
143.0
129.6
53
187.5
169.9
14
10.4
9.4
74
54.8
49.7
34
99.3
90.0
94
143.7
130.3
54
188.2
170.6
15
11.1
10.1
75
55.6
50.4
35
100.0
90.7
95
144.5
131.0
55
188. 9
171.2
16
11.9
10.7
76
56.3
51.0
36
100.8
91.3
96
145.2
131.6
56
189.7
171.9
17
12.6
11.4
77
57.1
51.7
37
101.5
92.0
97
146.0
132.3
57
190.4
172.6
18
13.3
12.1
78
57.8
52.4
38
102.3
92.7
98
146.7
133.0
58
191.2
173.3
19
14.1
12.8
79
58. 5 : 53. 1
39
103.0
93.3
99
147.4
133.6
59
191.9
173.9
20
14.8-
13.4
80
59. 3 ! 53. 7
40
103.7
94.0
200
148.2
134.3
60
192.6
174. 6
21
15.6
14.1
81
60.0 i 54.4
141
104.5
94.7
201
148.9
135.0
261
193.4
175.3
22
16.3
14.8
82
60. 8 55. 1
42
105.2
95.4
02
149.7
135.7
62
194.1
175.9
23
17.0
15.4
83
61.5
55.7
43
106.0
96.0
03
150.4
136.3
63
194.9
176.6
24
17.8
16.1
84
62.2
56.4
44
106.7
96.7
04
151.2
137.0
64
195.6
177.3
25
18.5
16.8
85
63.0
57.1
45
107.4
97.4
05
151.9
137.7
65
196.4
178.0
26
19.3
17.5
86
63.7
57.8
46
108.2
98.0
06
152.6
138.3
66
197.1
178.6
27
20.0
18.1
87
64.5
58.4
47
108.9
98.7
07
153.4
139.0
67
197.8
179.3
28
20.7
18.8
88
65.2
59.1
48
109.7
99.4
08
154.1
139.7
68
198.6
180.0
29
21.5
19.5
89
65.9
59.8
49
110.4
100.1
09
154. 9 ! 140. 4
69
199.3
180.6
30
22.2
20.1
90
66.7
60.4
50
111.1
100.7
10
155. 6 141. 0
70
200.1
181.3
31
23.0
20.8
91
67.4
61.1
151
111.9
101.4
211
156.3 141.7
271
200.8
182.0
32
23.7
21.5
92
68.2
61.8
52
112.6
102.1
12
157.1
142.4
72
201.5
182.7
33
24.5
22.2
93
68.9
62.5
53
113.4
102.7
13
157.8
143.0
73
202.3
183.3
34
25.2
22.8
94
69.6
63.1
54
114.1
103.4
14
158.6
143.7
74
203.0
184.0
35
25.9
23.5
95
70.4
63.8
55
114.8
104.1
15
159.3
144.4
75
203.8
184.7
36
26.7
24.2
96
71.1
64.5
56
115.6
104.8
16
160.0
145.1
76
204.5
185.4
37
27.4
24.8
97
71.9
65.1
57
116.3
105.4
17
160.8
145. 7
77
205.2
186.0
38
28.2
25.5
98
72.6
65.8
58
117.1
106.1
18
161.5
146.4
78
206.0
186.7
39
28.9
26.2
99
73.4
66.5
59
117.8
106.8
19
162.3
147.1
79
206.7
187.4
40
29.6
26.9
100
74.1
67.2
60
118.6
107.4
20
163.0
147.7
80
207.5
188.0
41
30.4
27.5
101
74.8
67.8
161
119.3
108.1
221
163.8
148.4
281
208.2
188.7
42
31.1
28.2
02
75.6
68.5
62
120.0
108.8
22
164.5
149.1
82
208.9
189.4
43
31.9
28.9
03
76.3
69.2
63
120.8 1109.5
23
165.2
149.8
83
209.7
190.1
44
32.6
29.5
04
77.1
69.8
64
121.5 1 110.1
24
166.0
150.4
84
210.4
190. 7
45
33.3
30.2
05
77.8
70.5
65
122.3
110.8
25
166.7
151.1
85
211.2
191.4
46
34.1
30.9
06
78.5 ! 71.2
66
123. 0
111.5
26
167.5
151. 8
86
211.9
192.1
47
34.8
31.6
07
79.3
71.9
67
123.7
112.2
27
168.2
152.4
87
212.7
192.7
48
35.6
32. 2
08
80.0
72.5
68
124.5
112.8
28
168.9
153.1
88
213.4
193.4
49
36.3
32] 9
09
80.8
73.2
69
125.2
113.5
29
169.7
153.8
89
214.1
194.1
50
37.0
33.6
10
81.5 ; 73.9
70
126.0
114.2
30
170.4
154.5
90
214.9
194.8
51
37.8
34.2
111
82.2
171
126.7
114.8
231
171.2
155.1
291
215.6
195.4
52
38.5
34.9
12
83. 0 75. 2
72 127. 4
115.5
32
171.9
155.8
92
216.4
196.1
53
39.3
35.6
13
83. 7 75. J'
73 128. 2
116.2
33
172.6
156.5
93
217.1
196.8
54
40.0
36.3
14
84.5
76.6
74 128. 9
116.9
34
173.4
157.1
94
217.8
197.4
55
40.8
36.9
15
85.2
77.2
75 ! 129. 7
117.5
35
174.1
157.8
95
218.6
198.1
56
41.5
37.6
16
86.0
77.9
76 130. 4
118.2
36
174.9
158.5
96
219.3
198.8
57
42.2
38.3
17
86.7
78.6
77
131.1
118.9
37
175.6
159.2
97
220.1
199.5
58
43.0
39.0
18
87.4
79.2
78
131.9
119.5
38
176.3
159.8
98
220.8
200.1
59
43.7
39.6
19
88.2
79.9
79
132.6
120.2
39
177.1
160.5
99
221.5
200.8
60
44.5
40.3
20
88.9 ! 80.6
80
133.4
120.9
40
177.8
161.2
300
222.3
201.5
Dist.
Dep.
Lat.
Dist. Dep. Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
NE. J E. SE. i- E. NW. } W. SW. \ W. [For 4\ Points.
Page 530] TABLE 1.
Difference of Latitude and Departure for 4 Points.
NE. NW. SE. SW.
DM.
Lat.
Dep.
Dist.
Lat.
Dep.
Diat.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.1
43.1
121
85.6
85.6
181
128.0
128.0
241
170.4
170.4
2
1.4
1.4
62
43.8
43.8
22
86.3
86.3
82
128.7
128.7
42
171.1
171.1
3
2.1
2.1
63
44.5
44.5
23
87.0
87.0
83
129.4
129.4
43
171.8
171.8
4
2.8
2.8
64
45.3
45.3
24
87.7
87.7
84
130.1
130.1
44
172.5
172.5
5
3.5
3.5
65
46.0
46.0
25
88.4
88.4
85
130.8
130.8
45
173.2
173.2
6
4.2
4.2
66
46.7
46.7
26
89.1
89.1
86
131.5
131.5
46
173.9
173.9
7
4.9
4.9
67
47.4
47.4
27
89.8
89.8
87
132.2
132.2
47
174.7
174.7
8
5.7
5.7
68
48.1
48.1
28
90.5
90.5
88
132.9
132.9
48
175.4
175.4
9
6.4
6.4
69
48.8
48.8
29
91.2
91.2
89
133.6
133.6
49
176.1
176.1
10
7.1
7.1
70
49.5
49.5
30
91.9
91.9
90
134.4
134.4
50
176.8
176.8
11
7.8
7.8
71
50.2
50.2
131
92.6
92.6
191
135.1
135.1
251
177.5
177.5
12
8.5
8.5
72
50.9
50.9
32
93.3
93.3
92
135.8
135.8
52
178.2
178.2
13
9.2
9.2
73
51.6
51.6
33
94.0
94.0
93
136.5
136.5
53
178.9
178.9
14
9.9
9.9
74
52.3
52.3
34
94.8
94.8
94
137.2
137.2
54
179.6
179.6
15
10.6
10.6
75
53.0
53.0
35
95.5
95.5
95
137.9
137.9
55
180.3
180.3
16
11.3
11.3
76
53.7
53.7
36
96.2
96.2
96
138.6
138.6
56
181.0
181.0
17
12.0
12.0
77
54.4
54.4
37
96.9
96.9
97
139.3
139.3
57
181.7
181.7
18
12.7
12.7
78
55.2
55.2
38
97.6
97.6
98
140.0
140.0
58
182.4
182.4
19
13.4
13.4
79
55.9
55.9
39
98.3
98.3
99
140.7
140.7
59
183.1
183.1
20
14.1
14.1
80
56.6
56.6
40
99.0
99.0
200
141.4
141.4
60
183.8
183.8
21
14.8
14.8
81
57.3
57.3
141
99.7
99.7
201
142.1
142.1
261
184.6
184.6
22
15.6
15.6
82
58.0
58.0
42
100.4
100.4
02
142.8
142.8
62
185.3
185.3
23
16.3
16.3
83
58.7
58.7
43
101.1
101.1
03
143.5
143.5
63
186.0
186.0
24
17.0
17.0
84
59.4
59.4
44
101.8
101.8
04
144.2
144.2
64
186.7
186.7
25
17.7
17.7
85
60.1
60.1
45
102.5
102.5
05
145.0
145.0
65
187.4
187.4
26
18.4
18.4
86
60.8
60.8
46
103.2
103.2
06
145.7
145.7
66
188.1
188.1
27
19.1
19.1
87
61.5
61.5
47
103.9
103.9
07
146.4
146.4
67
188.8
188.8
28
19.8
19.8
88
62.2
62.2
48
104.7
104.7
08
147.1
147.1
68
189.5
189.5
29
20.5
20.5
89
62.9
62.9
49
105.4
105.4
09
147.8
147.8
69
190.2
190.2
30
21.2
21.2
90
63.6
63.6
50
106.1
106.1
10
148.5
148.5
70
190.9
190.9
31
21.9
21.9
91
64.3
64.3
151
106.8
106.8
211
149.2
149.2
271
191.6
191.6
32
22.6
22.6
92
65.1
65.1
52
107.5
107.5
12
149.9
149.9
72
192.3
192.3
33
23.3
23.3
93
65.8
65.8
53
108.2
108.2
13
150.6
150.6
73
193.0
193.0
34
24.0
24.0
94
66.5
66.5
54
108.9
108.9
14
151.3
151.3
74
193.7
193.7
35
24.7
24.7
95
67.2
67.2
55
109.6
109.6
15
152.0
152.0
75
194.5
194.5
36
25.5
25.5
96
67.9
67.9
56
110.3
110.3
16
152.7
152.7
76
195.2
195.2
37
26.2
26.2
97
68.6
68.6
57
111.0
111.0
17
153.4
153.4
77
195.9
195.9
38
26.9
26.9
98
69.3
69.3
58
111.7
111.7
18
154.1
154.1
78
196.6
196.6
39
27.6
27.6
99
70.0
70.0
59
112.4
112.4
19
154.9
154.9
79
197.3
197.3
40
28.3
28.3
100
70.7
70.7
60
113.1
113.1
20
155.6
155.6
80
198.0
198.0
41
29.0
29.0
101
71.4
71.4
161
113.8
113.8
221
156.3
156.3
281
198.7
198.7
42
29.7
29.7
02
72.1
72.1
62
114.6
114.6
22
157.0
157.0
82
199.4
199.4
43
30.4
30.4
03
72.8
72.8
63
115.3
115.3
23
157.7
157.7
83
200.1
200.1
44
31.1
31.1
04
73.5
73.5
64
116.0
116.0
24
158.4
158.4
84
200.8
200.8
45
31.8
31.8
05
74.2
74.2
65
116.7
116.7
25
159.1
159.1
85
201.5
201.5
46
32.5
32.5
06
75.0
75.0
66
117.4
117.4
26
159.8
159.8
86
202.2
202.2
47
33.2
33.2
07
75.7
75.7
67
118.1
118.1
27
160.5
160.5
87
202.9
202.9
48
33.9
33.9
08
76.4
76.4
68
118.8
118.8
28
161.2
161.2
88
203.6
203.6
49
34.6
34.6
09
77.1
77.1
69
119.5
119.5
29
161.9
161.9
89
204.4
204.4
50
35.4
35.4
10
77.8
77.8
70
120.2
120.2
30
162.6
162.6
90
205.1
205.1
51
36.1
36.1
111
78.5
78.5
171
120.9
120.9
231
163.3
163.3
291
205.8
205.8
52
36.8
36.8
12
79.2
79.2
72
121.6
121.6
32
164.0
164.0
92
206.5
206.5
53
37.5
37.5
13
79.9
79.9
73
122.3
122.3
33
164.8
164.8
93
207.2
207.2
54
38.2
38.2
14
80.6
80.6
74
123.0
123.0
34
165.5
165.5
94
207.9
207.9
55
38.9
38.9
15
81.3
81.3
75
123.7
123.7
35
166.2
166.2
95
208.6
208.6
56
39.6
39.6
16
82.0
82.0
76
124. 5
124.5
36
166.9
166.9
96
209.3
209.3
57
40.3
40.3
17
82.7
82.7
77
125.2
125.2
37
167.6
167.6
97
210.0
210.0
58
41.0
41.0
18
83.4
83.4
78
125.9
125.9
38
168. 3
168.3
98
210.7
210.7
59
41.7
41.7
19
84.1
84.1
79
126.6
126.6
39
169.0
169.0
99
211.4
211.4
60
42.4
42.4
20
84.9
84.9
80
127.3
127.3
40
169.7
169.7
300
212.1
212.1
Dist.
Dep.
La,t.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. NW. SE. SW. [For 4 Points.
1
Page 532] TABLE 2.
Difference of Latitude and Departure for 1° (179°, 181°, 359°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. j Lat.
Dep.
Dist.
Lat. j Dep.
1
1.0
0.0
61
61.0
1.1
121
121.0
2.1
181
181.0
3.2
241
241.0
4.2
2
2.0
0.0
62
62.0
1.1
22
122.0
2.1
82
182.0
3.2
42
242. 0
4.2
3
3.0
0.1
63
63.0
1.1
23
123.0
2.1
83
183.0
3.2
43
243.0
4.2
4
4.0
0.1
64
64.0
1.1
24
124.0
2.2
84
184.0
3.2
44
244.0
4.3
5
5.0
0.1
65
65.0
1.1
25
125.0
2.2
85
185.0
3.2
45
245.0
4.3
6
6.0
0.1
66
66.0
1.2
26
126.0
2.2
86
186.0
3.2
46
246.0
4.3
7
7.0
0.1
67
67.0
1.2
27
127.0
2.2
87
187.0
3.3
47
247.0
4.3
8
8.0
0.1
68
68.0
1.2
28
128. 0
2.2
88
188.0
3.3
48
248.0
4.3
9
9.0
0.2
69
69.0
1.2
29
129.0
2.3
89
189. 0
3.3
49
249.0
4.3
10
10.0
0.2
70
70.0
1.2
30
130.0
2.3
90
190.0
3.3
50
250.0
4.4
11
11.0
0.2
71
71.0
1.2
131
131.0
2.3
191
191.0
3.3
251
251.0
4.4
12
12.0
0.2
72
72.0
1.3
32
132.0
2.3
92
192.0
3.4
52
252.0
4.4
13
13.0
0.2
73
73.0
1.3
33
133.0
2.3
93
193.0
3.4
53
253.0
4.4
14
14.0
0.2
74
74.0
1.3
34
134.0
2.3
94
194.0
3.4
54
254.0
4.4
15
15.0
0.3
75
75.0
1.3
35
135.0
2.4
95
195.0
3.4
55
255.0
4.5
16
16.0
0.3
76
76.0
1.3
36
136.0
2.4
96
196.0
3.4
56
256.0
4.5
17
17.0
0.3
77
77.0
1.3
37
137.0
2.4
97
197.0
3.4
57
257.0
4.5
18
18.. 0
0.3
78
78.0
1.4
38
138.0
2.4
98
198.0
3.5
58
258.0
4.5
19
19.0
0.3
79
79.0
1.4
39
139.0
2.4
99
199.0
3.5
59
259.0
4.5
20
20.0
0.3
80
80.0
1.4
40
140.0
2.4
200
200.0
3.5
60
260.0
4.5
21
21.0
0.4
81
81.0
1.4
141
141.0
2.5
201
201.0
3.5
261
261.0
4.6
22
22.0
0.4
82
82.0
1.4
42
142.0
2.5
02
202.0
3.5
62
262.0
4.6
23
23.0
0.4
83
83.0
1.4
43
143.0
2.5
03
203.0
3.5
63
263.0
4.6
24
24.0
0.4
84
84.0
1.5
44
144.0
2.5
04
204.0
3.6
64
264.0
4.6
25
25.0
0.4
85
85.0
1.5
45
145.0
2.5
05
205.0
3.6
65
265.0
4.6
26
26.0
0.5
86
86.0
1.5
46
146.0
2.5
06
206.0
3.6
66
266.0
4.6
27
27.0
0.5
87
87.0
1.5
47
147.0
2.6
07
207.0
3.6
67
267.0
4.7
28
28.0
0.5
88
88.0
1.5
48
148.0
2.6
Q8
208.0
3..6
68
268.0
4.7
29
29.0
0.5
89
89.0
1.6
49
149.0
2.6
09
209.0
3.6
69
269.0
4.7
30
30.0
0.5
90
90.0
1.6
50
150.0
2.6
10
210. 0
3.7
70
270.0
4.7
31
31.0
0.5
91
91.0
1.6
151
151.0
2.6
211
211.0
3.7
271
271.0
4.7
32
32.0
0.6
92
92.0
1.6
52
152.0
2.7
12
212.0
3.7
72
272.0
4.7
33
33.0
0.6
93
93.0
1.6
53
153.0
2.7
13
213.0
3.7
73
273.0
4.8
34
34.0
0.6
94
94.0
1.6
54
154.0
2.7
14
214.0
3.7
74
274.0
4.8
35
35.0
0.6
95
95.0
1.7
55
155.0
2.7
15
215.0
3.8
75
275.0
4.8
36
36.0
0.6
96
96.0
1.7
56
156.0
2.7
16
216.0
3.8
76
276.0
4.8
37
37.0
0.6
97
97.0
1.7
57
157.0
2.7
17
217.0
3.8
77
277.0
4.8
38
38.0
0.7
98
98.0
1.7
58
158.0
2.8
18
218.0
3.8
78
278.0
4.9
39
39.0
0.7
99
99.0
1.7
59
159.0
2.8
19
219.0
3.8
79
279.0
4.9
40
40.0
0.7
100
100.0
1.7
60
160.0
2.8
20
220.0
3.8
80
280.0
4.9
41
41.0
0.7
101
101.0
1.8
161
161.0
2.8
221
221.0
3.9
281
281.0
4.9
42
42.0
0.7
02
102.0
1.8
62
162.0
2.8
22
222.0
3.9
82
282.0
4.9
43
43.0
0.8
03
103.0
1.8
63
163.0
2.8
23
223.0
3.9
83
283.0
4.9
44
44.0
0.8
04
104.0
1.8
64
164.0
2.9
24
224.0
3.9
84
284.0
5.0
45
45.0
0.8
05
105.0
1.8
65
165.0
2.9
25
225.0
3.9
85
285.0
5.0
46
46.0
0.8
06
106.0
1.8
66
166.0
2.9
26
226.0
3.9
86
286.0
5.0
47
47.0
0.8
07
107.0
1.9
67
167.0
2.9
27
227.0
4.0
87
287.0
5.0
48
48.0
0.8
08
108.0
1.9
68
168.0
2.9
28
228.0
4.0
88
288.0
5.0
49
49.0
0.9
09
109.0
1.9
69
169.0
2.9
29
229.0
4.0
89
289.0
5.0
50
50.0
0.9
10
110.0
1.9
70
170.0
3.0
30
230.0
4.0
90
290.0
5.1
51
51.0
0.9
111
111.0
1.9
171
171.0
3.0
231
231.0
4.0
291
291.0
5.1
52
52.0
0.9
12
112.0
2.0
72
172.0
3.0
32
232.0
4.0
92
292.0
5.1
53
53.0
0.9
13
113.0
2.0
73
173.0
3.0
33
233.0
4.1
93
293.0
5.1
54
54.0
0.9
14
114.0
2.0
74
174.0
3.0
34
234.0
4.1
94
294.0
5.1
55
55.0
1.0
15
115.0
2.0
75
175.0
3.1
35
235.0
4.1
95
295.0
5.1
56
56.0
1.0
16
116.0
2.0
76
176.0
3.1
36
236.0
4.1
96
296.0
5.2
57
57.0
1.0
17
117.0
2.0
77
177.0
3.1
37
237.0
4.1
97
297.0
5.2
58
58.0
1.0
18
118.0
2.1
78
178.0
3.1
38
238.0
4.2
98
298.0
5.2
59
59.0
1.0
19
119.0
2.1
79
179.0
3.1
39
239.0
4.2
99
299.0
5.2
60
60.0
1.0
20
120.0
2.1
80
180.0
3.1
40
240.0
4.2
300
300.0
5.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
89° (91°, 269°, 271°).
TABLE 2. [Page 533
Difference of Latitude and Departure for 1° (179°, 181°, 359°).
Di*t.
Lat.
Dep.
Dist. Lat. Dep.
Dist. | Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
301.0 i 5.3
361 360.9
6.3
421
420.9
7.3
481
480.9
8.4
541
540.9
9.5
02 302.0 ! 5.3
62 361.9
6.3
22
421.9
7.4
82
481.9
8.4
42
541.9
9.5
03
303.0
5.3
63 362. 9
6.3
23
422.9
7.4
83
482.9
8.5
43
542.9
9.5
04
304.0
5.3
64
363.9
6.4
24
423.9
7.4
84
483.9
8.5
44
543.9
9.5
05 305. 0
5.3
65
364.9
6.4
25 424. 9
7.4
85 484. 9
8.5
45
544.9
9.5
06 306.0
5.3
66
365.9
6.4
26 425. 9
7.4
86 485. 9
8.5
46
545.9
9.5
07 307. 0
5.4
67
366.9
6.4
27
426.9
7.4
87 486. 9
8.5
47
546.9
9.6
08 308. 0
5.4
68
367.9
6.4
28
427.9
7.5
88 487. 9
8.6
48
547.9
9.6
09 309.0
5.4
69
368.9
6.4
29
428.9
7.5
89
488.9
8.6
49
548.9
9.6
10 310. 0
5.4
70 1 369. 9
6.5
30
429.9
7.5
90
489.9
8.6
50
549.9
9.6
311 311.0
5.4
371 370. 9
6.5
431
430.9 ! 7.5
491
490.9
8.6
551
550.9
9.6
12 312. 0
5.4
72 371.9
6.5
32
431. 9 i 7. 5
92
491.9
8.6
52
551.9
9.6
13 313. 0
5.5
73 372. 9
6.5
33
432.9 7.5
93 492. 9
8.7
53
552.9
9.7
14 I 314. 0
5.5
74 \ 373.9
6.5
34
433. 9 7. 6
94 493. 9
8.7
54
553.9
9.7
15 315. 0
5.5
75 ! 374.9
6.5
35
434. 9 7. 6
95 i 494.9
8.7
55
554.9
9.7
16 316.0
5.5
76 | 375.9
6.6
36
435. 9 7. 6
96 ! 495.9
8.7
56
555.9
9.7
17
317.0 5.5
77 376.9
6.6
37
436. 9 7. 6
97 496. 9
8.7
57
556.9
9.7
18
318.0 5.5
78 377. 9
6.6
38
437.9
7.6
98 | 497.9
8.7
58
557.9
9.7
19
319.0 5.6
79 378. 9
6.6
39
438. 9 7. 7
99 498.9
8.8
59
558.9
9.8
20
320.0
5.6
80 379. 9
6.6
40
439. 9 | 7. 7
500 499. 9
8.8
60
559.9
9.8
321
321.0
5.6
381 380. 9
6.7
441
440.9
7.7
501 500. 9
8.8
561
560.9
9.8
22 322.0
5.6
82
381.9
6.7
42
441.9
7.7
02 501. 9
8.8
62
561.9
9.8
23
323.0
5.6
83
382.9
6."
43
442.9
7.7
03
502.9
8.8
63
562.9
9.8
24
324.0
5.6
84
383.9
6."
44
443.9
7.7
04
503.9
8.8
64
563.9
9.8
25
325.0
5.7
85
384. 9 6. 7
45
444.9
7.8
05
504.9
8.8
65
564.9
9.9
26
326.0
5.7
86
385.9
6.7
46
445.9
7.8
06
505.9
8.9
66
565.9
9.9
27
327.0
5.1
87
386.9
6.8
47
446.9
7.8
07
506.9
8.9
67
566.9
9.9
28
328.0
5.7
88
387.9
6.8
48
447.9
7.8
08
507.9
8.9
68
567.9
9.9
29
329.0
5.7
89
388.9
6.8
49
448.9
7.8
09
508.9
8.9
69
568.9
9.9
30
330.0
5.8
90
389.9
6.8
50
449.9
7.8
10
509.9
8.9
70
569.9
9.9
331 ! 331.0
5.8
391
390.9
6.8
451
450.9
7.9
511
510.9
9.0
571
570.9
10.0
32 i 332. 0 5. 8
92
391.9
6.8
52
451.9
7.9
12
511.9
9.0
72
571.9
10.0
33 | 333. 0 5. 8
93
392.9
6.9
53
452.9
7.9
13
512.9
9.0
73
572.9
10.0
34
333.9 5.8
94
393.9
6.9
54
453.9
7.9
14
513.9
9.0
74
573.9
10.0
35
334. 9 5. 8
95
394.9
6.9
55
454. 9
7.9
15
514.9
9.0
75
574.9
10.0
36 335. 9 5. 9
96
395.9
6.9
56
455.9
8.0
16
515.9
9.0
76
575.9
10.0
37
336.9
5.9
97
396.9
6.9
57
456.9
8.0
17
516.9
9.1
77
576.9
10.1
38
337.9
5.9
98
397.9
6.9
58
457.9
8.0
18
517.9
9.1
78
577.9
10.1
39
338.9
5.9
99
398.9
7.0
59
458.9
8.0
19
518.9
9.1
79
578.9
10.1
40 339.9
5.9
400
399.9
7.0
60
459.9
8.0
20
519.9
9.1
80 579. 9
10.1
341 340. 9
6.0
401
400. 9 j 7. 0
461 460. 9
8.0
521
520.9
9.1
581 580. 9
10.1
42 l 341.9
6.0
02
401.9 7.0
62 461.9
8.1
22
521.9
9.1
82
581.9
10. lv
43 1 342.9
6.0
03
402.9
7.0
63
462.9
8.1
23
522.9
9.2
83 582. 9
10.2
44 343.9
6.0
04 403. 9
7.1
64
463.9
8.1
24
523.9
9.2
84
583.9
10.2
45 i 344.9
6.0
05 404. 9
7.1
65
464.9
8.1
25
524.9
9.2
85
584.9
10.2
46 ; 345. 9
6.0
06 405. 9 7. 1
66
465.9
8.1
26
525. 9
9.2
86
585.9
10.2
47 346.9
6.1
07
406.9 1 7.1
67
466.9
8.1
27
526.9
9.2
87
586.9
10.2
48 j 347.9
6.1
08
407.9 7.1
68
467.9
8.2
28
527.9
9.2
88
587.9
10.2
49 | 348.9
6.1
09 408. 9 1 7. 1
69
468.9
8.2
29
528.9
9.3
89
588.9
10.3
50 349. 9
6.1
10 409. 9 7.2
70
469.9
8.2
30
529.9
9.3
90
589.9
10.3
351 350.9 6.1
411 410.9 i 7.2
471
470.9
8.2
531
530.9
9.3
591
590.9
10.3
52
351.9
6.1
12 411.9 7.2
72
471.9
8.2
32
531.9
9.3
92 591. 9
10.3
53
352.9
6.2
13 412.9 ' 7.2
73
472.9
8.2
33
532.9
9.3
93 592.9
10.3
54
353. 9
6.2
14 413.9 i 7.2
74
473.9
8.3
34
533.9
9.3
94 593. 9
10.3
55
354.9
6.2
15 i 414.9 ! 7.2
75
474.9
8.3
35
534.9
9.4
95 594. 9
10.4
56
355.9
6.2
16 415.9 i 7.3
76
475.9
8.3
36
535.9
9.4
96 595. 9
10.4
57
356.9
6.2
17
416.9 1 7.3
77
476.9
8.3
37
536.9
9.4
97
596.9
10.4
58
357.9
6.2
18 417.9 i 7.3
78
477.9
8.3
38
537.9
9.4
98
597.9
10.4
59
358.9
6.3
19
418.9 7.3
79
478.9
8.4
39
538.9
9.4
99
598.9
10.4
60
359.9
6.3
20 419. 9 7. 3
80
479.9
8.4
40
539.9
9.4
600
599.9
10.5
Dist.
Dep.
Lat.
Dist.
Dep. | Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
89° (91°, 269°, 271°).
Page 534] TABLE 2.
Difference of Latitude and Departure for 2° (178°, 182°, 358°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
61.0
2.1
121
120.9
4.2
181
180.9
6.3
241
240.9
8.4
2
2.0
0.1
62
62.0
2.2
22
121.9
4.3
82
181.9
6.4
42
241.9
8.4
3
3.0
0.1
63
63.0
2.2
23
122.9
4.3
83
182.9
6.4
43
242.9
8.5
4
4.0
0.1
64
64.0
2.2
24
123.9
4.3
84
183.9
6.4
44
243.9
8.5
5
5.0
0.2
65
65.0
2.3
25
124.9
4.4
85
184.9
6.5
45
244.9
8.6
6
6.0
0.2
66
66.0
2.3
26
125.9
4.4
86
185.9
6.5
46
245.9
8.6
7
7.0
0.2
67
67.0
2.3
27
126.9
4.4
87
186.9
6.5
47
246.8
8.6
8
8.0
0.3
68
68.0
2.4
28
127.9
4.5
88
187.9
6.6
48
247.8
8.7
9
9.0
0.3
69
69.0
2.4
29
128.9
4.5
89
188.9
6.6
49
248.8
8.7
10
10.0
0.3
70
70.0
2.4
30
129.9
4.5
90
189.9
6.6
50
249.8
8.7
11
11.0
0.4
71
71.0
2.5
131
130.9
4.6
191
190.9
6.7
251
250.8
8.8
12
12.0
0.4
72
72.0
2.5
32
131.9
4.6
92
191.9
6.7
52
251.8
8.8
13
13.0
0.5
73
73.0
2.5
33
132.9
4.6
93
192.9
6.7
53
252.8
8.8
14
14.0
0.5
74
74.0
2.6
34
133.9
4.7
94
193.9
6.8
54
253.8
8.9
15
15.0
0.5
75
75.0
2.6
35
134.9
4.7
95
194. 9
6.8
55
254.8
8.9
16
16.0
0.6
76
76.0
2.7
36
135.9
4.7
96
195.9
6.8
56
255.8
8.9
17
17.0
0.6
77
77.0
2.7
37
136.9
4.8
97
196.9
6.9
57
256.8
9.0
18
18.0
0.6
78
78.0
2.7
38
137.9
4.8
98
197.9
6.9
58
257.8
9.0
19
19.0
0.7
79
79.0
2.8
39
138.9
4.9
99
198.9
6.9
59
258.8
9.0
20
20.0
0.7
80
80.0
2.8
40
139.9
4.9
200
199.9
7.0
60
259.8
9.1
21
21.0
0.7
81
81.0
2.8
141
140.9
4.9
201
200.9
7.0
261
260.8
9.1
22
22.0
0.8
82
82.0
2.9
42
141.9
5.0
02
201.9
7.0
62
261.8
9.1
23
23.0
0.8
83
82.9
2.9
43
142.9
5.0
03
202.9
7.1
63
262.8
9.2
24
24.0
0.8
84
83.9
2.9
44
143.9
5.0
04
203.9
7.1
64
263.8
9.2
25
25.0
0.9
85
84.9
3.0
45
144.9
5.1
05
204.9
7.2
65
264.8
9.2
26
26.0
0.9
86
85.9
3.0
46
145.9
5.1
06
205.9
7.2
66
265.8
9.3
27
27.0
0.9
87
86.9
3.0
47
146.9
5.1
07
206.9
7.2
67
266.8
9.3
28
28.0
1.0
88
87.9
3.1
48
147.9
5.2
08
207.9
7.3
68
267.8
9.4
29
29.0
1.0-
89
88.9
3.1
49
148.9
5.2
09
208.9
7.3
69
268.8
9.4
30
30.0
1.0
90
89.9
3.1
50
149.9
5.2
10
209.9
7.3
70
269.8
9.4
31
31.0
1.1
91
90.9
3.2
151
150.9
5.3
211
210.9
7.4
271
270.8
9.5
32
32.0
1.1
92
91.9
3.2
52
151.9
5.3
12
211.9
7.4
72
271.8
9.5
33
33.0
1.2
93
92.9
3.2
53
152.9
5.3
13
212.9
7.4
73
272.8
9.5
34
34.0
1.2
94
93.9
3.3
54
153.9
5.4
14
213.9
7.5
74
273.8
9.6
35
35.0
1.2
95
94.9
3.3
55
154.9
5.4
15
214.9
7.5
75
274.8
9.6
36
36.0
1.3
96
95.9
3.4
56
155.9
5.4
16
215.9
7.5
76
275.8
9.6
37
37.0
1.3
97
96.9
3.4
57
156.9
5.5
17
216.9
7.6
77
276.8
9.7
38
38.0
1.3
98
97.9
3.4
58
157.9
5.5
18
217.9
7.6
78
277.8
9.7
39
39.0
1.4
99
98.9
3.5
59
158.9
5.5
19
218.9
7.6
79
278.8
9.7
40
40.0
1.4
100
99.9
3.5
60
159.9
5.6
20
219.9
7.7
80
279.8
9.8
41
41.0
1.4
101
100.9
3.5
161
160.9
5.6
221
220.9
7.7
281
280.8
9.8
42
42.0
1.5
02
101.9
3.6
62
161.9
5.7
22
221.9
7.7
82
281.8
9.8
43
43.0
1.5
03
102.9
3.6
63
162.9
5.7
23
222.9
7.8
83
282.8
9.9
44
44.0
.5
04
103.9
3.6
64
163.9
5.7
24
223.9
7.8
84
283.8
9.9
45
45.0
.6
05
104.9
3.7
65
164.9
5.8
25
224.9
7.9
85
284.8
9.9
46
46.0
.6
06
105.9
3.7
66
165.9
5.8
26
225.9
7.9
86
285.8
10.0
47
47.0
.6
07
106.9
3.7
67
166.9
5.8
27
226.9
7.9
87
286.8
10.0
48
48.0
.7
08
107.9
3.8
68
167.9
5.9
28
227.9
8.0
88
287.8
10.1
49
49.0
.7
09
108.9
3.8
69
168.9
5.9
29
228.9
8.0
89
288.8
10.1
50
50.0
1.7
10
109.9
3.8
70
169.9
5.9
30
229.9
8.0
90
289.8
10.1
51
51.0
1.8
111
110.9
3.9
171
170.9
6.0
231
230.9
8.1
291
290.8
10.2
52
52.0
1.8
12
111.9
3.9
72
171.9
6.0
32
231.9
8.1
92
291.8
10.2
53
53.0
1.8
13
112.9
3.9
73
172.9
6.0
33
232.9
8.1
93
292.8
10.2
54
54.0
1.9
14
113.9
4.0
74
173.9
6.1
34
233.9
8.2
94
293.8
10.3
55
55.0
1.9
15
114.9
4.0
75
174.9
6.1
35
234.9
8.2
95
294.8
10.3
56
56.0
2.0
16
115.9
4.0
76
175.9
6.1
36
235.9
8.2
96
295.8
10.3
57
57.0
2.0
17
116.9
4.1
77
176.9
6.2
37
236.9
8.3
97
296.8
10.4
58
58.0
2.0
18
117.9
4.1
78
177.9
6.2
38
237.9
8.3
98
297.8
10.4
59
59.0
2.1
19
118.9
4.2
79
178.9
6.2
39
238.9
8.3
99
298.8
10.4
60
60.0
2.1
20
119.9
4.2
80
179.9
6.3
40
239.9
8.4
300
299.8
10.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
88° (92°, 268°, 272°).
TABLE 2. [Page 535
Difference of Latitude and Departure for 2° (178°, 182°, 358°).
Dist.
Lat
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
300.8
10.5
361
360.8
12.6
421
420.8
14.7
481
480.7
16.8
541
540.7
18.9
02
301.8
10.5
62
361.8
12.6
22
421.8
14.7
82
481.7
16.8
42
541.7
18.9
03
302.8
10.6
63
362.8
12.7
23
422.8
14.7
83
482.7
16.8
43
542.7
18.9
04
303.8
10.6
64
363.8
12.7
24
423.8
14.8
84
483.7
16.9
44
543.7
19.0
05
304.8
10.6
65
364.8
12.7
25
424.8
14.8
85
484.7
16.9
45
544.7
19.0
06
305.8
10.7
66
365.8
12.8
26
425.7
14.9
86
485.7
16.9
46
545.7
19.0
07
306.8
10.7
67
366.8
12.8
27
426.7
14.9
87
486.7
17.0
47
546.7
19.1
08
307.8
10.7
68
367.8
12.8
28
427.7
14.9
88
487.7
17.0
48
547.7
19.1
09
308.8
10.8
69
368.8
12.9
29
428.7
15.0
89
488.7
17.0
49
548.7
19.1
10
309.8
10.8
70
369.8
12.9
30
429.7
15.0
90
489.7
17.1
50
549.7
19.2
311
310.8
10.8
371
370.8
12.9
431
430.7
15.0
491
490.7
17.1
551
550.7
19.2
12
311.8
10.9
72
371.8
13.0
32
431.7
15.1
92
491.7
17.1
52
551.7
19.2
13
312.8
10.9
73
372.8
13.0
33
432.7
15.1
93
492.7
17.2
53
552.7
19.3
14
313.8
10.9
74
373.8
13.0
34
433.7
15.1
94
493.7
17.2
54
553.7
19.3
15
314.8
11.0
75
374.8
13.1
35
434.7
15.2
95
494.7
17.2
55 554. 7
19.3
16
315.8
11.0
76
375.8
13.1
36
435.7
15.2
96
495.7
17.3
56
555.7
19.4
17
316.8
11.0
77
376.8
13.1
37
436.7
15.2
97
496.7
17.3
57
556.7
19.4
18
317.8
11.1
78
377.8
13.2
38
437.7
15.3
98
497.7
17.3
58
557.7
19.4
19
318.8
11.1
79
378.8
13.2
39
438.7
15.3
99
498.7
17.4
59
558.7
19.5
20
319.8
11.2
80
379.8
13.2
40
439.7
15.3
500
499.7
17.4
60
559.7
19.5
321
320.8
11.2
381
380.8
13.3
441
440.7
15.4
501
500.7
17.5
561
560.7
19.5
22
321.8
11.2
82
381.8
13.3
42
441.7
15.4
02
501.7
17.5
62
561.7
19.6
23
322.8
11.3
83
382.8
13.3
43
442.7
15.4
03
502.7
17.5
63
562.7
19.6
24
323.8
11.3
84
383.8
13.4
44
443.7
15.5
04
503.7
17.6
64
563.7
19.6
25
324.8
11.3
85
384.8
13.4
45
444.7
15.5
05
504.7
17.6
65
564.7
19.7
26
325.8
11.4
86
385.8
13.5
46
445.7
15.6
06
505.7
17.6
66
565.7
19.7
27
326.8
11.4
87
386.8
13.5
47
446.7
15.6
07
506.7
17.7
67
566.7
19.7
28
327.8
11.4
88
387.8
13.5
48
447.7
15.6
08
507.7
17.7
68
567.7
19.8
29
328.8
11.5
89
388.8
13.6
49
448.7
15.7
09
508.7
17.7
69
568.7
19.8
30
329.8
11.5
90
389.8
13.6
50
449.7
15.7
10
509.7
17.8
70
569.7
19.9
331
330.8
11.5
391
390.8
13.6
451
450.7
15.7
511
510.7
17.8
571
570.7
19.9
32
331.8
11.6
92
391.8
13.7
52
451.7
15.8
12
511.7
17.8
72
571.7
19.9
33
332.8
11.6
93
392.8
13.7
53
452.7
15.8
13
512.7
17.9
73
572.7
20.0
34
333.8
11.6
94
393.8
13.7
54
453.7
15.8
14
513.7
17.9
74
573.6
20.0
35
334.8
11.7
95
394.8
13.8
55
454.7
15.9
15
514.7
17.9
75
574.6
20.0
36
335.8
11.7
96
395.8
13.8
56
455.7
15.9
16
515.7
18.0
76
575.6
20.1
37
336.8
11.7
97
396.8
13.8
57
456.7
15.9
17
516.7
18.0
77
576.6
20.1
38
337.8
11.8
98
397.8
13.9
58
457.7
16.0
18
517.7
18.1
78
577.6
20.1
39
338.8
11.8
99
398.8
13.9
59
458. 7
16.0
19
518.7
18.1
79
578.6
20.2
40
339.8
11.9
400
399.8
13.9
60
459.7
16.0
20
519.7
18.1
80
579.6
20.2
341 I 340.8
11.9
401
400.8
14.0
461
460.7
16.1
521
520.7
18.2
581
580.6
20.2
42 341.8
11.9
02
401.8
14.0
62
461.7
16.1
22
521.7
18.2
82
581.6
20.3
43 342. 8
12.0
03
402.8
14.0
63
462.7
16.1
23
522.7
18.2
83
582.6
20.3
44 343.8
12.0
04
403.8
14.1
64
463.7
16.2
24
523.7
18.3
84
583.6
20.3
45
344.8
12.0
05
404.8
14.1
65
464.7
16.2
25
524.7
18.3
85
584.6
20.4
46
345.8
12.1
06
405.8
14.2
66
465.7
16.2
26
525.7
18.4
86
585.6
20.4
47
346.8
12.1
07
406.8
14.2
67
466.7
16.3
27
526.7
18.4
87
586.6
20.4
48
347.8
12.1
08
407.8
14.2
68
467.7
16.3
28
527.7
18.4
88
587.6
20.5
49
348.8
12.2
09
408.8
14.3
69
468.7
16.4
29
528.7
18.5
89
588.6
20.5
50
349.8
12.2
10
409.8
14.3
70
469.7
16.4
30
529.7
18.5
90
589.6
20.5
351
350.8
12.2
411
410.8
14.3
471
470.7
16.4
531
530.7
18.5
591
590.6
20.6
52
351.8
12.3
12
411.8
14.4
72
471.7
16.5
32
531.7
18.6
92
591.6
20.6
53
352.8
12.3
13
412.8
14.4
73
472.7
16.5
33
532.7
18.6
93
592.6
20.6
54
353.8
12.3
14
413.8
14.4
74
473.7
16.5
34
533.7
18.6
94
593.6
20.7
55
354.8
12.4
15
414.8
14.5
75
474.7
16.6
35
534.7
18.7
95
594.6
20.7
56
355.8
12.4
16
415.8
14.5
76
475.7
16.6
36
535.7
18.7
96
595.6
20.7
57
356.8
12.4
17
416.8
14.5
77
476.7
16.6
37
536.7
18.7
97
596.6
20.8
58
357.8
12.5
18
417.8
14.6
78
477.7
16.7
38
537.7
18.8
98
597.6
20.8
59
358.8
12.5
19
418.8
14.6
79
478.7
16.7
39
538.7
18.8
99
598.6
20.8
60
359.8
12.5
20
419.8
14.6
80
479.7
16.7
40
539.7
18.8
600
599.6
20.9
Dist.
Dep.
Lat.
Diflt.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
88° (92°, 268°, 272°).
Page 536] TABLE 2.
Difference of Latitude and Departure for 3° (177°, 183°, 357°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.9
3.2
121
120.8
6.3
181
180.8
9.5
241
240.7
12.6
2
2.0
0.1
62
61.9
3.2
22
121.8
6.4
82
181.8
9.5
42
241.7
12.7
3
3.0
0.2
63
62.9
3.3
23
122.8
6.4
83
182.7
9.6
43
242.7
12.7
4
4.0
0.2
64
63.9
3.3
24
123.8
6.5
84
183.7
9.6
44
243.7
12.8
5
5.0
0.3
65
64.9
3.4
25
124. 8
6.5
85
184.7
9.7
45
244.7
12.8
6
6.0
0.3
66
65.9
3.5
26
125.8
6.6
86
185.7
9.7
46
245.7
12.9
7
7.0
0.4
67
66.9
3.5
27
126.8
6.6
87
186.7
9.8
47
246.7
12.9
8
8.0
0.4
68
67.9
3.6
28
127.8
6.7
88
187.7
9.8
48
247.7
13.0
9
9.0
0.5
69
68.9
3.6
29
128.8
6.8
89
188.7
9.9
49
248.7
13.0
10
10.0
0.5
70
69.9
3.7
30
129.8
6.8
90
189.7
9.9
50
249.7
13.1
11
11.0
0.6
71
70.9
3.7
131
130.8
6.9
191
190.7
10.0
251
250.7
13.1
12
12.0
0.6
72
71.9
3.8
32
131.8
6.9
92
191.7
10.0
52
251.7
13.2
13
13.0
0.7
73
72.9
3.8
33
132.8
7.0
93
192.7
10.1
53
252.7
13.2
14
14.0
0.7
74
73.9
3.9
34
133.8
7.0
94
193.7
10.2
54
253.7
13.3
15
15.0
. 0.8
75
74.9
3.9
35
134.8
7.1
95
194.7
10.2
55
254.7
13.3
16
16.0
0.8
76
75.9
4.0
36
135.8
7.1
96
195.7
10.3
56
255.6
13.4
17
17.0
0.9
77
76.9
4.0
37
136. 8
7.2
97
196.7
10.3
57
256.6
13.5
18
18.0
0.9
78
77.9
4.1
38
137.8
7.2
98
197.7
10.4
58
257.6
13.5
19
19.0
1.0
79
78.9
4.1
39
138.8
7.3
99
198.7
10.4
59
258.6
13.6
20
20.0
1.0
80
79.9
4.2
40
139.8
7.3
200
199.7
10.5
60
259.6
13.6
21
21.0
1.1
81
80.9
4.2
141
140.8
7.4
201
200.7
10.5
261
260.6
13.7
22
22.0
1.2
82
81.9
4.3
42
141.8
7.4
02
201.7
10.6
62
261.6
13.7
23
23.0
1.2
83
82.9
4.3
43
142.8
7.5
03
202.7
10.6
63
262.6
13.8
24
24.0
1.3
84
83.9
4.4
44
143.8
7.5
04
203.7
10.7
64
263.6
13.8
25
25.0
1.3
85
84.9
4.4
45
144.8
7.6
05
204.7
10.7
65
264.6
13.9
26
26.0
1.4
86
85.9
4.5
46
145.8
7.6
06
205.7
10.8
66
265.6
13.9
27
27.0
1.4
87
86.9
4.6
47
146.8
7.7
07
206.7
10.8
67
266.6
14.0
28
28.0
1.5
88
87.9
4.6
48
147.8
7.7
08
207.7
10.9
68
267.6
14.0
29
29.0
1.5
89
88.9
4.7
49
148.8
7.8
09
208.7
10.9
69
268.6
14.1
30
30.0
1.6
90
89.9
4.7
50
149.8
7.9
10
209.7
11.0
70
269.6
14.1
31
31.0
1.6
91
90.9
4.8
151
150.8
7.9
211
210.7
11.0
271
270.6
14.2
32
32.0
1.7
92
91.9
4.8
52
151.8
8.0
12
211.7
11.1
72
271.6
14.2
33
33.0
1.7
93
92.9
4.9
53
152.8
8.0
13
212.7
11.1
73
272.6
14.3
34
34.0
1.8
94
93.9
4.9
54
153.8
8.1
14
213.7
11.2
74
273.6
14.3
35
35.0
1.8
95
94.9
5.0
55
154.8
8.1
15
214.7
11.3
75
274.6
14.4
36
36.0
1.9
96
95.9
5.0
56
155.8
8.2
16
215.7
11.3
76
275.6
14.4
37
36.9
1.9
97
96.9
5.1
57
156.8
8.2
17
216.7
11.4
77
276.6
14.5
38
37.9
2.0
98
97.9
5.1
58
157.8
8.3
18
217.7
11.4
78
277.6
14.5
39
38.9
2.0
99
98.9
5.2
59
158.8
8.3
19
218.7
11.5
79
278.6
14.6
40
39.9
2.1
100
99.9
5.2
60
159.8
8.4
20
219.7
11.5
80
279.6
14.7
41
40.9
2.1
101
100.9
5.3
161
160.8
8.4
221
220.7
11.6
281
280.6
14.7
42
41.9
2.2
02
101.9
5.3
62
161.8
8.5
22
221.7
11.6
82
281.6
14.8
43
42.9
2.3
03
102.9
5.4
63
162.8
8.5
23
222.7
11.7
83
282.6
14.8
44
43.9
2.3
04
103.9
5.4
64
163.8
8.6
24
223.7
11.7
84
283.6
14.9
45
44.9
2.4
05
104.9
5.5
65
164.8
8.6
25
224.7
11.8
85
284.6
14.9
46
45.9
2.4
06
105.9
5.5
66
165.8
8.7
26
225.7
11.8
86
285.6
15.0
47
46.9
2.5
07
106.9
5.6
67
166.8
8.7
27
226.7
11.9
87
286.6
15.0
48
47.9
2.5
08
107.9
5.7
68
167.8
8.8
28
227.7
11.9
88
287.6
15.1
49
48.9
2.6
09
108.9
5.7
69
168.8
8.8
29
228.7
12.0
89
288.6
15.1
50
49.9
2.6
10
109.8
5.8
70
169.8
8.9
30
229.7
12.0
90
289.6
15.2
51
50.9
2.7
111
110.8
5.8
171
170.8
8.9
231
230.7
12.1
291
290.6
15.2
52
51.9
2.7
12
111.8
5.9
72
171.8
9.0
32
231.7
12.1
92
291.6
15.3
53
52.9
2.8
13
112.8
5.9
73
172.8
9.1
33
232.7
12.2
93
292.6
15.3
54
53.9
2.8
14
113.8
6.0
74
173.8
9.1
34
233.7
12.2
94
293.6
15.4
55
54.9
2.9
15
114.8
6.0
75
174.8
9.2
35
234.7
12.3
95
294.6
15.4
56
55.9
2.9
16
115.8
6.1
76
175.8
9.2
36
235.7
12.4
96
295.6
15.5
57
56.9
3.0
17
116.8
6.1
77
176.8
9.3
37
236.7
12.4
97
296.6
15.5
58
57.9
3.0
18
117.8
6.2
78
177.8
9.3
38
237.7
12.5
98
297.6
15.6
59
58.9
3.1
19
118.8
6.2
79
178.8
9.4
39
238.7
12.5
99
298.6
15.6
60
59.9
3.1
20
119.8
6.3
80
179.8
9.4
40
239.7
12.6
300
299.6
15.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
87° (93°, 267°, 273°).
TABLE -2. [Page 537
Difference of Latitude and Departure for 3° (177°, 183°, 357°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
300.6
15.7
361
360.5
18.9
421
420.4
22.0
481
480.3
25.2
541
540.2
28.3
02
301.6
15.8
62
361.5
19.0
22
421.4
22.1
82
481.3
25.2
42
541.2
28.4
03
302.6
15.9
63
362.5
19.0
23
422.4
22.2
83
482. 3 25. 3
43
542.2
28.4
04
303.5
15.9
64
363.5
19.1
24 423. 4
22.2
84
483. 3 25. 3
44
543.2
28.5
05 304. 5
16.0
65
364.5
19.1
25 424. 4
22.3
85
484. 3 | 25. 4
45
544.2
28.5
06 305. 5
16.0
66
365.5
19.2
26 : 425. 4
22.3
86
485.3 25.4
46
545.2
28.6
07 306. 5
16.1
67
366.5
19.2
27 426.4
22.4
87
486.3 i 25.5
47
546.2
28.6
08 307. 5
16.1
68
367.5
19.3
28 427. 4
22.4
88
487. 3 1 25. 5
48
547.2
28.7
09 308. 5
16.2
69
368. 5 19. 3
29 428. 4
22.5
89
488. 3 25. 6
49
548.2
28.7
10 309. 5
16.2
70
369. 5 19. 4
30 ! 429. 4
22.5
90
489. 3 25. 6
50
549.2
28.8
311 310. 5
16.3
371
370. 5 19. 4
431 | 430.4
22.6
491
490.3
25.7
551
550.2
28.8
12 311.5
16.3
72
371.5 I 19.5
32 431.4
22.6
92
491.3
25.7
52
551.2
28.9
13 312. 5
16.4
73
372.5 i 19.5
33 I 432.4
22.7
93
492.3
25.8
53
552.2
28.9
14
313.5
16.4
74
373.5
19.6
34
433.4
22.7
94
493.3
25.9
54
553.2
29.0
15
314.5
16.5
75
374.5
19.6
35
434.4
22.8
95
494.3
25.9
55
554.2
29.1
16
315.5
16.6
76
375.5
19.7
36
435.4
22.8
96
495.3
26.0
56
555.2
29.1
17
316.5
16.6
77
376.5
19.8
37
436.4
22.9
97
496.3
26.0
57
556.2
29.2
18
317.5
16.7
78
377.4
19.8
38
437.4
22.9
98
497.3
26.1
58
557.2
29.2
19
318.5
16.7
79
378.4
19.9
39
438.4
23.0
99
498.3
26.1
59
558.2
29.3
20
319.5
16.8
80
379.4
19.9
40
439.4
23.0
500
499.3
26.2
60 559. 2
29.3
321
320.5
16.8
381
380.4
20.0
441
440.4
23.1
501
500.3
26.2
561 560. 2
29.4
22
321.5
16.9
82
381.4
20.0
42
441.4
23.1
02
501. 3 26. 3
62 561. 2
29.4
23
322.5
16.9
83
382.4
20.1
43
442.4
23.2
03
502.3 i 26.3
63 562. 2
29.5
24
323.5
17.0
84
383.4
20.1
44
443.4
23.3
04
503. 3 26. 4
64 563. 2
29.5
25
324.5
17.0
85
384.4
20.2
45
444.4
23.3
05
504.3 '• 26.4
65 564.2
29.6
26
325.5
17.1
86
385.4
20.2
46
445.4
23.4
06
505.3 ! 26.5
66 565. 2
29.6
27
326.5
17.1
87
386.4
20.3
47
446.4
23.4
07
506.3
26.5
67 566. 2
29.7
28
327.5
17.2
88
387.4
20.3
48
447.4
23.5
08
507.3
26.6
68 567. 2 29. 7
29
328.5
17.2
89
388.4
20.4
49
448.4
23.5
09
508. 3
26.6
69 568.2 ' 29.8
30
329.5
17.3
90
389.4
20.4
50
449.3
23.6
10
509.3
26.7
70 569.2 29.8
331
330.5
17.3
391
390.4
20.5
451
450.3
23.6
511
510.3
26.7
571
570.2 j 29.9
32
331.5
17.4
92
391.4
20.5
52
451.3
23.7
12
511. 3 26. 8
72
571. 2| 29. 9
33
332.5
17.5
93
392.4
20.6
53
452.3
23.7
13
512.3
26.8
73
572.2
30.0
34
333.5
17.5
94
393.4
20.6
54
453.3
23.8
14
513.3
26.9
74
573.2
30.0
35
334.5
17.6
95
394.4
20.7
55
454.3
23.8
15
514.3
27.0
75
574.2
30.1
36
335.5
17.6
96
395.4
20.7
56
455.3
23.9
16
515.3
27.0
76
575.2
30.1
37
336.5
17.7
97
396.4
20.8
57
456.3
23.9
17
516.3
27.1
77
576.2
30.2
38
337.5
17.7
98
397.4
20.8
58
457.3
24.0
18
517. 3
27.1
78
577.2
30.2
39
338.5
17.8
99
398.4
20.9
59
458.3
24.0
19
518.3
27.2
79
578.2
30.3
40
339.5
17.8
400
399.4
20.9
60
459.3
24.1
20 519. 3
27.2
80
579.2
30.3
341
340.5
17.9
401
400.4
21.0
461
460.3
24.1
521
520.3 i 27.3
581
580.2
30.4
42
341.5
17.9
02
401.4
21.1
62
461.3
24.2
22
521. 3 27. 3
82
581.2
30.4
43
342.5
18.0
03
402.4
21.1
63
462.3
24.2
23
522.3
27.4
83
582.2
30.5
44
343.5
18.0
04
403.4
21.2
64
463.3
24.3
24 523. 3
27.4
84
583.2
30.5
45
344.5
18.1
05
404.4
21.2
65
464.3
24.4
25 524. 3
27.5
85
584.2
30.6
46
345.5
18.1
06
405.4
21.3
66
465.3
24.4
26
525.3
27.5
86
585.2
30.6
47
346.5
18.2
07
406.4
21.3
67
466.3
24.5
27
526.3
27.6
87
586.2
30.7
48
347.5
18.2
08
407.4
21.4
68
467.3
24.5
28
527.3
27.6
88
587.2
30.7
49
348.5
18.3
09
408.4
21.4
69
468.3
24.6
29
528.3
27.7
89
588.2
30.8
50
349.5
18.3
10
409.4
21.5
70
469.3
24.6
30
529.3
27.7
90
589.2
30.9
351
350.5
18.4
411
410.4
21.5
471
470. 3
24.7
531
530.3
27.8
591
590.2
30.9
52
351.5
18.4
12
411.4
21.6
72
471.3
24.7
32
531.3
27.8
92
591.2
31.0
53
352.5
18.5
13
412.4
21.6
73
472.3
24.8
33
532.3
27.9
93
592.2
31.0
54
353.5
18.5
14
413.4
21.7
74
473.3
24.8
34
533.3
27.9
94
593.2
31.1
55
354.5
18.6
15
414.4
21.7
75
474.3
24.9
35
534.3
28.0
95 594. 2
31.1
56
355.5
18.6
16
415.4
21.8
76
475.3
24.9
36
535.3
28.1
96 i 595.2
31.2
57
356.5
18.7
17
416.4
21.8
77
476.3
25.0
37
536.3
28.1
97
596.2
31.2
58
357. 5
18.8
18
417.4
21.9
78
477.3
25.0
38
537.3
28.2
98
597.2
31.3
59
358.5
18.8
19
418.4
21.9
79
478.3
25.1
39
538.3
28.2
99
598.2
31.3
60 359. 5
18.9
20
419.4
22.0
80
479.3
25.1
40
539.3
28.3
600
599.2
31.4
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
87° (93°, 267°, 273°).
Page 538] TABLE 2.
Difference of Latitude and Departure for 4° (176°, 184°, 356°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.9
4.3
121
120.7
8.4
181
180.6
12.6
241
240.4
16.8
2
2.0
0.1
62
61.8
4.3
22
121.7
8.5
82
181.6
12.7
42
241.4
16.9
3
3.0
0.2
63
62.8
4.4
23
122.7
8.6
83
182.6
12.8
43
242.4
17.0
4
4.0
0.3
64
63.8
4.5
24
123.7
8.6
84
183.6
12.8
44
243.4
17.0
5
5.0
0.3
65
64.8
4.5
25
124.7
8.7
85
184.5
12.9
45
244.4
17.1
6
6.0
0.4
66
65.8
4.6
26
125.7
8.8
86
185.5
13.0
46
245.4
17.2
7
7.0
0.5
67
66.8
4.7
27
126.7
8.9
87
186.5
13.0
47
246.4
17.2
8
8.0
0.6
68
67.8
4.7
28
127.7
8.9
88
187.5
13.1
48
247.4
17.3
9
9.0
0.6
69
68.8
4.8
29
128.7
9.0
89
188.5
13.2
49
248.4
17.4
10
10.0
0.7
70
69.8
4.9
30
129.7
9.1
90
189.5
13.3
50
249.4
17.4
11
11.0
0.8
71
70.8
5.0
131
130.7
9.1
191
190.5
13.3
251
250.4
17.5
12
12.0
0.8
72
71.8
5.0
32
131.7
9.2
92
191.5
13.4
52
251.4
17.6
13
13.0
0.9
73
72.8
5.1
33
132.7
9.3
93
192.5
13.5
53
252.4
17.6
14
14.0
1.0
74
73.8
5.2
34
133.7
9.3
94
193.5
13.5
54
253.4
17.7
15
15.0
1.0
75
74.8
5.2
35
134.7
9.4
95
194.5
13.6
55
254.4
17.8
16
16.0
1.1
76
75.8
5.3
36
135.7
9.5
96
195.5
13.7
56
255.4
17.9
17
17.0
1.2
77
76.8
5.4
37
136.7
9.6
97
196.5
13.7
57
256.4
17.9
18
18.0
1.3
78
77.8
5.4
38
137.7
9.6
98
197.5
13.8
58
257.4
18.0
19
19.0
1.3
79
78.8
5.5
39
138.7
9.7
99
198.5
13.9
59
258.4
18.1
20
20.0
1.4
80
79.8
5.6
40
139.7
9.8
200
199.5
14.0
60 | 259.4
18.1
21
20.9
1.5
81
80.8
5.7
141
140.7
9.8
201
200.5
14.0
261
260.4
18.2
22
21.9
1.5
82
81.8
5.7
42
141.7
9.9
02
201.5
14.1
62
261.4
18.3
23
22.9
1.6
83
82.8
5.8
43
142.7
10.0
03
202.5
14.2
63
262.4
18.3
24
23.9
1.7
84
83.8
5.9
44
143.6
10.0
04
203.5
14.2
64
263.4
18.4
25
24.9
1.7
85
84.8
5.9
45
144.6
10.1
05
204.5
14.3
65
264.4
18.5
26
25.9
1.8
86
85.8
6.0
46
145.6
10.2
06
205.5
14.4
66
265.4
18.6
27
26.9
1.9
87
86.8
6.1
47
146.6
10.3
07
206.5
14.4
67
266.3
18.6
28
27.9
2.0
88
87.8
6.1
48
147.6
10.3
08
207.5
14.5
68.
267.3
18.7
29
28.9
2.0
89
88.8
6.2
49
148.6
10.4
09
208.5
14.6
69
268.3
18.8
30
29.9
2.1
90
89.8
6.3
50
149.6
10.5
10
209.5
14.6
70
269.3
18.8
31
30.9
2.2
91
90.8
6.3
151
150.6
10.5
211
210.5
14.7
271 270. 3
18.9
32
31.9
2.2
92
91.8
6.4
52
151.6
10.6
12
211.5
14.8
72 271. 3
19.0
33
32.9
2.3
93
92.8
6.5
53
152.6
10.7
13
212.5
14.9
73 272. 3
19.0
34
33.9
2.4
94
93.8
6.6
54
153.6
10.7
14
213.5
14.9
74
273.3
19.1
35
34.9
2.4
95
94.8
6.6
55
154.6
10.8
15
214.5
15.0
75
274.3
19.2
36
35.9
2.5
96
95.8
6.7
56
155.6
10.9
16
215.5
15.1
76
275.3
19.3
37
36.9
2.6
97
96.8
6.8
57
156.6
11.0
17
216.5
15.1
77
276.3
19.3
38
37.9
2.7
98
97.8
6.8
58
157.6
11.0
18
217.5
15.2
78
277.3
19.4
39
38.9
2.7
99
98.8
6.9
59
158.6
11.1
19
218.5
15.3
79
278.3
19.5
40
39.9
2.8
100
99.8
7.0
60
159.6
11.2
20
219.5
15.3
80
279.3
19.5
41
40.9
2.9
101
100.8
7.0
161
160.6
11.2
221
220.5
15.4
281
280.3
19.6
42
41.9
2.9
02
101.8
7.1
62
161.6
11.3
22
221.5
15.5
82
281.3
19.7
43
42.9
3.0
03
102.7
7.2
63
162.6
11.4
23
222.5
15.6
83
282.3
19.7
44
43.9
3.1
04
103.7
7.3
64
163.6
11.4
24
223.5
15.6
84
283.3
19.8
45
44.9
3.1
05
104.7
7.3
65
164.6
11.5
25
224.5
15.7
85
284.3
19.9
46
45.9
3.2
06
105.7
7.4
66
165.6
11.6
26
225.4
15.8
86
285.3
20.0
47
46.9
3.3
07
106.7
7.5
67
166.6
11.6
27
226.4
15.8
87
286.3
20.0
48
47.9
3.3
08
107.7
7.5
68
167.6
11.7
28
227.4
15.9
88
287.3
20.1
49
48.9
3.4
09
108.7
7.6
69
168.6
11.8
29
228.4
16.0
89
288.3
20.2
50
49.9
3.5
10
109.7
7.7
70
169.6
11.9
30
229.4
16.0
90
289.3
20.2
51
50.9
3.6
111
110.7
7.7
171
170.6
11.9
231
230.4
16.1
291
290.3
20.3
52
51.9
3.6
12
111.7
7.8
72
171.6
12.0
32
231.4
16.2
92
291.3
20.4
53
52.9
3.7
13
112.7
7.9
73
172.6
12.1
33
232.4
16.3
93
292.3
20.4
54
53.9
3.8
14
113.7
8.0
74
173.6
12.1
34
233.4
16.3
94
293.3
20.5
55
54.9
3.8
15
114.7
8.0
75
174. 6 *
12.2
35
234.4
16.4
95
294.3
20.6
56
55.9
3.9
16
115.7
8.1
76
175.6
12.3
36
235.4
16.5
96
295.3
20.6
57
56.9
4.0
17
116.7
8.2
77
176.6
12.3
37
236.4
16.5
97
296. 3
20.7
58
57.9
4.0
18
117.7
8.2
78
177.6
12.4
38
237.4
16.6
98
297.3
20.8
59
58.9
4.1
19
118.7
8.3
79
178.6
12.5
39
238.4
16.7
99
298.3
20.9
60
59.9
4.2
20
119.7
8.4
80
179.6
12.6
40
239.4
16.7
300
299.3
20.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
86°; (94°, 266°, 274°).
TABLE 2. [Page 539
Difference of Latitude and Departure for 4° (176°, 184°, 356° .
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat
Dep.
301
300.3 1 21.0
361 360. 1
25.2
421
420.0
29.4
481
479.8
33.5
541
539.7
37.7
02
301.3
21.1
62 1 361.1
25.2
22
421.0
29.4
82
480.8
33.6
42
540.7
37.8
03
302.2
21.1
63 1 362. 1
25.3
23
422.0
29.5
83
481.8
33.7
43
541.7
37.9
04
303.2
21.2
64
363.1
25.4
24
423.0
29.6
84
482.8
33.7
44
542.7
37.9
05
304.2
21.3
65
364.1
25.5
25
424.0
29.6
85
483.8
33.8
45
543.7
38.0
06
305.2
21.3
66
365.1
25.5
26
424.9
29.7
86
484.8
33.9
46
544.7
38.1
07
306.2
21.4
67
366.1
25.6
27
425.9
29.8
87
485.8
33.9
47
545.7
38.1
08
307.2
21.5
68
367.1
25.7
28
426.9
29.9
88
486.8
34.0
48
546.7
38.2
09
308.2
21.6
69
368.1
25.7
29
427.9
29.9
89
487.8
34.1
49
547.7
38.3
10
309.2
21.6
70
369.1
25.8
30
428.9
30.0
90
488.8
34.2
50
548.7
38.3
311
310.2
21.7
371
370.1
25.9
431
429.9
30.1
491
489.8
34.2
551
549.7
38.4
12
311.2
21.8
72
371.1
25.9
32
430.9
30.1
92
490.8
34.3
52
550.7
38.5
13
312.2
21.8
73
372.1
26.0
33
431.9
30.2
93
491.8
34.4
53
551.7
38.5
14
313.2
21.9
74
373. 1
26.1
34
432.9
30.3
94
492.8
34.4
54
552.7
38.6
15
314.2
22.0
75
374.1
26.2
35
433.9
30.3
95
493.8
34.5
55
553.6
38.7
16
315.2
22.1
76
375.1
26.2
36
434.9
30.4
96
494.8
34.6
56
554.6
38.7
17
316.2
22.1
77
376.1
26.3
37
435.9
30.5
97
495.8
34.6
57
555.6
38.8
18
317.2
22.2
78
377.
26.4
38
436.9
30.6
98
496.8
34.7
58
556.6
38.9
19
318.2
22.3
79
378.
26.4
39
437.9
30.6
99
497.8
34.8
59
557.6
38.9
20
319.2
22.3
80
379.
26.5
40
438.9
30.7
500
498.8
34.8
60
558.6
39.0
321
320.2
22.4
381
380.
26.6
441
439.9
30.8
501
499.8
34.9
561
559.6
39.1
22
321.2
22.5
82
381.
26.6
42
440.9
30.8
02
500.8
35.0
62
560.6
39.2
23
322.2
22.5
83
382.
26.7
43
441.9
30.9
03
501.8
35.0
63
561.6
39.2
24
323.2
22.6
84
383.1
26.8
44
442.9
31.0
04
502.8
35.1
64
562.6
39.3
25
324.2
22.7
85
384.0
26.9
45
443.9
31.0
05
503.8
35.2
65
563.6
39.4
26
325.2
22.7
86
385.0
26.9
46
444.9
31.1
06
504.8
35.2
66
564.6
39.4
27
326.2
22.8
87
386.0
27.0
47
445.9
31.2
07
505.8
35.3
67
565. 6
39.5
28
327.2
22.9
88
387.0
27.1
48
446.9
31.2
08
506.8
35.4
68
566.6
39.6
29
328.2
23.0
89
388.0
27.1
49
447.9
31.3
09
507.8
35.5
69
567.6
39.7
30
329.2
23.0
90
389.0
27.2
50
448.9
31.4
10
508.8
35.6
70
568.6
39.8
331
330.2
23.1
391
390.0
27.3
451
449.9
31.5
511
509.8
35.6
571
569.6
39.8
32
331.2
23.2
92
391.0
27.3
52
450.9
31.5
12
510.8
35.7
72
570.6
39.9
33
332.2
23.2
93
392.0
27.4
53
451.9
31.6
13
511.8
35.8
73 571. 6
40.0
34
333.2
23.3
94
393.0
27.5
54
452.9
31.7
14
512.7
35.8
74 572. 6
40.0
35
334.2
23.4
95
394.0
27.6
55
453.9
31.7
15
513.7
35.9
75
573.6
40.1
36
335.2
23.4
96
395.0
27.6
56
454.9
31.8
16
514.7
36.0
76
574.6
40.2
37
336.2
23.5
97
396.0
27.7
57
455.9
31.9
17
515.7
36.0
77 | 575. 6
40.2
38
337.2
23.6
98
397.0
27.8
58
456.9
31.9
18
516.7
36.1
78 576. 6
40.3
39
338.2
23.6
99
398.0
27.8
59
457.9
32.0
19
517.7
36.2
79 577. 6
40.4
40
339.2
23.7
400
399.0
27.9
60
458.9
32.1
20
518.7
36.2
80
578.6
40.5
341
340.2
23.8
401
400.0
28.0
461
459.9
32.2
521
519.7
36.3
581
579.6
40.5
42
341.2
23.9
02
401.0
28.0
62
460.9
32.2
22
520.7
36.4
82
580.6
40.6
43
342.2
23.9
03
402.0
28.1
63
461.9
32.3
23
521.7
36.4
83
581.6
40.7
44
343.1
24.0
04
403.0
28.2
64
462.9
32.4
24
522.7
36.5
84
582.6
40.7
45
344.1
24.1
05
404.0 i 28.2
65
463.9
32.4
25
523.7
36.6
85
583.6
40.8
46
345.1
24.1
06
405.0
28.3
66
464.9
32.5
26
524.7
36.7
86
584.6
40.9
47
346.1
24.2
07
406.0
28.4
67
465.8
32.6
27
525.7
36.8
87
585.6
40.9
48
347.1
24.3
08
407.0
28.5
68
466.8
32.6
28
526.7
36.8
88
586.6
41.0
49
348.1
24.3
09
408.0
28.5
69
467.8
32.7
29
527.7
36.9
89
587.6
41.1
50
349. 1 24. 4
10
409.0
28.6
70,
468.8
32.8
30
528.7
37.0
90
588.6
41.2
351
350. 1 | 24. 5
411
410.0
28.7
471
469.8
32.9
531
529.7
37.0
591
589.6
41.3
52
351. 1 24. 6
12
411.0
28.7
72
470.8
32.9
32
530.7
37.1
92
590.6
41.3
53
352. 1 24. 6
13
412.0
28.8
73
471.8
33.0
33
531.7
37.2
93
591.6
41.4
54
353.1
24.7
14
413.0
28.9
74
4y2.8
33.1
34
532.7
37.2
94
592.6
41.5
55
354.1
24.8
15
414.0
28.9
75
473.8
33.1
35
533.7
37.3
95
593.6
41.5
56
355.1
24.8
16
415.0
29.0
76
474.8
33.2
36
534.7
37.4
96
594.6
41.6
57
356.1
24.9
17
416.0
29.1
77
475.8
33.3
37
535.7
37.5
97
595.6
41.7
58
357.1
25.0
18
417.0
29.2
78
476.8
33.3
38
536.7
37.5
98
596.6
41.7
59
358.1
25.0
19
418.0
29.2
79
477.8
33.4
39
537.7
37.6
99
597.6
41.8
60
359.1
25.1
20
419.0
29.3
80
478.8
35.5
40
538.7
37.7
600
598.6
41.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
86°; (94°, 266°, 274°).
Page 540] TABLE 2.
Difference of Latitude and Departure for 5° (175°, 185°, 355°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.8
5.3
121
120.5
10.5
181
180.3
15.8
241
240.1
21.0
2
2.0
0.2
62
61.8
5.4
22
121.5
10.6
82
181.3
15.9
42
241.1
21.1
3
3.0
0.3
63
62.8
5.5
23
122.5
10.7
83
182.3
15.9
43
242.1
21.2
4 J
4.0
0.3
64
63.8
5.6
24
123.5
10.8
84
183.3
16.0
44
243.1
21.3
5 I 5.0
0.4
65
64.8
5.7
25
124.5
10.9
85
184.3
16.1
45
244.1
21.4
6
6.0
0.5
66
65.7
5.8
26
125.5
11.0
86
185.3
16.2
46
245.1
21.4
7
7.0
0.6
67
66.7
5.8
27
126.5
11.1
87
186.3
16.3
47
246.1
21.5
8
8.0
0.7
68
67.7
5.9
28
127.5
11.2
88
187. 3.
16.4
48
247.1
21.6
9
9.0
0.8
69
68.7
6.0
29
128.5
11.2
89
188.3
16.5
49
248.1
21.7
10
10.0
0.9
70
69.7
6.1
30
129.5
11.3
90
189.3
16.6
50
249.0
21.8
11
11.0
1.0
71
70.7
6.2
131
130.5
11.4
191
190.3
16.6
251
250.0
21.9
12
12.0
1.0
72
71.7
6.3
32
131.5
11.5
92
191.3
16.7
52
251.0
22.0
13
13.0
1.1
73
72.7
6.4
33
132.5
11.6
93
192.3
16.8
53
252.0
22.1
14
13.9
1.2
74
73.7
6.4
34
133. 5
11.7
94
193.3
16.9
54
253.0
22.1
15
14.9
1.3
75
74.7
6.5
35
134.5
11.8
95
194. 3
17.0
55
254.0
22.2
16
15.9
1.4
76
75.7
6.6
36
135.5
11.9
96
195. 3
17.1
56
255.0
22.3
17
16.9
1.5
77
76.7
6.7
37
136.5
11.9
97
196.3
17.2
57
256.0
22.4
18
17.9
1.6
78
77.7
6.8
38
137.5
12.0
98
197.2
17.3
58
257.0
22.5
19
18.9
1.7
79
78.7
6.9
39
138.5
12.1
99
198.2
17.3
59
258.0
22.6
20
19.9
1.7
80
79.7
7.0
40
139.5
12.2
200
199.2
17.4
60
259.0
22.7
21
20.9
1.8
81
80.7
7.1
141
140. 5
12.3
201
200.2
17.5
261
260.0
22.7
22
21.9
1.9
82
81.7
7.1
42
141.5
12.4
02
201.2
17.6
62
261.0
22.8
23
22.9
2.0
83
82.7
7.2
43
142.5
12.5
03
202.2
17.7
63
262.0
22.9
24
23.9
2.1
84
83.7
7.3
44
143.5
12.6
04
203.2
17.8
64
263.0
23.0
25
24.9
2.2
85
84.7
7.4
45
144.4
12.6
05
204.2
17.9
65
264.0
23.1
26
25.9
2.3
86
85.7
7.5
46
145.4
12.7
06
205.2
18.0
66
265.0
23.2
27
26.9
2.4
87
86.7
7.6
47
146.4
12.8
07
206.2
18.0
67
266.0
23.3
28
27.9
2.4
88
87.7
7.7
48
147.4
12.9
08
207.2
18.1
68
267.0
23.4
29
28.9
2.5
89
88.7
7.8
49
148.4
13.0
09
208.2
18.2
69
268.0
23.4
30
29.9
2.6
90
89.7
7.8
50
149.4
13.1
10
209.2
18.3
70
269.0
23.5
31
30.9
2.7
91
90.7
7.9
151
150.4
13.2
211
210.2
18.4
271
270.0
23.6
32
31.9
2.8
92
91.6
8.0
52
151.4
13.2
12
211.2
18.5
72
271.0
23.7
33
32.9
2.9
93
92.6
8.1
53
152.4
13.3
13
212.2
18.6
73
272.0
23.8
34
33.9
3.0
94
93.6
8.2
54
153. 4
13.4
14
213.2
18.7
74
273.0
23.9
35
34.9
3.1
95
94.6
8.3
55
154.4
13.5
15
214.2
18.7
75
274.0
24.0
36
35.9
3.1
96
95.6
8.4
56
155.4
13.6
16
215.2
18.8
76
274.9
24.1
37
36.9
3.2
97
96.6
8.5
57
156.4
13.7
17
216.2
18.9
77
275.9
24.1
38
37.9
3.3
98
97.6
8.5
58
157.4
13.8
18
217.2
19.0
78
276.9
24.2
39
38.9
3.4
99
98.6
8.6
59
158.4
13.9
19
218.2
19.1
79
277.9
24.3
40
39.8
3.5
100
99.6
8.7
60
159.4
13.9
20
219.2
19.2
80
278.9
24.4
41
40.8
3.6
101
100.6
8.8
161
160.4
14.0
221
220.2
19.3
281
279.9
24.5
42
41.8
3.7
02
101.6
8.9
62
161.4
14.1
22
221.2
19.3
82
280.9
24.6
48
42.8
3.7
03
102.6
9.0
63
162.4
14.2
23
222.2
19.4
83
281.9
24.7
44
43.8
3.8
04
103.6
9.1
64
163.4
14.3
24
223.1
19.5
84
282.9
24.8
45
44.8
3.9
05
104.6
9.2
65
164.4
14.4
25
224.1
19.6
85
283.9
24.8
46
45.8
4.0
06
105.6
9.2
66
165.4
14.5
26
225.1
19.7
86
284.9
24.9
47
46.8
4.1
07
106.6
9.3
67
166.4
14.6
27
226.1
19.8
87
285.9
25.0
48
47.8
4.2
08
107.6
9.4
68
167.4
14.6
28
227.1
19.9
88
286.9
25.1
49
48.8
4.3
09
108.6
9.5
69
168.4
14.7
29
228.1
20.0
89
287.9
25.2
50
49.8
4.4
10
109.6
9.6
70
169.4
14.8
30
229.1
20.0
90
288.9
25.3
51
50.8
4.4
111
110.6
9.7
171
170.3
14.9
231
230.1
20.1
291
289.9
25.4
52
51.8
4.5
12
111.6
9.8
72
171.3
15.0
32
231.1
20.2
92
290.9
25.4
53
52.8
4.6
13
112.6
9.8
73
172.3
15.1
33
232.1
20.3
93
291.9
25.5
54
53.8
4.7
14
113'. 6
9.9
74
173.3
15.2
34
233.1
20.4
94
292.9
25.6
55
54.8
4.8
15
114.6
10.0
75
. 174. 3
15.3
35
234.1
20.5
95
293.9
25.7
56
55.8
4.9
16
115.6
10.1
76
175.3
15.3
36
235.1
20.6
96
294.9
25.8
57
56.8
5.0
17
116.6
10.2
77
176.3
15.4
37
236.1
20.7
97
295.9
25.9
58
57.8
5.1
18
117.6
10.3
78
177.3
15.5
38
237.1
20.7
98
296.9
26.0
59
58.8
5.1
19
118.5
10.4
79
178.3
15.6
39
238.1
20.8
99
297.9
26.1
60
59.8
5.2
20
119.5
10.5
80
179.3
15.7
40
239.1
20.9
300
298.9
26.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
85° (95°, 265°, 275°).
TABLE 2.
[Page 541
J^UKQ
LCiiOC \JL
J^tllill.1
J.C <VUV.
L J-'C^OJ. 1
C11C 1U1
• f*
1 V ; J.OO
. ouu
)-
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
| Lat.
Dep.
301
299.9
26.2
361
359.6
31.5
421
419.4
36.7
481
479.2
41.9
541
' 538.9
47.2
02
300.8
26.3
62
360.6
31.6
22
420.4
36.8
82
480.2
42.0
42
i 539.9
47.3
03
! 301. 8
26.4
63
361.6
31.6
23
421.4
36.9
83
481.2
42.1
43
540.9
47.4
04
I 302.8
I 26.5
64
362.6
31.7
24
422.4
37.0
84
482.2
42.2
44
541.9
47.5
05
303.8
j 26.6
65
363.6
31.8
25
423.4
i 37.1
85
483.2
42.3
45
542.9
47.6
06
304.8
! 26.7
66
364.6
31.9
26
424.4
37.1
86
484.1
42.4
46
543.9
47.7
07
305.8
26.8
67
365.6
32.0
27
425.4
37.2
87
485.1
42.4
47
i 544.9
47.7
08
306.8
26.9
68
! 366. 6
32.1
28
426.4
37.3
88
486.1
I 42.5
48
545.9
; 47.8
09
307.8
26.9
69
367.6
32.2
29
427.4
37.4
89
487.1
42.6
49
546.9
47.9
10
308.8
27.0
70
368.6
32.3
30
428.4
37.5
90
488.1
i 42.7
50
547.9
48.0
311
309.8
27.1
371
369.6
32.3
431
429.4
37.6
491
489.1
j 42.8
551
548.9
48.1
12
310.8
27.2
72
370.6
32.4
32
430.4
37.7
92
490.1
42.9
52
549.9
48.2
13
311.8
27.3
73
371.6
32.5
33
431.3
37.7
93
491.1
i 43.0
53
550.9
48.3
14
312.8
27.4
74
372.6
32.6
34
432.3
37.8
94
492.1
43.1
54
551.9
48.4
15
313.8
27.5
75
373.6
32.7
35
433.3
37.9
95
493.1
43.1
55
552.9
48.4
16
314.8
27.5
76
374.6
32.8
36
434. 3
38.0
96
494.1
43.2
56
553.9
48.5
17
315.8
27.6
77
375.6
32.9
37
435.3
38.1
97
495.1
43.3
57
554.9
48.6
18
316.8
27.7
78
376.6
33.0
38
436.3
38.2
98
496.1
43.4
58
555.9
i 48.7
19
317.8
27.8
79
377.6
33.0
39
437.3
38.3
99
497.1
43.5
59
556.9
i 48.8
20
318.8
27.9
80
378. 6
33.1
40
438.3
38.4
500
498.1
43.6
60
557.9
48.8
321
319.8
28.0
381
379.5
33.2
441
439.3
38.4
501
499.1
43.7
561
568.8
48.9
22
320.8
28.1
82
380.5
33.3
42
440.3
38.5
02
500.1
43.8
62
559. 8
. 49.0
23
321.8
28.2
83
381.5
33.4
43
441.3
38.6
03
501.1
43.8
63
560.8
49.1
24
322.8
28.2
84
382.5
33.5
44
442.3
38.7
04
502.1
43.9
64
561.8
49.2
25
323.8
28.3
85
383.5
33.6
45
443.3
38.8
05
503.1
44.0
65
562.8
49.3
26
324.8
28.4
86
384.5
33.7
46
444.3
38.9
06
504.1
44.1
66
563.8
49.4
27
325.8
28.5
87
385.5
33.7
47
445.3
39.0
07
505.1
44.2
67
564.8
49.5
28
326.7
28.6
88
386.5
33.8
48
446.3
39.1
08
506.1
44.3
68
565.8
49.6
29
327.7
28.7
89
387.5
33.9
49
447.3
39.1
09
507.1
44.4
69
566.8
49.7
30
328.7
28.8
90
388.5
34.0
50
AAQ Q
T±O. O
39.2
10
508.1
44.5
70
567.8
49.7
331
329.7
28.9
391
389.5
34.1
451
449.3
39.3
511
509.0
44.5
571
568.8
49.8
32
330.7
28.9
92
390.5
34.2
52
450.3
39.4
12
510.0
44.6
72
569.8
49.9
33
331.7
29.0
93
391.5
34.3
53
451.3
39.5
13
511.0
44.7
73
570.8
50.0
34
332.7
29.1
94
392.5
34.3
54
452.3
39.6
14
512.0
44.8
74
571.8
50.1
35
333. 7
29.2
95
393.5
34.4
55
453.3
39.7
• 15
513.0
44.9
75
572.8
50.2
36
334.7
29.3
96
394.5
34.5
56
454. 3
39.8
16
514.0
45.0
76
573.8
50.3
37
335.7
29.4
97
395.5
34.6
57
455.3
39.8
17
515.0
45.1
77
574.8
50.4
38
336.7
29.5
98
396.5
34.7
58
456.3
39.9
18
516.0
45.2
78
575.8
50.4
39
337.7
29.6
99
397.5
34.8
59
457.3
40.0
19
517.0
45.2
79
576.8
50.5
40
338.7
29.6
400
398.5
34.9
60
458.2
40.1
20
518.0
45.3
80
577.8
50.6
341
339.7
29.7
401
399.5
35.0
461
459.2
40.2
521
519.0
45.4
581
578.8
50.7
42
340.7
29.8
02
400.5
35.0
62
460.2
40.3
22
520.0
45.5
82
579.8
50.8
43 j
341.7
29.9
03
401.5
35.1
63
461.2
40.4
23
521.0
45.6
83
580.8
50.9
44
342.7
30.0
04
402.5
35.2
64
462.2
40.4
24
522.0
45.7
84
581.8
50.9
45
343.7
30.1
05
403.5
35.3
65
463.2
40.5
25
523.0
45.8
85
582.8
51.0
46
344.7
30.2
06
404.5
35.4
66
464.2
40.6
26
524.0
45.9
86
583. 8
51.1
47
345.7
30.3
07
405.4 !
35.5
67
465.2
40.7
27
525.0
45.9
87
584.8
51.2
48
346.7
30.3
08
406.4
35.6
68
466.2
40.8
28
526.0
46.0
88
585.8
51.3
49
347.7
30.4
09
407.4
35.7
69
467.2
40.9
29
527.0
46.1
89
586.8
51.4
50
348.7
30.5
10
408.4
35.7
70
468.2
41.0
30
528.0
46.2
90
587.8
51.5
351
349.7
30.6
411
409.4
35.8
471
469.2
41.1
531
529.0
46.3
591
588.7
51.6
52
350.7
30.7
12
410.4
35.9
72
470.2
41.1
32
530.0
46.4
92
589.7
51.6
53
351.7
30.8
13
411.4
36.0
73
471.2
41.2
33
531.0
46.5
93
590.7
51.7
54
352.6
30.9
14
412.4
36.1
74
472.2
41.3
34
532.0
46.6
94
591.7
51.8
55
353.6
30.9
15
413.4
36.2
75
473.2
41.4
35
533.0
46.6
95
592.7
51.9
56
354.6
31.0
16
414.4
36.3
76
474.2
41.5
36
533.9
46.7
96
593.7
52.0
57
355.6
31.1
17
415.4
36.4
77
475.2
41.6
37
534.9
46.8
97
594.7
52.1
58
356.6
31.2
18
416.4
36.4
78
476.2
41.7
38
535.9
46.9
98
595. 7
52.2
59
357.6
31.3
19
417.4
36.5
79
477.2
41.8
39
536.9
47.0
99
596.7
52.3
60
358.6
31.4
20
418.4
36.6
80
478.2
41.8
40
537.9
47.1
600
597.7
52.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. j
Lat.
Dist.
Dep.
Lat.
!
35° (9
5°, 265°
, 275°)
Page 542] TABLE 2.
Difference of Latitude and Departure for 6° (174°, 186°, 354°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.7
6.4
121
120.3
12.6
181
180.0
18.9
241
239.7
25.2
2
2.0
0.2
62
61.7
6.5
22
121.3
12.8
82
181.0
19.0
42
240.7
25.3
3
3.0
0.3
63
62.7
6.6
23
122.3
12.9
83
182.0
19.1
43
241.7
25.4
4
4.0
0.4
64
63.6
6.7
24
123.3
13.0
84
183.0
19.2
44
242.7
25.5
5
5.0
0.5
65
64.6
6.8
25
124.3
13.1
85
184.0
19.3
45
243.7
25.6
6
6.0
0.6
66
65.6
6.9
26
125.3
13.2
86
185.0
19.4
46
244.7
25.7
7
7.0
0.7
67
66.6
7.0
27
126.3
13.3
87
186.0
19.5
47
245.6
25.8
8
8.0
0.8
68
67.6
7.1
28
127.3
13.4
88
187.0
19.7
48
246.6
25.9
9
9.0
0.9
69
68.6
7.2
29
128.3
13.5
89
188.0
19.8
49
247.6
26.0
10
9.9
1.0
70
69.6
7.3
30
129.3
13.6
90
189.0
19.9
50
248.6
26.1
11
10.9
.1
71
70.6
7.4
131
130.3
13.7
191
190.0
20.0
251
249.6
26.2
12
11.9
.3
72
71.6
7.5
32
131.3
13.8
92
190.9
20.1
52
250.6
26.3
13
12.9
.4
73
72.6
7.6
33
132.3
13.9
93
191.9
20.2
53
251.6
26.4
14
13.9
.5
74
73.6
7.7
34
133.3
14.0
94
192.9
20.3
54
252.6
26.6
15
14.9
.6
75
74.6
7.8
35
134.3
14.1
95
193.9
20.4
55
253.6
26.7
16
15.9
1.7
76
75.6
7.9
36
135.3
14.2
96
194.9
20.5
56
254.6
26.8
17
16.9
1.8
77
76.6
8.0
37
136.2
14.3
97
195.9
20.6
57
255.6
26.9
18
17.9
1.9
78
77.6
8.2
38
137.2
14.4
98
196.9
20.7
58
256.6
27.0
19
18.9
2.0
79
78.6
8.3
39
138.2
14.5
99
197.9
20.8
59
257.6
27.1
20
19.9
2.1
80
79.6
8.4
40
139.2
14.6
200
198.9
20.9
60
258.6
27.2
21
20.9
2.2
81
80.6
8.5
141
140.2
14.7
201
199.9
21.0
261
259.6
27.3
22
21.9
2.3
82
81.6
8.6
42
141.2
14.8
02
200.9
21.1
62
260.6
27.4
23
22.9
2.4
83
82.5
8.7
43
142.2
14.9
03
201.9
21.2
63
261.6
27.5
24
23.9
2.5
84
83.5
8.8
44
143.2
15.1
04
202.9
21.3
64
262.6
27.6
25
24.9
2.6
85
84.5
8.9
45
144.2
15.2
05
203.9
21.4
65
263.5
27.7
26
25.9
2.7
86
85.5
9.0
46
145.2
15.3
06
204.9
21.5
66
264.5
27.8
27
26.9
2.8
87
86.5
9.1
47
146.2
15.4
07
205.9
21.6
67
265.5
27.9
28
27.8
2.9
88
87.5
9.2
48
147.2
15.5
08
206.9
21.7
68
266.5
28.0
29
28.8
3.0
89
88.5
9.3
49
148.2
15.6
09
207.9
21.8
69
267.5
28.1
30
29.8
3.1
90
89.5
9.4
50
149.2
15.7
10
208.8
22.0
70
268.5
28.2
31
30.8
3.2
91
90.5
9.5
151
150.2
15.8
211
209.8
22.1
271
269.5
28.3
32
31.8
3.3
92
91.5
9.6
52
151.2
15.9
12
210.8
22.2
72
270.5
28.4
33
32.8
3.4
93
92.5
9.7
53
152.2
16.0
13
211.8
22.3
73
271.5
28.5
34
33.8
3.6
94
93.5
9.8
54
153.2
16.1
14
212.8
22.4
74
272.5
28.6
35
34.8
3.7
95
94.5
9.9
55
154.2
16.2
15
213.8
22.5
75
273.5
28.7
36
35.8
3.8
96
95.5
10.0
56
155.1
16.3
16
214.8
22.6
76
274.5
28.8
37
36.8
3.9
97
96.5
10.1
57
156.1
16.4
17
215.8
22.7
77
275.5
29.0
38
37.8
4.0
98
97.5
10.2
58
157.1
16.5
18
216.8
22.8
78
276.5
29.1
39
38.8
4.1
99
98.5
10.3
59
158.1
16.6
19
217.8
22.9
79
277.5
29.2
40
39.8
4.2
100
99.5
10.5
60
159.1
16.7
20
218.8
23.0
80
278.5
29.3
41
40.8
4.3
101
100.4
10.6
161
160.1
16.8
221
219.8
23.1
281
279.5
29.4
42
41.8
4.4
02
101.4
10.7
62
161.1
16.9
22
220.8
23.2
82
280.5
29.5
43
42.8
4.5
03
102.4
10.8
63
162.1
17.0
23
221.8
23.3
83
281.4
29.6
44
43.8
4.6
04
103.4
10.9
64
163.
17.1
24
222.8
23.4
84
282.4
29.7
45
44.8
4.7
05
104.4
11.0
65
164.
17.2
25
223.8
23.5
85
283.4
29.8
46
45.7
4.8
06
105.4
11.1
66
165.
17.4
26
224.8
23.6
86
284.4
29.9
47
46.7
4.9
07
106.4
11.2
67
166.
17.5
27
225.8
23.7
87
285.4
30.0
48
47.7
5.0
08
107.4
11.3
68
167.
17.6
28
226.8
23.8
88
286.4
30.1
49
48.7
5.1
09
108.4
11.4
69
168.
17.7
29
227.7
23.9
89
287.4
30.2
50
49.7
5.2
10
109.4
11.5
70
169.
17.8
30
228.7
24.0
90
288.4
30.3
51
50.7
5.3
111
110.4
11.6
171
170.1
17.9
231
229.7
24.1
291
289.4
30.4
52
51.7
5.4
12
111.4
11.7
72
171.1
18.0
32
230.7
24.3
92
290.4
30.5
53
52.7
5.5
13
112.4
11.8
73
172.1
18.1
33
231.7
24.4
93
291.4
30.6
54
53.7
5.6
14
113.4
11.9
74
173.0
18.2
34
232.7
24.5
94
292.4
30.7
55
54.7
5.7
15
114.4
12.0
75
174.0
18.3
35
233.7
24.6
95
293.4
30.8
56
55.7
5.9
16
115.4
12.1
76
175.0
18.4
36
234.7
24.7
96
294.4
30.9
57
56.7
6.0
17
116.4
12.2
77
176.0
18.5
37
235.7
24.8
97
295.4
31.0
58
57.7
6.1
18
117.4
12.3
78
177.0
18.6
38
236.7
24.9
98
296.4
31.1
59
58.7
6.2
19
118.3
12.4
79
178.0
18.7
39
237.7
25.0
99
297.4
31.3
60
59.7
6.3
20
119.3
12.5
80
179.0
18.8
40
238.7
25.1
300
298.4
31.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
84° (96°, 264°, 276°).
TABLE 2. [Page 643
Difference of Latitude and Departure for 6° (174°, 186°, 354°).
Dist.
Lat. Dep.
Dist. Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
299.3 I 31.5
361
359.0
37.7
421
418. 7 44. 0
481
478.4
50.3
541
538.0
56.5
02
300.3 31.6
62
360.0
37.8
22
419.7 ! 44.1
82
479.4
50.4
42
539.0
56.6
03
301. 3 i 31. 7
63
361.0
37.9
23
420.7 i 44.2
83
480.4
50.5
43
540.0
56.7
04
302.3
31.8
64
362.0
38.0
24
421.7 1 44.3
84
481.3
50.6
44
541.0
56.8
05
303.3
31.9
65
363.0
38.1
25
422.7
44.4
85
482.3
50.7
45
542.0
56.9
06
304.3
32.0
66
364.0
38.3
26
423.7
44.5
86
483.3
50.8
46
543.0
57.0
07
305.3
32.1
67
365.0
38.4
27
424. 7 44. 6
87
484.3
50.9
47
544.0
57.1
08
306.3
32.2
68
366.0
38.5
28
425. 7 44. 7
88
485.3
51.0
48
545. 0
57.2
09
307.3
32.3
69
367.0
38.6
29
426. 6 44. 8
89
486.3
51.1
49
546.0
57.3
10
308.3 j 32.4
70
368.0
38.7
30
427. 6 44. 9
90
487.3
51.2
50
547.0
57.4
311
309.3
32.5
371
369.0
38.8
431
428. 6 45. 0
491
488.3
51.3
551
548.0
57.5
12
310.3
32.6
72
370.0
38.9
32
429. 6 i 45. 2
92
489.3
51.4
52
549.0
57.6
13
311.3
32.7
73
371.0
39.0
33
430.6
45.3
93
490.3
51.5
53
550. 0
57.7
14
312.3
32.8
74
371.9
39.1
34
431.6
45.4
94 491. 3
51.6
54
551.0
57.9
15
313.3
32.9
75
372.9
39.2
35
432.6
45.5
95
492.3
51.7
55
552.0
58.0
16
314.3
33.0
76
373.9
39.3
36
433.6
45.6
96
493.3
51.8
56
553.0
58.1
17
315.3
33.1
77
374.9
39.4
37
434.6
45.7
97
494.3
51.9
57
554.0
58.2
18
316.3
33.2
78
375.9
39.5
38
435.6
45.8
98 495. 3
52.0
58
555.0
58.3
19
317.3
33.3
79
376.9
39.6
39
436.6
45.9
99 496. 3
52.1
59
556.0
58.4
20
318.2
33.4
80
377.9
39.7
40
437.6
46.0
500 497. 3
52.3
60
556.9
58.5
321
319.2
33.6
381
378.9
39.8
441
438.6
46.1
501
498.3
52.4
561
557.9
58.6
22
320.2
33.7
82
379.9
39.9
42
439.6
46.2
02
499.3
52.5
62
558.9
58.7
23
321.2 i 33.8
83
380.9
40.0
43
440.6
46.3
03
500. 2 52. 6
63
559.9
58.8
24
322.2 33.9
84
381.9
40.1
44
441.6
46.4
04
501.2
52.7
64
560.9
59.0
25
323.2 1 34.0
85
382.9
40.2
45
442.6
46.5
05
502.2
52.8
65
561.9
59.1
26
324.2
34.1
86
383.9
40.3
46
443.6
46.6
06
503.2
52.9
66
562.9
59.2
27
325.2
34.2
87
384.9
40.5
47
444.5
46.7
07
504.2
53.0
67
563.9
59.3
28 326. 2
34.3
88
385.9
40.6
48
445.5
46.8
08
505.2
53.1
68
564.9
59.4
29
327.2
34.4
89
386.9
40.7
49
446.5
46.9
09
506.2 53.2
69
565.9
59.5
30
328.2
34.5
90
387.9
40.8
50
447.5
47.0
10
507.2 53.3
70
566.9
59.6
331 | 329.2
34.6
391
388.9
40.9
451
448.5
47.1
511
508.2
53.4
571
567.9
59.7
32 1 330.2
34.7
92
389.9
41.0
52
449.5
47.2
12
509.2
53.5
72
568.9
59.8
33 1 331.2
34.8
93
390.8
41.1
53
450. 5
47.3
13
510.2
53.6
73
569.9
59.9
34 332. 2
34.9
94
391.8
41.2
54
451.5
47.5
14
511.2
53.7
74
570.9
60.0
35 333. 2
35.0
95
392.8
41.3
55
452.5
47.6
15
512.2
53.8
75
571.9 ! 60.1
36 334. 2
35.1
96
393.8
41.4
56
453.5
47.7
16
513.2
53.9
76
572.9 ! 60.2
37
335.2
35.2
97
394.8
41.5
57
454. 5
47.8
17
514.2
54.0
77
573.9
60.3
38
336.1
35.3
98
395.8
41.6
58
455. 5
47.9
18
515.2
54.1
78
574.9
60.4
39 337. 1
35.4
99
396.8
41.7
59
456.5
48.0
19
516.2
54.2
79
575. 8
60.5
40 338. 1
35.5
400
397.8
41.8
60
457.5
48.1
20
517.2
54.3
80
576.8
60.6
341
339.1
35.6
401
398.8
41.9
461
458.5
48.2
521
518.1
54.5
581
577. 8
60.7
42
340.1
35.7
02
399.8
42.0
62
459.5
48.3
22
519.1
54.6
82
578.8
60.8
43 341. 1
35.8
03
400.8
42.1
63
460.5
48.4
23
520.1
54.7
83
579.8
60.9
44
342.1
36.0
04
401.8
42 9
64
461.5
48.5
24
521.1
54.8
84
580. 8 61. 1
45
343.1
36.1
05
402.8
42.3
65
462.5
48.6
25
522.
54.9
85
581. 8 61. 2
46
344.1
36.2
06
403.8
42.4
66
463.4
48.7
26
523.
55.0
86
582. 8 61. 3
47 345. 1
36.3
07
404.8
42.5
67
464.4
48.8
27
524.
55.1
87
583. 8 61. 4
48
346.1
36.4
08
405.8
42.6
68
465.4
48.9
28
525.
55.2
88
584. 8 61. 5
49
347.1
36.5
09
406.8
42.7
69
466.4
49.0
29
526.
55.3
89
585. 8 61. 6
50
348.1
36.6
10
407.8
42.9
70
467.4
49.1
30
527.
55.4
90
586. 8 61. 7
351
349.1
36.7
411
408.7
43.0
471
468.4
49.2
531
528.1
55.5
591
587. 8 61. 8
52
350.1
36.8
12
409.7
43.1
72
469.4
49.3
32
529.1
55.6
92
588. 8 61. 9
53
351. I
36.9
13
410.7
43.2
73
470.4
49.4
33
530.1
55.7
93
589. 8 62. 0
54
352.1
37.0
14
411.7
43.3
74
471.4
49.5
34
531.1
55.8
94
590. 8 62. 1
55
353.1
37.1
15
412.7
43.4
75
472.4
49.6
35
532.1
55.9
95
591. 8 62. 2
56
354. 0
37.2
16
413.7
43.5
76
473.4
49.8
36
533.1
56.0
96
592. 8 62. 3
57
355.0
37.3
17
414.7
43.6
77
474.4
49.9
37
534.1
56.1
97
593. 8 62. 4
58
356.0
37.4
18
415.7
43.7
78
475.4
50.0
38
535.1
56.2
98
594. 7 62. 5
59
357.0
37.5
19
416.7
43.8
79
476.4
50.1
39
536.1
56.3
99
595. 7 62. 6
60
358.0
37.6
20
417.7
43.9
80
477.4
50.2
40
537.1
56.4
600
596.7
62.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
84° (96°, 264°, 276°).
61828°—
Page 544] TABLE 2.
Difference of Latitude and Departure for 7° (173°, 187°, 353°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.5
7.4
121
120.1
14.7
181
179.7
22.1
241
239.2
29.4
2
2.0
0.2
62
61.5
7.6
22
121.1
14.9
82
180.6
22.2
42'
240.2
29.5
3
3.0
0.4
63
62. -6
7.7
23
122.1
15.0
83
181.6
22.3
43
241.2
29.6
4
4.0
0.5
64
63.5
7.8
24
123.1
15.1
84
182.6
22.4
44
242.2
29.7
5
5.0
0.6
65
64.5
7.9
25
124.1
15.2
85
183.6
22.5
45
243.2
29.9
6
6.0
0.7
66
65.5
8.0
26
125.1
15.4
86
184.6
22.7
46
244.2
30.0
7
6.9
0.9
67
66.5
8.2
27
126.1
15.5
87
185.6
22.8
47
245.2
30.1
8
7.9
1.0
68
67.5
8.3
28
127.0
15.6
88
186.6
22.9
48
246.2
30.2 .
9
8.9
1.1
69
68.5
8.4
29
128.0
15.7
89
187.6
23.0
49
247.1
30.3
10
9.9
1.2
70
69.5
8.5
30
129.0
15.8
90
188.6
23.2
50
248.1
30.5
11
10.9
1.3
VI
70.5
8.7
131
130.0
16.0
191
189.6
23.3
251
249.1
30.6
12
11.9
1.5
72
71.5
8.8
32
131.0
16.1
92
190.6
23.4
52
250.1
30.7
13
12.9
1.6
73
72.5
8.9
33
132.0
16.2
93
191.6
23.5
53
251.1
30.8
14
13.9
1.7
74
73.4
9.0
34
133.0
16.3
94
192.6
23.6
54
252.1
31.0
15
14.9
1.8
75
74.4
9.1
35
134.0
16.5
95
193.5
23.8
55
253. 1
31.1
16
15.9
1.9
76
75.4
9.3
36
135.0
16.6
96
194.5
23.9
56
254.1
31.2
17
16.9
2.1
77
76.4
9.4
37
136.0
16.7
97
195.5
24.0
57
255.1
31.3
18
17.9
2.2
78
77.4
9.5
38
137.0
16.8
98
196.5
24.1
58
256.1
31.4
19
18.9
2.3
79
78.4
9.6
39
138.0
16.9
99
197.5
24.3
59
257.1
31.6
20
19.9
2.4
80
79.4
9.7
40
139.0
17.1
200
198.5
24.4
60
258.1
31.7
21
20.8
2.6
81
80.4
9.9
141
139.9
17.2
201
199.5
24.5
261
259.1
31.8
22
21.8
2.7
82
81.4
10.0
42
140.9
17.3
02
200.5
24.6
62
260.0
31.9
23
22.8
2.8
83
82.4
10.1
43
141.9
17.4
03
201.5
24.7
63
261.0
32.1
24
23.8
2.9
84
83.4
10.2
44
142.9
17.5
04
202.5
24.9
64
262.0
32.2
25
24.8
3.0
85
84.4
10.4
45
143.9
17.7
05
203.5
25.0
65
263.0
32.3
26
25.8
3.2
86
85.4
10.5
46
144.9
17.8
06
204.5
25.1
66
264.0
32.4
27
26.8
3.3
87
86.4
10.6
47
145.9
17.9
07
205.5
25.2
67
265.0
32.5
28
27.8
3.4
88
87.3
10.7
48
146.9
18.0
08
206.4
25.3
68
266.0
32.7
29
28.8
3.5
89
88.3
10.8
49
147.9
18.2
09
207.4
25.5
69
267.0
32.8
30
29.8
3.7
90
89.3
11.0
50
148.9
18.3
10
208.4
25.6
70
268.0
32.9
31
30.8
3.8
91
90.3
11.1
151
149.9
18.4
211
209.4
25.7
271
269.0
33.0
32
31.8
3.9
92
91.3
11.2
52
150. 9
18.5
12
210.4
25.8
72
270.0
33.1
33
32.8
4.0
93
92.3
11.3
53
151.9
18.6
13
211.4
26.0
73
271.0
33.3
34
33.7
4.1
94
93.3
11.5
54
152.9
18.8
14
212.4
26.1
74
272.0
33.4
35
34.7
4.3
95
94.3
11.6
55
153.8
18.9
15
213.4
26.2
75
273.0
33.5
36
35.7
4.4
96
95.3
11.7
56
154.8
19.0
16
214.4
26.3
76
273.9
33.6
37
36.7
4.5
97
96.3
11.8
57
155.8
19.1
17
215.4
26.4
77
274.9
33.8
38
37.7
4.6
98
97.3
11.9
58
156.8
19.3
18
216.4
26.6
78
275.9
33.9
39
38.7
4.8
99
98.3
12.1
59
157.8
19.4
19
217.4
26.7
79
276.9
34.0
40
39.7
4.9
100
99.3
12.2
60
158.8
19.5
20
218.4
26.8
80
277.9
34.1
41
40.7
5.0
101
100.2
12.3
161
159.8
19.6
221
219.4
26.9
281
278.9
34.2
42
41.7
5.1
02
101.2
12.4
62
160.8
19.7
22
220.3
27.1
82
279.9
34.4
43
42.7
5.2
03
102.2
12.6
63
161.8
19.9
23
221.3
27.2
83
280.9
34.5
44
43.7
5.4
04
103.2
12.7
64
162.8
20.0
24
222.3
27.3
84
281.9
34.6
45
44.7
5.5
05
104.2
12.8
65
163.8
20.1
25
223.3
27.4
85
282.9
34.7
46
45.7
5.6
06
105.2
12.9
66
164.8
20.2
26
224.3
27.5
86
283.9
34.9
47
46.6
5.7
07
106.2
13.0
67
165.8
20.4
27
225.3
27.7
87
284.9
35.0
48
47.6
5.8
08
107.2
13.2
68
166.7
20.5
28
226.3
27.8
88
285.9
35.1
49
48.6
6.0
09
108.2
13.3
69
167.7
20.6
29
227.3
27.9
89
286.8
35.2
50
49.6
6.1
10
109.2
13.4
70
168.7
20.7
30
228.3
28.0
90
287.8
35.3
51
50.6
6.2
111
110.2
13.5
171
169.7
20.8
231
229.3
28.2
291
288.8
35.5
52
51.6
6.3
12
111.2
13.6
72
170.7
21.0
32
230.3
28.3
92
289.8
35.6
53
52.6
6.5
13
112.2
13.8
73
171.7
21.1
33
231.3
28.4
93
290.8
35.7
54
53.6
6.6
14
113.2
13.9
74
172.7
21.2
34
232.3
28.5
94
291.8
35.8
55
54.6
6.7
15
114.1
14.0
75
173.7
21.3
35
233.2
28.6
95
292.8
36.0
56
55.6
6.8
16
115.1
14.1
76
174.7
21.4
36
234.2
28.8
96
293.8
36.1
57
56.6
6.9
17
116.1
14.3
77
175. 7
21.6
37
235.2
28.9
97
294.8
36.2
58
57.6
7.1
18
117.1
14.4
78
176.7
21.7
38
236.2
29.0
98
295.8
36.3
59
58.6
7.2
19
118.1
14.5
79
177.7
21.8
39
237.2
29.1
99
296.8
36.4
60
59.6
7.3
20
119.1
14.6
80
178.7
21.9
40
238.2
29.2
300
297.8
36.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
83° (97°, 263°, 277°).
TABLE 2. [Page 545
Difference of Latitude and Departure for 7° (173°, 187°, 363°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
298.7
36.7
361
358.3
44.0
421
417.9
51.3
481
477.4
58.6
541
537.0
65.9
02
299.7
36.8
62
359.3
44.1
22
418.8
51.4
82
478.4
58.7
42
537.9
66.0
03
300.7
36.9
63
360.3
44.2
23
419. 8 51. 5
83 479. 4
58.8
43
538. 9 66. 2
04
301. 7 37. 0
64
361.3
44.4
24
420.8 i 51.7
84 480. 4
59.0
44
539. 9
66.3
05
302. 7 37. 2
65
362.3
44.5
25
421.8
51.8
85 481. 4
59.1
45
540.9
66.4
06
303.7
37.3
66
363.3
44.6
26
422.8
51.9
86 482. 4
59.2
46
541.9
66.6
07
304.7
37.4
67
364.3
44.7
27
423.8
52.0
87 483.4
59.4
47
542.9
66.7
• 08
305.7
37.5
68
365.2
44.8
28
424. 8 52. 2
88
484.3
59.5
48
543.9
66.8
09
306.7
37.7
69
366.2
45.0
29
425.8 52.3
89
485.3
59.6
49
544.9
66.9
10
307.7
37.8
70
367. 2
45.1
30
426.8 52.4
90
486.3
59.7
50
545.9
67.0
311
308.7
37.9
3V i
368.2
45.2
431
427. 8 52. 5
491
487. 3 59. 8
551
546.9
67.1
12
309.7
38.0
72
369.2
45.3
32
428. 8 52. 6
92
488. 3 59. 9
52
547.9
67.2
13
310.7
38.1
73
370.2
45.5
33
429. 8 52. 8
93
489. 3 60. 1
53
548.9
67.4
14
311. 7
38.3
74
371.2
45.6
34
430. 8 52. 9
94
490. 3 60. 2
54
549.9
67.5
15
312.6
38.4
75
372.2
45.7
35
431.7 ! 53.0
95
491. 3 60. 3
55
550.8
67.6
16
313.6
38.5
76
373.2 | 45.8
36 432.7 | 53.1
96 492. 3 60. 5
56
551.8
67.8
17
314.6
38.6
77 374.2 1 45.9
37 433.7 i 53.3
97
493.3 i 60.6
57
552.8
67.9
18
315.6
38.7
78 1 375. 2 46. 1
38 434.7 53.4
98
494.3 ! 60.7
58
553.8
68.0
19
316.6
38.9
79 376. 2
46.2
39 435.7 53.5
99
495.3 | 60.8
59
554.8
68.1
20
317.6
39.0
80 377. 2
46.3
40 436. 7 53. 6
500
496.3
61.0
60
555.8
68.3
321
318.6
39.1
381 1 378.1
46.4
441 437. 7 53. 7
501
497. 2 61. 1
561
556.8
68.4
22
319.6
39.2
82
379.1
46.5
42 i 438.7 53.9
02
498. 2 61. 2
62
557.8
68.5
23 320. 6
39.4
83 380. 1
46.7
43 i 439.7 54.0
03
499. 2 61. 3
63
558.8
68.6
24 321. 6
39.5
84 381. 1
46.8
44 1 440. 7 54. 1
04
500. 2 61. 4
64
559.8
68.7
25 322. 6
39.6
85 382. 1
46.9
45 1 441. 7 54. 2
05
501.2
61.5
65
560.8
68.9
26
323.6
39.7
86 383. 1
47.0
46 442.7 54.3
06
502.2
61.6
66
561.8
69.0
27
324. 6 39. 8
87 384. 1
47.2
47 443. 7 j 54. 5
07 1 503. 2
61.8
67
562.8
69.1
28 325. 5 40. 0
88 385. 1
47.3
48 1 444.7 54.6
08 504.2
61.9
68
563.8
69.2
29 1 326.5
40.1
89
386.1
47.4
49 445.6 54.7
09 505.2
62.0
69
564.8
69.3
30 327. 5
40.2
90
387.1
47.5
50 1 446.6 54.8
10 506.2
62.1
70
565.8
69.4
331 328. 5 40. 3
391 ! 388. 1
47.6
451 447.6 I 55.0
511 507. 2
62.3
571
566.7
69.6
32
329.5
40.5
92 389. 1
47.8
52 448. 6 55. 1
12
508.2
62.4
72
567.7
69.7
33
330.5
40.6
93 390.1
47.9
53 i 449.6 1 55.2
13
509.2
62.5
73
568.7
69.8
34
331.5
40.7
94 i 391. 1
48.0
54 i 450.6 j 55.3
14
510.2
62.6
74
569.7
69.9
35
332.5
40.8
95 392. 0 48. 1
55 451.6 55.4
15
511.1
62.7
75
570.7
70.1
36
333.5
40.9
96 393. 0 48. 3
56 452.6 1 55.6
16
512.1
62.9
76
571.7
70.2
37
334.5
41.1
97 394. 0
48.4
57 1 453. 6
55. 7
17
513.1
63.0
77
572.7
70.3
38
335.5 41.2
98
395.0
48.5
58
454.6
55.8
18
514.1
63.1
78
573.7
70.4
39
336.5 j 41.3
99
396.0
48.6
59
455.6
55.9
19
515.1
63.2
79
574.7
70.5
40
337. 5 41. 4
400
397.0
48.7
60
456.6 i 56.1
20
516.1
63.4
80
575.7
70.7
341
338. 4 41. 6
401
398.0
48.9
461
457.6
56.2
521
517.1
63.5
581
576.7
70.8
42
339.4
41.7
02
399.0
49.0
62
458.5
56.3
22
518.1
63.6
82
577.6
70.9
43
340.4
41.8
03
400.0
49.1
63
459.5
56.4
23
519.1
63.7
83
578.6
71.0
44
341.4
41.9
04
401.0
49.2
64
460.5
56.5
24
520.1
63.8
84
579.6
71.2
45
342. 4 42. 0
05
402.0
49.4
65
461.5
56.7
25
521.1
64.0
85
580.6
71.3
46
343. 4 42. 2
06
403.0
49.5
66
462.5
56.8
26 522. 1
64.1
86
581.6
71.4
47
344. 4 42. 3
07
404.0
49.6
67
463.5
56.9
27
523.1
64.2
87
582.6
71.5
48
345. 4 42. 4
08
405.0
49.7
68
464.5
57.0
28
524.1
64.3
88
583.6
71.6
49
346.4
42.5
09
405.9
49.8
69
465.5
57.2
29
525.0
64.5
89
584.6
71.8
50
347. 4 42. 6
10
406.9
50.0
70
466.5
57.3
30 526. 0
64.6
90
585.6
71.9
351
348. 4 42. 8
411
407.9
50.1
471
467.5
57.4
531
527.0
64.7
591
586.6
72.0
52
349.4
42.9
12
408.9
50.2
72
468.5
57. 5
32
528.0
64.8
92
587.6
72.1
53
350.4
43.0
13
409.9
50.3
73
469.5
57.6
33
529.0
64.9
93
588.6
72.2
54
351.4
43.1
14
410.9
50.4
74 470.5
57.8
34
530. 0 65. 1
94
589.6
72.4
55
352.3
43.3
15 411.9
50.6
75 471. 5
57.9
35
531.0 65.2
95
590.6
72.5
56
353.3
43.4
16 412. 9
50.7
76 472. 4
58.0
36
532. 0 65. 3
96
591.5
72.6
57
354.3
43.5
1.7 413. 9
50.8
77 1 473.4
58.1
37
533.0 i 65.4
97
592.5
72.7
58
355.3
43.6
18 414. 9 50. 9
78 ! 474.4
58.2
38
534. 0
65.6
98
593.5
72.9
59
356.3
43.7
19
415.9 51.1
79
475.4
58.4
39
535.0
65.7
99
594.5
73.0
60
357.3
43.9
20
416.9
51.2
80
476.4
58.5
40
536.0
65.8
600
595.5
73.1
Dist.
Dep. j Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
83° (97°, 263°, 277°).
Page 546] TABLE 2.
Difference of Latitude and Departure for 8° (172°, 188°, 352°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.4
8.5
121
119.8
16.8
181
179.2
25.2
241
238.7
33.5
2
2.0
0.3
62
61.4
8.6
22
120.8
17.0
82
180.2
25.3
42
239.6
33.7
3
3.0
0.4
63
62.4
8.8
23
121.8
17.1
83
181.2
25.5
43
240.6
33.8
4
4.0
0.6
64
63.4
8.9
24
122.8
17.3
84
182.2
25.6
44
241.6
34.0
5
5.0
0.7
65
64.4
9.0
25
123.8
17.4
85
183.2
25.7
45
242.6
34.1
6
5.9
0.8
66
65.4
9.2
26
124.8
17.5
86
184.2
25.9
46
243.6
34.2
7
6.9
1.0
67
66.3
9.3
27
125.8
17.7
87
185.2
26.0
47
244.6
34.4
8
7.9
1.1
68
67.3
9.5
28
126.8
17.8
88
186.2
26.2
48
245.6
34.5
9
8.9
1.3
69
68.3
9.6
29
127.7
18.0
89
187.2
26.3
49
246.6
34.7
10
9.9
1.4
70
69.3
9.7
30
128.7
18.1
90
188.2
26.4
50
247.6
34.8
11
10.9
1.5
71
70.3
9.9
131
129.7
18.2
191
189.1
26.6
251
248.6
34.9
12
11.9
1.7
72
71.3
10.0
32
130.7
18.4
92
190.1
26.7
52
249.5
35.1
13
12.9
1.8
73
72.3
10.2
33
131.7
18.5
93
191.1
26.9
53
250.5
35.2
14
13.9
1.9
74
73.3
10.3
34
132.7
18.6
94
192.1
27.0
54
251. 5
35.3
15
14.9
2.1
75
74.3
10.4
35
133.7
18.8
95
193.1
27.1
55
252.5
35.5
16
15.8
2.2
76
75.3
10.6
36
134.7
18.9
96
194.1
27.3
56
253.5
35.6
17
16.8
2.4
77
76.3
10.7
37
135.7
19.1
97
195.1
27.4
57
254.5
35.8
18
17.8
2.5
78
77.2
10.9
38
136.7
19.2
98
196.1
27.6
58
255.5
35.9
19
18.8
2.6
79
78.2
11.0
39
137.7
19.3
99
197.1
27.7
59
256.5
36.0
20
19.8
2.8
80
79.2
11.1
40
138.6
19.5
200
198.1
27.8
60
257.5
36.2
21
20.8
2.9
81
80.2
11.3
141
139.6
19.6
201
199.0
28.0
261
258.5
36.3
22
21.8
3.1
82
81.2
11.4
42
140.6
19.8
02
200.0
28.1
62
259.5
36.5
23
22.8
3.2
83
82.2
11.6
43
141.6
19.9
03
201.0
28.3
63
260.4
36.6
24
23.8
3.3
84
83.2
11.7
44
142.6
20.0
04
202.0
28.4
64
261.4
36.7
25
24.8
3.5
85
84.2
11.8
45
143. 6
20.2
05
203.0
28.5
65
262.4
36.9
26
25.7
3.6
86
85.2
12.0
46
144.6
20.3
06
204.0
28.7
66
263.4
37.0
27
26.7
3.8
87
86.2
12.1
47
145.6
20.5
07
205.0
28.8
67
264.4
37.2
28
27.7
3.9
88
87.1
12.2
48
146.6
20.6
08
206.0
28.9
68
265.4
37.3
29
28.7
4.0
89
88.1
12.4
49
147.5
20.7
09
207'. 0
29.1
69
266.4
37.4
30
29.7
4.2
90
89.1
12.5
50
148.5
20.9
10
208.0
29.2
70
267.4
37.6
31
30.7
4.3
91
90.1
12.7
151
149.5
21.0
211
208.9
29.4
271
268.4
37.7
32
31.7
4.5
92
91.1
12.8
52
150.5
21.2
12
209.9
29.5
72
269.4
37.9
33
32.7
4.6
93
92.1
12.9
53
151.5
21.3
13
210.9
29.6
73
270.3
38.0
34
33.7
4.7
94
93.1
13.1
54
152.5
21.4
14
211.9
29.8
74
271.3
38.1
35
34.7
4.9
95
94.1
13.2
55
153.5
21.6
15
212.9
29.9
75
272.3
38.3
36
35.6
5.0
96
95.1
13.4
56
154. 5
21.7
16
213.9
30.1
76
273.3
38.4
37
36.6
5.1
97
96.1
13.5
57
155.5
21.9
17
214.9
30.2
77
274.3
38.6
38
37.6
5.3
98
97.0
13.6
58
156.5
22.0
18
215.9
30.3
78
275.3
38.7
39
38.6
5.4
99
98.0
13.8
59
157.5
22.1
19
216.9
30.5
79
276.3
38.8
40
39.6
5.6
100
99.0
13.9
60
158.4
22.3
20
217.9
30.6
80
277.3
39.0
41
40.6
5.7
101
100.0
14.1
161
159.4
22.4
221
218.8
30.8
281
278.3
39.1
42
41.6
5.8
02
101.0
14.2
62
160.4
22.5
22
219.8
30.9
82
279.3
39.2
43
42.6
6.0
03
102.0
14.3
63
161.4
22.7
23
220.8
31.0
83
280.2
39.4
44
43.6
6.1
04
103. 0
14.5
64
162.4
22.8
24
221.8
31.2
84
281.2
39.5
45
44.6
6.3
05
104.0
14.6
65
163.4
23.0
25
222.8
31.3
85
282.2
39.7
46
45.6
6.4
06
105.0
14.8
66
164.4
23.1
26
223.8
31.5
86
283.2
39.8
47
46.5
6.5
07
106.0
14.9
67
165. 4
23.2
27
224.8
31.6
87
284.2
39.9
48
47.5
6.7
08
106.9
15.0
68
166.4
23.4
28
225.8
31.7
88
285.2
40.1
49
48.5
6.8
09
107.9
15.2
69
167.4
23.5
29
226.8
31.9
89
286.2
40.2
50
49.5
7.0
10
108.9
15.3
70
168. 3
23.7
30
227.8
32.0
90
287.2
40.4
51
50.5
7.1
111
109.9
15.4
171
169.3
23.8
231
228.8
32.1
291
288.2
40.5
52
51.5
7.2
12
110.9
15.6
72
170.3
23.9
32
229.7
32.3
92
289.2
40.6
53
52.5
7.4
13
111.9
15.7
73
171.3
24.1
33
230.7
32.4
93
290.1
40.8
54
53.5
7.5
14
112.9
15.9
74
172.3
24.2
34
231.7
32.6
94
291.1
40.9
55
54.5
7.7
15
113.9
16.0
75
173.3
24.4
35
232.7
32.7
95
292.1
41.1
56
55.5
7.8
16
114.9
16.1
76
174.3
24.5
36
233.7
32.8
96
293.1
41.2
57
56.4
7.9
17
115.9
16.3
77
175.3
24.6
37
234.7
33.0
97
294.1
41.3
58
57.4
8.1
18
116.9
16.4
78
176.3
24.8
38
235.7
33.1
98
295.1
41.5
59
58.4
8.2
19
117.8
16.6
79
177.3
24.9
39
236.7
33.3
99
296.1
41.6
60
59.4
8.4
20
118.8
16.7
80
178.2
25.1
40
237.7
33.4
300
297.1
41.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
82° (98°, 262°, 278°).
TABLE 2. [Page 547
Difference of Latitude and Departure for 8° (172°, 188°, 352°).
Dist.
Lat.
Dep.
Dist.
Lat. | Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
J
301
298.0
41.9
361
357.5
50.2
421
416.9
58.6
481
476.3
66.9
541
535.7
75»2
02
299.0
42.0
62
358.5
50.4
22
417.9
58.7
82
477.3
67.1
42
536.7
75.4
03
300.0
42. 2
63
359.4
50.5
23
418.9
58.9
83
478.3
67.2
43
537.7
75. 5
04
301.0
42^3
64
360.4
50.7
24
419.8
59.0
84
479.3
67.4
44
538.7
75.7
05
302.0
42.5
65
361.4
50.8
25
420.8
59.2
85
480.3
67.5
45
539.7
75.8
1 06
303.0
42.6
66
362.4
50.9
26
421.8
59.3
86
481.2
67.6
46
540.6
75.9
1 07
304.0
42.7
67
363.4
51.1
27
422.8
59.4
87
482.2
67.8
47
541.6
76.1
08
305.0
42.9
68
364.4
51.2
28
423.8
59.6
88
483.2
67.9
48
542.6
76.2
09
306.0
43.0
69
365.4
51.4
29
424.8
59.7
89
484.2
68.1
49
543. 6
76.4
1 10
307.0
43.1
70
366.4
51.5
30
425.8
59.8
90
485.2
68.2
50
544.6
76.5
1 311
307.9
43.3
371
367.4
51.6
431
426.8
60.0
491
486.2
68.3
551
545.6
76.6
12
308.9
43.4
72
368. 4 | 51. 8
32
427.8
60.1
92
487.2
68.5
52
546.6
76.8
13
309.9
43.6
73
369.3
51.9
33
428.8
60.3
93
488. 2
68.6
53
547.6
76.9
14
310.9
43.7
74
370.3
52.1
34
429.8
60.4
94
489.2
68.8
54
548.6
77.1
15
311.9
43.8
75
371.3
52.2
35
430.7
60.5
95
490.2
68.9
55
549.6
77.2
16
312.9
44.0
76
372.3
52.3
36
431.7
60.7
96
491.2
69.0
56
550.6
77.4
1 17
313.9
44.1
77
373.3
52.5
37
432.7
60.8
97
492.1
69.2
57
551. 5
77.5
1 18
314.9
44.3
78
374.3
52.6
38
433.7
61.0
98
493.1
69.3
58
552.5
77.6
19
315.9
44.4
79
375.3
52.7
39
434.7
61.1
99
494.1
69.5
59
553.5
77.8
20
316.9
44.5
80
376.3
52.9
40
435.7
61.2
500
495.1
69.6
60
554. 5
77.9
r32i
317.9
44.7
381
377.3
53.0
441
436.7
61.4
501
496.1
69.7
561
OOO. 0
78.1
22
318.8
44.8
82
378.3
53.2
42
437.7
61.5
02
497.1
69.9
62
556.5
78.2
23
319.8
45.0
83
379.2
53.3
43
438.7
61.7
03
498.1
70.0
63
557.5
78.3
24
320.8
45.1
84
380.2
53.4
44
439.7
61.8
04
499.1
70.2
64
558.5
78.5
25
321.8
45.2
85
381.2
53.6
45
440.6
61.9
05
500.1
70.3
65
559.5
78.6
26
322.8
45.4
86
382.2
53.7
46
441.6
62.1
06
501.0
70.4
66
560.5
78.8
27
323.8
45.5
87
383.2
53.9
47
442.6
62.2
07
502.0
70.6
67
561.5
78.9
28
324.8
45.7
88
384.2
54.0
48
443.6
62.4
08
503.0
70.7
68
562.5
79.0
29
325.8
45.8
89
385.2
54.1
49
444.6
62.5
09
504.0
70.8
69
563.5
79.1
30
326.8
45.9
90
386.2
54.3
50
445.6
62.6
10
505.0
70.9
70
564.5
79.3
|33T
327.8
46.1
391
387.2
54.4
451
446.6
62.8
511
506.0
71.1
571
565.4
79.4
32
328.7
46.2
92
388.2
54.6
52
447.6
62.9
12
507.0
71.2
72
566.4
79.6
33
329.7
46.3
93
389.1
54.7
53
448.6
63.0
13
508.0
71.4
73
567.4
79.7
34
330.7
46.5
94
390.1
54.8
54
449.6
63.2
14
509.0
71.5
74
568.4
79.8
35
331.7
46.6
95
391.1
55.0
55
450.5
63.3
15
510.0
71.6
75
569.4
80.0
36
332.7
46.8
96
392.1
55.1
56
451.5
63.5
16
510.9
71.8
76
570.4
80.1
37
333.7
46.9
97
393.1
55.3
57
452.5
63.6
17
511.9
71.9
77
571.4
80.2
38
334.7
47.0
98
394.1
55.4
58
453.5
63.7
18
512.9
72.0
78
572.4
80.4
39
335.7
47.2
99
395.1
55.5
59
454.5
63.9
19
513.9
72.2
79
573.4
80.5
40
336.7
47.3
400
396.1
55.7
60
455.5
64.0
20
514.9
72.3
80
574.4
80.6
341
337.7
47.5
401
397.1
55.8
461
456.5
64.2
521
515.9
72.4
581
575.4
80.8
42
338.6
47.6
02
398.1
56.0
62
457.5
64.3
22
516.9
72.6
82
576.4
80.9
43
339.6
47.7
03
399.1
56.1
63
458.5
64.4
23
517.9
72.8
83
577.4
81.1
44
340.6
47.9
04
400.0
56.2
64
459.5
64.6
24
518.9
73.0
84
578.4
81.3
45
341.6
48.0
05
401.0
56.4
65
460.4
64.7
25
519.9
73.1
85
579.4
81.4
46
342.6
48.2
06
402.0
56.5
66
461.4
64.9
26
520.9
73.2
86
580.3
81.6
47
343.6
48.3
07
403.0
56.6
67
462.4
65.0
27
521.8
73.4
87
581.3
81.7
48
344.6
48.4
08
404.0
56.8
68
463.4
65.1
28
522.8
73.5
88
582.3
81.8
49
345.6
48.6
09
405.0
56.9
69
464.4
65.3
29
523.8
73.7
89
583.3
82.0
50
346.6
48.7
10
406.0
57.1
70
465.4
65.4
30
524.8
73.8
90
584.3
82.1
pJST 347.6
48.9
411
407.0
57.2
471
466.4
65.6
531
525.8
73.9
591
585.3
82.2
52 348. 5
49.0
12
408.0
57.3
72
467.4
65.7
32
526.8
74.1
92
586.3
82.4
53 ! 349.5
49.1
13
409.0
57. 5
73
468.4
65.8
33
527.8
74.2
93
587.3
82.5
54
350.5
49.3
14
409.9
57.6
74
469.4
66.0
34
528.8
74.3
94
588.3
82.6
55
351.5
49.4
15
410.9
57.8
75
470.4
66.1
35
529.8
74.5
95
589.3
82.8
56
352.5
49.5
16
411.9
57.9
76
471.3
66.2
36
530.8
74.6
96
590.3
83.0
57
353.5
49.7
17
412.9
58.0
77
472.3
66.4
37
531.7
74.7
97
591.2
83.1
58
354.5
49.8
18
413.9
58.2
78
473.3
66.5
38
532.7
74.9
98
592.2
83.2
59
355.5
50.0
19
414.9
58.3
79
474.3
66.7
39
533.7
75.0
99
593.2
83.3
1 60
356.5
50.1
20
415.9
58.5
80
475.3
66.8
40
534.7
75.1
600
594.2
83.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
82° (98°, 262°, 278°).
' Page 548] TABLE 2.
Difference of Latitude and Departure for 9° (171°, 189°, 351°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
60.2
9.5
121
119.5
18.9
181
178.8
28.3
241
238.0
37.7
2
2.0
0.3
62
61.2
9.7
22
120.5
19.1
82
179.8
28.5
42
239.0
37.9
3
3.0
0.5
63
62.2
9.9
23
121.5
19.2
83
180.7
28.6
43
240.0
38.0
4
4.0
0.6
64
63.2
10.0
24
122.5
19.4
84
181.7
28.8
44
241.0
38.2
5
4.9
0.8
65
64.2
10.2
25
123.5
19.6
85
182.7
28.9
45
242.0
38.3
6
5.9
0.9
66
65.2
10.3
26
124.4
19.7
86
183.7
29.1
46
243.0
38.5
7
6.9
1.1
67
66.2
10.5
27
125.4
19.9
87
184.7
29.3
47
244.0
38.6
8
7.9
1.3
68
67.2
10.6
28
126.4
20.0
88
185.7
29.4
48
244.9
38.8
9
8.9
1.4
69
68.2
10.8
29
127.4
20.2
89
186.7
29.6
49
245.9
39.0
10
9.9
1.6
70
69.1
11.0
30
128.4
20.3
90
187.7
29.7
50
246.9
39.1
11
10.9
1.7
71
70.1
11.1
131
129.4
20.5
191
188.6
29.9
251
247.9
39.3
12
11.9
1.9
72
71.1
11.3
32
130.4
20.6
92
189.6
30.0
52
248.9
39.4
13
12.8
2.0
73
72.1
11.4
33
131.4
20.8
93
190.6
30.2
53
249.9
39.6
14
13.8
2.2
74
73.1
11.6
34
132.4
21.0
94
191.6
30.3
54
250.9
39.7
15
14.8
2.3
75
74.1
11.7
35
133.3
21.1
95
192.6
30.5
55
251.9
39.9
16
15.8
2.5
76
75.1
11.9
36
134.3
21.3
96
193.6
30.7
56
252.8
40.0
17
16.8
2.7
77
76.1
12.0
37
135.3
21.4
97
194.6
30.8
57
253.8
40.2
18
17.8
2.8
78
77.0
12.2
38
136.3
21.6
98
195.6
31.0
58
254.8
40.4
19
18.8
3.0
79
78.0
12.4
39
137.3
21.7
99
196.5
31.1
59
255.8
40.5
20
19.8
3.1
80
79.0
12.5
40
138.3
21.9
200
197.5
31.3
60
256.8
40.7
21
20.7
3.3
81
80.0
12.7
141
139.3
22.1
201
198.5
31.4
261
257.8
40.8
22
21.7
3.4
82
81.0
12.8
42
140.3
22.2
02
199.5
31.6
62
258.8
41.0
23
22.7
3.6
83
82.0
13.0
43
141.2
22.4
03
200.5
31.8
63
259.8
41.1
24
23.7
3.8
84
83.0
13.1
44
142.2
22.5
04
201.5
31.9
64
260.7
41.3
25
24.7
3.9
85
84.0
13.3
45
143.2
22.7
05
202.5
32.1
65
261.7
41.5
26
25.7
4.1
86
84.9
13.5
46
144.2
22.8
06
203.5
32.2
66
262.7
41.6
27
26.7
4.2
87
85.9
13.6
47
145.2
23.0
07
204.5
32.4
67
263.7
41.8
28
27.7
4.4
88
86.9
13.8
48
146.2
23.2
08
205.4
32.5
68
264.7
41.9
29
28.6
4.5
89
87.9
13.9
4$
147.2
23.3
09
206.4
32.7
69
265.7
42.1
30
29.6
4.7
90
88.9
14.1
50
148.2
23.5
10
207.4
32.9
70
266.7
42.2
31
30.6
4.8
91
89.9
14.2
151
149.1
23.6
211
208.4
33.0
271
267.7
42.4
32
31.6
5.0
92
90.9
14.4
52
150.1
23.8
12
209.4
33.2
72
268.7
42.6
33
32.6
5.2
93
91.9
14.5
53
151.1
23.9
13
210.4
33.3
73
269.6
42.7
34
33.6
5.3
94
92.8
14.7
54
152.1
24.1
14
211.4
33.5
74
270.6
42.9
35
34.6
5.5
95
93.8
14.9
55
153.1
24.2
15
212.4
33.6
75
271.6
43.0
36
35.6
5.6
96
94.8
15.0
56
154.1
24.4
16
213.3
33.8
76
272.6
43.2
37
36.5
5.8
97
95.8
15.2
57
155.1
24.6
17
214.3
33.9
77
273.6
43.3
38
37.5
5.9
98
96.8
15.3
58
156.1
24.7
18
215.3
34.1
78
274.6
43.5
39
38.5
6.1
99
97.8
15.5
59
157.0
24.9
19
216.3
34.3
79
275.6
43.6
40
39.5
6.3
100
98.8
15.6
60
158.0
25.0
20
217.3
34.4
80
276.6
43.8
41
40.5
6.4
101
99.8
15.8
161
159.0
25.2
221
218.3
34.6
281
277.5
44.0
42
41.5
6.6
02
100.7
16.0
62
160.0
25.3
22
219.3
34.7
82
278.5
44.1
43
42.5
6.7
03
101.7
16.1
63
161.0
25.5
23
220.3
34.9
83
279.5
44.3
44
43.5
6.9
04
102.7
16.3
64
162.0
25.7
24
221.2
35.0
84
280.5
44.4
45
44.4
7.0
05
103.7
16.4
65
163.0
25.8
25
222.2
35.2
85
281.5
44.6
46
45.4
7.2
06
104.7
16.6
66
164.0
26.0
26
223.2
35.4
86
282.5
44.7
47
46.4
7.4
07
105.7
16.7
67
164.9
26.1
27
224.2
35.5
87
283.5
44.9
48
47.4'
7.5
08
106.7
16.9
68
165.9
26.3
28
225.2
35.7
88
284.5
45.1
49
48.4
7.7
09
107.7
17.1
69
166.9
26.4
29
226.2
35.8
89
285.4
45.2
50
49.4
7.8
10
108.6
17.2
70
167.9
26.6
30
227.2
36.0
90
286.4
45.4
51
50.4
8.0
111
109.6
17.4
171
168.9
26.8
231
228.2
36.1
291
287.4
45.5
52
51.4
8.1
12
110.6
17.5
72
169.9
26.9
32
229.
36.3
92
288.4
45.7
53
52.3
8.3
13
111.6
17.7
73
170.9
27.1
33
230.
36.4
93
289.4
45.8
54
53.3
8.4
14
112.6
17.8
74
171.9
27.2
34
231.
36.6
94
290.4
46.0
55
54.3
8.6
15
113.6
18.0
75
172.8
27.4
35
232.
36.8
95
291.4
46.1
56
55.3
8.8
16
114.6
18.1
76
173.8
27.5
36
233.
36.9
96
292.4
46.3
57
56.3
8.9
17
115.6
18.3
77
174.8
27.7
37
234.
37.1
97
293.3
46.5
58
57.3
9.1
18
116.5
18.5
78
175.8
27.8
38
235.
37.2
98
294.3
46.6
59
58.3
9.2
19
117.5
18.6
79
176.8
28.0
39
236.
37.4
99
295.3
46.8
60
59.3
9.4
20
118.5
18.8
80
177.8
28.2
40
237.0
37.5
300
296.3
46.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
81° (99°, 261°, 279°).
TABLE 2. [Page 549
Difference of Latitude and Departure for 9° (171°, 189°, 351°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
297.3
47.1
361
356.6
56.5
421 415.8
65.9
481
475.1
75.2
541
534.4
84.6
02
298.3
47.2
62
357.5
56.7
22 416.8
66.0
82
476.1
75.3
42
535.4
84.7
03
299.3
47.4
63
358.5
56.8
23 417. 8
66.2
83
477.1
75.5
43
536.3
84.9
04
300.3
47.6
64
359.5
56.9
24
418.8
66.3
84
478.0
75.6
44
537.3
85.1
05
301.2
47.7
65
360.5
57.1
25
419.8
66.5
85
479.0
75.8
45
538.3
85.3
06
302.2
47.9
66
361.5
57.3
26
420.8
66.6
86
480.0
75.9
46
539.3
85.4
07
303.2
48.0
67
362.5
57.4
27
421.7
66.8
87
481.0
76.1
47
540.3
85.6
08
304.2
48.2
68
363.5
57.6
28
422.-
67.0
88
482.0
76.2
48
541.3
85.7
09
305.2
48.3
69
364.5
57. 7
29
423."
67.1
89
483.0
76.4
49
542.3
85.9
10
306.2 ! 48.5
70
365.4
57.9
30
424."
67.3
90
484.0
76.5
50
543.3
86.0
311
307.2
48.7
371
366.4
58.1
431
425."
67.4
491
485.0
76.7
551
544.3
86.2
12
308.2
48.8
72
367.4
58.2
32
426."
67.6
92
485.9
76.8
52
545.2
86.3
13
309.1
49.0
73
368.4
58.4
33
427."
67.7
93
486.9
77.0
53
546.2
86.5
14
310.1
49.1
74
369.4
58.5
34
428."
67.9
94
487.9
77.1
54
547.2
86.6
15
311.1
49.3
75
370.4
58.7
35
429.6
68.1
95
488.9 77.3
55
548.2
86.8
16
312.1
49.4
76
371.4
58.8
36
430.6
68.2
96
489.9
77.5
56
549.2
87.0
17
313.1
49.6
77
372.4
59.0
37
' 431. 6
68.4
97
490.9
77.7
57
550.2
87.1
18
314.1
49.8
78
373.3
59.1
38
432.6
68.5
98
491.9
77.9
58
551.2
87.3
19
315.1
49.9
79
374. 3
59.3
39
433.6
68.7
99
492.9
78.0
59
552.2
87.4
20
316.1
50.1
80 375. 3 59. 5
40
434.6
68.8
500
493.8
78.2
60
553.1
87.6
321
317.0
50.2
381
376. 3
59.6
441
435.6
69.0
501
494.8
78.4
561
554.1
87.7
22
318.0
50.4
82
377.3
59.8
42
436.6
69.1
02
495.8
78.5
62
555.1
87.9
23
319.0
50.5
83
378.3
59.9
43
437.5
69.3
03
496.8
78.7
63
556.1
88.0
24
320.0
50.7
84
379.3
60.1
44
438.5
69.5
04
497.8
78.8
64
557.1
88.2
25
321.0
50.8
85
380.3
60.2
45
439.5
69.6
05
498.8
79.0
65
558.1
88.3
26
322.0
51.0
86
381.2
60.4
46
440.5
69.8
06
499.8
79.1
66
559.1
88.5
27
323.0
51.2
87
382.2
60.5
47
441.5
69.9
07
500.8
79.2
67
560.1
88.6
28
324.0
51.3
88
383.2
60.7
48
442.5
70.1
08
501.7
79.4
68
561.0
88.8
29
324.9
51.5
89
384.2
60.9
49
443.5
70.2
09
502.7
79.5
69
562.0
88.9
30
325.9
51.7
90
385.2
61.0
50
444.5
70.4
10
503.7
79.7
70
563.0
89.1
331
326.9
51.8
391
386.2
61.2
451
445.4
70.6
511
504.7
79.8
571
564.0
89.2
32
327.9
51.9
92
387.2
61.3
52
446.4
70.7
12
505.7
80.1
72
565.0
89.4
33
328. 9 52. 1
93
388.2
61.5
53
447.4
70.9
13
506.7
80.2
73
566.0
89.5
34
329. 9 52. 3
94
389.
61.6
54
448.4
71.0
14
507.7
80.3
74
567.0
89.7
35
330. 9 52. 4
95
390.
61.8
55
449.4
71.2
15
508.7
80.5
75
568.0
89.9
36
331. 9 52. 6
96
391.
62.0
56
450.4
71.3
16
509.6
80.6
76
568.9
90.1
37
332. 8 52. 7
97
392.
62.1
57
451.4
71.5
17
510.6
80.8
77
569.9
90.2
38
333.8 ! 52.9
98
393.
62.3
58
452.4
71.7
18
511.6
80.9
78
570.9
90.3
39
334.8
53.0
99
394.
62.4
59
453.3
71.8
19
512.6
81.1
79
571.9
90.5
40
335.8
53.2
400
395.1
62.6
60
454.3
72.0
20
513.6
81.3
80
572.9
90.7
341
336.8
53.3
401
396.1
62.7
461
455.3
72.1
521
514.6
81.4
581 573. 9
90.9
42 337. 8
53.5
02
397.0
62.9
62
456.3
72.3
22
515.6
81.6
82 574. 9
91.0
43
338.8
53.7
03
398.0
63.0
63
457.3
72.4
23
516.6
81.8
83 575. 9
91.2
44
339.8
53.8
04
399.0
63.2
64
458.3
72.6
24
517.6
81.9
84 576. 9
91.3
45
340.8
54.0
05
400.0
63.4
65
459.3
72.7
25
518.6
82.1
85 j 577. 9
91.5
46
341.7
54.1
06
401.0
63.5
66
460.3
72.9
26
519.5
82.3
86 578. 8
91.7
47
342. "
54.3
07
402.0
63.7
67
461.2
73.1
27
520.5
82.4
87
579.8
91.8
48
343."
54.4
08
403.0
63.8
68
462.2
73.2
28
521.5
82.6
88
580.8
92.0
49
344. " 54. 6
09
404.0
64.0
69
463.2
73.4
29
522.5
82.7
89
581.8
92.1
50
345. 7 54. 8
10
405.0
64.1
70
464.2
73.5
30
523.5
82.9
90
582.8
92.2
351
346. 7 54. 9
411
405.9
64.3
471
465.2
73.7
531
524.5
83.1
591
583.8
92.4
52
347. " 55. 1
12
406.9
64.5
72
466.2
73.8
32
525.5
83.2
92
584.8
92.5
53
348. " 55. 2
13
407.9
64.6
73
467.2
74.0
33
526.5
83.4
93
585.7
92.7
54
349.6
55. 4
14
408.9
64.8
74
468.2
74.2
34
527.5
83.5
94
586.7
92.9
55
350.6
55.5
15
409.9
64.9
75
469.2
74.3
35
528.4
83.7
95
587.7
93.1
56
351.6
55.7
16
410.9
65.1
76
470.1
74.5
36
529.4
83.8
96
588.7
93.2
57
352.6
55.9
17
411.9
65.2
77
471.1
74.6
37
530.4
84.0
97
589.7
93.4
58
353. 6 56. 0
18
412.9
65.4
78
472.1
74.8
38
531.4
84.1
98
590.7
93.5
59
354. 6 56. 2
19
413.8
65.6
79
473.1
74.9
39
532.4
84.3
99
591.7
93.7
60
355. 6 56. 3
20
414.8
65.7
80
474.1
75.0
40
533.4
84.4
600
592.6
93.8
Dist. \ Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
81° (99°, 261°, 279°).
Page 550] TABLE 2.
Difference of Latitude and Departure for 10° (170°, 190°, 350°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
60.1
10.6
121
119.2
21.0
181
178.3
31.4
241
237.3
41.8
2
2.0
0.3
62
61.1
10.8
22
120.1
21.2
82
179.2
31.6
42
238. 3
42.0
3
3.0
0.5
63
62.0
10.9
23
121.1
21.4
83
180.2
31.8
43
239.3
42.2
4
3.9
0.7
64
63.0
11.1
24
122.1
21.5
84
181.2
32.0
44
240.3
42.4
5
4.9
0.9
65
64.0
11.3
25
123.1
21.7
85
182.2
32.1
45
241.3
42.5
6
5.9
1.0
66
65.0
11.5
26
124.1
21.9
86
183. 2
32.3
46
242.3
42.7
7
6.9
1.2
67
66.0
11.6
27
125.1
22.1
87
184.2
32.5
47
243.2
42.9
8
7.9
1.4
68
67.0
11.8
28
126.1
22.2
88
185.1
32.6
48
244.2
43.1
9
8.9
1.6
69
68.0
12.0
29
127.0
22.4
89
186.1
32.8
49
245.2
43.2
10
9.8
1.7
70
68.9
12.2
30
128.0
22.6
90
187.1
33.0
50
246.2
43.4
"11
10.8
1.9
71
69.9
12.3
131
129.0
22.7
191
188.1
33.2
251
247.2
43.6
12
11 8
2.1
72
70.9
12.5
32
130.0
22.9
92
189.1
33.3
52
248.2
43.8
13
12.8
2.3
73
71.9
12.7
33
131.0
23.1
93
190.1
33.5
53
249.2
43.9
14
13.8
2.4
74
72.9
12.8
34
132.0
23.3
94
191.1
33.7
54
250.1
44.1
15
14.8
2.6
75
73.9
13.0
35
132.9
23.4
95
192.0
33.9
55
251.1
44.3
16
15.8
2.8
76
74.8
13.2
36
133.9
23.6
96
193.0
34.0
56
252.1
44.5
17
16.7
3.0
77
75.8
13.4
37
134.9
23.8
97
194.0
34.2
57
253.1
44.6
18
17.7
3.1
78
76.8
13.5
38
135.9
24.0
98
195.0
34.4
58
254.1
44.8
19
18.7
3.3
79
77.8
13.7
39
136.9
24.1
99
196.0
34.6
59
255.1
45.0
20
19.7
3.5
80
78.8
13.9
40
137.9
24.3
200
197.0
34.7
60
256.1
45.1
21
20.7
3.6
81
79.8
14.1
141
138.9
24.5
201
197.9
34.9
261
257.0
45.3
22
21.7
3.8
82
80.8
14.2
42
139.8
24.7
02
198.9
35.1
62
258.0
45.5
23
22.7
4.0
83
81.7
14.4
43
140.8
24.8
03
199.9
35.3
63
259.0
45.7
24
23.6
4.2
84
82.7
14.6
44
141.8
25.0
04
200.9
35.4
64
260.0
45.8
25
24.6
4.3
85
83.7
14.8
45
142.8
25.2
05
201.9
35.6
65
261.0
46.0
26
25.6
4.5
86
84.7
14.9
46
143.8
25.4
06
202.9
35.8
66
262.0
46.2
27
26.6
4.7
87
85.7
15.1
47
144.8
25.5
07
203.9
35.9
67
262.9
46.4
28
27.6
4.9
88
86.7
15.3
48
145.8
25.7
08
204.8
36.1
68
263.9
46.5
29
28.6
5.0
89
87.6
15.5
49
146.7
25.9
09
205.8
36.3
69
264.9
46.7
30
29.5
5.2
90
88.6
15.6
50
147.7
26.0
10
206.8
36.5
70
265.9
46.9
31
30.5
5.4
91
89.6
15.8
151
148.7
26.2
211
207.8
36.6
271
266.9
47.1
32
31.5
5.6
92
90.6
16.0
52
149.7
26.4
12
208.8
36.8
72
267.9
47.2
33
32.5
5.7
93
91.6
16.1
53
150.7
26.6
13
209.8
37.0
73
268.9
47.4
34
33.5
5.9
94
92.6
16.3
54
151.7
26.7
14
210.7
37.2
74
269.8
47.6
35
34.5
6.1
95
93.6
16.5
55
152.6
26.9
15
211.7
37.3
75
270.8
47.8
36
35.5
6.3
96
94.5
16.7
56
153.6
27.1
16
212.7
37.5
76
271.8
47.9
37
36.4
6.4
97
95.5
16.8
57
154.6
27.3
17
213.7
37.7
77
272.8
48.1
38
37.4
6.6
98
96.5
17.0
58
155.6
27.4
18
214.7
37.9
78
273.8
48.3
39
38.4
6.8
99
97.5
17.2
59
156.6
27.6
19
215. 7
38.0
79
274.8
48.4
40
39.4
6.9
100
98.5
17.4
60
157.6
27.8
20
216.7
38.2
80
275.7
48.6
41
40.4
7.1
101
99.5
17.5
161
158.6
28.0
221
217.6
38.4
281
276.7
48.8
42
41.4
7.3
02
100.5
17.7
62
159.5
28,1
22
218.6
38.5
82
277.7
49.0
43
42.3
7.5
03
101.4
17.9
63
160.5
28.3
23
219.6
38.7
83
278.7
49.1
44
43.3
7.6
04
102.4
18.1
64
161.5
28.5
24
220.6
38.9
84
279.7
49.3
45
44.3
7.8
05
103.4
18.2
65
162.5
28.7
25
221.6
39.1
85
280.7
49.5
46
45.3
8.0
06
104.4
18.4
66
163.5
28.8
26
222.6
39.2
86
281.7
49.7
47
46.3
8.2
07
105.4
18.6
67
164.5
29.0
27
223.6
39.4
87
282.6
49.8
48
47.3
8.3
08
106.4
18.8
68
165.4
29.2
28
224.5
39.6
88
283.6
50.0
49
48.3
8.5
09
107.3
18.9
69
166.4
29.3
29
225.5
39.8
89
284.6
50.2
50
49.2
8.7
10
108.3
19.1
70
167.4
29.5
30
226.5
39.9
90
285. 6
50.4
51
50.2
8.9
111
109.3
19.3
171
168.4
29.7
231
227.5
40.1
291
286.6
50.5
52
51.2
9.0
12
110.3
19.4
72
169.4
29.9
32
228.5
40.3
92
287.6
50.7
53
52.2
9.2
13
111.3
19.6
73
170.4
30.0
33
229.5
40.5
93
288.5
50.9
54
53.2
9.4
14
112.3
19.8
74
171.4
30.2
34
230.4
40.6
94
289.5
51.1
55
54.2
9.6
15
113.3
20.0
75
172.3
30.4
35
231.4
40.8
95
290.5
51.2
56
55.1
9.7
16
114.2
20.1
76
173.3
30.6
36
232.4
41.0
96
291.5
51.4
57
56.1
9.9
17
115.2
20.3
77
174.3
30.7
37
233.4
41.2
97
292.5
51.6
58
57.1
10.1
18
116.2
20.5
78
175.3
30.9
38
234.4
41.3
98
293.5
51.7
59
58.1
10.2
19
117.2
20.7
79
176.3
31.1
39
235.4
41.5
99
294.5
51.9
60
59.1
10.4
20
118.2
20.8
80
177.3
31.3
40
236.4
41.7
300
295.4
52.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
80° (100°, 260°, 280°).
TABLE 27 [Page 551
Difference of Latitude and Departure for 10° (170°, 190°, 350°)
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
296.4
52.3
361
355.5
62.7
421
414.6
73.1
481
473.7
83.5
541
532.8
93.9
02
297.4
52.5
62
356.5
62.9
22
415.6
73.3
82
474.7
83.7
42
533.8
94.1
03
298.4
52.6
63
357.5
63.0
23
416.6
73.5
83
475.7
83.9
43
534.8
94.3
04
299.4
52.8
64
358. 5
63.2
24
417.6
73.6
84
476.6
84.1
44
535.7
94.5
05
300.4
53.0
65
359.5
63.4
25
418.5
73.8
85
477.6
84.2
45
536.7
94.6
06
301.4
53.1
66
360.4
63.6
26
419.5
74.0
86
478.6
84.4
46
537.7
94.8
07
302.3
53.3
67
361.4
63.7
27
420.5
74.2
87
479.6
84.6
47
538.7
95.0
08
303.3
53.5
68
362.4
63.9
28
421.5
74.3
88
480.6
84.7
48
539.7
95.1
09
304.3
53.7
69
363.4
64.1
29
422.5
74.5
89
481.6
84.9
49
540.7
95.3
10
305.3
53.8
70
364.4
64.3
30
423.5
74.7
90
482.6
85.1
50"
541.6
95.5
311
306.3
54.0
371
365.4
64.4
431
424.5 I 74.9
491
483.5
85.2
551
542.6
95.6
12
307.3
54.2
72
366.4
64.6
32
425.4
75.0
92
484.5
85.4
52
543.6
95.8
13
308.2
54.3
73
367.3
64.8
33
426.4
75.2
93
485.5
85.6
53
544.6
96.0
14
309.2
54.5
74
368.3
65.0
34
427.4
75.4
94
486.5
85.8
54
545.6
96.2
15
310.2
54.7
75
369.3
65.1
35
428.4
75. 5
95
487.5
85.9
55
546.6
96.3
16
311.2
54.9
76
370.3
65.3
36
429.4
75.7
96
488.5
86.1
56
547.5
96.5
17
312.2
55.1
77
371.3
65.5
37
430.4
75.9
97
489.4
86.3
57
548.5
96.7
18
313.2
55.2
78
372. 3
65.6
38
431.3
76.1
98
490.4
86.5
58
549.5
96.9
19
314.2
55.4
79
373.2
65.8
39
432.3
76.2
99
491.4
86.6
59
550.5
97.0
20
315.1
55.6
80
374.2
66.0
40
433.3
76.4
500
492.4
86.8
60
551.5
97.2
321
316.1
55.8
381
375.2
66.2
441
434.3
76.6
501
493.4
87.0
561
552.5
97.4
22
317.1
55.9
82
376.2
66.3
42
435.3
76.8
02
494.4
87.2
62
553.5
97.6
23
318.1
56.1
83
377.2
66.5
43
436.3
76.9
03
495.3
87.3
63
554.4
97.7
24
319.1
56.3
84
378.2
66.7
44
437.3
77.1
04
496.3
87.5
64
555.4
97.9
25
320.1
56.4
85
379.2
66.9
45
438.2
77.3
05
497.3
87.7
65
556.4
98.1
26
321.0
56.6
86
380.1
67.0
46
439.2
77.5
06
498.3
87.9
66
557. 4
98.3
27
322.0
56.8
87
381.1
67.2
47
440.2
77.6
07
499.3
88.0
67
558.4
98.4
28
323.0
57.0
88
382.1
67.4
48
441.2
77.8
08
500.3
88.2
68
559.4
98.6
29 324. 0
57.1
89
383.1
67.6
49
442.2
78.0
09
501.3
88.4
69
560.3
98.8
30
325. 0
57.3
90
384.1
67.7
50
443.2
78.2
10
502.2
88.6
70
561.3
99.0
331 326. 0
o/. o
391
385.1
67.9
451
444.2
78.3
511
503.2
88.7
571
562.3
99.1
32 327. 0
57.7
92
386.0
68.1
52
445.1
78.5
12
504.2
88.9
72
563.3
99.3
33 327. 9
57.8
93
387.0
68.2
53
446.1
78.7
13
505.2
89.1
73
564.3
99.5
34 328. 9
58.0
94
388.0
68.4
54
447.1
78.8
14
506.2
89.2
74
565.3
99.6
35
329.9
58.2
95
389.0
68.6
55
448.1
79.0
15
507.2
89.4
75
566.3
99.8
36
330.9
58.4
96
390.0
68.8
56
449.1
79.2
16
508.2
89.6
76
567.2
100.0
37
331.9
58.5
97
391.0
68.9
57
450.1
79.4
17
509.1
89.8
77
568.2
100.2
38
332.9
58.7
98
392.0
69.1
58
451.0
79.5
18
510.1
89.9
78
569.2
100.3
39
333.9
58.9
99
392.9
69.3
59
452.0
79.7
19
511.1
90.1
79
570.2
100.5
40
334.8
59.1
400
393.9
69.5
60
453.0
79.9
20
512.1
90.3
80
571.2
100.7
341
335.8
59.2
401
394.9
69.6
461
454.0
80.1
521
513.1
90.5
581
572.2
100.9
42
336.8
59.4
02
395.9
69.8
62
455.0
80.2
22
514.1
90.6
82
573.2
101.0
43
337.8
59.6
03
396.9
70.0
63
456.0
80.4
23
515.1
90.8
83
574.1
101.2
44
338.8
59.8
04
397.9
70.2
64
457.0
80.6
24
516.0
91.0
84
575.1
101.4
45
339.8
59.9
05
398.9
70.3
65
457.9
80.8
25
517.0
91.2
85
576.1
101.6
46
340.7
60.1
06
399.8
70.5
66
458.9
80.9
26
518.0
91.3
86
577. 1
101.7
47
341.7
60.3
07
400.8
70.7
67
459.9
81.1
27
519.0
91.5
87
578.1
101.9
48
342.
60.4
08
401.8
70.9
68
460.9
81.3
28
520.0
91.7
88
579.1
102.1
49
343.
60.6
09
402.8
71.0
69
461.9
81.5
29
521.0
91.9
89
580.0
102.3
50
344.
60.8
10
403.8
71.2
70
462.9
81.6
30
521.9
92.0
90
581.0
102.4
351
345.
61.0
411
404.8
71.4
471
463.8
81.8
531
522.9
92.2
591
582.0
102.6
52
346.
61.1
12
405.7
71.6
72
464.8
82.0
32
523.9
92.4
92
583.0
102.8
53
347.6
61.3
13
406.7
71.7
73
465.8
82.1
33
524.9
92.5
93
584.0
102.9
54
348.6
61.5
14
407.7
71.9
74
466.8
82.3
34
525.9
92.7
94
585.0
103.1
55
349.6
61.7
15
408.7
72.1
75
467.8
82.5
35
526.9
92.9
95
586.0
103.3
56
350.6
61.8
16
409.7
72.2
76
468. 8
82.7
36
527.9
93.1
96
586.9
103.5
57
351.6
62.0
17
410.7
72.4
77
469.8
82.8
37
528.8
93.2
97
587.9
103.6
58
352.6
62.2
18
411.7
72.6
78
470.7
83.0
38
529.8
93.4
98
588.9
103.8
59
353.5
62 4
19
412.6
72.8
79
471.7
83.2
39
530.8
93.6
99
589.9
104.0
60
354.5
62.5
20
413.6
72.9
80
472.7
83.4
40
531.8
93.8
600
590.9
104.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist. Dep.
Lat.
80° (100°, 260°, 280°).
Page 552] TABLE 2.
Difference of Latitude and Departure for 11° (169°, 191°, 349°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.9
11.6
121
118.8
23.1
181
177.7
34.5
241
236.6
46.0
2
2.0
0.4
62
60.9
11.8
22
119.8
23.3
82
178.7
34.7
42
237.6
46.2
3
2 9
0.6
63
61.8
12.0
23
120.7
23.5
83
179.6
34.9
43
238.5
46.4
4
3.9
0.8
64
62.8
12.2
24
121.7
23.7
84
180.6
35.1
44
239.5
46.6
5
4.9
1.0
65
63.8
12.4
25
122.7
23.9
85
181.6
35.3
45
240.5
46.7
6
5.9
1.1
66
64.8
12.6
26
123.7
24.0
86
182.6
35.5
46
241.5
46.9
7
6.9
1.3
67
65.8
12.8
27
124.7
24.2
87
183.6
35.7
47
242.5
47.1
8
7.9
1.5
68
66.8
13.0
28
125.6
24.4
88
184.5
35.9
48
243.4
47.3
9
8.8
1.7
69
67.7
13.2
29
126.6
24.6
89
185.5
36.1
49
244.4
47.5
10 9.8
1.9
70
68.7
13.4
30
127.6
24.8
90
186.5
36.3
50
245.4
47.7
11
10.8
2.1
71
69.7
13.5
131
128.6
25.0
191
187.5
36.4
251
246.4
47.9
12
11.8
2.3
72
70.7
13.7
32
129.6
25.2
92
188.5
36.6
52
247.4
48.1
13
12.8
2.5
73
71.7
13.9
33
130.6
25.4
93
189.5
36.8
53
248.4
48.3
14
13.7
2.7
74
72.6
14.1
34
131. 5
25.6
94
190.4
37.0
54
249.3
48.5
15
14.7
2.9
75
73.6
14.3
35
132.5
25.8
95
191.4
37.2
55
250.3
48.7
16
15.7
3.1
76
74.6
14.5
36
133.5
26.0
96
192.4
37.4
56
251.3
48.8
17
16.7
3.2
77
75.6
14.7
37
134.5
26.1
97
193.4
37.6
57
252.3
49.0
18
17.7
3.4
78
76.6
14.9
38
135.5
26.3
98
194.4
37.8
58
253.3
49.2
19
18.7
3.6
79
77.5
15.1
39
136.4
26.5
99
195.3
38.0
59
254.2
49.4
20
19.6
3.8
80
78.5
15.3
40
137.4
26.7
200
196.3
38.2
60
255.2
49.6
21
20.6
4.0
81
79.5
15.5
141
138.4
26.9
201,
197.3
38.4
261
256.2
49.8
22
21.6
4.2
82
80.5
15.6
42
139.4
27.1
-^Q.2,'
198.3
38.5
62
257.2
50.0
23
22.6
4.4
83
81.5
15.8
43
140.4
27.3
0^
199.3
38.7
63
258.2
50.2
24
23.6
4.6
84
82.5
16.0
44
141 4
27.5
04
200.3
38.9
64
259.1
50.4
25
24.5
4.8
85
83.4
16.2
45
142.3
27.7
05
201.2
39.1
65
260.
50.6
26
25.5
5.0
86
84.4
16.4
46
143.3
27.9
06
202.2
39.3
66
261.
50.8
27
26.5
5.2
87
85.4
16.6
47
144.3
28.0
07
203.2
39.5
67
262.
50.9
28
27.5
5.3
88
86.4
16.8
48
145.3
28.2
08
204.2
39.7
68
263.
51.1
29
28.5
5.5
89
87.4
17.0
49
146.3
28.4
09
205.2
39.9
69
264.
51.3
30
29.4
5.7
90
88.3
17.2
50
147.2
28.6
10
206.1
40.1
70
265.0
51.5
31
30.4
5.9
91
89.3
17.4
151
148.2
28.8
211
207.1
40.3
271
266. 0
51.7
32
31.4
6.1
92
90.3
17.6
52
149.2
29.0
12
208.1
40.5
72
267.0
51.9
33
32.4
6.3
93
91.3
17.7
53
150.2
29.2
13
209.1
40.6
73
268.0
52.1
34
33.4
6.5
94
92.3
17.9
54
151.2
29.4
14
210.1
40.8
74
269.0
52.3
35
34.4
6.7
95
93.3
18.1
55
152.2
29.6
15
211.0
41.0
75
269.9
52.5
36
35.3
6.9
96
94.2
18.3
56
153.1
29.8
16
212.0
41.2
76
270.9
52.7
37
36.3
7.1
97
95.2
18.5
57
154.1
30.0
17
213.0
41.4
77
271.9
52.9
38
37.3
7.3
98
96.2
18.7
58
155.1
30.1
18
214.0
41.6
78
272.9
53.0
39
38.3
7.4
99
97.2
18.9
59
156.1
30.3
19
215.0
41.8
79
273.9
53.2
40
39.3
7.6
100
98.2
19.1
60
157.1
30.5
20
216.0
42.0
80
274.9
53.4
41
40.2
7.8
101
99.1
19.3
161
158.0
30.7
221
216.9
42.2
281
275.8
53.6
42
41.2
8.0
02
100.1
19.5
62
159.0
30.9
22
217.9
42.4
82
276. 8
53.8
• 43
42.2
8.2
03
101.1
19.7
63
160.0
31.1
23
218.9
42.6
83 277. 8
54.0
44
43.2
8.4
04
102.1
19.8
64
161.0
31.3
24
219.9
42.7
84
278.8
54.2
45
44.2
8.6
05
103. 1
20.0
65
162.0
31.5
25
220.9
42.9
85
279.8
54.4
46
45.2
8.8
06
104.1
20.2
66
163.0
31.7
26
221.8
43.1
86
280.7
54.6
47
46.1
9.0
07
105.0
20.4
67
163.9
31.9
27
222.8
43.3
87
281.7
54.8
48
47.1
9.2
08
106.0
20.6
68
164.9
32.1
28
223.8
43.5
88
282.7
55.0
49
48.1
9.3
09
107.0
20.8
69
165.9
32.2
29
224.8
43.7
89
283.7
55.1
50
49.1
9.5
10
108.0
21.0
70
166.9
32.4
30
225.8
43.9
90
284.7
55.3
51
50.1
9.7
111
109.0
21.2
171
167.9
32.6
231
226.8
44.1
291
285.7
55.5
52
51.0
9.9
12
109.9
21.4
72
168.8
32.8
32
227.7
44.3
92
286 6
55.7
53
52.0
10.1
13
110.9
21.6
73
169.8
33.0
33
228.7
44.5
93
287.6
55.9
54
53.0
10.3
14
111.9
21.8
74
170.8
33.2
34
229.7
44.6
94
288. 6
56.1
55
54.0
10.5
15
112.9
21.9
75
171.8
33.4
35
230.7
44.8
95
289.6
56.3
56
55.0
10.7
16
113.9
22. 1
76
172.8
33.6
36
231.7
45.0
96
290.6
56.5
57
56.0
10.9
17
114.9
22^3
77
173.7
33.8
37
232.6
45.2
97
291.5
56.7
58
56.9
11.1
18
115.8
22.5
78
174 7
34.0
38
233.6
45.4
98
292.5
56.9
59
57.9
11.3
19
116. 8
22.7
79
175.7
34.2
39
234.6
45.6
99
293.5
57.1
60
58.9
11.4
20
117.8
22.9
80
176.7
34.3
40
235.6
45.8
300
294.5
57.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
79° (101°, 259°, 281°).
TABLE 2. [Page 553
Difference of Latitude and Departure for 11° (169°, 191°, 349°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
295.4
57.4
361
354. 3 68. 9
421
413.2
80.3
481
472.1
91.8
541
531.0
103.2
02
296.4
57.6
62
355. 3 69. 1
22
414.2
80.5
82
473.1
92.0
42
532.0
103.4
03
297.4
57.8
63
356. 3 69. 3
23
415.2
80.7
83
474.1
92.2
43
533.0
103.6
04
298.4
58.0
64
357. 3 69. 5
24
416.2 i 80.9
84
475.1
92.4
44
534. 0
103.8
05
299.4
58.2
65
358. 3 69. 6
25
417.2 81.1
85
476.1
92.6
45
535.0
104.0
06
300.3
58.4
66
359. 2 69. 8
26
418. 1 81. 3
86
477.0
92.8
46
535.9
104.2
07
301.3
58.6
67
360. 2 70. 0
27
419.1 i 81.5
87
478.0
93.0
47
536.9
104.4
08
302.3
58.8
68
361. 2 70. 2
28
420.1 81.7
88
479.0
93.2
48
537.9
104.6
09
303.3
59.0
69
362. 2 70. 4
29
421.1 81.9
89
480.0
93.3
49
538.9
104.8
10
304.3
59.2
70
363. 2 70. 6
30
422. 1 82. 1
90
481.0
93.5
50
539.9
105.0
311
305.3
59.3
371
364.1
70.8
431
423.0
82.2
491
481.9
93.6
551
540.8
105.1
12
306.2
59.5
72
365.1
71.0
32
424.0
82.4
92
482.9
93.8
52
541.8
105. 3
13
307.2
59.7
73
366.1
71.2
33
425. 0
82.6
93
483.9
94.0
53
542.8
105.5
14
308.2
59.9
74
367.1
71.4
34
426.0
82.8
94
484.9
94.2
54
543.8
105.7
15
309.2
60.1
75
368.1
71.6
35
427.0
83.0
95
485.9
94.4
55
544.8
105.9
16
310.2
60.3
76
369.1
71.7
36
428.0
83.2
96
486.9
94.6
56
545.8
106.1
17
311.1
60.5
77
370.0
71.9
37
428.9
83.4
97
487.8
94.8
57
546.7
106.3
18
312.1
60.7
78
371.0
72.1
38
429.9
83.6
98
488.8
95.0
58
547.7
106.5
19
313.1
60.9
79
372.0
72.3
39
430.9
83.8
99
489.8
95.2
59
548.7
106.7
20
314.1
61.1
80
373.0
72.5
40
431.9
84.0
500
490.8
95.4
60
549.7
106.9
321
315.1
61.3
381
374.0
72.7
441
432.9
84.1
501
491.8
95.6
561
550.7
107.1
22
316.1
61.4
82
374.9
72.9
42
433.8
84.3
02
492.7
95.8
62
551.6
107.2
23
317.0
61.6
83
375.9
73.1
43
434.8
84.5
03
493.7
96.0
63
552.6
107.4
24
318.0
61.8
84
376.9
73.3
44
435.8
84.7
04
494.7
96.2
64
553.6
107.6
25
319.0
62.0
85
377.9
73.5
45
436.8
84.9
05
495. 7
96.4
65
554.6
107.8
26
320.0
62.2
86
378.9
73.7
46
437.8
85.1
06
496.7
96.6
66
555.6
108.0
27
321.0
62.4
87
379. 9
73.8
47
438.8
85.3
07
497.7
96.8
67
556. 6
108.2
28
321.9
62.6
88
380.8
74.0
48
439."
85.5
08
498.6
97.0
68
557.6
108.4
29
322.9
62.8
89
381.8
74.2
49
440."
85.7
09
499.6
97.2
69
558.6
108.6
30
323.9
63.0
90
382.8
74.4
50
441."
85.9
10
500.6
97.3
70
559.5
108.8
331
3*1.9
63.2
391
383.8
74.6
451 442. "
86.1
511
501.6
97.5
571
560.5
109.0
32 325. 9
63.4
92 384. 8
74.8
52
443."
86.2
12
502.6
97.6
72
561.5
109.1
33 326. 8
63.5
93 385."
75.0
53
444.6
86.4
13
503.5 i 97.8
73
562.5
109.3
34 327. 8
63.7
94 386. "
75.2
54
445. 6
86.6
14 504. 5 98. 0
74
563.5
109.5
35 328. 8
63.9
95 387. "
75.4
55
446.6
86.8
15
505.5
98.2
75
564.5
109.7
36 329. 8
64.1
96 , 388. "
75.6
56
447.6
87.0
16
506.5
98.4
76
565.4
109.9
37 330. 8
64.3
97 i 389. -
75.8
57
448.6
87.2
17
507.5
98.6
i i
566.4
110.1
38 331. 8
64.5
98 390. -
75.9
58
449.6
87.4
18
508.5
98.8
78
567.4
110.3
39 332. 7
64.7
99 391. 6
76.1
59
450. 5
87.6
19
509.4
99.0
79
568.3
110.5
40 333. 7
64.9
400 ! 392. 6
76.3
60
451.5
87.8
20
510.4
99.2
80
569.3
110.7
341 334. 7
65.1
401 | 393.6
76. 5
461
452.5
88.0
521
511.4
99.4
581
570.3
110.9
42
335.7
65.3
02 i 394.6
76.7
62
453.5
88.2
22
512.4
99.6
82
571.3
111.1
43
336.7
65.5
03 i 395.6
76.9
63
454.5
88.3
23
513.4
99.8
83
572.3
111.3
44 337. 6
65.6
04 i 396.5
77.1
64
455.4
88.5
24
514.3
100.0
84
573.2
111.5
45 338. 6
65.8
05 i 397. 5
77.3
65
456. 4
88.7
25
515. 3
100.2
85
574.2
111.7
46
339.6
66.0
06 j 398. 5
77.5
66
457. 4
88.9
26
516.3
100.4
86
575.2
111.8
47
340.6
66.2
07 399. 5
77.7
67
458.4
89.1
27
517.3 [100.6
87
576.2
112.1
48
341.6
66.4
08 | 400.5
77.9
68
459.4
89.3
28
518. 3 ! 100. 8
88
577.2
112.3
49 342. 6
66.6
09 401.5
78.1
69
460.4
89.5
29
519.3 101.0
89
578. 2
112.4
50 343. 5
66.8
10 402. 4
78.2
70
461.3
89.7
30
520.2
101.2
90
579.1
112.6
351
344.5
67.0
411 403. 4
78.4
471
462.3
89.9
531
521.2
101.4
591
580. 1 112. 8
52
345. 5
67.2
12
404.4
78.6
72
463.3
90.1
32
522.2
101.6
92
581.1
113.0
53 346. 5
67.4
13
405.4
78.8
73
464.3
90.3
33
523.2
101.7
93
582. 1 113. 2
54 347. 5
67.5
14 406. 4
79.0
74
465.3
90.4
34 524. 2
101.8
94
583. 1 113. 3
55 348.4
67.7
15 407. 3
79.2
75
466.2
90.6
35
525.1
102.0
95
584. 0 113. 5
56 349. 4
67.9
16 408. 3
79.4
76
467.2
90.8
36
526.1
102.2
96
585. 0 113. 7
57 350. 4
68.1
17
409.3
79.6
1 1
468.2
91.0
37
527.1
102.4
97
586.0 113.9
58 1 351.4
68.3
18
410.3
79.8
78
469.2
91.2
38
528.1
102.6
98
587.0 114.1
59 352. 4
68.5
19
411.3
80.0
79
470.2
91.4
39
529.1
102.8
99
588.0
114.3
60 353.4
68.7
20
412.3
80.1
80
471.1
91.6
40
530.1
103.0
600
589.0
114.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
79° (101°, 259°, 281° .
Page 554] TABLE 2.
Difference of Latitude and Departure for 12° (168°, 192°, 348°).
Dl8t.
Lat.
Dep
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Difit.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.7
12.7
121
118.4
25.2
181
177.0
37.6
241
235. 7
50.1
2
2.0
0.4
62
60.6
12.9
22
119.3
25.4
82
178.0
37.8
42
2:;o. 7
50.3
3
2.9
0.6
63
61.6
13.1
23
120. 3
25.6
83
179.0
38.0
43
237.7
50. 5
4
3.9
0.8
64
62.6
13.3
24
121.3
25.8
84
180.0
38. 3
44
238. 7
50. 7
5
4.9
.0
66
63.6
13.5
25
122.3
26.0
85
181.0
38.5
45
239.6
50.9
6
5.9
.2
66
64.6
13.7
26
123.2
26.2
86
181.9
38.7
46
240.6
51.1
7
6.8
.5
67
65. 5
13.9
27
124.2
26.4
87
182.9
38.9
47
241.6
51.4
8
7.8
.7
68
66.5
14.1
28
125. 2
26.6
88
183. 9
39.1
48
242.6
51.6
9
8.8
.9
69
67.5
14.3
29
126.2
26.8
89
184.9
39.3
49
243.6
51.8
10
9.8
2.1
70
68.5
14.6
30
127.2
27.0
90
185. 8
39.5
50
244. 5
52.0
11
10.8
2.3
71
69.4
14.8
131
128.1
27.2
191
186.8
39.7
251
245. 5 1 52. 2
12
11.7
2.5
72
70.4
15.0
32
129. 1
27.4
92
187.8
39.9
52
246.5 i 52.4
13
12.7
2.7
73
71.4
15.2
33
130. 1
27.7
93
188.8
40.1
53
247. 5 52. 6
14
13.7
2.9
74
72.4
15.4
34
131.1
27.9
94
189.8
40.3
54
248. 4 52. 8
15
14.7
3.1
75
73.4
15.6
35
132.0
28.1
95
190.7
40.5
55
249. 4 53. 0
16
15.7
3.3
76
74.3
15.8
36
133.0
28.3
96
191.7
40.8
56
250.4
53. 2
17
16.6
3.5
.77
75.3
16.0
37
134.0
28.5
97
192.7
41.0
57
251. 4
53. 4
18
17.6
3.7
78
76.3
16.2
38
135. 0
28.7
98
193.7
41.2
58
252. 4
53.6
19
18.6
4.0
79
77.3
16.4
39
136.0
28.9
99
194.7
41.4
59
253. 3
53.8
20
19.6
4.2
80
78.3
16. 0
40
136.9
29.1
200
195.6
41.6
60
254.3
54.1
21
20.5
4.4
81
79.2
16.8
141
137.9
29.3
201
190. 6
41.8
261
255. 3
54.3
22
21.5
4.6
82
80.2
17.0
42
138.9
29.5
02
197.6
42.0
62
256. 3
54.5
28
22.5
4.8
83
81.2
17.3
43
139.9
29.7
03
198.6
42.2
63
257. 3
54.7
24
23.5
5.0
84
82.2
17.5
44
140.9
29.9
04
199.5
42.4
64
258. 2
54.9
25
24.5
5.2
85
83.1
17.7
45
141.8
30.1
05
200.5
42.6
65
259. 2
55.1
26
25.4
5.4
86
84.1
17.9
46
142.8
30.4
06
201. 5
42.8
66
200.2
55. 3
27
26.4
5. 0
87
85.1
18.1
47
143. 8
30.6
07
202. 5
43.0
67
261.2
55. 5
28
27.4
5.8
88
86.1
18.3
48
144.8
30.8
08
203.5
43.2
68
262.1
55. 7
29
28.4
6.0
89
87.1
18.5
49
145. 7
31.0
09
204.4
43.5
69
263. 1
55. 9
30
29.3
6.2
90
88. 0
18.7
50
146.7
31.2
10
205.4
43.7
70
264.1
56.1
31
30.3
6.4
91
89.0
18.9
151
147.7
31.4
211
206.4
43.9
271 265. 1
56.3
32
31.3
6.7
92
90.0
19.1
52
148.7
31.6
12
207.4
44.1
72 266. 1
56.6
33
32.3
6.9
93
91.0
19.3
53
149.7
31.8
13
208.3
44.3
73 267. 0
56.8
34
33.3
7.1
94
91.9
19.5
54
150. 6
32.0
14
209.3
44.5
74
268.0
57.0
35
34.2
7.3
95
92.9
19.8
55
151. 6
32.2
15
210. 3
44.7
75
269.0
57.2
36
35. 2
7.5
96
93.9
20.0
56
152. 6
32. 4
16
211.3
44.9
76
270.0
57.4
37
36.2
7.7
97
94.9
20.2
57
153. 6
32. 6
17
212.3
45.1
77
270.9
57.6
38
37.2
7.9
98
95.9
20.4
58
154. 5
32.9
18
213.2
45.3
78
271.9
57.8
39
38.1
8.1
99
96.8
20.6
59
155. 5
33. 1
19
214.2
45.5
79
272.9
58.0
40
39.1
8. 3
100
07.8
20.8
60
156.5
33.3
20
215.2
45.7
80
273. 9
58.2
41
40.1
8.5
101
98.8
21.0
161
157.5
33.5
221
216.2
45.9
281
274.9
58.4
42
41.1
8.7
02
99.8
21.2
62
158. 5
33.7
22
217.1
46.2
82
275. 8
58.6
43
42.1
8.9
03
100.7
21.4
63
159. 4
33.9
23
218.1
46.4
83
276.8
58.8
44
43.0
9.1
04
101.7
21.6
64
160.4
34.1
24
219.1
46.6
84
277.8
59.0
45
44.0
9.4
05
102.7
21.8
65
161.4
34.3
25
220.1
46.8
85
278.8
59.3
46
45.0
9.6
06
103. 7
22.0
66
162.4
34.5
26
221.1
47.0
86
279.8
59.5
47
46.0
9.8
07
104.7
22.2
67
163.4
34.7
27
222.0
47.2
87
280.7
59.7
48
47.0
10.0
08
105.7
22.5
68
164.3
34.9
28
223.0
47.4
88
281.7
59.9
49
47.9
10.2
09
106.6
22.7
69
165.3
35.1
29
224.0
47.6
89
282.7
60.1
50
48.9
10.4
10
107.6
22.9
70
166.3
35.3
30
225.0
47.8
90
283. 7
60.3
51
49. 9
10.0
111
108.6
23.1
171
107.8
35.6
231
220. 0
48.0
291
284.6
60.5
52
50.9
10.8
12
109.6
23. 3
72
168.2
35.8
32
226.9
48.2
92
285. 6
60.7
53
51.8
11.0
13
110.5
23.5
73
169.2
36.0
33
227.9
48.4
93
286.6
60.9
54
52.8
11.2
14
111.5
23.7
74
170.2
36.2
34
228.9
48.7
94
287.6
61.1
55
53.8
11.4
16
112.5
23.9
75
171.2
36.4
35
229.9
48.9
95
288.6
61.3
56
54.8
11.6
16
113.5
24.1
76
172.2
36.6
36
230.8
49.1
96
289.5
61.5
57
55. 8
11.9
17
114.4
24.3
77
173.1
36.8
37
231.8
49.3
97
290.5
61.7
58
56.7
12.1
18
115.4
24.5
78
174.1
37.0
38
232. 8
49.5
98
291.5
62.0
59
57.7
12.3
19
116.4
24.7
79
175.1
37.2
39
233.8
49.7
99
292.5
62.2
60
58.7
12.5
20
117.4
24.9
80
176.1
37.4
40
234.8
49.9
300
293.4
62.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
78° (102°, 258°, 282°).
TABLE 2. [Page 555
Difference of Latitude and Departure for 12° (168°, 192°, 348°).
Dist.
Lat. Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
294.4
62.6
361
353.1
75.0
421
411.8
87.5
481
470.5
100.0
541
529.2
112.5
02 295. 4
62.8
62
354.1
75.2
22
412.8
87.7
82
471.5
100.2
42
530.2
112.7
03
296.4
63.0
63
355.1
75.4
23
413.8
87.9
83
472.5
100.4
43
531.1
112.9
04
297.4
63.2
64
356.0
75. 7
24
414.7
88.1
84
473.4
100.6
44
532.1
113.1
05
298.3
63.4
65
357.0
75.9
25
415.7
88.3
85
474.4
100.8
45
533.1
113.3
06
299.3
63.6
66
358.0
76.1
26
416.7
88.6
86
475.4
101.0
46
534.1
113.5
07
300.3
63.8
67
359.0
76.3
27
417.7
88.8
87
476.4
101.2
47
535. 1
113.7
08
301.3
64.0
68
360.0
76.5
28
418.6
89.0
88
477.3
101.4
48
536.0
113.9
09
302.2
64.2
69
360.9
76.7
29
419.6
89.2
89
478.3
101.6
49
537.0
114.1
10
303. 2
64.4
70
361.9
76.9
30
420.6
89.4
90
479.3
101.9
50
538.0
114.4
311
304. 2 , 64. 6
371
362.9
77.1
431
421.6
89.6
491
480.3
102.1
551
538.9
114.6
12
305.2
64.8
72
363.9
77.3
32
422.6
89.8
92
481.2
102.3
52
539.9
114.3
13
306.2
65.1
73
364.8
77.5
33
423.5
90.0
93
482.2
102.5
53
540.9
115.0
14
307. 1 65. 3
74
365.8
77.7
34
424.5
90.2
94
483.2
102.7
54
541.9
115.2
15
308.1
65.5
75
366.8
77.9
35
425.5
90.4
95
484.2
102.9
55
542.9
115.4
16
309.1
65.7
76
367.8
78.2
36
426. 5
90.6
96
485.2
103.1
56
543.8
115.6
17
310. 1 j 65. 9
77
368.8
78.4
37
427.5
90.8
97
486.1
103.3
57
544.8
115.8
18
311. 1 66. 1
78
369.7
78.6
38
428.4
91.0
98
487.1
103.5
58
545.8
116.0
19
312. 0 ! 66. 3
79
370.7
78.8
39
429.4
91.3
99
488.1
103.8
59
546.8
116.2
20
313.0
66.5
80
371.7
79.0
40
430.4
91.5
500
489.1
104.0
60
547.8
116.4
321
314.0
66.7
381
372.7
79.2
441
431.4
91.7
501
490.0
104.2
561
548.7
116.6
22
315.0
66.9
82
373.7
79.4
42
432.3
91.9
02
491.0
104.4
62
549.7
116.8
23
315. 9
67.1
83
374.6
79.6
43
433.3
92.1
03
492.0
104.6
63
550.7
117.0
24
316.9
67.3
84
375.6
79.8
44
434.3
92.3
04
493.0
104.8
64
551.7
117.2
25
317.9
67.6
85
376.6
80.0
45
435. 3
92.5
05
494.0
105.0
65
552.7
117.4
26
318.9
67.8
86
377.6
80.2
46
436.3
92.7
06
495.0
105.2
66
553.7
117.6
27
319.9
68.0
87
378.5
80.4
47
437.2
92.9
07
495.9
105.4
67
554.6
117.8
28
320.8
68.2
88
379.5
80.7
48
438.2
93.1
08
496.9
105.6
68
555.6
118.0
29
321.8 68.4
89
380.5
80.9
49
439.2
93.3
09
497.9
105.8
69
556.6
118.2
30
322. 8 68. 6
90
381.5
81.1
50
440.2
93.5
10
498.9
106.0
70
557.5
118.5
331
323. 8 68. 8
391
382.5
81.3
451
441.1
93.7
511
499.8
106.2
571
558.5
118.7
32
324. 7 69. 0
92
383.4
81.5
52
442.1
93.9
12
500.8
106.4
72
559.5
118.9
33
325. 7 69. 2
93
384.4
81.7
53
443.1
94.1
13
501.8
106.6
73
560.5
119.1
34
326. 7 69. 4
94
385.4
81.9
54
444.1
94.4
14
502.8
106.8
74
561.5
119.3
35
327. 7 69. 6
95
386.4
82.1
55
445.1
94.6
15
503.7
107.0
75
562.4
119.5
36
328. 7 69. 8
96
387.3
82.3
56
446.0
94.8
16
504.7
107.2
76
563.4
119.7
37
329. 6 70. 0
97
388.3
82.5
57
447.0
95.0
17
505.7
107.4
77
564.4
119.9
38
330. 6 70. 3
98
389.3
82.7
58
448.0
95.2
18
506.7
107.6
78
565.4
120.1
39 331. 6
70.5
99
390.3
82.9
59
449.0
95.4
19
507.7
107.8
79
566.4
120.3
40
332.6
70.7
400
391.3
83.1
60
450.0
95.6
20
508.7
108.1
80
567.4
120.6
341
333.5
70.9
401
392.2
83.4
461
450.9
95.8
521
509.6
108.3
581
568.3
120.8
42
334.5
71.1
02
393.2
83.6
62
451.9
96.0
22
510.6
108.5
82
569.3
121.0
43
335.5
71.3
03
394.2
83.8
63
452.9
96.2
23
511.6
108.7
83
570.3
121.2
44
336.5
71.5
04
395.2
84.0
64
453.9
96.5
24
512.5
108.9
84
571.2
121.4
45
337.5
71.7
05
396.2
84.2
65
454.8
96.7
25
513.5
109.2
85
572.2
121.6
46
338.4
71.9
06
397.1
84.4
66
455.8
96.9
26
514.5
109.4
86
573.2
121.8
47
339.4
72.1
07
398.1
84.6
67
456.8
97.1
27
515.5
109.6
87
574.2
122.0
48
340.4
72.3
08
399.1
84.8
68
457.8
97.3
28
516.5
109.8
88
575.2
122.2
49
341.4
72.5
09
400.1
85.0
69
458. 8
97.5
29
517.5
110.0
89
576.2
122.4
50
342.4
72.7
10
401.0
85.2
70
459.7
97.7
30
518.4
110.2
90
577.1
122.6
351
343.3
73.0
411
402.0
85.4
471
460.7
97.9
531
519.4
110.4
591
578.1
122.8
52
344.3
73.2
12
403.0
85.6
72
461.7
98.1
32
520.4
110.6
92
579.1
123.0
53
345.3
73.4
13
404.0
85.8
73
462.7
98.3
33
521.3
110.8
93
580.0
123.2
54
346.3
73.6
14
405.0
86.1
74
463.6
98.5
34
522.3
111.0
94
581.0
123.4
55
347.2
73.8
15
405.9
86.3
75
464.6
98.7
35
523.3
111.2
95
582.0
123.6
56
348.2
74.0
16
406.9
86.5
76
465.6
98.9
36
524.3
111.4
96
583.0
123.9
57
349.2
74.2
17
407.9
86.7
77
466.6
99.1
37
525.3
111.6
97
584.0
124.1
58
350.2
74.4
18
408.9
86.9
78
467.6
99.4
38
526.2
111.8
98
584.9
124.3
59
351.2
74.6
19
409.8
87.1
79
468.5
99.6
39
527.2
112.0
99
585.9
124.5
60
352.1
74.8
20
410.8
87.3
80
469.5
99.8
40
528.2
112.3
600
586.9
124.7
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. | Lat.
Dist. Dep. Lat.
78° (102°, 258°, 282°).
Page 556] TABLE 2.
Difference of Latitude and Departure for 13° (167°, 193°, 347°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.4
13.7
121
117.9
27.2
181
176.4
40.7
241
234.8
54.2
2
1.9
0.4
62
60.4
13.9
22
118.9
27.4
82
177.3
40.9
42
235. 8
54.4
3
2.9
0.7
63
61.4
14.2
23
119.8
27.7
83
178.3
41.2
43
236.8
54.7
4
3.9
0.9
64
62.4
14.4
24
120.8
27.9
84
179.3
41.4
44
237.7
54.9
5
4.9
1.1
65
63.3
14.6
25
121.8
28.1
85
180.3
41.6
45
238.7
55.1
6
5.8
1.3
66
64.3
14.8
26
122.8
28.3
86
181.2
41.8
46
239.7
55.3
7
6.8
1.6
67
65.3
15.1
27
123.7
28.6
87
182.2
42.1
47
240.7
55.6
8
7.8
1.8
68
66.3
15.3
28
124.7
28.8
88
183.2
42.3
48
241.6
55.8
9
8.8
2.0
69
67.2
15.5
29
125.7
29.0
89
184.2
42.5
49
242.6 56.0
10
9.7
2.2
70
68.2
15.7
30
126.7
29.2
90
185.1
42.7
50
243. 6
56.2
11
10.7
2.5
71
69.2
16.0
131
127.6
29.5
191
186.1
43.0
251
244.6
56.5
12
11.7
2.7
72
70.2
16.2
32
128.6
29.7
92
187.1
43.2
52
245.5
56.7
13
12.7
2.9
73
71.1
16.4
33
129.6
29.9
93
188.1
43.4
53
246.5
56.9
14
13.6
3.1
74
72.1
16.6
34
130.6
30.1
94
189.0
43.6
54
247.5
57.1
15
14.6
3.4
75
73.1
16.9
35
131.5
30.4
95
190.0
43.9
55
248.5
57.4
16
15.6
3.6
76
74.1
17.1
36
132.5
30.6
96
191.0
44.1
56
249.4
57.6
17
16.6
3.8
77
75.0
17.3
37
133.5
30.8
97
192.0
44.3
57
250.4
57.8
18
17.5
4.0
78
76.0
17.5
38
134.5
31.0
98
192.9
44.5
58
251.4
58.0
19
18.5
4.3
79
77.0
17.8
39
135.4
31.3
99
193.9
44.8
59
252.4
58.3
20
19.5
4.5
80
77.9
18.0
40
136.4
31.5
200
194.9
45.0
60
253.3
58.5
21
20.5
4.7
81
78.9
18.2
141
137.4
31.7
201
195.8
45.2
261
254.3
58.7
22
21.4
4.9
82
79.9
18.4
42
138.4
31.9
02
196.8
45.4
62
255.3
58.9
23
22.4
5.2
83
80.9
18.7
43
139.3
32.2
03
197.8
45.7
63
256.3
59.2
24
23.4
5.4
84
81.8
18.9
44
140.3
32.4
04
198.8
45.9
64
257.2
59.4
25
24.4
5.6
85
82.8
19.1
45
141.3
32.6
05
199.7
46.1
65
258.2
59.6
26
25.3
5.8
86
83.8
19.3
46
142.3
32.8
06
200.7
46.3
66
259.2
59.8
27
26.3
6.1
87
84.8
19.6
47
143.2
33.1
07
201.7
46.6
67
260.2
60.1
28
27.3
6.3
8S
85.7
19.8
48
144.2
33.3
08
202.7
46.8
68
261.1
60.3
29
28.3
6.5
89
86.7
20.0
49
145.2
33.5
09
203. 6
47.0
69
262.1
60.5
30
29.2
6.7
90
87.7
20.2
50
146.2
33.7
10
204.6
47.2
70
263.1
60.7
31
30.2
7.0
91
88.7
20.5
151
147.1
34.0
211
205.6
47.5
271
264.1
61.0
32
31.2
7.2
92
89.6
20.7
52
148.1
34.2
12
206.6
47.7
72
265.0
61.2
33
32.2
7.4
93
90.6
20.9
53
149.1
34.4
13
207.5
47.9
73
266.0
61.4
34
33.1
7.6
94
91.6
21.1
54
150.1
34.6
14
208.5
48.1
74
267.0
61.6
35
34.1
7.9
95
92.6
21.4
55
151.0
34.9
15
209.5
48.4
75
268.0
61.9
36
35.1
8.1
96
93.5
21.6
56
152.0
35.1
16
210.5
48.6
76
268.9
62.1
37
36.1
8.3
97
94.5
21.8
57
153.0
35.3
17
211.4
48.8
77
269.9
62.3
38
37.0
8.5
98
95.5
22.0
58
154.0
35.5
18
212.4
49.0
78
270.9
62.5
39
38.0
8.8
99
96.5
22.3
59
154.9
35.8
19
213.4
49.3
79
271.8
62.8
40
39.0
9.0
100
97.4
22.5
60
155.9
36.0
20
214.4
49.5
80
272.8
63.0
41
39.9
9.2
101
98.4
22.7
161
156.9
36.2
221
215.3
49.7
281
273.8
63.2
42
40.9
9.4
02
99.4
22.9
62
157.8
36.4
22
216.3
49.9
82
274.8
63.4
43
41.9
9.7
03
100.4
23.2
63
158.8
36.7
23
217.3
50.2
83
275.7
63.7
44
42.9
9.9
04
101.3
23.4
64
159.8
36.9
24
218.3
50.4
84
276.7
63.9
45
43.8
10.1
05
102.3
23.6
65
160.8
37.1
25
219.2
50.6
85
277.7
64.1
46
44.8
10.3
06
103.3
23.8
66
161.7
37.3
26
220.2
50.8
86
278.7
64.3
47
45.8
10.6
07
104.3
24.1
67
162.7
37.6
27
221.2
51.1
87
279.6
64.6
48
46.8
10.8
08
105.2
24.3
68
163.7
37.8
28
222.2
51.3
88
280.6
64.8
49
47.7
11.0
09
106.2
24.5
69
164.7
38.0
29
223.1
51.5
89
281.6
65.0
50
48.7
11.2
10
107.2
24.7
70
165.6
38.2
30
224.1
51.7
90
282.6
65.2
51
49.7
11.5
111
108.2
25.0
171
166.6
38.5
231
225.1
52.0
291
283.5
65.5
52
50.7
11.7
12
109.1
25.2
72
167.6
38.7
32
226.1
52.2
92
284.5
65.7
53
51.6
11.9
13
110.1
25.4
73
168.6
38.9
33
227.0
52.4
93
285.5
65.9
54
52.6
12.1
14
111.1
25.6
74
169.5
39.1
34
228.0
52.6
94
286.5
66.1
55
53.6
12.4
15
112.1
25.9
75
170. 5
39.4
35
229.0
52.9
95
287.4
66.4
56
54.6
12.6
16
113.0
26.1
76
171.5
39.6
36
230.0
53.1
96
288.4
66.6
57
55.5
12.8
17
114.0
26.3
77
172.5
39.8
37
230.9
53.3
97
289.4
66.8
58
56.5
13.0
18
115.0
26.5
78
173.4
40.0
38
231.9
53.5
98
290.4
67.0
59
57.5
13.3
19
116.0
26.8
79
174.4
40.3
39
232.9
53.8
99
291.3
67.3
60
58.5
13.5
20
116.9
27.0
80
175.4
40.5
40
233. 8 .
54.0
300
292.3
67.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
77° (103°, 257°, 283°).
TABLE 2.
[Page 557
Difference of Latitude and Departure for 13° (167°, 193
°, 347°).
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
301 293. 3
67.7
361
351.8
81.2
421
410.2
94.7
481
468.7
108.2
541
527.2
121.7
02 294. 3
67.9
62
352.7
81.4
22
411.2
94.9
82
469.7
108.4
42
528.1
121.9
03 295. 2
68.1
63
353.7
81.6
23 :
412.2
95.1
83
470.6
108.6
43
529.1
122.1
04 296.2
68.4
64
354.7
81.9
24 !
413.1
95.3
84
471.6
108.8
44
530. 1 122. 3
05 ; 297.2
68.6
65
355.6
82.1
25
414.1
95.6
85
472.6
109.0
45 531. 1 122. 5
06 ; 298. 2
68.8
66
356. 6
82.3
26
415.1
95.8
86
473.6
109.3
46 532. 0 122. 8
07 299. 1
69.0
67
357.6
82.5
27 !
416.1
96.0
87
474.5
109.5
47 533.0 123.0
08 300. 1
69.3
68 358.6
82.8
28
417.0
96.2
88
475. 5
109.7
48 534.0 123.2
09 301.1
69.5
69 359. 5
83.0
29
418.0
96.5
89
476.5
109.9
49 535.0 123.4
10 302. 1
69.7
70 | 360.5
83.2
30 i
419.0
96.7
90
477.5
110.1
50 535. 9 123. 7
311 303.0 69.9
371
361.5
83.4
431 i
420.0
96.9
491
478.4
110.4
551 536. 9 123. 9
12 304.0
70.2
72
362.5
83.7
32
420.9
97.1
92
479.4
110.6
52 537. 9 124. 1
13 305. 0
70.4
73
363.4
83.9
33
421.9
97.4
93
480.4
110.9
53 538. 9 124. 4
14 306. 0
70.6
74
364.4
84.1
34 i
422.9
97.6
94
481.4
111.1
54
539. 8 124. 6
15 306. 9
70.8
^
<o
365.4
84.3
35 i
423.9
97.8
95
482.3
111.3
55
540. 8 124. 9
16
307.9
71.1
76
366.4
84.6
36 |
424.8
98.0
96
483.3
111.5
56 541. 8
125. 1
17
308.9
71.3
77
367.3
84.8
37
425.8
98.3
97
484.3
111.8
57 542. 8
125.3
18
309.9
71.5
78
368.3
85.0
38
426.8
98.5
98
485.3
112.0
58 543. 7
125. 5
19
310.8
71.7
79
369.3
85.2
39
427.8
98.7
99
486.2
112.2
59 j 544. 7
125.8
20 311. 8
72.0
80 370. 3
85.5
40
428.7
98.9
500
487.2
112.4
60 ; 545.7
126.0
321
312.8
72.2
381 371.2
85.7
441
429. 7
99.2
501
488 2
112.6
561 546. 7 126. 2
22
313.8
72.4
82 ; 372.2
85.9
42
430.7
99.4
02
489.2
112.9
62 547. 6
126.4
23
314.7
72.6
83 i 373. 2
86.1
43
431.6
99.6
03
490.1
113.1
63 548. 6
126.7
24
315.7
72.9
84 374. 2
86.4
44
432.6
99.8
04
491.1
113.3
64 549.6
126.9
25
316. 7 73. 1
85 375. 1
86.6
45
433.6
100.1
05
492.1
113.5
65 550.6
127.1
26
317.6
73.3
86
376.1
86.8
46
434.6
100.3
06
493.1
113.8
66 I 551.5
127.3
27
318. 6 73. 5
87
377.1
87.0
47
435.5
100.5
07
494.0
114.0
67 552.5
127. 6
28
319. 6 73. 8
88
378.1
87.3
48
436.5
100.7
08
495.0
114.2
68 i 553.5
127.8
29
320.6 | 74.0
89
379.0
87. 5
49
437.5
101.0
09
496.0
114.5
69 ! 554. 5
128.0
30
321.5 i 74.2
90
380.0
87.7
50
438.5
101.2
10
496.9
114.7
70 555.4
128.3
331 | 322.5 j 74.4
391 i 381.0
87.9
451
439.4
101.4
511
497.9
114.9
571 : 556.4
128.5
32 323.5 74.7
92 382. 0
88.2
52
440.4
101.6
12
498.9
115.1
72 557. 4
128.7
33 324.5 ; 74.9
93 382. 9
88.4
53
441.4
101.9
13
499.9
115.4
73 558.4
128.9
34 325.4 75.1
94
383.9
88.6
54
442. 4
102.1
14
500.8
115.6
74 ; 559. 3
129.2
35
326,4 75.3
95
384.9
88.8
55
443.3
102.3
15
501.8
115.8
75 560. 3
129.4
36
327.4
75.6
96
385.9
89.1
56
444.3
102.5
16
502.8
116.0
76
561.3
129.6
37
328.4
75.8
97
386.8
89.3
57
445.3
102.8
17
503.8
116.3
77
562.3
129.8
38
329.3 76.0
98
387.8
89.5
58
446.3
103.0
18
504.7
116.5
78
563.2
130.0
39
330. 3 76. 2
99
388.8
89.7
59
447.2
103.2
19
505.7
116.7
79
564.2
130.2
40
331.3 i 76.5
400
389.8
90.0
60
448.2
103.4
20
506.7
116.9
80
565.2
130.4
341
332.3 j 76.7
401
390.7
90.2
461
449.2
103.7
521
507.7
117.2
581
566.2
130.7
42
333.2 1 76.9
02
391.7
90.4
62
450.2
103.9
22
508.6
117.5
82
567.1
131.0
43
334.2 77.1
03
392.7
90.6
63
451.1
104.1
23
509.6
117.7
83
568. 1 131. 2
44
335.2 77.4
04
393.6
90.8
64
452. 1
104.3
24
510.6
117.9
84
569. 1 131. 4
45
336.2 j 77.6
05
394.6
91.1
65
453.1
104.6
25
511.6
118.1
85
570.1 131.6
46
337.1 77.8
06
395.6
91.3
86
454.1
104.8
26
512.5
118.3
86
571.0
131.8
47
338.1 78.0
07
396.6
91.5
67
455.0
105.0
27
513.5
118.5
87
572.0
132.0
48
339.1 78.3
08
397.5
91.7
68
456.0
105.2
28
514.5
118.7
88
573.0
132.3
49
340.1 78.5
09
398.5
92.0
69
457.0
105.5
29
515.5
119.0
89 573. 9
132.5
50
341. 0 ! 78. 7
10
399.5
92.2
70
458.0
105.7
30
516.4
119.2
90 ! 574.9 ! 132.8
351
342.0 78.9
411
400.5
92.4
471
458.9
105.9
531
517.4
119.4
591 575. 9
133.0
52
343.0 79.2
12
401.4
92.6
72
459.9
106.1
32
518.4
119.6
92 576. 9
133.2
53
344.0 79.4
13
402.4
92.9
73
460.9
106.4
33
519.4
119.9
93 577. 8
133.4
54
344.9 | 79.6
14
403.4
93.1
74
461.9
106.6
34
520.3
120.1
94 578. 8
133.6
55
345. 9 79. 8
15
404.4
93.3
75
462.8
106.8
35
521.3
120.3
95
579.8
133.8
56
346.9 i 80.1
16
405.3
93.5
76
463.8
107.0
36
522.3
120.5
96
580.8
134.0
57
347.9 ; 80.3
17
406.3
93.8
77
464.8
, 107. 3
37
523.3
120.8
97
581.7
134.3
58
348.8 i 80.5
18
407.3
94.0
78
465.8
107. 5
38
524.2
121.0
98
582.7
134.5
59
349. 8 ; 80. 7
19
408.3
94.2
79
466.7
i 107. 7
39
525.2
121.2
99
583.7
134.8
60
350. 8 81. 0
20
409.2
94.4
80
467.7
107.9
40
526.2
121.5
600
584.6
135.0
Dist.
Dep. Lat.
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
77° (103°, 257
°, 283°).
Page 558] TABLE 2.
Difference of Latitude and Departure for 14° (166°, 194°, 346°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
10
0.2
61
59.2
14.8
121
117.4
29.3
181
175.6
43.8
241
233.8
58.3
2
1.9
0.5
62
60.2
15.0
22
118.4
29.5
82
176.6
44.0
42
234.8
58.5
3
2.9
0.7
63
61.1
15.2
23
119.3
29.8
83
177.6
44.3
43
235. 8
58.8
4
3.9
1.0
64
62.1
15.5
24
120.3
30.0
84
178.5
44.5
44
236. 8
59.0
5
4.9
1.2
65
63.1
15.7
25
121.3
30.2
85
179.5
44.8
45
237.7
59.3
6
5.8
1.5
66
64.0
16.0
26
122.3
30.5
86
180.5
45.0
46
238.7
59.5
7
6.8
1.7
67
65.0
16.2
27
123.2
30.7
87
181.4
45.2
47
239.7
59.8
8
7.8
1.9
68
66.0
16.5
28
124.2
31.0
88
182.4
45.5
48
240.6
60.0
9
8.7
2.2
69
67.0
16.7
29
125. 2
31.2
89
183.4
45.7
49
241.6
60.2
10
9.7
2.4
70
67.9
16.9
30
126.1
31.4
90
184.4
46.0
50
242.6
60.5
11
10.7
2.7
71
68.9
17.2
131
127.1
31.7
191
185. 3
46.2
251
243.5
60.7
12
11.6
2.9
72
69.9
17.4
32
128.1
31.9
92
186.3
46.4
52
244.5
61.0
13
12.6
3.1
73
70.8
17.7
33
129.0
32.2
93
187.3
46.7
53
245.5
61.2
14
13.6
3.4
74
71.8
17.9
34
130.0
32.4
94
188.2
46.9
54
246.5
61.4
15
14.6
3.6
75
72.8
18.1
35
131.0
32.7
95
189.2
47.2
55
247.4
61.7
16
15.5
3.9
76
73.7
18.4
36
132.0
32.9
96
190.2
47.4
56
248.4
61.9
17
16.5
4.1
77
74.7
18.6
37
132.9
33.1
97
191.1
47.7
57
249.4
62.2
18
17.5
4.4
78
75.7
18.9
38
133.9
33.4
98
192.1
47.9
58
250.3
62.4
19
18.4
4.6
79
76.7
19.1
39
134.9
33.6
99
193.1
48.1
59
251.3
62.7
20
19.4
4.8
80
77.6
19.4
40
135.8
33.9
200
194.1
48.4
60
252.3
62.9
21
20.4
5.1
81
78.6
19.6
141
136.8
34.1
201
195.0
48.6
261
253.2
63.1
22
21.3
5.3
82
79.6
19.8
42
137.8
34.4
02
196.0
48.9
62
254.2
63.4
23
22.3
5.6
83
80.5
20.1
43
138.8
34.6
03
197.0
49.1
63
255.2
63.6
24
23.3
5.8
84
81.5
20.3
44
139.7
34.8
04
197.9
49.4
64
256.2
63.9
25
24.3
6.0
85
82.5
20.6
45
140.7
35.1
05
198.9
49.6
65
257. 1
64.1
26
25.2
6.3
86
83.4
20.8
46
141.7
35.3
06
199.9
49.8
66
258.1
64.4
27
26.2
6.5
87
84.4
21.0
47
142.6
35.6
07
200.9
50.1
67
259.1
64.6
28
27.2
6.8
88
85.4
21.3
48
143.6
35.8
08
201.8
50.3
68
260.0
64.8
29
28.1
7.0
89
86.4
21.5
49
144.6
36.0
09
202.8
50.6
69
261.0
65.1
30
29.1
7.3
90
87.3
21.8
50
145.5
36.3
10
203.8
50.8
70
262.0
65.3
31
30.1
7.5
91
88.3
22.0
151
146.5
36.5
211
204.7
51.0
271
263.0
65.6
32
31.0
7.7
92
89.3
22.3
52
147.5
36.8
12
205.7
51.3
72
263.9
65.8
33
32.0
8.0
93
90.2
22.5
53
148.5
37.0
13
206.7
51.5
73
264.9
66.0
34
33.0
8.2
94
91.2
22.7
54
149.4
37.3
14
207.6
51.8
74
265.9
66.3
35
34.0
8.5
95
92.2
23.0
55
150.4
37.5
15
208.6
52.0
75
266.8
66.5
36
34.9
8.7
96
93.1
23.2
56
151.4
37.7
16
209.6
52.3
76
267.8
66.8
37
35.9
9.0
97
94.1
23.5
57
152.3
38.0
17
210.6
52.5
77
268.8
67.0
38
36.9
9.2
98
95.1
23.7
58
153.3
38.2
18
211.5
52.7
78
269.7
67.3
39
37.8
9.4
99
96.1
24.0
59
154.3
38.5
19
212.5
53.0
79
270.7
67.5
40
38.8
9.7
100
97.0
24.2
60
155.2
38.7
20
213.5
53.2
80
271.7
67.7
41
39.8
9.9
101
98.0
24.4
161
156.2
38.9
221
214.4
53.5
281
272.7
68.0
42
40.8
10.2
02
99.0
24.7
62
157.2
39.2
22
215.4
53.7
82
273.6
68.2
43
41.7
10.4
03
99.9
24.9
63
158.2
39.4
23
216.4
53.9
83
274.6
68.5
44
42.7
10.6
04
100.9
25.2
64
159.1
39.7
24
217.3
54.2
84
275.6
68.7
45
43.7
10.9
05
101.9
25.4
65
160.1
39.9
25
218.3
54.4
85
276.5
68.9
46
44.6
11.1
06
102.9
25.6
66
161.1
40.2
26
219.3
54.7
86
277.5
69.2
47
45.6
11.4
07
103.8
25.9
67
162.0
40.4
27
220.3
54.9
87
278.5
69.4
48
46.6
11.6
08
104.8
26.1
68
163.0
40.6
28
221.2
55.2
88
279.4
69.7
49
47.5
11.9
09
105.8
26.4
69
164.0
40.9
29
222.2
55.4
89
280.4
69.9
50
48.5
12.1
10
106.7
26.6
70
165.0
41.1
30
223.2
55.6
90
281.4
70.2
51
49.5
12.3
111
107.7
26.9
171
165.9
41.4
231
224.1
55.9
291
282.4
70.4
52
50.5
12.6
12
108.7
27.1
72
166.9
41.6
32
225. 1
56.1
92
283.3
70.6
53
51.4
12.8
13
109.6
27.3
73
167.9
41.9
33
226.1
56.4
93
284.3
70.9
54
52.4
13.1
14
110.6
27.6
74
168.8
42.1
34
227.0
56.6
94
285.3
71.1
55
53.4
13.3
15
111.6
27.8
75
169.8
42.3
35
228.0
56.9
95
286.2
71.4
56
54.3
13.5
16
112.6
28.1
76
170.8
42.6
36
229.0
57.1
96
287.2
71.6
57
55.3
13.8
17
113.5
28.3
77
171.7
42.8
37
230.0
57.3
97
288.2
71.9
58
56.3
14.0
18
114.5
28.5
78
172.7
43.1
38
230.9
57.6
98
289.1
72.1
59
57.2
14.3
19
115.5
28.8
79
173.7
43.3
39
231.9
57.8
99
290.1
72.3
60
58.2
14.5
20
116.4
29.0
80
174.7
43.5
40
232.9
58.1
300
291.1
72.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
76° (104°, 256°, 284°).
TABLE 2. [Page 559
Difference of Latitude and Departure for 14° (166°, 194°, 346°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
292.0
72.8
361
350. 2
87.3
421
408.5
101.8
481
466.7
116.3
541
525. 0
130.9
02
293.0
73.0
62
351.2
87.6
22
409.4
102.1
82
467.7
116.6
42
525.9
131.2
03
294.0
73.3
63
352.2
87.8
23
410.4
102.3
83
468.6
116.8
43
526. 9
131.4
04
294.9
73.5
64
353.2
88.0
24
411.4
102.6
84
469.6
117.1
44
527. 9
131.6
05
295. 9
73.8
65
354.1
88.3
25
412.3
102.8
85
470.6
117.3
45
528. 8
131.9
06
296.9 ! 74.0
66
355.1
88.5
26
413.3
103.0
86
471.5
117.6
46
S2v>. 8
132.1
07
297. 8
74.2
67
356. 1
88.8
27
414.3
103.3
87
472.5
117.8
47
530.8
132.3
08
298.8
74.5
68
357.0
89.0
28
415.3
103.5
88
473.5
118.0
48
531.7
132.6
09
299.8
74.7
69
358.0
89.2
29
416.2
103.8
89
474.5
118.3
49
532.7
132.8
10
300.8
75.0
70
359.0
89.5
30
417.2
104.0
90
475.4
118.5
50
533.7
133.0
311
301.7
75.2
371
359.9
89.7
431
418.2
104.2
491
476.4
118.8
551
534.6
133.3
12
302.7
75.5
72
360.9
90.0
32
419.1
104.5
92
477.4
119.0
52
535.6
133.6
13
303.7
75.7
73
361.9
90.2
33
420.1
104.7
93
478.3
119.2
53
536. 6
133.8
14
304.6
75.9
74
362.9
90.5
34
421.1
105.0
94
479.3
119.5
54
537. 5
134. 0'
15
305.6
76.2
75
363.8
90.7
35
422.0
105.2
95
480.3
119.7
55
538.5
134.3
16
306.6
76.4
76
364.8
90.9
36
423.0
105.5
96
481.3
120.0
56
539.5
134.5
17
307.6
76.7
77
365.8
91.2
37
424.0
105.7
97
482.2
120.2
57
540.5
134.8
18
308.5
76.9
78
366.7
91.4
38
425. 0
105.9
98
483.2
120.4
58
541.4
135.0
19
309.5
77.2
79
367.7
91.7
39
425.9
106.2
99
484.2
120.7
59
542.4
135.2
20
310.5
77.4
80
368.7
91.9
40
426.9
106.4
500
485.1
121.0
60
543.4
135.5
321
311.4
77.6
381
369.6
92.2
441
427.9
106.7
501
486.1
121.2
561
544.3
135.7
22
312.4
77.9
82
370.6
92.4
42
428.8
106.9
02
487.1
121.4
62
545.3
135.9
23
313.4
78.1
83
371.6
92.6
43
429.8
107.1
03
488.0
121.7
63
546.3
136.2
24
314.3
78.4
84
372.6
92.9
44
430.8
107.4
04
489.0
122.0
64
547.2
136.5
25
315.3
78.6
85
373.5
93.1
45
431.7
107.6
05
490.0
122.1
65
548.2
136.6
26
316.3
78.8
86
374.5
93.4
46
432.7
107.9
06
491.0
122.4
66
549.2
136.9
27
317.3
79.1
87
375.5
93.6
47
433.7
108.1
07
491.9
122.6
67
550.1
137.1
28
318.2
79.3
88
376.4
93.8
48
434.7
108.4
08
492.9
122.9
68
551.1
137.4
29
319.2
79.6
89
377.4
94.1
49
435.6
108.6
09
493.9
123.1
69
552. 1
137.6
30
320.2
79.8
90
378.4
94.3
50
436.6
108.8
10
494.9
123.4
70
553.1
137.9
331
321. 1 80. 1
391
379.4
94.6
451
437.6
109.1
511
495.8
123.6
571
554. 0
138.1
32
322.1
80.3
92
380.3
94.8
52
438.5
109.3
12
496.8
123.8
72
555.0
138.3
33
323.1
80.5
93
381.3
95.1
53
439.5
109.6
13
497.8
124.1
73
556.0
138.6
34
324. 0 80. 8
94
382. 3
95.3
54
440.5
109.8
14
498.7
124.3
74
557.0
138.8
35
325.0 81.0
95
383.2
95.5
55
441.5
110.1
15
499.7
124.6
75
557.9
139.1
36
326. 0 1 81. 3
96
384. 2
95.8
56
442.4
110.3
16
500.7
124.8
76
558.9
139.3
37
327.0
81.5
97 385. 2
96.0
57
443.4
110.5
17
501.7
125.0
77
559.9
139.5
38
327.9
81.7
98 386. 1
96.3
58
444.4
110.8
18
502.6
125.3
78
560.9
139.8
39
328.9
82.0
99
387.1
96.5
59
445.3
111.0
19
503.6
125.6
79
561.8
140.0
40
329.9
82.2
400
388.1
96.7
60
446.3
111.3
20
504.6
125. 8
80
562.8
140.3
341
330.8
82.5
401 389. 1
97.0
461
447.3
111.5
521
505. 5
126.0
581 563. 8
140.5
42
331.8
82.7
02 390. 0
97.2
62
448.2
111.7
22
506.5
126.2
82 564. 7
140.8
43
332.8
83.0
03 I 391. 0
97.5
63
449.2
112.0
23
507.5
126.5
83
565.7
141.0
44
333.7
83.2
04 i 392.0
97.7
64
450. 2
112.2
24
508.4
126.8
84
566.7
141.3
45
334.7
83.4
05 i 392.9
98.0
65
451.2
112.5
25
509.4
127.0
85
567.6
141.5
46
335.7
83.7
06 393. 9
98.2
66
452.1
112.7
26
510.4
127.2
86
568.6
141.8
47
336.7
83.9
07 394. 9
98.4
67
453.1
113.0
27
511.4
127.5
87
569.6
142.0
48
337.6
84.2
08 395. 8
98.7
68
454.1
113.2
28
512.3
127.8
88
570.6
142.3
49
338.6
84.4
09 396. 8
98.9
69
455.0
113.4
29
513.3
128.0
89
571.5
142.5
50
339.6
84.7
10 j 397.8
99.2
70
456.0
113.7
30
514.3
128.2
90
572.5
142.8
351
340.5 i 84.9
411 398. 8
99.4
4V 1
457.0
113.9
531
515.3
128.5
591
573. 5 143. 0
52
341.5
85.1
12
399.7
99.7
72
457.9
114.2
32
516.2
128.8
92
574.4 143.3
53
342.5
85.4
13
400.7
99.9
73
458. 9
114.4
33
517.2
129.0
93
575.4 j 143.5
54
343. 5 85. 6
14
401.7
100.1
74
459.9
114.6
34
518.2
129.2
94
576.4
143.8
55
344.4 ! 85.9
15
402.6
100.4
75
460.9
114.9
35
519.1
129.4
95
577. 3
144.0
56
345. 4 86. 1
16
403.6
100.6
76
461.8
115.1
36
520.1
129.7
96
578.3
144.2
57
346. 4 86. 3
17
404.6
100.9
77
462.8
115.4
37
521.1
129.9
97
579.3
144.5
58
347.3 i 86.6
18
405. 5
101.1
78
463.8
115.6
38
522.1
130.2
98
580.3
144.7
59
348.3 ; 86.8
19
406.5
101.3
79
464.7
115.9
39
523.0
130.4
99
581.2
144.9
60
349. 3 87. 1
20
407.5
101.6
80
465.7
116.1
40
524.0
130.6
600
582.2
145.1
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep. j Lat.
76° (104°, 256°, 284°).
61828°— 16 29
Page 560] TABLE 2.
Difference of Latitude and Departure for 15° (165°, 195°, 345°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.9
15.8
121
116.9
31.3
181
174.8
46.8
241
232.8
62.4
2
1.9
0.5
62
59.9
16.0
22
117.8
31.6
82
175.8
47.1
42
233.8
62.6
3
2.9
0.8
63
60.9
16.3
23
118.8
31.8
83
176.8
47.4
43
234.7
62.9
4
3.9
1.0
64
61.8
16.6
24
119.8
32.1
84
177.7
47.6
44
235.7
63.2
5
4.8
1.3
65
62.8
16.8
25
120.7
32.4
85
178.7
47.9
45
236.7
63.4
6
5.8
1.6
66
63.8
17.1
26
121.7
32.6
86
179.7
48.1
46
237.6
63.7
7
6.8
1.8
67
64.7
17.3
27
122.7
32.9
87
180.6
48.4
47
238.6
63.9
8
7.7
2.1
68
65.7
17.6
28
123.6
33.1
88
181.6
48.7
48
239.5
64.2
9
8.7
2.3
69
66.6
17.9
29
124.6
33.4
89
182.6
48.9
49
240.5
64.4
10
9.7
2.6
70
67.6
18.1
30
125. 6
33.6
90
183.5
49.2
50
241.5
64.7
11
10.6
2.8
71
68.6
18.4
131
126.5
33.9
191
184.5
49.4
251
242.4
65.0
12
11.6
3.1
72
69.5
18.6
32
127.5
34.2
92
185.5
49.7
52
243.4
65.2
13
12.6
3.4
73
70.5
18.9
33
128.5
34.4
93
186.4
50.0
53
244.4
65.5
14
13.-5
3.6
74
71.5
19.2
34
129.4
34.7
94
187.4
50.2
54
245.3
65.7
15
14.5
3.9
75
72.4
19.4
35
130.4
34.9
95
188.4
50.5
55
246.3
66.0
16
15.5
4.1
76
73.4
19.7
36
131.4
35.2
96
189.3
50.7
56
247.3
66.3
17
16.4
4.4
77
74.4
19.9
37
132.3
35.5
97
190.3
51.0
57
248.2
66.5
18
17.4
4.7
78
75.3
20.2
38
133.3
35.7
98
191.3
51.2
58
249.2
66.8
19
18.4
4.9
79
76.3
20.4
39
134.3
36.0
99
192.2
51.5
59
250.2
67.0
20
19.3
5.2
80
77.3
20.7
40
135.2
36.2
200
193.2
51.8
60
251.1
67.3
21
20.3
5.4
81
78.2
21.0
141
136.2
36.5
201
194.2
52.0
261
252.1
67.6
22
21.3
5.7
82
79.2
21.2
42
137.2
36.8
02
195.1
52.3
62
253.1
67.8
23
22.2
6.0
83
80.2
21.5
43
138. 1
37.0
03
196.1
52.5
63
254.0
68.1
24
23.2
6.2
84
81.1
21.7
44
139.1
37.3
04
197.0
52.8
64
255.0
68.3
25
24.1
6.5
85
82.1
22.0
45
140.1
37.5
05
198.0
53.1
65
256.0
68.6
26
25.1
6.7
86
83.1
22.3
46
141.0
37.8
06
199.0
53.3
66
256.9
68.8
27
26.1
7.0
87
84.0
22.5
47
142.0
38.0
07
199.9
53.6
67
257.9
69.1 i
28
27.0
7.2
88
85.0
22.8
48
143.0
38.3
08
200.9
53.8
68
258.9
69.4
29
28.0
7.5
89*
86.0
23.0
49
143.9
38.6
09
201.9
54.1
69
259.8
69.6
30
29.0
7.8
90
86.9
23.3
50
144.9
38.8
10
202.8
54.4
70
260.8
69.9
31
29.9
8.0
91
87.9
23.6
151
145.9
39.1
211
203.8
54.6
271
261.8
TOjTi
32
30.9
8.3
92
88.9
23.8
52
146.8
39.3
12
204.8
54.9
72
262.7
70.4
33
31.9
8.5
93
89.8
24.1
53
147.8
39.6
13
205. 7
55.1
73
263.7
70.7
34
32.8
8.8
94
90.8
24.3
54
148.8
39.9
14
206.7
55.4
74
264.7
70.9
35
33.8
9.1
95
91.8
24.6
55
149.7
40.1
15
207.7
55.6
75
265.6
71.2
36
34.8
9.3
96
92.7
24.8
56
150.7
40.4
16
208.6
55.9
76
266.6
71.4
37
35.7
9.6
97
93.7
25.1
57
151.7
40.6
17
209.6
56.2
77
267.6
71.7
38
36.7
9.8
98
94.7
25.4
58
152.6
40.9
18
210.6
56.4
78
268.5
72.0
39
37.7
10.1
99
95.6
25.6
59
153.6
41.2
19
211.5
56.7
79
269.5
72.2
40
38.6
10.4
100
96.6
25.9
60
154.5
41.4
20
212.5
56.9
80
270.5
72.5
41
39.6
10.6
101
97.6
26.1
161
155.5
41.7
221
213.5
57.2
281
271.4
72.7
42
40.6
10.9
02
98.5
26.4
62
156.5
41.9
22
214.4
57.5
82
272.4
73.0
43
41.5
11.1
03
99.5
26.7
63
157.4
42.2
23
215.4
57.7
83
273.4
73.2
44
42.5
11.4
04
100.5
26.9
64
158.4
42.4
24
216.4
58.0
84
274.3
73.5
45
43.5
11.6
05
101.4
27.2
65
159.4
42.7
25
217.3
58.2
85
275.3
73.8
46
44.4
11.9
06
102.4
27.4
66
160.3
43.0
26
218.3
58.5
86
276.3
74.0
47
45.4
12.2
07
103.4
27.7
67
161.3
43.2
27
219.3
58.8
87
277.2
74.3
48
46.4
12.4,
08
104.3
28.0
68
162.3
43.5
28
220.2
59.0
88
278.2
74.5
49
47.3
12.7
09
105.3
28.2
69
163.2
43.7
29
221.2
59.3
89
279.2
74.8
50
48.3
12.9
10
106.3
28.5
70
164.2
44.0
30
222.2
59.5
90
280.1
75.1
51
49.3
13.2
111
107.2
28.7
171
165.2
44.3
231
223.1
59.8
291
281.1
75.3
52
50.2
13.5
12
108.2
29.0
72
166.1
44.5
32
224.1
60.0
92
282.1
75.6
53
51.2
13.7
13
109.1
29.2
73
167.1
44.8
33
225.1
60.3
93
283. 0
75.8
54
52.2
14.0
14
110.1
29.5
74
168.1
45.0
34
226.0
60.6
94
284.0
76.1
55
53.1
14.2
15
111.1
29.8
75
169.0
45.3
35
227.0
60.8
95
284.9
76.4
56
54.1
14.5
16
112.0
30.0
76
170.0
45.6
36
228.0
61.1
96
285.9
76.6
57
55.1
14.8
17
113.0
30.3
77
171.0
45.8
37
228.9
61.3
97
286.9
76.9
58
56.0
15.0
18
114.0
30.5
78
171.9
46.1
38
229.9
61.6
98
287.8
77.1
59
57.0
15.3
19
114.9
30.8
79
172.9
46.3
39
230.9
61.9
99
288.8
77.4
60
58.0
15.5
20
115.9
31.1
80
173.9
46.6
40
231.8
62.1
300
289.8
77.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
75° (105°, 255°, 285°).
TABLE 2. [Page 561
Difference of Latitude and Departure for 15° (166°, 195°, 345°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
290.7
77.9
361
348.7
93.4
421
406.6
109.0
481
464.6
124.5
541
522.6
140.0
02
291.7
78.2
62
349.6
93.7
22
407.6
109.2
82
465.6
124.8
42
523.5
140.3
03
292.7
78.4
63
350.6
94.0
23
408.6
109.5
83
466.5
125.0
43
524.5
140.5
04
293.6
78.7
64
351.6
94.2
24
409.5
109. 7
84
467.5
125.3
44
525.5
140.8
05
294.6
78.9
65
352.5
94.5
25
410.5
110.0
85
468.5
125.6
45
526.4
141.1
06
295.6
79.2
66
353.5
94.7
26
411.5
110.3
86
469.4
125.8
46
527.4
141.4
07 i 296. 5
79.5
67
354.5
95.0
27
412.4
110.5
87
470.4
126.1
47
528.4
141.6
08
297.5
79.7
68
355. 4
95.3
28
413.4
110.8
88
471.4
126.4
48
529.3
141.9
09
298.4
80.0
69
356.4
95.5
29
414.4
111.0
89
472.3
126.6
49
530.3
142.1
10
299.4
80.2
70
357. 4
95.8
30
415.3
111.3
90
473. 3
126.9
50
531.3
142.4
311
300.4
80.5
371
358.3
96.0
431
416.3
111.6
491
474.3
127.1
551
532.2
142.6
12
301.3
80.8
72 [ 359.3
96.3
32
417.3
111.8
92
475.2
127.4
52
533.2
142.9
13
302.3
81.0
73 1 360.3
96.5
33
418.2
112.1
93
476.2
127.6
53
534.2
143.1
14
303.3
81.3
74
361.2
96.8
34
419.2
112.3
94
477.2
127.9
54
535.1
143.4
15
304.2
81.5
75
362.2
97.1
35
420.2
112.6
95
478.1
128.1
55
536.1
143.7
16
305.2
81.8
76
363.2
97.3
36
421.1
112.9
96
479.1
128.4
56
537.1
143.9
17
306.2
82.1
77 364. 1
97.6
37
422. 1 1 113. 1
97
480.1
128.6
57
538.0
144.2
18
307.1
82.3
78 365. 1
97.8
38
423. 1 113. 4
98
481.0
128.9
58
539.0
144.4
19
308.1
82.6
79 366. 1
98.1
39
424.0 113.6
99
482.0
129.1
59
540.0
144.7
20
309.1
82.8
80 367. 0
98.4
40
425,0 ill3. 9
500
483.0
129.4
60
540.9
144.9
321 310.0
83.1
381 368. 0
98.6
441
426. 0 114. 1
501
483.9
129.7
561
541.9
145.2
22
311.0
83.3
82 369. 0
98.9
42
426. 9 ! 114. 4
02
484.9
129.9
62
542.9
145.4
23
312.0
83.6
83 369. 9
99.1
43
427. 9 i 114. 7
03
485.9
130.2
63
543.8
145.7
24
312.9
83.9
84 370. 9
99.4
44
428. 8 j 114. 9
04
486.8
130.4
64
544.8
146.0
25
313.9
84.1
85 371. 9
99.6
45
429. 8 i 115. 2
05
487.8
130.7
65
545.8
146.2
26
314.9
84.4
86
372.8
99.9
46
430.8
115.4
06
488.8
131.0
66
546.7
146.5
27
315.8
84.6
87
373.8
100.2
47
431.7
115.7
07
489.7
131.2
67
547.7
146.7
28
316.8
84.9
88
374.8
100.4
48
432.7
116.0
08
490.7
131.5
68
548.7
147.0
29
317.8
85.1
89
375.7
100.7
49
433.7
116.2
09
491.7
131.7
69
549.6
147.2
30 ! 318. 7
85.4
90
376.7
100.9
50
434.6
116.5
10
492.6
132.0
70
550.6
147.5
331 1 319.7
85.7
391
377. 7
101.2
451
435.6
116.7
511
493.6
132.3
571
551.6
147.8
32 320. 7
85.9
92
378.6
101.5
52
436.6
117.0
12
494.5
132.5
72
552.5
148.0
33 1 321.6
86.2
93
379.6
101.7
53
437.5
117.3
13
495.5
132.8
73
553.5
148.3
34
322.6
86.5
94
380.6
102.0
54
438.5
117.5
14
496.5
133.0
74
554.4
148.5
35
323.6
86.7
95
381.5
102.2
55
439.5
117.8
15
497.4
133.3
75
555.4
148.8
36
324.5
87.0
96
382.5 1102.5
56
440.4
118.0
16
498. 4 j 133. 5
76
556.4
149.0
37
325.5
87.2
97
383.4 102.8
57
441.4
118.3
17
499. 4 i 133. 8
77
557.3
149.3
38
326.5
87.5
98
384.4 1103.0
58
442.4
118.5
18
500. 3 i 134. 0
78
558.3
149.5
39
327.4
87.7
99
385.4
103.3
59
443.3
118.8
19
501. 3 j 134. 3
79
559.3
149.8
40
328.4
88.0
400
386.3
103.5
60
444.3
119.1
20
502. 3 i 134. 6
80
560.2
150.1
341
329.4
88.3
401
387.3
103.8
461
445.3
119.3
521
503.2 134.8
581
561.2
150.3
42
330.3
88.5
02
388.3
104.1
62
446.2
119.6
22
504. 2 i 135. 1
82
562.2
150.6
43
331.3
88.8
03
389.2
104.3
63
447.2
119.8
23
505. 2 135. 3
83
563.1
150.8
44
332.3
89.0
04
390.2
104.6
64
448.2
120.1
24
506.1
135.6
84
564.1
151.1
45
333.2
89.3
05
391.2
104.8
65
449.1
120.4
25
507.1
135.9
85
565.1
151.4
46
334.2
89.6
06
392.1
105.1
66
450.1
120.6
26
508.1
136.1
86
566.0
151.6
47
335.2
89.8
07
393.1
105.3
67
451.1
120.9
27
509.0
136.4
87
567.0
151.9
48
336.1
90.1
08
394.1
105.6
68
452.0
121.1
28
510.0
136.6
88
568.0
152.2
49
337.1
90.3
09
395.0
105.9
69
453.0
121.4
29
511.0
136.9
89
568.9
152.4
50
338.1
90.6
10
396.0
106.1
70
454.0
121.7
30
511.9
137.2
90
569.9
152.7
351
339. 0
90.9
411
397. 0 106. 4
4V 1
454.9
121.9
531
512.9
137.4
591
570.9
153.0
52
340.0
91.1
12
397. 9 ' 106. 6
72
455.9
122.2
32
513.9
137.7
92
571.8
153.2
53
340.9
91.4
13
398. 9 : 106. 9
73
456.9
122.4
33
514.8
137.9
93
572.8
153.5
54
341.9
91.6
14
399. 9 : 107. 2
74
457.8
122.7
34
515.8
138.2
94
573.8
153.7
55
342.9
91.9
15
400. 8 i 107. 4
75
458.8
122.9
35
516.8
138.4
95
574.7
154.0
56
343.8
92.1
16
401. 8 1 107. 7
76
459.8
123.2
36
517.7
138.7
96
575.7
154.2
57
344.8
92.4
17
402.8 107.9
77
460.7
123.5
37
518.7
139.0
97
576.7
154.5
58
345.8
92.7
18
403.7 108.2
78
461.7
123.7
38
519.7
139.2
98
577.6
154.8
59
346.7
92.9
19
404. 7 i 108. 5
79
462. 7
124.0
39
520.6
139.5
99
578.6
155.0
60
347.7
93. 2
20
405. 7
108.7
80
463.6
124.2
40
521.6
139.7
600
579.5
155.3
Dist.
Dep.
Lav.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
75° (105°, 255°, 285°) .
Page 562] TABLE 2.
Difference of Latitude and Departure for 16° (164°, 196°, 344°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.6
16.8
121
116.3
33.4
181
174.0
49.9
241
231. 7
66.4
2
1.9
0.6
62
59.6
17.1
22
117.3
33.6
82
174.9
50.2
42
232. 6
66.7
3
2.9
0.8
63
60.6
17.4
23
118.2
33.9
83
175.9
50.4
43
233. 6
67.0
4
3.8
1.1
64
61.5
17.6
24
119.2
34.2
84
176.9
50.7
44
234.5
67.3
5
4.8
1.4
65
62.5
17.9
25
120.2
34.5
85
177.8
51.0
45
235.5
67.5
6
5.8
1.7
66
63.4
18.2
26
121.1
34.7
86
178.8
51.3
46
236. 5
67.8
7
6.7
1.9
67
64.4
18.5
27
122.1
35.0
87
179.8
51.5
47
237.4
68.1
8
7.7
2.2
68
65.4
18.7
28
123.0
35.3
88
180.7
51.8
48
238.4
68.4
9
8.7
2.5
69
66.3
19.0
29
124.0
35.6
89
181.7
52.1
49
239.4
68.6
10
9.6
2.8
70
67.3
19.3
30
125.0
35.8
90
182.6
52.4
50
240. 3
68.9
11
10.6
3.0
71
68.2
19.6
131
125. 9 36. 1
191 183. 6
52.6
251
241.3
69.2
12
11.5
3.3
72
69.2
19.8
32
126.9
36.4
92
184.6
52.9
52
242.2
69.5
13
12.5
3.6
73
70.2
20.1
33
127.8
36.7
93
185.5
53.2
53
243. 2
69.7
14
13.5
3.9
74
71.1
20.4
34
128.8
36.9
94
186.5
53.5
54
244.2
70.0
15
14.4
4.1
75
72.1
20.7
35
129.8
37.2
95
187.4
53.7
55
245.1
70.3
16
15.4
4.4
76
73.1
20.9
36
130.7
37.5
96
188.4
54.0
56
246.1
70.6
17
16.3
4.7
77
74.0
21.2
37
131. 7
37.8
97
189.4
54.3
57
247.0
70.8
18
17.3
5.0
78
75.0
21.5
38
132.7
38.0
98
190.3
54.6
58
248.0
71.1
19
18.3
5.2
79
75.9
21.8
39
133.6
38.3
99
191.3
54.9
59
249.0
71.4
20
19.2
5.5
80
76.9
22.1
40
134.6
38.6
200
192.3
55.1
60
249.9
71.7
21
20.2
5.8
81
77.9
22.3
141
135.5
38.9
201
193.2
55.4
261
250.9
71.9 •
22
21.1
6.1
82
78.8
22.6
42
136.5
39.1
02
194.2
55.7
62
251.9
72.2
23
22.1
6.3
83
79.8
22.9
43
137.5
39.4
03
195.1
56.0
63
252.8
72.5
24
23.1
6.6
84
80.7
23.2
44
138.4
39.7
04
196.1
56.2
64
253.8
72.8
25
24.0
6.9
85
81.7
23.4
45
139.4
40.0
05
197.1
56.5
65
254.7
73.0
26
25.0
7.2
86
82.7
23.7
46
140.3
40.2
06
198.0
56.8
66
255. 7
73.3
27
26.0
7.4
87
83.6
24.0
47
141.3
40.5
07
199.0
57.1
67
256.7
73.6
28
26.9
7.7
88
84.6
24.3
48
142.3
40.8
08
199.9
57.3
68
257.6
73.9
29
27.9
8.0
89
85.6
24.5
49
143.2
41.1
09
200.9
57.6
69
258.6
74.1
30
28.8
8.3
90
86.5
24.8
50
144.2
41.3
10
201.9
57.9
70
259.5
74.4
31
29.8
8.5
91
87.5
25.1
151
145.2
41.6
211
202.8
58.2
271
260.5
74.7
32
30.8
8.8
92
88.4
25.4
52
146.1
41.9
12
203.8
58.4
72
261.5
75.0
33
31.7
9.1
93
89.4
25.6
53
147.1
42.2
13
204.7
58.7
73
262.4
75.2
34
32.7
9.4
94
90.4
25.9
54
148.0
42.4
14
205.7
59.0
74
263.4
75.5
35
33.6
9.6
95
91.3
26.2
55
149.0
42.7
15
206.7
59.3
75
264.3
75.8
36
34.6
9.9
96
92.3
26.5
56
150.0
43.0
16
207.6
59.5
76
265.3
76.1
37
35.6
10.2
97
93.2
26.7
57
150.9
43.3
17
208.6
59.8
77
266.3
76.4
38
36.5
10.5
98
94.2
27.0
58
151.9
43.6
18
209.6
60.1
78
267.2
76.6
39
37.5
10.7
99
95.2
27.3
59
152.8
43.8
19
210. 5
60.4
79
268.2
76.9
40
38.5
11.0
100
96.1
27.6
60
153. 8
44.1
20
211.5
60.6
80
269.2
77.2
41
39.4
11.3
101
97.1
27.8
161
154.8
44.4
221
212.4
60.9
281
270.1
77.5
42
40.4
11.6
02
98.0
28.1
62
155.7
44.7
22
213.4
61.2
82
271.1
77.7
43
41.3
11.9
03
99.0
28.4
63
156.7
44.9
23
214.4
61.5
83
272.0
78.0
44
42.3
12.1
04
100.0
28.7
64
157. 6
45.2
24
215.3
61.7
84
273.0
78.3
45
43.3
12.4
05
100.9
28.9
65
158.6
45.5
25
216.3
62.0
85
274.0
78.6
46
44.2
12.7
06
101.9
29.2
66
159.6
45.8
26
217.2
62.3
86
274.9
78.8
47
45.2
13.0
07
102.9
29.5
67
160.5
46.0
27
218.2
62.6
87
275.9
79.1
48
46.1
13.2
08
103.8
29.8
68
161.5
46.3
28
219.2
62.8
88
276.8
79.4
49
47.1
13.5
09
104.8
30.0
69
1 62. 5
46.6
29
220.1
63.1
89
277.8
79.7
50
48.1
13.8
10
105.7
30.3
70
163.4
46.9
30
221.1
63.4
90
278.8
79.9
51
49.0
14.1
111
106.7
30.6
171
164.4
47.1
231
222.1
63.7
291
279.7
80.2
52
50.0
14.3
12
107.7
30.9
72
165.3
47.4
32
223.0
63.9
92
280.7
80.5
53
50.9
14.6
13
108.6
31.1
73
166.3
47.7
33
224.0
64.2
93
281.6
80.8
54
51.9
14.9
14
109.6
31.4
74
167.3
48.0
34
224.9
64.5
94
282.6
81.0
55
52.9
15.2
15
110.5
31.7
75
168.2
48.2
35
225.9
64.8
95
283.6
81.3
56
53.8
15.4
16
111.5
32.0
76
169.2
48.5
36
226.9
65.1
96
284.5
81.6
57
54.8
15.7
17
112.5
32.2
77
170.1
48.8
37
227.8
65.3
97
285.5
81.9
58
55.8
16.0
18
113.4
32.5
78
171.1
49.1
38
228.8
65.6
98
286.5
82.1
59
56.7
16.3
19
114.4
32.8
79
172.1
49.3
39
229.7
65.9
99
287.4
82.4
60
57.7
16.5
20
115.4
33.1
80
173.0
49.6
40
230.7
66.2
300
288.4
82.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
74° (106°, 254°, 286°).
TABLE 2. [Page 563
Difference of Latitude and^Departure for 16° (164°, 196°, 344°).
Dist.
Lat.
Dep.
Di3t. Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat. | Dep.
Dist.
Lat. Dep.
301
289.3
82.9
361
347.0
99.5
421
404.7
116.0
481
462.4
132.5
541
520.1
149.1
02
290.3
83.2
62
348.0
99.7
22
405.6
116.3
82
463.3
132.8
42
521.0
149.4
03
291.2
83.5
63
348.9
100.0
23
406.6
116.6
83
464.3
133.1
43
522.0
149.7
04
292.2
83.8
64
349.9
100.3
24 407. 6
116.8
84
465.2
133.4
44
523.0
150.0
05
293.2
84.0
65
350.8
100.6
25 408. 5
117.1
85
466.2
133.6
45
523.9
150.2
06
294.1
84.3
66
351.8
100.8
26 409.5
117.4
86
467.2
133.9
46
524.9
150.4
07
295. 1 84. 6
67
352.8
101.1
27 410. 4
117.7
87 468. 1
134.2
47
525.9
150.7
08
296.0
84.9
68
353.7
101.4
28
411.4
117.9
88 469. 1
134.5
48
526.8
151.0
09
297.0
85.1
69
354.7
101.7
29
412.4
118.2
89 470. 1
134.8
49
527.8
151.3
10
298.0
85.4
70 355. 6
101.9
30
413.3
118.5
90
471.0
135.0
50
528.7
151.6
311
298.9
85.7
371
356.6
102.2
431
414.3
118.8
491
472.0
135.3
551
529.7
151.9
12
299.9
86.0
72
357.6
102.5
32
415.2
119.0
92
472.9
135.6
52
530.6
152.2
13
300.9
86.2
73
358.5
102.8
33 j 416. 2
119.3
93
473.9
135.9
53
531.6
152.5
14
301.8
86.5
74
359.5
103.1
34 ! 417.2
119.6
94
474.9
136.2
54
532.6
152.8
15
302.8
86.8
75
360.4
103.3
35 ! 418. 1
119.9
95
475. 8
136.4
55
533.5
153.0
16
303.7
87.1
76
361.4
103.6
36 j 419. 1
120.1
96
476.8
136.7
56
534.5
153.2
17
304.7
87.3
77
362.4
103.9
37 420. 0
120.4
97
477.7
137.0
57
535.4
153.5
18
305.7
.87.6
78
363.3
104.2
38 421. 0
120.7
98
478.7
137.3
58
536.4
153.8
19
306.6
87.9
79
364.3
104.4
39
422.0
121.0
99
479.7
137.5
59
537.4
154.1
20
307.6
88.2
80
365.3
104.7
40
422.9
121.2
500
480.6
137.8
60
538.3
154.4
321
308.5
88.4
381
366.2
105.0
441 423. 9
121.5
501
481.6 138.1
561
539.3
154.7
09
309.5
88.7
82
367.2
105.3
42
424.9
121.8
02
482.6
138.3
62
540.3
154.9
23
310.5
89.0
83
368.1
105.5
43
425.8
122.1
03
483.5
138.6
63
541.2
155.2
24
311.4
89.3
84
369.1
105. 8
44
426.8
122. 3
04
484.5
138.9
64
542.2
155. 4
25
312.4
89.5
85
370.1
106.1
45
427.7
122.6
05
485.4
139.2
65
543.1
155. 7
26
313.3
89.8
86
371.0
106.4
46
428.7
122.9
06
486.4
139.4
66
544.1
156.0
27
314.3
90.1
87
372.0
106.6
47
429.7
123.2
07
487.3
139.7
67
545. 1
156. 3
28
315.3
90.4
88
372.9
106.9
48
430.6
123.4
08
488.3
140.0
68
546.0
156.6
29
316.2
90.6
89
373.9
107.2
49
431.6
123.7
09
489.3
140.3
69
547.0
156.9
30
317.2
90.9
90
374.9
107.5
50
432.6
124.0
10
490.2
140.6
70
547.9
157.1
331
318.2
91.2
391
375.8
107.7
451 433. 5
124.3
511
491.2
140.8
571 548. 9
157.3
3'7
319.1
91.5
92
376.8
108.0
52 434. 5
124.6
12
492.1
141.1
72
549.8
157.6
33
320.1
91.8
93
377.8
108.3
53 435. 4
124.8
13
493.1
141.4
73
550.8
157.9
34
321.0
92.0
94
378.7 108.6
54 436. 4
125. 1
14
494.1
141.7
74
551.8
158.2
35
322. 0
92.3
95
379.7 1108.8
55
437.4
125.4
15
495.0
141.9
75
552.7
158.4
36
323.0
92.6
96
380. 6 : 109. 1
56
438.3
125.7
16
496.0
142.2
76
553.7
158.7
37
323.9
92.9
97
381.6 109.4
57
439.3
125.9
17
496.9
142.5
77
554.6
159.0
38
324.9
93.1
98
382.6 109.7
58
440.2
126.2
18
497.9
142.8
78
555.6
159.3
39
325.8
93.4
99
383. 5 109. 9
59
441.2
126.5
19
498.9
143.0
79
556.5
159.5
40
326.8
93.7
400
384.5 110.2
60
442.2
126.8
20
499.8
143.3
80
557.5
159.8
341
32-7. 8
94.0
401
385.4 110.5
461
443.1
127.0
521
500.8
143.6
581
558.4
160.1
42
328.7
94.2
02
386.4 110.8
62
444.1
127.3
22
501.7
143.9
82 , 559.4
160.4
43
329.7
94.5
03
387.4 111.0
63
445.0
127.6
23
502. 7
144.1
83 560. 4
160.6
44
330.7
94.8
04
388. 3 111. 3
64
446.0
127.9
24
503.7
144.4
84 561. 3
161.0
45
331.6
95.1
05
389.3 111.6
65
447.0
128.1
25
504.6
144.7
85 562. 3
161.3
46
332.6
95.3
06
390.2 111.9
66
447.9
128.4
26
505.6
145.0
86
563.2
161.6
47
333.5
95.6
07
391.2
112.1
67
448.9
128.7
27
506.6
145.3
87
564.2
161.8
48
334.5
95.9
08
392.2
112.4
68
449.8
129.0
28
507.5
145.6
88
565.2
162.1
49
335. 5 96. 2
09
393.1
112.7
69
450.8
129.2
29
508.5
145.8
89
566.1
162.4
50
336.4 | 96.4
10
394.1
113.0
70
451.8
129.5
30
509.4
146.1
90
567.1
162.7
|3oT
337. 4 1 96. 7
411
395.1
113.3
471
452.7
129.8
531
510.4
146.4
591
568.1
162.9
52
338.3
97.0
12
396.0
113.5
72
453.7
130.1
32
511.4
146.7
92
569.0
163.2
53
339.3
97.3
13
397.0
113.8
73
454.7
130.3
33
512.3
146.9
93
570.0
163.5
54
340.3
97.5
14
397.9
114.1
74
455. 6
130.6
34
513.3
147.2
94
571.0
163.8
55
341.2
97.8
15
398.9
114.4
75
456.6
130.9
35
514.3
147.5
95
571.9
164.0
56
342.2
98.1
16
399.9
114.6
76
457.5
131.2
36
515.2
147.8
96
572.9
164.3
57
343.1
98.4
17
400.8
114.9
77
458.5
131.4
37
516.2
148.0
97
573.9
164.6
58
344.1
98.6
18
401.8
115.2
78
459.5
131.7
38
517.2
148.2
98
574.8
164.9
59
345.1
98.9
19
402.7
115.5
79
460.4
132.0
39
518.1
148.5
99
575.8
165.1
60
346.0
99.2
20
403.7
115.8
80
461.4
132.3
40
519.1
148.8
600
576.8
165.4
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
I 74° (106°, 254°, 286°).
Page 564] TABLE 2.
Difference of Latitude and Departure for 17° (163°, 197°, 343°). .
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.3
17.8
121
115.7
35.4
181
173.1
52.9
241
230.5
70.5
2
1.9
0.6
62
59.3
18.1
22
116.7
35.7
82
174.0
53.2
42
231.4
70.8
3
2.9
0.9
63
60.2
18.4
23
117.6
36.0
83
175.0
53.5
43
232.4
71.0
4
3.8
1.2
64
61.2
18.7
24
118.6
36.3
84
176.0
53.8
44
233.3
71.3
5
4.8
1.5
65
62.2
19.0
25
119.5
36.5
85
176.9
54.1
45
234.3
71.6
6
5.7
1.8
66
63.1
19.3
26
120.5
36.8
86
177.9
54.4
46
235.3
71.9
7
6.7
2.0
67
64.1
19.6
27
121.5
37.1
87
178.8
54.7
47
236.2
72.2
8
7.7
2.3
68
65.0
19.9
28
122.4
37.4
88
179.8
55.0
48
237.2
72.5
9
8.6
2.6
69
66.0
20.2
29
123.4
37.7
89
180.7
55.3
49
238.1
72.8
10
9.6
2.9
70
66.9
20.5
30
124.3
38.0
90
181.7
55.6
50
239.1
73.1
11
10.5
3.2
71
67.9
20.8
131
125.3
38.3
191
182.7
55.8
251
240.0
73.4
12
11.5
3.5
72
68.9
21.1
32
126.2
38.6
92
183.6
56.1
52
241.0
73.7
13-
12.4
3.8
73
69.8
21.3
33
127.2
38.9
93
184.6
56.4
53
241.9
74.0
14
13.4
4.1
74
70.8
21.6
34
128.1
39.2
94
185.5
56.7
54
242.9
74.3
15
14.3
4.4
75
71.7
21.9
35
129.1
39.5
95
186.5
57.0
55
243.9
74.6
16
15.3
4.7
76
72.7
22.2
36
130.1
39.8
96
187.4
57.3
56
244.8
74.8
17
16.3
5.0
77
73.6
22.5
37
131.0
40.1
97
188.4
57.6
57
245.8
75.1
18
17.2
5.3
78
74.6
22.8
38
132.0
40.3
98
189.3
57.9
58
246.7
75.4
19
18.2
5.6
79
75.5
23.1
39
132.9
40.6
99
190.3
58.2
59
247.7
75.7
20
19.1
5.8
80
76.5
23.4
40
133.9
40.9
200
191.3
58.5
60
248.6
76.0
21
20.1
6.1
81
77.5
23.7
141
134.8
41.2
201
192.2
58.8
261
249.6
76.3
22
21.0
6.4
82
78.4
24.0
42
135.8
41.5
02
193.2
59.1
62
250.6
76.6
23
22.0
6.7
83
79.4
24.3
43
136.8
41.8
03
194.1
59.4
63
251.5
76.9
24
23.0
7.0
84
80.3
24.6
44
137.7
42.1
04
195.1
59.6
64
252.5
77.2
25
23.9
7.3
85
81.3
24.9
45
138.7
42.4
05
196.0
59.9
65
253.4
77.5
26
24.9
7.6
86
82.2
25.1
46
139.6
42.7
06
197.0
60.2
66
254.4
77.8
27
25.8
7.9
87
83.2
25.4
47
140.6
43.0
07
198.0
60.5
67
255.3
78.1
28
26.8
8.2
88
84.2
25.7
48
141.5
43.3
08
198.9
60.8
68
256.3
78.4
29
27.7
8.5
89
85.1
26.0
49
142.5
43.6
09
199.9
61.1
69
257.2
78.6
30
28.7
8.8
90
86.1
26.3
50
143.4
43.9
10
200.8
61.4
70
258.2
78.9
31
29.6
9.1
91
87.0
26.6
151
144.4
44.1
211
201.8
61.7
271
259.2
79.2
32
30.6
9.4
92
88.0
26.9
52
145.4
44.4
12
202.7
62.0
72
260.1
79.5
33
31.6
9.6
93
88.9
27.2
53
146.3
44.7
13
203.7
62.3
73
261.1
79.8
34
32.5
9.9
94
89.9
27.5
54
147. 3
45.0
14
204.6
62.6
74
262.0
80.1
35
33.5
10.2
95
90.8
27.8
55
148.2
45.3
15
205.6
62.9
75
263.0
80.4
36
34.4
10.5
96
91.8
28.1
56
149.2
45.6
16
206.6
63.2
76
263.9
80.7
37
35.4
10.8
97
92.8
28.4
57
150.1
45.9
17
207.5
63.4
77
264.9
81.0
38
36.3
11.1
98
93.7
28.7
58
151.1
46.2
18
208.5
63.7
78
265.9
81.3
39
37.3
11.4
99
94.7
28.9
59
152.1
46.5
19
209.4
64.0
79
266.8
81.6
40
38.3
11.7
100
95.6
29.2
60
153.0
46.8
20
210.4
64.3
80
267.8
81.9
41
39.2
12.0
101
96.6
29.5
161
154.0
47.1
221
211.3
64.6
281
268.7
82.2
42
40.2
12.3
02
97.5
29.8
62
154.9
47.4
22
212.3
64.9
82
269.7
82.4
43
41.1
12.6
03
98.5
30.1
63
155.9
47.7
23
213.3
65.2
83
270.6
82.7
44
42.1
12.9
04
99.5
30.4
64
156.8
47.9
24
214.2
65.5
84
271.6
83.0
45
43.0
13.2
05
100.4
30.7
65
157.8
48.2
25
215.2
65.8
85
272.5
83.3
46
44.0
13.4
06
101.4
31.0
66
158.7
48.5
26
216.1
66.1
86
273.5
83.6
47
44.9
13.7
07
102.3
31.3
67
159.7
48.8
27
217.1
66.4
87
274.5
83.9
48
45.9
14.0
08
103.3
31.6
68
160.7
49.1
28
218.0
66.7
88
275.4
84.2
49
46.9
14.3
09
104.2
31.9
69
161.6
49.4
29
219.0
67.0
89
276.4
84.5
50
47.8
14.6
10
105.2
32.2
70
162.6
49.7
30
220.0
67.2
90
277.3
84.8
51
48.8
14.9
111
106.1
32.5
IV I
163.5
50.0
231
220.9
67.5
291
278.3
85.1
52
49.7
15.2
12
107.1
32.7
72
164.5
50.3
32
221.9
67.8
92
279.2
85.4
53
50.7
15.5
13
108.1
33.0
73
165.4
50.6
33
222.8
68.1
93
280.2
85.7
54
51.6
15.8
14
109.0
33.3
74
166.4
50.9
34
223.8
68.4
94
281.2
86.0
55
52.6
16.1
15
110.0
33.6
75
167.4
51.2
35
224.7
68.7
95
282.1
86.2
56
53.6
16.4
16
110.9
33.9
76
168.3
51.5
36
225.7
69.0
96
283.1
86.5
57
54.5
16.7
17
111.9
34.2
77
169.3
51.7
37
226.6
69.3
97
284.0
86.8
58
55.5
17.0
18
112.8
34.5
78
170.2
52.0
38
227.6
,69.6
98
285.0
87.1
59
56.4
17.2
19
113.8
34.8
79
171.2
52.3
39
228.6
69.9
99
285.9
87.4
60
57.4
17.5
20
114.8
35.1
80
172.1
52.6
40
229.5
70.2
300
286.9
87.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist,
Dep.
Lat.
Dist.
Dep.
Lat.
73° (107°, 253°, 287°).
TABLE 2. [Page 565
Difference of Latitude and Departure for 17° (163°, 197°, 343°).
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat. ! Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
301
287.8
88.0
361
345.2
105. 5
421
402.6
123.1
481
460.0
140.6
541
517.3
158.2
02
288.8
88.3
62
346.1
105.8
22
403.5
123.4
82
460.9
140.9
42
518.3
158.5
03
289.7
88.6
63
347.1
106.1
23
404.5
123. 7
83
461.9
141.2
43
519.2
158.8
04
290.7
88.9
64
348.1
106.4
24
405.4
124.0
84
462.8
141.5
44
520.2
159.1
05
291.6
89.2
65
349.0
106.7
25
406.4
124.3
85
463.8
141.8
45
521.2
159.3
06
292.6
89.5
66
350.0
107.0
26
407.3
124.6
86
464.7
142.1
46
522.1
159.6
07
293.5
89.8
67
350.9
107.3
27
408.3
124.8
87
465.7
142.3
47
523.1
159.9
08
294.5
90.1
68
351.9
107.6
28
409.3
125.1
88
466.7
142.6
48
524.0
160.2
09
295.5'
90.3
69
352.8
107.9
29
410.2
125. 4
89
467.6
142.9
49
525.0
160.5
10
296.4
90.6
70 353. 8
108.2
30
411.2
125.7
90
468.6
143.2
50
526.0
160.8
311
297.4 1 90.9
371 354. 8
108.5
431
412.1
126.0
491
469.5
143.5
551
526.9
161.1
12
298.3
91.2
72 355. 7
108.8
32
413.1
126.3
92
470.5
143. 8
52
527.9
161.4
13
299.3
91.5
73 1 356.7
109.1
33
414.0
126.6
93
471.4
144.1
53
528.8
161.7
14
300.2
91.8
74
357.6
109.4
34
415.0
126.9
94
472.4
144.4
54
529.8
162.0
15
301.2
92.1
75
358.6
109.6
35
416.0
127.2
95
473.4
144.7
55
530.8
162.3
16
302.2
92.4
76
359.5
109.9
36
416.9
127.5
96
474.3
145.0
56
531.7
162.6
17
303.1
92.7
77 360. 5
110.2
37
417.9
127.8
97
475.3
145.3
57
532.7
162.9
18
304.1
93.0
78
361.4
110.5
38
418.8
128.1
98
476.2
145.6
58
533.6
163.2
19
305.0
93.3
79
362.4
110.8
39
419.8
128.4
99
477.2
145. 9
59
534.6
163.5
20
306.0
93.6
80
363.4
111.1
40
420. 7'
128.6
500
478.1
146.2
60 535. 5
163.8
321
306.9
93.9
381 i 364.3
111.4
441
421. 7 i 128. 9
501
479.1
146.5
561
536.5
164.1
22
307.9
94.1
82 365. 3
111.7
42
422. 7 1 129. 2
02
480.1
146.8
62
537.5
164.4
23
308.8
94.4
83 366. 2
112.0
43
423. 6 1 129. 5
03
481.0
147.1
63
538.4
164.6
24
309.8
94.7
84
367.2
112.3
44
424.6
129.8
04
482.0
147.4
64
539.4
164.8
25
310.8
95.0
85
368.1
112.6
45
425.5
130.1
05
482.9
147.7
65
540.3
165.1
26
311.7
95.3
86
369.1
112.9
46
426.5
130.4
06
483.9
148.0
66
541.3
165.4
27
312.7
95.6
87
370.1
113.2
47
427.4
130.7
07
484.8
148.3
67
542.2
165.7
28
313.6
95.9
88
371.0
113.4
48
428.4
131.0
08
485.8
148.6
68
543.2
166.0
29
314.6
96.2
89
372.0
113.7
49
429.3
131.3
09
486.7
148.9
69
544.1
166.4
30
315.5
96.5
90
372.9
114.0
50
430.3
131.6
10
487.7
149.1
70
545.1
166.7
331
316.5
96.8
391
373.9
114.3
451
431.3
131.9
511
488.7
149.4
571 I 546. 1
167. 0
32
317.5
97.1
92
374.8
114.6
52
432.2
132.2
12
489.6
149.7
72
547.0
167.2
33
318.4
97.4
93
375.8
114.9
53
433.2
132.4
13
490.6
150.0
73
548.0
167.5
34
319.4
97.7
94
376.7
115.2
54
434.1
132.7
14
491.5
150.2
74
548.9
167.8
35
320.3
97.9
95
377. 7
115.5
55
435.1
133.0
15
492.5
150.5
75
549.9
168.1
36
321.3
98.2
96
378.7
115.8
56
436.0
133.3
16
493.4
150.8
76
550.8
168.4
37
322.2
98.5
97
379.6
116.1
57
437.0
133.6
17
494.4
151.1
77
551.8
168.7
38
323.2
98.8
98
380.6
116.4
58
438.0
133. 9
18
495.3
151. 4
78
552.7
169.0
39
324. 2 99. 1
99
381.5
116.7
59
438.9
134.2
19
496.3
151.7
79
553.7
169.3
40
325.1 j 99.4
400
382.5
117.0
60
439.9
134.5
20
497.2
152.0
80
554.6
169.6
341
326. 1 99. 7
401
383.4
117.2
461
440.8
134.8
521
498.2
152.3
581
555. 6 169. 9
42
327.0 100.0
02
384.4
117.5
62
441.8
135.1
22
499.2
152.6
82
556. 5 170. 2
43
328.0
100.3
03
385.4 117.8
63
442.7
135.4
23
500.1
152.9
83
557.5
170.5
44
328.9
100.6
04
386.3
118.1
64
443.7
135.7
24
501.1
153.2
84
558.4
170.8
45
329.9
100.9
05
387.3
118.4
65
444.6
136.0
25
502.0
153.5
85
559.4
171.1
46
330.8
101.2
06
388.2
118.7
66 445. 6
136.2
26
503.0
153.8
86
560.4
171.3
47
331.8
101.5
07
389.2
119.0
67 446. 6
136.5
27
503.9
154.1
87
561.3
171.6
48
332.8
101.8
08
390.1
119.3
68 447. 5
136.8
28
504.9
154.4
88
562.3
171.9
49
333.7
102.0
09 391.1 119.6
69
448.5
137.1
29
505.9
154.7
89
563.2
172.2
50
334.7
102.3
10 392. 0
119.9
70
449.4
137.4
30
506.8
155.0
90
564.2
172.5
351
335.6
102.6
411
393.0
120.2
471
450.4
137.7
531
507.8
155.3
591
565.1
172.8
52
336.6
102.9
12
394.0
120.5
72
451.3
138.0
32
508.7
155.6
92
566.1
173.1
53
337.5
103.2
•13
394.9
120.8
73
452.3
138.3
33
509.7
155.9
93
567.1
173.4
54
338.5
103.5
14
395.9
121.0
74 453. 3
138.6
34
510.6
156. 2
94
568.0
173.7
55
339.5
103.8
15
396.8
121.3
75
454.2
138.9
35
511.6
156. 5
95
569.0
174.0
56
340.4
104.1
16
397.8
121.6
76
455.2
139.2
36
512.6
156. 8
96
569.9
174.3
57
341.4
104.4
17
398.7
121.9
77
456.1
139.5
37
513.5
157.1
97
570.9
174.6
58
342.3
104.7
18
399.7
122.2
78
457.1
139.8
38
514.5
157.3
98
571.8
174.9
59
343.3
105.0
19
400.7
122.5
79
458.0
140.0
39
515.4
157.6
99
572.8
175.2
60
344.2
105.3
20
401.6
122.8
80
459.0
140.3
40
516.4
157.9
600
573.8
175.4
Dist.
Dep.
Lat.
Dist. | Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
73° (107°, 253°, 287°).
Page 566] TABLE 2.
Difference of Latitude and Departure for 18° (162°, 198°, 342°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.0
18.9
121
115.1
37.4
181
172.1
55.9
241
229.2
74.5
2
1.9
0.6
62
59.0
19.2
22
116.0
37.7
82
173.1
56.2
42
230^2
74.8
3
2.9
0.9
63
59.9
19.5
23
117.0
38.0
83
174.0
56.6
43
231.1
75.1
4
3.8
1.2
64
60.9
19.8
24
117.9
38.3
84
175.0
56.9
44
232.1
75.4
5
4.8
1.5
65
61.8
20.1
25
118.9
38.6
85
175.9
57.2
45
233.0
75.7
6
5.7
1.9
66
62.8
20.4
26
119.8
38.9
86
176.9
57.5
46
234.0
76.0
7
6.7
2.2
67
63.7
20.7
27
120.8
39.2
87
177.8
57.8
47
234.9
76.3
8
7.6
2.5
68
64.7
21.0
28
121. 7
39.6
88
178.8
58.1
48
235.9
76.6
9
8.6
2.8
69
65.6
21.3
29
122.7
39.9
89
179.7
58.4
49
286.8
76.9
10
9.5
3.1
70
66.6
21.6
30
123.6
40.2
90
180.7
58.7
50
237.8
77.3
11
10.5
3.4
71
67.5
21.9
131
124.6
40.5
191
181.7
59.0
251
238.7
77.6
12
11.4
3.7
72
68.5
22.2
32
125.5
40.8
92
182.6
59.3
52
239. 7
77.9
13
12.4
4.0
73
69.4
22.6
33
126.5
41.1
93
183.6
59.6
53
240.6
78.2
14
13.3
4.3
74
70.4
22.9
34
127.4
41.4
94
184.5
59.9
54
241.6
78.5
15
14.3
4.6
75
71.3
23.2
35
128.4
41.7
95
185.5
60.3
55
242.5
78.8
16
15.2
4.9
76
72.3
23.5
36
129.3
42.0
96
186.4
60.6
56
243.5
79.1
17
16.2
5.3
77
73.2
23.8
37
130.3
42.3
97
187.4
60.9
57
244.4
79.4
18
17.1
5.6
78
74.2
24.1
38
131.2
42.6
98
188. 3
61.2
58
245.4
79.7
19
18.1
5.9
79
75.1
24.4
39
132.2
43.0
99
189.3
61.5
59
246.3
80.0
20
19. ,0
6.2
80
76.1
24.7
40
133. 1
43.3
200
190.2
61.8
60
247.3
80.3
21
20.0
6.5
81
77.0
25.0
141
134.1
43.6
201
191.2
62.1
261
248.2
80.7
22
20.9
6.8
82
78.0
25.3
42
135.1
43.9
02
192.1
62.4
62
249.2
81.0
23
21.9
7.1
83
78.9
25.6
43
136.0
44.2
03
193.1
62.7
63
250.1
81.3
24
22.8
7.4
84
79.9
26.0
44
137.0
44.5
04
194.0
63.0
64
251.1
81.6
25
23.8
7.7
85
80.8
26.3
45
137.9
44.8
05
195.0
63.3
65
252.0
81.9
26
24.7
8.0
86
81.8
26.6
46
138.9
45.1
06
195.9
63.7
66
253.0
82.2
27
25.7
8.3
87
82.7
26.9
47
139.8
45.4
07
196.9
64.0
67
253.9
82.5
28
26.6
8.7
88
83.7
27.2
48
140.8
45.7
08
197.8
64.3
68
254.9
82.8
29
27.6
9.0
89
84.6
27.5
49
141.7
46.0
09
198.8
64.6
69
255.8
83.1
30
28.5
9.3
90
85.6
27.8
50
142.7
46.4
10
199.7
64.9
70
256.8
83.4
31
29.5
9.6
91
86.5
28.1
151
143.6
46.7
211
200.7
65.2
271
257.7
83.7
32
30.4
9.9
92
87.5
28.4
52
144.6
47.0
12
201.6
65.5
72
258.7
84.1
33
31.4
10.2
93
88.4
28.7
53
145.5
47.3
13
202.6
65.8
73
259.6
84.4
34
32.3
10.5
94
89.4
29.0
54
146.5
47.6
14
203.5
66.1
74
260.6
84.7
35
33.3
10.8
95
90.4
29.4
55
147.4
47.9
15
204.5
66.4
75
261.5
85.0
36
34.2
11.1
96
91.3
29.7
56
148.4
48.2
16
205.4
66.7
76
262.5
85.3
37
35.2
11.4
97
92.3
30.0
57
149.3
48.5
17
206.4
67.1
77
263. 4
85.6
38
36.1
11.7
98
93.2
30.3
58
150.3
48.8
18
207.3
67.4
78
264.4
85.9
39
37.1
12.1
99
94.2
30.6
59
151.2
49.1
19
208. 3
67.7
79
265.3
86.2
40
38.0
12.4
100
95.1
30.9
60
152.2
49.4
20
209.2
68.0
80
266.3
86.5
41
39.0
12.7
101
96.1
31.2
161
153.1
49.8
221
210.2
68.3
281
267.2
86.8
42
39.9
13.0
02
97.0
31.5
62
154.1
50.1
22
211.1
68.6
82
268.2
87.1
43
40.9
13.3
03
98.0
31.8
63
155.0
50.4
23
212. 1
68.9
83
269.1
87.5
44
41.8
13.6
04
98.9
32.1
64
156.0
50.7
24
213.0
69.2
84
270.1
87.8
45
42.8
13/9
05
99.9
32.4
65
156.9
51.0
25
214.0
69.5
85
271.1
88.1
46
43.7
14.2
06
100.8
32.8
66
157.9
51.3
26
214.9
69.8
86
272.0
88.4
47
44.7
14.5
07
101.8
33.1
67
158.8
51.6
27
215.9
70.1
87
273.0
88.7
48
45.7
14.8
08
102.7
33.4
68
159.8
51.9
28
216.8
70.5
88
273.9
89.0
49
46.6
15.1
09
103.7
33.7
69
160.7
52.2
29
217.8
70.8
89
274.9
89.3
50
47.6
15.5
10
104.6
34.0
70
161.7
52.5
30
218.7
71.1
90
275.8
89.6
51
48.5
15.8
111
105.6
34.3
171
162.6
52.8
231
219.7
71.4
291
276.8
89.9
52
49.5
16.1
12
106.5
34.6
72
163.6
53.2
32
220.6
71.7
92
277.7
90.2
53
50.4
16.4
13
107.5
34.9
73
164.5
53.5
33
221.6
72.0
93
278.7
90.5
54
51.4
16.7
14
108.4
35.2
74
165.5
53.8
34
222.5
72.3
94
279.6
90.9
55
52.3
17.0
15
109.4
35.5
75
166.4
54.1
35
223.5
72.6
95
280.6
91.2
56
53.3
17.3
16
110.3
35.8
76
167.4
54.4
36
224.4
72.9
96
281.5
91.5
57
54.2
17.6
17
111.3
36.2
77
168.3
54.7
37
225.4
73.2
97
282.5
91.8
58
55.2
17.9
18
112.2
36.5
78
169.3
55.0
38
226.4
73.5
98
283.4
92.1
59
56.1
18.2
19
113.2
36.8
79
170.2
55.3
39
227.3
73.9
99
284.4
92.4
60
57.1
18.5
20
114.1
37.1
80
171.2
55.6
40
228.3
74.2
300
285.3
92.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
72° (108°, 252°, 288°).
TABLE 2. [Page 567
Difference of Latitude and Departure for 18° (162°, 198°, 342°).
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist. , lat. Dep.
Dist.
Lat. , Dep.
Dist. Lat.
Dep.
301
286.3
93.0
361 j 343.3
111.6
421 i 400.4 130.1
481
457.5
148.6
541 j 514.5
167.2
02
287. 2
93.3
62 344. 3
111.9
22 401.4 i 130. 4
82
458. 5
148.9
42
515.5
167.5
03
288.2
93.7
63 ! 345. 2
112.2
23 402. 3 i 130. 7
83
459.4
149.3
43
516.4
167.9
04
289.1
94.0
64 346.2
112.5
24 403.3 1131.0
84
460.4
149.6
44 517.4
168.2
05
290.1
94.3
65 347. 1
112.8
25 404.2 1131.3
85
461.3
149.9
45
518.3
168.5
06
291.0
94.6
66 348. 1
113.1
26
405.2 '131.7
86
462.3
150.2
46
519.3
168.8
07
292.0
94.9
67 i 349.0
113.4
27
406.1
132.0
87
463.2
150.5
47
520.2
169.1
08
292.9
95.2
68
350.0
113.7
28
407.1
132.3
88
464.2 150.8
48
521.2
169.4
09
293.9
95.5
69
350.9
114.0
29
408.0 132.6
89
465. 1 151. 1
49
522.1
169.7
10
294.8
95.8
70
351.9
114.3
30
409.0 132.9
90
466.1 151.4
50
523.1
170.0
311
295.8
96.1
371
352.9
114.7
431
409.9
133.2
491
467.0
151. 7
551
524.0
170. 3
12
296.7
96.4
72
353.8
115.0
32
410.9
133.5
92
468.0
152.0
52
525. 0
170. 6
13
297.7
96.7
73
354.8
115.3
33
411.8
133.8
93
468.9
152. 3
53
525. 9
170.9
14
298.6
97.0
74
355.7
115.6
34
412.8
134.1
94
469.8
152.6
54
526.9
171.2
15
299.6
97.4
75
356.7
115.9
35
413.7
134.4
95
470.8
153.0
55
527.8
171.5
16
300.5
97.7
76
357.6
116.2
36
414.7
134.7
96
471.7
153.3
56
528.8
171.8
17
301.5
98.0
77
358.6
116.5
37
415.6
135.1
97
472.7
153. 6
57
529.7
172.1
18
302.4
98.3
78
359.5
116.8
38
416.6 135.4
98
473.6
153.9
58
530.7
172.4
19
303.4
98.6
79
360.5
117.1
39
417. 5 ; 135. 7
99
474.6
154.2
59
531.6
172.7
20
304.3
98.9
80
361.4
117.4-
40
418.5 ,136.0
500
475.5
154.5
60
532.6
173.0
321
305.3
99.2
381
362.4
117.7
441
419.4 136.3
501
476. 5
154.8
561
533.5
173.3
22
306.2
99.5
82
363.3
118.1
42
420. 4 ! 136. 6
02
477.4
155.1
62
534.5
173.6
23
307.2
99.8
83
364.3
118.4
43
421.3
136.9
03
478.4
155.4
63
535.4
173.9
24
308.2
100.1
84
365.2
118.7
44
422.3
137.2
04
479.3
155. 7
64
536.4
174.2
25
309.1
100.4
85
366.2
119.0
45
423.2
137.5
05
480.3
156. 1
65
537.3
174.6
26
310.1
100.7
86
367.1
119.3
46
424.2
137.8
Q6
481.2
156.4
66
538.3
174.9
27
311.0
101.1
87
368.1
119.6
47
425. 1
138.1
07
482.2
156. 7
67
539.2
175. 2
28
312.0
101.4
88
369.0
119.9
48
426.1
138.4
08
483.2
157.0
68
540.2
175.5
29
312.9
101.7
89
370.0
120.2
49
427.0
138.8
09
484.1
157. 3
69
541. 1
175.8
30
313.9
102.0
90
370.9
120.5
50
428.0
139.1
10
485.1
157. 6
70
542.1
176.1
331
314.8
102.3
391
371.9
120.8
451
428.9
139.4
511
486.0
157.9
571
543.0 i 176.4
32
315.8
102.6
92
372.8 121.1
52
429.9
139.7
12
487.0
158.2
72
544.0 176.7
33
316.7
102.9
93
373.8 121.5
53
430.8
140.0
13
487.9
158.5
73
544.9 177.0
34
317.7
103.2
94
374.7 121.8
54
431.8
140.3
14
488.9
158. 8
74
545. 9 177. 3
35
318.6
103.5
95
375.7 122.1
55
432.7
140.6
15
489.8
159.1
75
546. 8 177. 6
36
319.6
103.8
96
376.6 122.4
56
433.7
140.9
16
490.8
159.4
76
547.8 178.0
37
320.5
104.1
97
377. 6 122. 7
57
434.6
141.2
17
491.7
159. 7
77
548. 7 178. 3
38
321.5
104.5
98
378. 5 123. 0
58
435.6
141.5
18
492.7
160.0
78
549. 7 178. 6
39
322. 4
104.8
99
379.5 123.3
59
436.5
141.8
19
493.6
160.3
79
550. 6 178. 9
40
323.4
105.1
400
380. 4 123. 6
60
437. 5
142.2
20
494.6
160.7
80
551. 6 179. 2
341
324.3
105.4
401
381.4 123.9
461
438.4
142.5
521
495.5
161.0
581
552. 5 179. 5
42
325.3
105. 7
02
382.3 ;124.2
62
439.4
142.8
22
496.5
161.3
82
553. 5 179. 8
43
326.2
106.0
03
383.3 124.5
63 440. 3
143.1
23
497.4
161.6
83
554. 4 180. 1
44
327.2
106.3
04
384. 2
124.9
64 441.3
143. 4
24
498.4
161.9
84
555. 4
180.4
45 | 328.1
106.6
05
385.2
125.2
65
442.2
143.7
25
499.3
162.2
85
556.3
180.7
46 1 329. 1
106.9
06
386.1
125. 5
66
443.2
144.0
26
500.3
162.5
86
557. 3
181.1
47
330.0
107.2
07
387. 1 125. 8
67 444.2
144.3
27
501.2
162.9
87
558. 2
181.4
48
331.0
107.5
08
388. 0 126. 1
68
445.1
144.6
28
502.2
163.2
88
559.2
181.7
49
331.9
107.9
09
389. 0 126. 4
69
446.1
144.9
29 503. 1
163.5
89
560.1
182.0
50
332. 9 1 108. 2
10
389.9 126.7
70
447.0
145. 2
30 504. 1
163.8
90
561.1
182.3
351
333.8
108.5
411
390. 9 i 127. 0
471
448.0
145. 6
531 505. 0
164.1
591
562.0
182.7
52
334.8
108.8
12
391.8 127.3
72
448.9
145. 9
32 I 506.0
164.4
92
563.0
J83.0
53
335.7
109.1
13
392.8
127.6
73
449.9
146.2
33 I 506.9
164.7
93
563.9
183.3
54
336.7
109.4
14
393.7
127.9
74
450.8
146.5
34 507. 9
165.0
94
564.9
183.6
55
337.6
109.7
15
394.7
128. 3
75
451.8
146.8
35 1 508. 8
165.3
95
565.8
183.9
56
338.6
110.0
16
395.6
128.6
76
452. 7
147.1
36 509. 8
165.6
96
566.8
184.2
57
339.5
110.3
17
396.6
128.9
77
453. 7
147.4
37 510. 7
165.9
97
567.7
184.5
58
340.5
110.6
18
397.5
129.2
78
454. 6
147.7
38 511. 7
166.2
98
568.7
184.8
59
341.4
110.9
19
398.5
129.5
79
455. 6
148.0
39 512. 6
166.5
99
569.6
185.1
60
342.4
111.3
20
399.5
129.8
80
456. 5
148.3
40
513.6
166.9
600
570.6
185.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
72° (108, 252°, 288°).
Page 568] TABLE 2.
Difference of Latitude and Departure for 19° (161°, 199°, 341°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.7
19.9
121
114.4
39.4
181
171.1
58.9
241
227.9
78.5
2
1.9
0.7
62
58.6
20.2
22
115.4
39.7
82
172.1
59.3
42
228.8
78.8
3
2.8
1.0
63
59.6
20.5
23
116.3
40.0
83
173.0
59.6
43
229.8
79.1
4
3.8
1.3
64
60.5
20.8
24
117.2
40.4
84
174.0
59.9
44
230.7
79.4
5
4.7
1.6
65
61.5
21.2
25
118.2
40.7
85
174.9
60.2
45
231.7
79.8
6
5.7
2.0
66
62.4
21.5
26
119.1
41.0
86
175.9
60.6
46
232.6
80.1
7
6.6
2.3
67
63.3
21.8
27
120.1
41.3
87
176.8
60.9
47
233.5
80.4
8
7.6
2.6
68
64.3
22.1
28
121.0
41.7
88
177.8
61.2
48
234.5
80.7
9
8.5
2.9
69
65.2
22.5
29
122.0
42.0
89
178.7
61.5
49
235.4
81.1
10
9.5
3.3
70
66.2
22.8
30
122.9
42.3
90
179.6
61.9
50
236. 4
81.4
11
10.4
3.6
71
67.1
23.1
131
123.9
42.6
191
180.6
62.2
251
237.3
81.7
12
11.3
3.9
72
68.1
23.4
32
124.8
43.0
92
181.5
62.5
52
238.3
82.0
13
12.3
4.2
73
69.0
23.8
33
125.8
43.3
93
182.5
62.8
53
239.2
82.4
14
13.2
4.6
74
70.0
24.1
34
126.7
43.6
94
183.4
63.2
54
240.2
82.7
15
14.2
4.9
75
70.9
24.4
35
127.6
44.0
95
184.4
63.5
55
241.1
83.0
16
15.1
5.2
76
71.9
24.7
36
128.6
44.3
96
185.3
63.8
56
242.1
83.3
17
16.1
5.5
77
72.8
25.1
37
129.5
44.6
97
186.3
64.1
57
243.0
83.7
18
17.0
5.9
78
73.8
25.4
38
130.5
44.9
98
187.2
64.5
58
243.9 ! 84.0
19
18.0
6.2
79
74.7
25.7
39
131.4
45.3
99
188.2
64.8
59
244.9
84.3
20
18.9
6.5
80
75.6
26.0
40
132.4
45.6
200
189.1
65.1
60
245.8
84.6
21
19.9
6.8
81
76.6
26.4
141
133.3
45.9
201
190.0
65.4
261
246.8
85.0
22
20.8
7.2
82
77.5
26.7
42
134.3
46.2
02
191.0
65.8
62
247.7
85.3
23
21.7
7.5
83
78.5
27.0
43
135.2
46.6
03
191.9
66.1
63
248.7
85.6
24
22.7
7.8
84
79.4
27.3
44
136.2
46.9
04
192.9
66.4
64
249.6
86.0
25
23.6
8.1
85
80.4
27.7
45
137.1
47.2
05
193.8
66.7
65
250.6
86.3
26
24.6
8.5
86
81.3
28.0
46
138.0
47.5
06
194.8
67.1
66
251.5
86.6
27
25.5
8.8
87
82.3
28.3
47
139.0
47.9
07
195.7
67.4
67
252.5
86.9
28
26.5
9.1
88'
83.2
28.7
48
139.9
48.2
08
196.7
67.7
68
253.4
87.3
29
27.4
9.4
89
84.2
29.0
49
140.9
48.5
09
197.6
68.0
69
254.3
87.6
30
28.4
9.8
90
85.1
29.3
50
141.8
48.8
10
198.6
68.4
70
255.3
87.9
31
29.3
10.1
91
86.0
29.6
151
142.8
49.2
211
199.5
68.7
271
256.2
88.2
32
30.3
10.4
92
87.0
30.0
52
143.7
49.5
12
200.4
69.0
72
257.2
88.6
33
31.2
10.7
93
87.9
30.3
53
144.7
49.8
13
201.4
69.3
73
258.1
88.9
34
32.1
11.1
94
88.9
30.6
54
145.6
50.1
14
202.3
69.7
74
259.1
89.2
35
33.1
11.4
95
89.8
30.9
55
146.6
50.5
15
203.3
70.0
75
260.0
89.5
36
34.0
11.7
96
90.8
31.3
56
147.5
50.8
16
204.2
70.3
76
261.0
89.9
37
35.0
12.0
97
91.7
31.6
57
148.4
51.1
17
205.2
70.6
77
261.9
90.2
38
35.9
12.4
98
92.7
31.9
58
149.4
51.4
18
206.1
71.0
78
262.9
90.5
39
36.9
12.7
99
93.6
32.2
59
150.3
51.8
19
207.1
71.3
79
263.8
90.8
40
37.8
13.0
100
94.6
32.6
60
151.3
52.1
20
208.0
71.6
80
264.7
91.2
41
38.8
13.3
101
95.5
32.9
161
152. 2
52.4
221
209.0
72.0
281
265.7
91.5
42
39.7
13.7
02
96.4
33.2
62
153.2
52.7
22
209.9
72.3
82
266.6
91.8
43
40.7
14.0
03
97.4
33.5
63
154.1
53.1
23
210.9
72.6
83
267.6
92.1
44
41.6
14.3
04
98.3
33.9
64
155.1
53.4
24
211.8
72.9
84
268.5
92.5
45
42.5
14.7
05
99.3
34.2
65
156.0
53.7
25
212.7
73.3
85
269.5
92.8
46
43.5
15.0
06
100.2
34.5
66
157.0
54.0
26
213.7
73.6
86
270.4
93.1
47
44.4
15.3
07
101.2
34.8
67
157.9
54.4
27
214.6
73.9
87
271.4
93.4
48
45.4
15.6
08
102.1
35.2
68
158.8
54.7
28
215.6
74.2
88
272.3
93.8
49
46.3
16.0
09
103.1
35.5
69
159. 8
55.0
29
216.5
74.6
89
273.3
94.1
50
47.3
16.3
10
104.0
35.8
70
160.7
55.3
30
217.5
74.9
90
274.2
94.4
51
48.2
16.6
111
105.0
36.1
171
161.7
55.7
231
218.4
75.2
291
275.1
94.7
52
49.2
16.9
12
105.9
36.5
72
162.6
56.0
32
219.4
75.5
92
276.1
95.1
53
50.1
17.3
13
106.8
36.8
73
163.6
56.3
33
220.3
75.9
93
277.0
95.4
54
51.1
17.6
14
107.8
37.1
74
164.5
56.6
34
221.3
76.2
94
278.0
95.7
55
52.0
17.9
15
108.7
37.4
75
165.5
57.0
35
222.2
76.5
95
278.9
96.0
56
52.9
18.2
16
109.7
37.8
76
166.4
57.3
36
223.1
76.8
96
279.9
96.4
57
53.9
18.6
17
110.6
38.1
77
167.4
57.6
37
224.1
77.2
97
280.8
96.7
58
54.8
18.9
18
111.6
38.4
78
168.3
58.0
38
225.0
77.5
98
281.8
97.0
59
55.8
19.2
19
112.5
38.7
79
169.2
58.3
39
226.0
77.8
99
282.7
97.3
60
56.7
19.5
20
113.5
39.1
80
170.2
58.6
40
226.9
78.1
300
283.7
97.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
71° (109°, 251°, 289°).
TABLE 2. [Page 569
Difference of Latitude and Departure for 19° (161°, 199°, 341°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
284.6
98.0
361
341.3
117.5
421
398.1
137.0
481
454.8
156.6
541
511.5
176.1
02
285.5
98.3
62
342.3
117.8
22
399.0
137.4
82
455.7
156.9
42
512.4
176.4
03
286.5
98.6
63
343.2
118.2
23
400.0
137.7
83
456.7
157.2
43
513.4
176.8
04
287.4
99.0
64
344.2
118.5
24
400.9
138.0
84
457.6
157.6
44
514.3
177.1
05
288.4
99.3
65
345.1
118.8
25
401.8
138.4
85
458.6
157.9
45
515.3
177.4
06
289.3
99.6
66
346.1
119.1
26
402.8
138.7
86
459.5
158.2
46
516.2
177.7
07
290.3
99.9
67
347.0
119.5
27
403.7
139.0
87
460.5
158.5
47
517.2
178.1
08
291.2
100.3
68-
348.0
119.8
28
404.7
139.3
88
461.4
158.9
48
518.1
178.4
09
292.2
100.6
69
348.9
120.1
29
405.6
139.7
89
462.4
159.2
49
519.1
178.7
10
293.1
100.9
70
349.8
120.4
30
406.6
140.0
90
463.3
159.5
50
520.0
179.0
311
294.1
101.2
371
350.8
120.8
431
407.5
140.3
491
464.3
159.8
551
521.0
179.4
12
295.0
101.6
72
351.7
121.1
32
408.5
140.6
92
465.2
160.2
52
521.9
179.7
13
295.9
101.9
73
352. 7
121.4
33
409.4
141.0
93
466.1
160.5
53
522.8
180.0
14
296.9
102.2
74
353.6
121.7
34
410.4
141.3
94
467.1
160.8
54
523.8
180.3
15
297. 8'
102.5
75
354.6
122.1
35
411.3
141.6
95
468.0
161.1
55
524.7
180.7
16
298.8
102.9
76
355.5
122.4
36
412.2
141.9
96
469.0
161.5
56
525.7
181.0
17
299.7
103.2
77
356.5
122.7
37
413.2
142.3
97
469.9
161.8
57
526.6
181.3
18
300.7
103.5
78
357.4
123.0
38
414.1
142.6
98
470.9
162.1
58
527.6
181.6
19
301.6
103.8
79
358.4
123.4
39
415.1
142.9
99
471.8
162.4
59
528.5
182.0
20
302.6
104.2
80
359.3
123.7
40
416.0
143.2
500
472.8
162.8
60
529. 5
182.3
321
303.5
104.5
381
360.2
124.0
441
417.0
143.6
501
473.7
163.1
561
530.4
182.6
22
304.5
104.8
82
361.2
124.4
42
417.9
143.9
02
474.7
163.4
62
531.4
182.9
23
305.4
105.1
83
362.1
124.7
43
418.9
144.2
03
475.6
163.7
63
532.3
183.3
24
306.3
105.5
84
363.1
125.0
44
419.8
144.5
04
476.5
164.1
64
533.2
183.6
25
307.3
105.8
85
364.0
125.3
45
420.8
144.9
05
477.5
164.4
65
534.2
183.9
26
308.2
106.1
86
365.0
125.7
46
421.7
145.2
06
478.4
164.7
66
535.1
184.2
27
309.2
106.4
87
365.9
126.0
47
422.6
145.5
07
479.4
165.0
67
536.1
184.6
28
310.1
106.8
88
366.9
126.3
48
423.6
145.8
08
480.3
165.4
68
537.0
184.9
29
311.1
107.1
89
367.8
126.6
49
424.5
146.2
09
481.2
165.7
69
538.0
185.2
30
312.0
107.4
90
368.8
127.0
50
425.5
146.5
10
482.2
166.1
70
538.9
185.6
331
313.0
107.7
391
369.7
127.3
451
426.4
146.8
511
483.1
166.4
571
539.9
185.9
32
313.9
108.1
92
370.6
127.6
52
427.4
147.1
12
484.1
166.7
72
540.8
186.2
33
314.9
108.4
93
371.6
127.9
53
428.3
147.5
13
485.0
167.0
73
541.7
186.5
34
315.8
108.7
94
372.5
128.3
54
429.3
147.8
14
486.0
167.4
74
542.7
186.9
35
316.7
109.1
95
373.5
128.6
55
430.2
148.1
15
486.9
167.7
75
543.6
187.2
36
317.7
109.4
96
374.4
128.9
56
431.2
148.4
16
487.9
168.0
76
544.6
187.5
37
318.6
109.7
97
375.4
129.2
57
432.1
148.8
17
488.8
168.3
77
545.5
187.8
38
319.6
110.0
98
376.3
129.6
58
433.0
149.1
18
489.7
168.7
78
546.5
188.2
39
320.5
110.4
99
377.3
129.9
59
434.0
149.4
19
490.7
169.0
79
547.4
188.5
40
321.5
110.7
400
378.2
130.2
60
434.9
149.7
20
491.6
169.3
80
548.4
188.8
341
322.4
111.0
401
379.2
130.5
461
435.9
150.1
521
492.6
169.6
581
549.3
189.1
42
323.4
111.3
02
380.1
130.9
62
436.8
150.4
22
493.5
170.0
82
550.3
189.5
43
324.3
111.7
03
381.0
131.2
63
437.8
150.7
23
494.5
170.3
83
551.2
189.8
44
325.3
112.0
04
382.0
131.5
64
438.7
151.0
24
495.4
170.6
84
552.2
190.1
45
326.2
112.3
05
382.9
131.8
65
439.7
151.4
25
496.4
170.9
85
553.1
190.4
46
327.1
112.6
06
383.9
132.2
66
440.6
151.7
26
497.3
171.2
86
554.1
190.8
47
328.1
113.0
07
384.8
132.5
67
441.6
152.0
27
498.3
171.6
87
555.0
191.1
48
329.0
113.3
08
385.8
132.8
68
442.5
152.4
28
499.2
171.9
88
555.9
191.4
49
330.0
113.6
09
386.7
133.1
69
443.4
152.7
29
500.1
172.2
89
556.9
191.7
50
330.9
113.9
10
387.7
133.5
70
444.4
153.0
30
501.1
172.5
90
557.8
192.1
351
331.9
114.3
411
388.6
133.8
471
445.3
153.3
531
502.0
172.9
591
558.8
192.4
52
332.8
114.6
12
389.6
134.1
72
446.3
153.7
32
503.0
173.2
92
559.7
192.7
53
333.8
114.9
13
390.5
134.4
73
447.2
154.0
33
503.9
173.5
93
560.7
193.0
54
334.7
115.2
14
391.4
134.8
74
448.2
154.3
34
504.9
173.8
94
561.6
193.4
55
335.7
115.6
15
392.4
135.1
75
449.1
154.6
35
505.8
174.2
95
562.6
193.7
56
336.6
115.9
16
393.3
135.4
76
450.1
155.0
36
506.8
174.5
96
563.5
194.0
57
337.5
116.2
17
394.3
135.7
77
451.0
155.3
37
507.7
174.8
97
564.5
194.3
58
338.5
116.5
18
395.2
136.1
78
452.0
155.6
38
508.7
175.1
98
565.4
194.7
59
339.4
116.9
19
396.2
136.4
79
452.9
155.9
39
509.6
175.5
99
566.4
195.0
60
340.4
117.2
20
397.1
136.7
80
453.8
156.3
40
510.6
175.8
600
567.3
195.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
71° (109°, 251°, 289°).
Page 570] TABLE 2.
Difference of Latitude and Departure for 20° (160°, 200°, 340°) .
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.3
20.9
121
113.7
41.4
181
170.1
61.9
241
226.5
82.4
2
1.9
0.7
62
58.3
21.2
22
114.6
41.7
82
171.0
62.2
42
227.4
82.8
3
2.8
1.0
63
59.2
21.5
23
115.6
42.1
83
172.0
62.6
43
228.3
83.1
4
3.8
1.4
64
60.1
21.9
24
116.5
42.4
84
172.9
62.9
44
229.3
83.5
5
4.7
1.7
65
61.1
22.2
25
117.5
42.8
85
173.8
63.3
45
230.2
83.8
6
5.6
2.1
66
62.0
22.6
26
118.4
43.1
86
174.8
63.6
46
231.2
84.1
7
6.6
2.4
67
63.0
22.9
27
119.3
43.4
87
175.7
64.0
47
232.1
84.5
8
7.5
2.7
68
63.9
23.3
28
120.3
43.8
88
176.7
64.. 3
48
233.0
84.8
9
8.5
3.1
69
64.8
23.6
29
121.2
44.1
89
177.6
64.6
49
234. 0
85.2
10
9.4
3.4
70
65.8
23.9
30
122.2
44.5
90
178.5
65.0
50
234.9
85.5
11
10.3
3.8
71
66.7
24.3
131
123.1
44.8
191
179.5
65.3
251
235.9
85.8
12
11.3
4.1
72
67.7
24.6
32
124.0
45.1
92
180.4
65.7
52
236.8
86.2
13
12.2
4.4
73
68.6
25.0
33
125.0
45.5
93
181. 4
66.0
53
237.7
86.5
14
13.2
4.8
74
69.5
25.3
34
125.9
45.8
94
182. 3
66.4
54
238.7
86.9
15
14.1
5.1
75
70.5
25.7
35
126.9
46.2
95
183.2
66.7
55
239.6
87.2
16
15.0
5.5
76
71.4
26.0
36
127.8
46.5
96
184.2
67.0
56
240.6
87.6
17
16.0
5.8
77
72.4
26.3
37
128.7
46.9
97
185.1
67.4
57
241.5
87.3
18
16.9
6.2
78
73.3
26.7
38
129.7
47.2
98
186.1
67.7
58
242.4
88.2
19
17.9
6.5
79
74.2
27.0
39
130.6
47.5
99
187.0
68.1
59
243.4
88.6
20
18.8
6.8
80
75.2
27.4
40
131.6
47.9
200
187.9
68.4
60
244.3
88.9
21
19.7
7.2
81
76.1
27.7
141
132.5
48.2
201
188.9
68.7
261
245.3
89.3
22
20.7
7.5
82
77.1
28.0
42
133.4
48.6
02
189.8
69.1
62
246.2
89.6
23
21.6
7.9
83
78.0
28.4
43
134.4
48.9
03
190.8
69.4
63
247.1
90.0
24
22.6
8.2
84
78.9
28.7
44
135.3
49.3
04
191.7
69.8
64
248.1
90.3
25
23.5
8.6
85
79.9
29.1
45
136.3
49.6
05
192. 6
70.1
65
249.0
90.6
26
24.4
8.9
86
80.8
29.4
46
137.2
49.9
06
193.6
70.5
66
250.0
91.0
27
25.4
9.2
87
81.8
29.8
47
138.1
50.3
07
194.5
70.8
67
250.9
91.3
28
26.3
9.6
88
82.7
30.1
48
139.1
50.6
08
195.5
71.1
68
251.8
91.7
29
27.3
9.9
89
83.6
30.4
49
140. 0
51.0
09
196.4
71.5
69
252.8
92.0
30
28.2
10.3
90
84.6
30.8
50
140.9
51.3
10
197.3
71.8
70
253.7
92.3
31
29.1
10.6
91
85.5
31.1
151
141.9
51.6
211
198.3
72.2
271
254.7
92.7
32
30.1
10.9
92
86.5
31.5
52
142.8
52.0
12
199.2
72.5
72
255.6
93.0
33
31.0
11.3
93
87.4
31.8
53
143.8
52.3
13
200.2
72.9
73
256.5
93.4
34
31.9
11.6
94
88.3
32.1
54
144.7
52.7
14
201.1
73.2
74
257.5
93.7
35
32.9
12.0
95
89.3
32.5
55
145.7
53.0
15
202.0
73.5
75
258.4
94.1
36
33.8
12.3
96
90.2
32.8
56
146.6
53.4
16
203.0
73.9
76
259.4
94.4
37
34.8
12.7
97
91.2
33.2
57
147.5
53.7
17
203.9
74.2
77
260. 3
94.7
38
35.7
13.0
98
92.1
33.5
58
148. 5
54.0
18
204.9
74.6
78
261.2
95.1
39
36.6
13.3
99
93.0
33.9
59
149.4
54.4
19
205.8
74.9
79
262.2
95.4
40
37.6
13.7
100
94.0
34.2
60
150. 4
54.7
20
206.7
75.2
80
263.1
95.8
41
38.5
14.0
101
94.9
34.5
161
151.3
55.1
221
207.7
75.6
281
264.1
96.1
42
39.5
14.4
02
95.8
34.9
62
152.2
55.4
22
208.6
75.9
82
265.0
96.4
43
40.4
14.7
03
96.8
35.2
63
153.2
55.7
23
209.6
76.3
83
265.9
96.8
44
41.3
15.0
04
97.7
35.6
64
154.1
56.1
24
210.5
76.6
84
266.9
97.1
45
42.3
15.4
05
98.7
35.9
65
155.0
56.4
25
211.4
77.0
85
267.8
97.5
46
43.2
15.7
06
99.6
36.3
66
156.0
56.8
26
212.4
77.3
86
268.8
97.8
47
44.2
16.1
07
100.5
36.6
67
156.9
57.1
27
213.3
77.6
87
269.7
98.2
48
45.1
16.4
08
101.5
36.9
68
157.9
57.5
28
214.2
78.0
88
270.6
98.5
49
46.0
16.8
09
102.4
37.3
69
158'. 8
57.8
29
215. 2
78.3
89
271.6
98.8
50
47.0
17.1
10
103.4
37.6
70
159.7
58.1
30
216.1
78.7
90
272.5
99.2
51
47.9
17.4
111
104.3
38.0
171
160.7
58.5
231
217.1
79.0
291
273.5
99.5
52
48.9
17.8
12
105.2
38.3
72
161.6
58.8
32
218.0
79.3
92
274.4
99.9
53
49.8
18.1
13
106.2
38.6
73
162.6
59.2
33
218. 9
79.7
93
275.3
100.2
54
50.7
18.5
14
107.1
39.0
74
163.5
59.5
34
219.9
80.0
94
276.3
100.6
55
51.7
18.8
15
108.1
39.3
75
164.4
59.9
35
220.8
80.4
95
277.2
100.9
56
52.6
19.2
16
109.0
39.7
76
165.4
60.2
36
221. 8
80.7
96
278.1
101.2
57
53.6
19.5
17
109.9
40.0
77
166.3
60.5
37
222.7
81.1
97
279.1
101.6
58
54.5
19.8
18
110.9
40.4
78
167.3
60.9
38
223.6
81.4
98
280.0
101.9
59
55.4
20.2
19
111.8
40.7
79
168.2
61.2
39
224.6
81.7
99
281.0
102.3
60
56.4
20.5
20
112.8
41.0
80
169.1
61.6
40
225.5
82.1
300
281.9
102.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
70° (110°, 250°, 250°).
[ TABLE 2. [Page 571
Difference of Latitude and Departure for 20° (160°, 200°, 340°).
1 Dist.
Lat. Dep.
Dist
Lat. < Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Isoi
282.9
103.0
361
339.2 123.5
421 395. 6
144.0
481
452.0
164.5
541
508. 4 185. 0
02
283.8
103.3
62
340.2
123.8
22 396.6
144.3
82
453.0
164.8
42
509. 3 185. 4
03
284.7 103.6
63
341.1
124.2
23
397.5
144.7
83
453.9
165.2
43
510.3
185.7
1 04
285. 7 104. 0
64
342.1
124.5
24
398.4
145.0
84
454.8
165.5
44
511.2
186.0
05
286.6
104.3
65
343.0
124.8
25
399.4
145.4
85
455.8
165.9
45
512.1
186.4
06
287.6
104.7
66
343.9
125.2
26
400.3
145.7
86
456.7
166.3
46
513.1
186.8
07
288.5
105.0
67
344.9
125.5
27
401.3
146.1
87
457.7
166.6
47
514.0
187. 1
08
289.4
105.4
68
345.8
125. 9
28
402.2
146.4
88
458.6
166.9
48
515.0 1 187.4
09
290.4
105.7
69
346.8
126.2
29
403.1
146.7
89
459.5
167.3
49 $15.9 | 187.8
10
291.3
106.0
70
347.7
126.6
30 404. 1
147.1
90
460.5
167.7
50 516. 8 188. 2
rsir
292. 3 i 106. 4
371
348.6
126.9
431 405. 0
147.4
491
461.4
168.0
551
517.8 188.5
12
293.2 106.7
72
349.6
127.2
32
406.0
147.8
92
462.4
168.3
52
518.7
188.8
13
294. 1 107. 1
73
350.5 127.6
33
406.9
148.1
93
463.3
168.6
53
519. 7
189.1
14
295.1 107.4
74
351. 5 127. 9
34
407.8
148.4
94
464.2
168.9
54
520.6
189.4
15
296.0 107.7
75
352.4 128.3
35
408.8
148.8
95
465.2
169.3
55 521. 5
189.8
16
297.0 108.1
76
353.3
128.6
36
409.7
149.1
96
466.1
169.6
56 522. 5
190.2
17
297.9
108.4
77
354.3
129.0
37
410.7
149.5
97
467.0
170.0
57 523. 4
190.5
18
298.8
108.8
78
355.2
129.3
38
411.6
149.8
98
468.0
170.3
58 524. 4
190.8
19
299.8
109.1
79
356.2
129.6
39
412.5
150.2
99
468.9
170.7
59 525. 3
191.2
20
300.7
109. 5
80
357.1
130.0
40
413.5
150.5
500
469.9
171.0
60 526. 2
191.6
321
301.6
109.8
381
358.0
130.3
441
414.4
150.8
501
470.8
171.3
561 527. 2
191.9
22
302.6
110.1
82
359. 0
130.7
42
415.4
151.2
02
471.7
171.7
62 528. 1
192.2
23
303.5
110.5
83
359.9
131.0
43
416.3
151.5
03
472.7
172.0
63 529. 0
192.5
24
304.5
110.8
84
360.8
131.3
44
417.2
151.9
04
473.6
172.4
64 530. 0
192.9
25
305. 4
111.2
85
361.8
131.7
45
418.2
152.2
05
474.5
172.7
65 530. 9
193.2
26
306.3
111.5
86
362.7
132.0
46
419.1
152.5
06
475.4
173.0
66 531. 8
193.6
27
307.3
111.8
87
363. 7
132.4
47
420.0
152.9
07
476.4
173.4
67 532. 8
193.9
28
308.2
112.2
88
364.6
132.7
48
421.0
153.2
08
477.3
173. 7
68 533. 7
194.2
29
309.2
112.5
89
365.5
133.1
49
421.9
153.6
09
478.3
174.1
69 1 534. 7
194.6
30
310.1
112.9
90
366.5
133.4
50
422.9
153.9
10
479.2
174.4
70 I 535.6
195.0
331
311.0
113.2
391
367.4
133.7
451
423.8
154.3
511
480.2
174.8
571
536.6
195.3
32
312.0
113.6
92 368.4
134.1
52
424.7
154.6
12
481.1
175.1
72
537.5
195.6
33
312.9
113.9
93 369. 3
134.4
53
425.7
154.9
13
482.1
175.4
73
538.5
195.9
34
313.9
114.2
94 370. 2
134.8
54
426.6
155.3
14
483.0
175.8
74
539.4
196.3
35
314.8
114.6
95 371.2
135.1
55
427.6
155.6
1.5
484.0
176.1
75
540.3
196.6
36
315.7
114.9
96 372. 1
135.4
56
428.5
156.0
16
484.9
176.5
76
541.3
197.0
37
316.7
115.3
97 I 373. 1
135.8
57
429.4
156.3
17
485.8
176.8
77
542.2
197.3
38
317.6
115.6
98 i 374.0
136.1
58
430.4
156.7
18
486.8
177.2
78
543.2
197.7
39
318.6
116.0
99 i 374.9
136.5
59
431.3
157.0
19
487.7
177.5
79
544.1
198.0
40
319.5
116.3
400 i 375. 9
136.8
60
432.3
157.4
20
488.7
177.9
80
545.0
198.4
341
320.4
116.6
401 376. 8
137.2
461
433.2
157.7
521 489. 6
178.2
581
546.0
198.7
42
321.4
117.0
02
377.8
137.5
62
434.1
158.0
22
490.5
178.5
82
546.9
199.0
43
322.3
117.3
03
378.7
137. 8
63
435.1
158.4
23
491.5
178.9
83
547.9
199.4
44
323.3
117.7
04
379.6
138.2
64
436.0
158.7
24
492.4
179.2
84
548.8
199.8
45 324. 2
118.0
05 380. 6
138.5
65
437.0
159.0
25
493.4
179.6
85
549.8
200.1
46
325. I
118.4
06 381. 5
138.9
66
437.9
159.4
26
494.3
179.9
86
550.7
200.4
47
326.1
118. 7
07 382. 5
139.2
67
438.8
159.7
27
495.3
180.2
87
551.7
200.8
48
327.0
119.0
08
383.4
139.6
68
439.8
160.1
28
496.2
180.6
88
552.6
201.2
49
328.0
119.4
09
384.3
139.9
69
440.7
160.4
29
497.1
181.0
89
553.5
201.5
50
328.9
119.7
10.
385.3
140.2
70
441.7
160.8
30
498.1
181.3
90
554.4
201.8
1 351
329.8
120.1
411
386.2
140.6
471
442.6
161.1
531
499.0
181.6
591
555.4
202.1
52
330.8
120.4
12
387.2
140.9
72
443.5
161.4
32
499.9
181.9
92
556.3
202.4
53 i 331. 7
120.7
13
388.1
141.3
73
444.5
161.8
33
500.9
182.3
93
557.3
202.8
54 332. 7
121.1
14
389.0
141.6
74
445.4
162.1
34
501.8
182.6
94
558.2
203.2
55 333. 6
121.4
15
390.0
141.9
75
446.4
'162. 5
35
502.7
183.0
95
559.1
203.5
56 334. 5
121.8
16
390.9
142.3
76
447.3
162.8
36
503.7
183.3
96
560.0
203.8
57 335. 5
122.1
17
391.9
142.6
77
448.2
163.2
37
504.6
183.7
97
561.0
204.2
58 336. 4
122.5
18
392.8
143.0
78
449.2
163.5
38
505.5
184.0
98
561.9
204.6
59 337. 4
122.8
19
393.7
143.3
79
450.1
163.8
39
506.5
184.3
99
562.9
204.9
60 338. 3
123.1
20
394.7
143.7
80
451.1
164.2
40
507.4
184.7
600
563.8
205.2
Dist. | Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
I 70° (110°, 250°, 290° ),
Page 572] TABLE 2.
Difference of Latitude and Departure for 21° (159°, 201°, 339°).
Dist
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
1
0.9
0.4
61
56.9
21.9
121
113.0
43.4
181
169.0
64.9
241
225.0
86.4
n
Li
1.9
0.7
62
57.9
22. 2
22
113.9
43.7
82
169.9
65.2
12
225.9
86.7
3
2.8
1.1
63
58.8
22.' 6
23
114.8
44.1
83
170.8
65.6
43
226.9
87.1
4
3.7
1.4
64
59.7
22.9
24
115.8
44.4
84
171.8
65.9
44
227.8
87.4
5
4.7
1.8
65
60.7
23.3
25
116.7
44.8
85
172. 7
66.3
45
228.7
87.8
6
5.6
2.2
66
61.6
23.7
26
117.6
45.2
86
173.6
66.7
46
229.7
88.2
7
6.5
2.5
67
62.5
24.0
27
118.6
45.5
87
174.6
67.0
47
230.6
88.5
8
7.5
2.9
68
63.5
24.4
28
119.5
45.9
88
175.5
67.4
48
231.5
88.9
9
8.4
3.2
69
64.4
24.7
29
120.4
46.2
89
176.4
67.7
49
232.5
89.2
10
9.3
3.6
70
65.4
25.1
30
121.4
46.6
90
177.4
68.1
50
233.4
89.6
11
10.3
3.9
71
66.3
25.4
131
122.3
46.9
191
178.3
68.4
251
234.3
90.0
12
11.2
4.3
72
67.2
25.8
32
123.2
47.3
92
179.2
68.8
52
235.3
90.3
13
12.1
4.7
73
68.2
26.2
33
124.2
47.7
93
180.2
69.2
53
236.2
90.7
14
13.1
5.0
74
69.1
26.5
34
125.1
48.0
94
181.1
69.5
54
237.1
91.0
15
14.0
5.4
75
70.0
26.9
35
126.0
48.4
95
182.0
69.9
55
238.1
91.4
16
14.9
5.7
76
71.0
27.2
36
127.0
48.7
96
183.0
70.2
56
239.0
91.7
17
15.9
6.1
77
71.9
27.6
37
127.9
49.1
97
183.9
70.6
57
239.9
92.1
18
16.8
6.5
78
72.8
28.0
38
128.8
49.5
98
184.8
71.0
58
240.9
92.5
19
17.7
6.8
79
73.8
28.3
39
129.8
49.8
99
185.8
71.3
59
241.8
92.8
20
18.7
7.2
80
74.7
28.7
40
130.7
50.2
200
186.7
71.7
60
242.7
93.2
21
19.6
7.5
81
75.6
29.0
141
131.6
50.5
201
187.6
72.0
261
243.7
93.5
22
20.5
7.9
82
76.6
29.4
42
132.6
50.9
02
188.6
72.4
62
244.6
93.9
23
21.5
8.2
83
77.5
29.7
43
133.5
51.2
03
189.5
72.7
63
245.5
94.3
24
22.4
8.6
84
78.4
30.1
44
134.4
51.6
04
190.5
73.1
64
246.5
94.6
25
23.3
9.0
85
79.4
30.5
45
135.4
52.0
05
191.4
73.5
65
247.4
95.0
26
24.3
9.3
86
80.3
30.8
46
136.3
52.3
06
192.3
73.8
66
248.3
95.3
27
25.2
9.7
87
81.2
31.2
47
137.2
52.7
07
193.3
74.2
67
249.3
95.7
28
26.1
10.0
88
82.2
31.5
48
138.2
53.0
08
194.2
74.5
68
250.2
96.0
29
27.1
10.4
89
83.1
31.9
49
139.1
53.4
09
195.1
74.9
69
251.1
96.4
30
28.0
10.8
90
84.0
32.3
50
140.0
53.8
10
196.1
75.3
70
252.1
96.8
31
28.9
11.1
91
85.0
32.6
151
141.0
54.1
211
197.0
75.6
271
253.0
97.1
32
29.9
11.5
92
85.9
33.0
52
141.9
54.5
12
197.9
76.0
72
253.9
97.5
33
30.8
11.8
93
86.8
33.3
53
142.8
54.8
13
198.9
76.3
73
254.9
97.8
34
31.7
12.2
94
87.8
33.7
54
143.8
55.2
14
199.8
76.7
74
255.8
98.2
35
32.7
12.5
95
88.7
34.0
55
144.7
55.5
15
200.7
77.0
75
256.7
98.6
36
33.6
12.9
96
89.6
34.4
56
145.6
55.9
16
201.7
77.4
76
257.7
98.9
37
34.5
13.3
97
90.6
34.8
57
146.6
56.3
17
202.6
77.8
77
258.6
99.3
38
35.5
13.6
98
91.5
35.1
58
147.5
56.6
18
203.5
78.1
78
259.5
99.6
39
36.4
14.0
99
92.4
35.5
59
148.4
57.0
19
204.5
78.5
79
260.5
100.0
40
37.3
14.3
100
93.4
35.8
60
149.4
57.3
20
205.4
78.8
80
261.4
100.3
41
38.3
14.7
101
94.3
36.2
161
150.3
57.7
221
206.3
79.2
281
262.3
100.7
42
39.2
15.1
02
95.2
36.6
62
151.2
58.1
22
207.3
79.6
82
263.3
101.1
43
40.1
15.4
03
96.2
36.9
63
152.2
58.4
23
208.2
79.9
83
264.2
101.4
44
41.1
15.8
04
97.1
37.3
64
153.1
58.8
24
209.1
80.3
84
265.1
101.8
45
42.0
16.1
05
98.0
37.6
65
154.0
59.1
25
210.1
80.6
85
266.1
102.1
46
42.9
16.5
06
99.0
38.0
66
155.0
59.5
26
211.0
81.0
86
267.0
102.5
47
43.9
16.8
07
99.9
38.3
67
155.9
59.8
27
211.9
81.3
87
267.9
102.9
48
44.8
17.2
08
100.8
38.7
68
156.8
60.2
28
212.9
81.7
88
268.9
103.2
49
45.7
17.6
09
101.8
39.1
69
157.8
60.6
29
213. 8
82.1
89
269.8
103.6
50
46.7
17.9
10
102.7
39.4
70
158.7
60.9
30
214.7
82.4
90
270.7
103.9
51
47.6
18.3
111
103.6
39.8
171
159. 6
61.3
231
215.7
82.8
291
271.7
104. 3
52
48.5
18.6
12
104.6
40.1
72
160.6
61.6
32
216.6
83.1
92
272.6
104.6
53
49.5
19.0
13
105.5
40.5
73
161.5
62.0
33
217.5
83.5
93
273.5
105.0
54
50.4
19.4
14
106.4
40.9
74
162.4
62.4
34
218.5
83.9
94
274.5
105.4
55
51.3
19.7
15
107.4
41.2
75
163.4
62.7
35
219.4
84.2
95
275.4
105.7
56
52.3
20.1
16
108.3
41.6
76
164.3
63.1
36
220.3
84.6
96
276.3
106.1
57
53.2
20.4
17
109.2
41.9
77
165. 2
63.4
37
221.3
84.9
97
277.3
106.4
58
54.1
20.8
18
110.2
42.3
78
166.2
63.8
38
222.2
85.3
98
278.2
106.8
59
55.1
21.1
19
111.1
42.6
79
167.1
64.1
39
223.1
85.6
99
279.1
107.2
60
56.0
21.5
20
112.0
43.0
80
168.0
64.5
40
224.1
86.0
300
280.1
107.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
69° (111°, 249°, 291°).
TABLE 2. [Page 573
Difference of Latitude and Departure for 21° (159°, 201°, 339°).
Dist.
Lat.
Dep.
Dist. Lat. I Dep.
Dist. j Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. | Dep.
301
281.0
107.9
361
337.0
129.4
421 393.0
150.9
481
449.0
172.4
541
505.1
193.9
02
281.9
108.2
62
337.9
129.7
22 1 394.0
151.2
82
450.0
172.7
42
506.0
194.2
03
282.9
108.6
63
338.9
130.1
23
394.9
151.6
83
450.9
173.1
43
507.0
194.6
04 283. 8
108.9
64
339.8
130.4
24
395.8
152.0
84
451.8
173.5
44
507.9
195.0
05 284. 7
109.3
65
340.7
130.8
25
396.8
152.3
85
452.8
173.8
45
508.8
195.3
06
285.7
109.7
66
341.7
131.2
26
397.7
152.7
86
453.7
174.2
46
509.8
195.7
07
286.6
110.0
67
342.6
131.5
27
398.6
153.0
87
454.6
174.5
47
510.7
196.0
08
287.5 110.4
68
343.5
131.9
28
399.6
153.4
88
455.6
174.9
48
511.6
196.4
09
288.5
110.7
79
344.5
132.2
29
400.5
153.7
89
456.5
175.2
49
512.6
196.8
10
289.4
111.1
70
345.4
132.6
30
401.4
154.1
90
457.4
175.6
50
513.5
197.1
311
290.3 111.5
371
346.3 133.0
431
402.4
154.5
491
458.4
176.0
551
514.4
197.5
12
291.3 Jill. 8
72
347. 3 133. 3
32
403.3
154.8
92
459.3
176.3
52
515.4
197.8
13
292.2
112.2
73
348. 2 ! 133. 7
33
404.2
155.2
93
460.2
176.7
53
516.3
198.2
14
293.1
112.5
74
349. 1 i 134. 0
34
405.2
155. 5
94
461.2
177.0
54
517.2
198.6
15
294. 1 112. 9
75
350. 1 i 134. 4
35
406.1
155.9
95
462.1
177.4
55
518.2
198.9
16
295.0 113.2
76
351. 0 i 134. 7
36
407.0
156.3
96
463.0
177.8
56
519.1
199.3
17
295.9 113.6
77
351. 9 i 135. 1
37
408.0
156.6
97
464.0
178.1
57
520.0
199.6
18
296.9 114.0
78
352. 9 i 135. 5
38
408.9
157.0
98
464.9
178.5
58
521.0
200.0
19
297.8 114.3
79
353. 8 1 135. 8
39
409.8
157.3
99
465.8
178.8
59
521.9
200.3
20
298. 7 114. 7
80
354. 7 ! 136. 2
40
410.8
157. 7
500
466.8
179.2
60
522.8
200.7
321
299.7
115.0
381
355. 7 1 136. 5
441
411.7
158.0
501 467. 7
179.5
561 523. 8
201.0
22 300.6 115.4
82
356. 6 1 136. 9
42
412.6
158.4
02
468.6
179.9
62
524.7
201.4
23 301. 5 i 115. 8
83
357. 5
137.3
43
413.6
158.8
03
469.6
180.3
63
525. 6
201.8
24
302.5 116.1
84
358.5
137.6
44
414.5
159.1
04
470.5
180.6
64
526.6
202.1
25
303.4
116.5
85
359.4
138.0
45
415.4
159.5
05
471.5
181.0
65
527.5
202.5
26
304.3
116.8
86
360.3
138.3
46
416.4
159.8
06
472.4
181.3
66
528.4
202.8
27
305.3 117.2
87
361.3
138.7
47
417.3
160.2
07
473.3
181.7
67
529.4
203.2
28
306.2 117.5
88
362.2
139. 1
48
418.2
160.5
08
474.3
182.0
68
530.3
203.5
29
307. 1 117. 9
89
363.1
139.4
49
419.2
160.9
09
475.2
182.4
69
531.2
203.9
30
308.1 118.3
90 364. 1
139. 8
50 420. 1
161.3
10
476.1
182.8
70
532.2
204.3
331
309.0
118.6
391 365. 0
140.1
451 421.0 161.6
511
477. 1 183. 1
571
533.1
204.6
32
309.9
119.0
92 365. 9
140.5
52
422.0 162.0
12
478. 0 1 183. 5
72
534.0
205.0
33
310.9
119.3
93 366. 9
140.8
53
422.9 !162.3
13
478.9
183.8
73
535.0
205.4
34
311.8
119.7
94 367.8
141.2
54
423. 8 1 162. 7
14
479.9
184.2
74
535.9
205.7
35
312.7
120.1
95 368. 7
141.6
55
424.8 !163. 1
15
480.8
184.6
75
536.8
206.1
36
313.7
120.4
96 369. 7
141.9
56
425.7 :163.4
16
481.7
184.9
76
537.8
206.4
37
314.6
120.8
97 370. 6
142.3
57
426.6 163.8
17
482.7
185.3
77
538.7
206.8
38
315.5
121.1
98 371.5
142.6
58
427. 6 ! 164. 1
18
483.6
185.6
78
539.6
207.1
39
316.5
121.5
99 372. 5
143.0
59
428. 5 1 164. 5
19
484.5
186.0
79
540.6
207.5
40
317.4
121.8
400 373. 4
143.4
60
429.4 164.9
20
485.5 186.4
80
541.5
207.9
341
318.3 122.2
401 374.3 143.7
461
430.4 165.2
521
486.4 186.7
581
542.4
208.2
42
319.3 122.6
02 375.3 144.1
62
431.3 165.6
22
487.3
187.1
82
543.4
208.6
43
320.2 122.9
03 376.2 144.4
63
432.2 165.9
23
488. 3 1 187. 4
83
544.3
208.9
44
321. 1 123. 2
04
377. 1 144. 8
64
433.2 166.3
24
489.2
187.8
84
545.2
209.3
45
322. 1
123.6
05
378. 1 145. 1
65
434.1 1166.6
25
490.1
188.1
85
546.2
209.6
46
323.0
124.0
06
379.0 145.5
66
435.0 167.0
26
491.1
188.5
86
547.1
210.0
47
323.9 124.4
07
379.9 145.9
67
436.0 167.4
27
492.0
188.9
87
548.0
210.4
48
324. 9 124. 7
08 380.9 146.2
68
436.9 167.7
28
492.9
189.2
88
549.0
210.7
49
325.8 125.1
09
381.8
146.6
69
437. 8 1 168. 1
29
493.9
189.6
89
549.9
211.1
50
326.7 ;125.4
10 382. 7
146.9
70 438.8 168.4
30
494.8
189.9
90
550.8
211.4
351
327. 7 125. 8
411 383. 7
147.3
471
439. 7 168. 8
531
495.7
190.3
691
551.8
211.8
52
328.6 126.1
12 384. 6
147.7
72
440.6 169.2
32
496.7
190.7
92
552.7
212.2
53
329.5 126.5
13 385. 5
148.0
73
441.6
169.5
33
497.6
191.0
93
553.6
212.5
54
330.5 126.9
14 386. 5
148.4
74
442.5
169.9
34
498.5
191.4
94
554.6
212.9
55
331.4 127.2
15
387.4
148.7
75
443.4
170.2
35
499.5
191.7
95
555.5
213.2
56
332.3 127.6
16
388.4
149.1
76 444.4 170.6
36
500.4
192.1
96
556.4
213.6
57
333.3
127.9
17 389. 3
149.4
77 445.3 !l70.9
37
501.3
192.4
97
557.4
213.9
58
334.2
128.3
18 390. 2
149.8
78 446. 2
171.3
38
502.3
192.8
98
558.2
214.3
59
335.1
128.7
19
391.2
150.2
79 447. 2
171.7
39
503.2
193.2
99
559.2
214.7
60
336.1
129.0
20
392.1
150.5
80 448. 1
172.0
40
504.1
193.5
600
560.1
215.0
Dist.
Dep.
Lat.
Dist.
. Dep. Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
69° (111°, 249°, 291°).
Page 574] TABLE 2.
Difference of Latitude and Departure for 22° (158°, 202, 338°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.6
22.9
121
112.2
45.3
181
167.8
67.8
241
223.5
90.3
2
1.9
0.7
62
57.5
23.2
22
113.1
45.7
82
168. 7
68.2
42
224.4
90.7
3
2:8
1.1
63
58.4
23.6
23
114.0
46.1
83
169.7
68.6
43
225.3
91.0
4
3.7
1.5
64
59.3
24.0
24
115.0
46.5
84
170.6
68.9
44
226.2
91.4
5
4.6
1.9
65
60.3
24.3
25
115.9
46.8
85
171.5
69.3
45
227 2
91.8
6
5.6
2.2
66
61.2
24.7
26
116.8
47.2
86
172.5
69.7
46
228*. 1
92.2
7
6.5
2.6
67
62.1
25.1
27
117.8
47.6
87
173.4
70.1
47
229.0
92.5
8
7.4
3.0
68
63.0
25.5
28
118.7
47.9
88
174.3
70.4
48
229.9
92.9
9
8.3
3.4
69
64.0
25.8
29
119.6
48.3
89
175.2
70.8
49
230.9
93.3
10
9.3
3.7
70
64.9
26.2
30
120.5
48.7
90
176.2
71.2
50
231.8
93.7
11
10.2
4.1
71
65.8
26.6
131
121.5
49.1
191
177.1
71.5
251
232.7
94.0
12
11.1
4.5
72
66.8
27.0
32
122.4
49.4
92
178.0
71.9
52
233.7
94.4
13
12.1
4.9
73
67.7
27.3
33
123.3
49.8
93
178.9
72.3
53
234.6
94.8
14
13.0
5.2
74
68.6
27.7
34
124.2
50.2
94
179.9
72.7
54
235. 5
95/2
15
13.9
5.6
75
69.5
28.1
35
125.2
50.6
95
180.8
73.0
55
236.4
95.5
16
14.8
6.0
76
70.5
28.5
36
126.1
50.9
96
181.7
73.4
56
237.4
95.9
17
15.8
6.4
77
71.4
28.8
37
127.0
51.3
97
182.7
73.8
57
238.3
96.3
18
16.7
6.7
78
72.3
29.2
38
128.0
51.7
98
183.6
74.2
58
239.2
96.6
19
17.6
7.1
79
73.2
29.6
39
128.9
52.1
99
184.5
74.5
59
240.1
97.0
20
18.5
7.5
80
74.2
30.0
40
129.8
52.4
200
185.4
74.9
60
241.1
97.4
21
19.5
7.9
81
75.1
30.3
141
130.7
52.8
201
186.4
75.3
261
242.0
97.8
22
20.4
8.2
82
76.0
30.7
42
131.7
53.2
02
187.3
75.7
62
242.9
98.1
23
21.3
8.6
83
77.0
31.1
43
132.6
53.6
03
188.2
76.0
63
243.8
98.5
24
22.3
9.0
84
77.9
31.5
44
133.5
53.9
04
189.1
76.4
64
244.8
98.9
25
23.2
9.4
85
78.8
31.8
45
134.4
54.3
05
190.1
76.8
65
245.7
99.3
26
24.1
9.7
86
79.7
32.2
46
135.4
54.7
06
191.0
77.2
66
246.6
99.6
27
25.0
10.1
87
80.7
32.6
47
136.3
55.1
07
191.9
77.5
67
247.6
100.0
28
26.0
10.5
88
81.6
33.0
48
137.2
55.4
08
192.9
77.9
68
248.5
100.4
29
26. &
10.9
89
82.5
33.3
49
138. 2
55.8
09
193.8
78.3
69
249.4
100.8
30
27.8
11.2
90
83.4
33.7
50
139. 1
56.2
10
194.7
78.7
70
250.3
101.1
31
28.7
11.6
91
84.4
34.1
151
140.0
56.6
211
195.6
79.0
271
251.3
101.5
32
29.7
12.0
92
85.3
34.5
52
140.9
56.9
12
196.6
79.4
72
252.2
101.9
33
30.6
12.4
93
86.2
34.8
53
141.9
57.3
13
197.5
79.8
73
253.1
102.3
34
31.5
12.7
94
87.2
35.2
54
142.8
57.7
14
198.4
80.2
74
254.0
102.6
35
32.5
13.1
95
88.1
35.6
55
143.7
58.1
15
199.3
80.5
75
255.0
103.0
36
33.4
13.5
96
89.0
36.0
56
144.6
58.4
16
200.3
80.9
76
255.9
103.4
37
34.3
13.9
97
89.9
36.3
57
145.6
58.8
17
201.2
81.3
77
256.8
103.8
38
35.2
14.2
98
90.9
36.7
58
146.5
59.2
18
202.1
81.7
78
257.8
104.1
39
36.2
14.6
99
91.8
37.1
59
147.4
59.6
19
203.1
82.0
79
258.7
104.5
40
37.1
15.0
100
92.7
37.5
60
148.3
59.9
20
204.0
82.4
80
259.6
104.9
A\
38.0
15.4
101
93.6
37.8
161
149.3
60.3
221
204.9
82.8
281
260.5
105.3
42
38.9
15.7
02
94.6
38.2
62
150.2
60.7
22
205.8
83.2
82
261.5
105.6
43
39.9
16.1
03
95.5
38.6
63
151.1
61.1
23
206.8
83.5
83
262.4
106.0
44
40.8
16.5
04
96.4
39.0
64
152.1
61.4
24
207.7
83.9
84
263.3
106.4
45
41.7
16.9
05
97.4
39.3
65
153.0
61.8
25
208.6
84.3
85
264.2
106.8
46
42.7
17.2
06
98.3
39.7
66
153.9
62.2
26
209.5
84.7
86
265.2
107.1
47
43.6
17.6
07
99.2
40.1
67
154.8
62.6
27
210.5
85.0
87
266.1
107. 5
48
44.5
18.0
08
100.1
40.5
68
155.8
62.9
28
211.4
85.4
88
267.0
107.9
49
45.4
18.4
09
101.1
40.8
69
156.7
63.3
29
212.3
85.8
89
268.0
108.3
50
46.4
18.7
10
102.0
41.2
70
157.6
63.7
30
213.3
86.2
90
268.9
108. 6
51
47.3
19.1
111
102. 9
41.6
171
158.5
64.1
231
214.2
86.5
291
269.8
109.0
52
48.2
19.5
12
103.8
42.0
72
159.5
64.4
32
215.1
86.9
92
270.7
109.4
53
49.1
19.9
13
104.8
42.3
73
160.4
64.8
33
216.0
87.3
93
271. 7
109.8
54
50.1
20.2
14
105.7
42.7
74
161.3
65.2
34
217.0
87.7
94
272.6
110.1
55
51.0
20.6
15
106.6
43.1
75
162.3
65.6
35
217.9
88.0
95
273.5
110.5
56
51.9
21.0
16
107.6
43.5
76
163.2
65.9
36
218.8
88.4
96
274.4
110.9
57
52.8
21.4
17
108.5
43.8
77
164.1
66.3
37
219.7
88.8
97
275.4
111.3
58
53.8
21.7
18
109.4
44.2
78
165.0
66.7
38
220. 7
89.2
98
276.3
111.6
59
54.7
22.1
19
110.3
44.6
79
166.0
67.1
39
221.6
89.5
99
277.2
112.0
60
55.6
22.5
20
111.3
45.0
80
166.9
67.4
40
222.5
89.9
300
278.2
112.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
68° (112°, 248°, 292°).
TABLE 2.
[Page 575
Difference of Latitude and Departure for 22° (158°, 202°, 338°).
Dfat
Lat.
Dep.
Dist. ; Lat. j Dep.
Dist. Lat.
Dep.
Dist.
Lat. ! Dep.
Dist. Lat.
Dep.
301
279.1
112.7
361
334.7
135.2
421
390.3
157.7
481
446.0
180.2
541 501. 6
202.7
02
280.0
113.1
62
3.35. 6
135.6
22
391.3
158.1
82
446.9 180.6
42
502.5
203.1
03
280.9
113.5
63
336.6
136.0
23
392.2
158.4
83
447.8 180.9
43
503.4
203.5
04
281.9
113.9
64
337.5
136.3
24
393.1
158.8
84
; 448.8 181.3
44
504.4
203.8
05
282.8
114.2
65
338.4
136.7
25
394.1
159.2
85
i 449.7 181.7
45
505. 3 204. 2
06
283.7
114.6
66
339.3
137.1
26
395.0
159.6
86
! 450.6 182.1
46
506. 2 204. 6
07
284.6
115.0
67
340.3
137.5
27
395.9
159.9
87
i 451.6 182.4
47
507.2
205.0
08
285.6
115.4
68
341.2
137.8
28
396.8
160.3
88
452. 5
182.8
48
508.1
205.3
09
286.5
115.7
69
342.1
138.2
29
397.8
160.7
89
453.4
183.2
49
509.0
205.7
10
287.4
116.1
70
343.1
138.6
30
398.7
161.1
90
454.3 183.6
50
510.0
206.1
311 288. 4
116.5
371
344.0 139.0
431
399.6
161.4
491
455. 3 184. 0
551
510.9
206.5
12 289.3
116.8
72
344.9
139.3
32
400. 5
161.8
92
456. 2
184.3
52
511.8
206.8
13 290.2
117.2
73
345.8
139.7
33
401.5
162.2
93
457. 1
184. 7
53
512.7
207.2
14 291. 1
117.6
74
346.8
140.1
34
402.4
162.6
94
458.0
185.1
54
513.6
207.6
15 i 292.1
118.0
75
347.7
140.5
35
403.3
162.9
95
459. 0
185.4
55
514.6
208.0
16 | 293. 0
118.3
76
348.6
140.8
36
404.3
163.3
96
459.9
185.8
56
515. 5
208.3
17
293.9
118.7
77
349.5 141.2
37
405.2
163.7
97
460.8
186.2
57
516.4
208.7
18 294. 8
119.1
78
350. 5 ; 141. 6
38
406.1
164.1
98
461.8
186.6
58
517.4
209.1
19 295. 8
119.5
79
351.4 141.9
39
407.0
164.4
99
462.7
186.9
59
518.3
209.4
20 296. 7
119.8
80
352.3 142.3
40
408.0 164.8
500
463.6
187.3
60
519.2
209.8
321 297. 6
120.2
381
353. 3 142. 7
441
408.9
165.2
501
464.5
187.7
561
520.1
210.2
22 ! 298. 6
120.6
82
354.2 1 143.1
42
409.8
165.5
02
465.4
188.0
62
521.0
210.5
23 299.5 121.0
83
355.1
143.4
43
410.7
165.9
03
466.4
188.4
63
522.0
210.9
24 300. 4
121.3
84
356.0
143.8
44
411.7
166.3
04
467.3
188.8
64
522.9
211.3
25 301.3
121.7
85
357.0
144.2
45
412.6
166.7
05
468.2
189.2
65
523.8
211.7
26 j 302.3
122.1
86
357.9
144.6
46
413.5
167.0
06
469.2
189.5
66
524.8
212.0
27 ; 303.2
122.5
87
358.8
144.9
47
414.5
167.4
07
470.1
189.9
67
525.7
212.4
28 304. 1
122.8
88
359.7
145. 3
48
415.4
167.8
08
471.0
190.3
68
526.6
212.8
29 305. 0
123. 2
89'
360.7
145. 7
49
416.3
168.2
09
471. 9
190.7
69
527. 5
213.2
30
306.0
123.6
90
361.6
146.1
50
417.2
168.5
10
472.9
191.1
70
528.5
213.5
331
306.9
124.0
391
362.5
146.4
451
418.2
168.9
oil
473.8
191.4
571
529.4
213.9
32
307. S 124. 3
92
363.5
146.8
52
419.1
169.3
12
474.7
191.8
72
530.3
214.3
33
308.8 124.7
93
364.4
147.2
53
420.0
169.7
13
475.6
192.2
73
531.2
214.7
34
309.7 125.1
94
365.3
147.6
54
420.9
170.0
14
476.6
192.5
74
532.2
215. 0
35
310.6 125.5
95
366.2
147.9
55
421.9
170.4
15
477. 5
19 9 9
75
533.1
215.4
36
311.5 125.8
96
367. 2
148.3
56
422.8
170.8
16
478.4
193.3
76
534.0
215.8
37
312. 5 126. 2
97
368.1
148. 7
57
423.7
171.2
17
479.3
193.7
77
534.9
216.2
38
313.4 :126.6
98
369.0
149.1
58
424.6 171.5
18
480.3
194.0
78
535.9
216.5
39
314. 3 127. 0
99
369.9
149. 4
59
425.6 171.9
19
481.2
194.4
79 536. 8
216.9
40
315.2 127.3
400
370.9
149.8
60
426. 5 172. 3
20
482.1
194.8
80 537. 7
217.3
341
316. 2 127. 7
401
371.8
150.2
461
427. 4
172.7
o21
483. 0 195. 2
581
538.6
217.7
42
317. 1 128. 1
02
372.7
150.6
62
42S. 4
173.0
"22
484.0 195.5
82
539.6
218.0
43
318.0 128.5
03
373.7
150.9
63
429.3
173.4
23
484. 9 195.9
83
540. 5 218. 4
44
319.0 128. 8
04
374.6
151.3
64
430.2
173.8
24
485.8
196. 3
84
541.4
218.8
45
319.9 129.2
05
375. 5
151.7
65
431.1
174.2
25
486. 7
196.7
85
542.4
219.2
46
320.8 129.6
06
376.4
152.1
66
432.1
174. 5
26
4S7. 7
197.0
86
543.3
219.5
47
321.7 130/0
07
377.4
152.4
67
433.0
174.9
27
488.6
197.4
87
544.2
219.9
48
322.7 130.3
08
378.3 152.8
68
433.9
175.3
28
489. 5
197.8
88
545. 1
220.3
49 323.6 J130. 7
09
379.2 153.2
69
434.8
175. 7
29
490.4
198.2
89
546.1
220. 7
50 324.5 131.1
10
380.1 153.6
70
435.8
176.0
30
491.4
198.5
90
547.0
221.0
351 325. 4 131. 5
411 381. 1 153. 9
471
436.7
176. 4
531
492.3
198.9
591
547.9
221.4
52
326.4 131.8
12
382.0 154.3
72
437.6
176.8
32
493.2
199.3
92
548.9
221.8
53 327.3 132.2
13
382.9 154.7
73
438.6
177.2
33
494.2
199.7
93
549.8
222. 2
54 1 328. 2 132. 6
14
383. 9 ! 155. 1
74
439.5
177.5
34
495.1
200.0
94
550.7
222"! 5
55 329.2 ! 133:0
15
384.8 ;155.4
75
440.4
177.9
35
496.0
200.4
95
551. 7
222.9
56
330.1 133.3
16
385. 7 j 155. 8
76
441.3
178.3
36
496.9
200.8
96
552. 6
223.3
57
331. 0 '' 133. 7
17
386. 6 i 156. 2
i /
442.3
178.7
37
497.9
201.2
97
553.5
223. 7
58 332.0 134.1
18
387. 6 156. 6
78
443.2
179.0
38
498.8
201.5
98
554.4
224. 0
59
332.9 134.5
19
388. 5 156. 9
79
444.1
179.4
39
499.7
201.9
99
555.4
224.4
60 333.8 134.8
20
389.4 157.3
80
445.0
179.8
40
500.7
202.3
600
556.3
224.8
Dist. Dep. Lat.
Dist. Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
68° (112°, 248°, 292° .
61828°—
Page 576] TABLE 2.
Difference of Latitude and Departure for 23° (157°, 203°, 337°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.2
23.8
121
111.4
47.3
181
166.6
70.7
241
221.8
94.2
2
1.8
0.8
62
57.1
24.2
22
112. 3
47.7
82
167.5
71.1
42
222.8
94.6
3
2.8
1.2
63
58.0
24.6
23
113.2
48.1
83
168.5
71.5
43
223.7
94.9
4
3.7
1.6
64
58.9
25.0
24
114.1
48.5
84
169.4
71.9
44
224.6
95.3
o
4.6
2.0
65
59.8
25.4
25
115.1
48.8
85
170.3
72.3
45
225.5
95.7
6
5.5
2.3
66
60.8
25.8
26
116.0
49.2
86
171.2
72.7
46
226.4
96.1
7
6.4
2.7
67
61.7
26.2
27
116.9
49.6
87
172.1
73.1
47
227.4
96.5
8
7.4
3.1
68
62.6
26.6
28
117.8
50.0
88
173.1
73.5
48
228.3
96.9
9
8.3
3.5
69
63.5
27.0
29
118.7
50.4
89
174.0
73.8
49
229.2
97.3
10
9.2
3.9
70
64.4
27.4
30
119.7
50.8
90
174.9
74.2
50
230.1
97.7
11
10.1
4.3
71
65.4
27.7
131
120.6
51.2
191
175.8
74.6
251
231.0
98.1
12
11.0
4.7
72
66.3
28.1
32
121.5
51.6
92
176.7
75.0
52
232.0
98.5
13
12.0
5.1
73
67.2
28.5
33
122.4
52.0
93
177.7
75.4
53
232.9
98.9
14
12.9
5.5
74
68.1
28.9
34
123.3
52.4
94
178.6
75.8
54
233.8
99.2
15
13.8
5.9
75
69.0
29.3
35
124.3
52.7
95
179.5
76.2
55
234.7
99.6
16
14.7
6.3
76
70.0
29.7
36
125.2
53.1
96
180.4
76.6
56
235.6
100.0
17
15.6
6.6
77
70.9
30.1
37
126.1
53.5
97
181.3
77.0
57
236.6
100.4
18
16.6
7.0
78
71.8
30.5
38
127.0
53.9
98
182. 3
77.4
58
237.5
100.8
19
17.5
7.4
79
72.7
30.9
39
128.0
54.3
99
183.2
77.8
59
238.4
101.2
20
18.4
7.8
80
73.6
31.3
40
128.9
54.7
200
184.1
78.1
60
239.3
101.6
21
19.3
8.2
81
74.6
31.6
141
129.8
55.1
201
185.0
78.5
261
240.3
102.0
22
20.3
8.6
82
75.5
32.0
42
130.7
55.5
02
185.9
78.9
62
241.2
102.4
23
21.2
9.0
83
76.4
32.4
43
131.6
55.9
03
186.9
79.3
63
242.1
102.8
24
22.1
9.4
84
77.3
32.8
44
132.6
56.3
04
187.8
79.7
64
243.0
103.2
25
23.0
9.8
85
78.2
33.2
45
133.5
56.7
05
188.7
80.1
65
243.9
103.5
26
23.9
10.2
86
79.2
33.6
46
134.4
57.0
06
189.6
80.5
66
244.9
103.9
27
24.9
10.5'
87
80.1
34.0
47
135.3
57.4
07
190.5
80.9
67
245.8
104.3
28
25.8
10.9
88
81.0
34.4
48
136.2
57.8
08
191.5
81.3
68
246.7
104.7
29
26.7
11.3
89
81.9
34.8
49
137.2
58.2
09
192.4
81.7
69
247.6
105.1
30
27.6
11.7
90
82.8
35.2
50
138.1
58.6
10
193.3
82.1
70
248.5
105.5
31
28.5
12.1
91
83.8
35.6
151
139.0
59.0
211
194.2
82.4
271
249.5
105.9
32
29.5
12.5
92
84.7
35.9
52
139.9
59.4
12
195.1
82.8
72
250.4
106.3
33
30.4
12.9
93
85.6
36.3
53
140.8
59.8
13
196.1
83.2
73
251.3
106.7
34
31.3
13.3
94
86.5
36.7
54
141.8
60.2
14
197.0
83.6
74
252.2
107.1
35
32.2
13.7
95
87.4
37.1
55
142.7
60.6
15
197.9
84.0
75
253.1
107.5
36
33.1
14.1
96
88.4
37.5
56
143.6
61.0
16
198.8
84.4
76
254.1
107.8
37
34.1
14.5
97
89.3
37.9
57
144.5
61.3
17
199.7
84.8
77
255.0
108.2
38
35.0
14.8
98
90.2
38.3
58
145.4
61.7
18
200.7
85.2
78
255.9
108.6
39
35.9
15.2
99
91.1
38.7
59
146.4
62.1
19
201.6
85.6
79
256.8
109.0
40
36.8
15.6
100
92.1
39.1
60
147.3
62.5
20
202.5
86.0
80
257.7
109.4
41
37.7
16.0
101
93.0
39.5
161
148.2
62.9
221
203.4
86.4
281
258.7
109.8
42
38.7
16.4
02
93.9
39.9
•62
149.1
63.3
22
204.4
86.7
82
259.6
110.2
43
39.6
16.8
03
94.8
40.2
63
150.0
63.7
23
205.3
87.1
83
260.5
110.6
44
40.5
17.2
04
95.7
40.6
64
151.0
64.1
24
206.2
87.5
84
261.4
111.0
45
41.4
17.6
05
96.7
41.0
65
151.9
64.5
25
207.1
87.9
85
262.3
111.4
46
42.3
18.0
06
97.6
41.4
66
152.8
64.9
26
208.0
88.3
86
263.3
111.7
47
43.3
18.4
07
98.5
41.8
67
153.7
65.3
27
209.0
88.7
87
264.2
112.1
48
44.2
18.8
08
99.4
42.2
68
154.6
65.6
28
209.9
89.1
88
265.1
112.5
49
45.1
19.1
09
100.3
42.6
69
155.6
66.0
29
210.8
89.5
89
266.0
112.9
50
46.0
19.5
10
101.3
43.0
70
156.5
66.4
30
211.7
89.9
90
266.9
113.3
51
46.9
19.9
111
102.2
43.4
171
157.4
66.8
231
212.6
90.3
291
267.9
113.7
52
47.9
20.3
12
103.1
43.8
72
158.3
67.2
32
213.6
90.6
92
268.8
114.1
53
48.8
20.7
13
104.0
44.2
73
159.2
67.6
33
214.5
91.0
93
269.7
114.5
54
49.7
21.1
14
104.9
44.5
74
160.2
68.0
34
215.4
91.4
94
270.6
114.9
55
50.6
21.5
15
105.9
44.9
75
161.1
68.4
35
216.3
91.8
95
271.5
115.3
56
51.5
21.9
16
106.8
45.3
76
162.0
68.8
36
217.2
92.2
96
272.5
115.7
57
52.5
22.3
17
107.7
45.7
77
162.9
69.2
37
218.2
92.6
97
273.4
116.0
58
53.4
22.7
18
108.6-
46.1
78
163.8
69.6
38
219.1
93.0
98
274.3
116.4
59
54.3
23.1
19
109.5
46.5
79
164. 8
69.9
39
220.0
93.4
99
275.2
116.8
60
55.2
23.4
20
110.5
46.9
80
165.7
70.3
40
220.9
93.8
300
276.2
117.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. 1 Lat.
67° (113°, 247°, 293°).
TABLE 2. [Page 577
Difference of Latitude and Departure for 23° (157°, 203°, 337°).
Dist.
Lat.
Dep.
Dirt. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
277.1
117.6
361 33213
141.1
421
387.5
164.5
481
442.7
188.0
541
498.0
211.4
02
278.0
118.0
62 333.2
141.5
22
388.5 |164.9
82
443.7
188.4
42
498.9
211.8
03
278.9
118.4
63
334.1
141.8
23
389.4
165.3
83
444.6
188.8
43
499.8
212.2
04
279.8
118.8
64
335.1
142.2
24
390.3
165.7
84
445.5
189.2
44
500.7
212.6
05
280.8
119.2
65
336.0 142.6
25
391.2
166.1
85
446.4
189.5
45
501.7
213.0
06
281.7
119. 6
66
336.9
143.0
26
392.1
166.5
86
447.3
189.9
46
502.6
213.4
07
282.6
120.0
67
337.8
143.4
27
393.1
166.8
87
448.3
190.2
47
503.5
213.8
08
283.5
120.4
68
338.7
143. 8
28
394.0 J167.2
88
449.2 190.6
48
504.4
214.2
09
284.4
120.8
69
339.7
144.2
29
394.9 167.6
89
450.1 i 191.0
49
505.3
214.6
10
285.4
121.2
70
340.6 144.6
30
395.8 168.0
90
451.0 191.4
50
506.3
215.0
311
286.3
121.6
3V 1
341.5
431
396.7 168.4
491
451.9 191.8
551
507.2
215.3
12
287.2
121.9
72
342.4 145.4
32
397.7 168.8
92
452.9 ;192.2
52
508.1
215.6
13
288.1
122.3
73
343. 4 145. 7
33
398. 6 1 169. 2
93
453. 8 192. 6
53
509.0
216.0
14
289.0
122.7
74
344.3 14(1.1
34
399.5 J169.6
94
454. 7 193. 0
54
509.9
216.4
15
290.0
123.1
75
345.2 146.5
35
400.4 170.0
95
455.6
193.4
55 1 510. 9
216.8
16
290.9
123.5
76
346. 1 146. 9
36
401.3 170.4
96
456.6
193.8
56 511. 8
217.2
17
291.8
123.9
77
317.0 147.3
37
402. 3 170. 8
97
457.5
194.2
57 512. 7
217.6
18
292. 7
124.3
78
348.0 147.7
38
403.2 171.1
98
458.4
194.6
58 ! 513. 6
218.0
19
293.6
124.6
79
348.9
148.1
39
404.1 1171.5
99
459.3
195.0
59 514. 5
218.4
20
294.6
125.0
80
349.8
148. 5
40
405.0 j 171. 9
500
460.2
195.4
60 515. 5
218.8
321
295. 5
125.4
381
350. 7
148.9
441
405. 9 1 172. 3
501
461.2
195.8
561 516. 4
219.2
22
296.4
125.8
82
351.6
149.3
42
406.9 172.7
02
462.1
196.2
62 517. 3
219.6
23
297.3
126.2
83
352. 6
149.7
43
407.8 '173.1
03
463.0
196.6
63 518. 2
220.0
24
298.2
126.6
84 353. 5
150.0
44
408.7 173.5
04
463.9
197.0
64 519. 2
220. 4
25
299.2
127.0
85 354. 4
150.4
45
409.6
173.9
05
464.9
197.4
65 520. 1
220. 8
26
300.1
127.4
86 355. 3
150. 8
46
410.5
174.3
06
465.8
197.8
66 521. 0
221.2
27
301.0
127.8
87 356.2 151.2
47 411. 5
174.7
07
466.7
198.1
67 521.9
221.6
28
301.9
128.2
88 i 357.2 151.6
48 412. 4
175.1
08
467.6
198.5
68
522.8
222.0
29
302.8
128.6
89 358. 1
152.0
49 413. 3
175. 4
09
468.5
198.8
69 523. 8
222.3
30
303.8
128.9
90 359.0
152.4
50 414. 2
175.8
10
469.5
199.3
70 524. 7
222. 7
331
304.7
129.3
391 359.9
152. 8
451 415. 2
176.2
511
470.4
199.7
571 525. 6
223. 1
32
305.6
129. 7
92 i 360.8
153.2
52 416. 1
176.6
12
471.3
200.0
72 526. 5
223.4
33
306.5
130. 1
93 361. 8
153. 6
53 417.0
177.0
13
472.2
200.4
73 527. 4
223.8
34
307.5
130.5
94 362. 7
154.0
54 417. 9
177.4
14
473.1
200.8
74 528. 4
224. 2
35
308.4
130.9
95 363. 6
154.3
55
418.8
177.8
15
474.0
201.2
75 529. 3
224.6
36
309.3
131.3
96 364. 5
154.7
56
419.8
178.2
16
475.0
201.6
76 530. 2
225. 0
37
310. 2
131.7
97 365. 4
155. 1
57
420.7
178.6
17
475.9
202.0
77 531. 1
225.4
38
311.1
132.1
98 : 366.4
155.5
58
421.6
179.0
18
476.8
202.4
78 532. 0
225. 8
39
312.1
132.5
99 ! 367.3
155.9
59
422. 5
179.4
19
477.7
202.8
79
533.0
226.2
40 313. 0
132.9
400 368. 2
156.3
60
423.4
179.7
20
478.6
203.2
80
533.9
226.6
341
313.9
133.2
401 1 369.1
156.7
461
424.4
180.1
521
479.6
203.6
581 | 534.8
227.0
42
314.8
133.6
02 I 370. 0
157. 1
62
425.3
180.5
22
480.5
204.0
82
535. 7
227.4
43
315.7
134.0
03 1 371.0
157. 5
63
426.2
180.9
23
481.4
204.4
83
536.6
227.8
44
316.7
134.4
04 i 371.9
157. 9
64
427. 1 181. 3
24
482.3
204.8
84
537.6
228.2
45
317.6
134.8
05 i 372.8
158.3
65
428.0
181.7
25
483.2
205.2
85
538.5
228.6
46
318.5
135.2
06 373. 7
158.6
66
429.0
182.1
26
484.2
205.5
86
539.4
229.0
47
319.4
135.6
07
374.6
159.0
67
429.9
182.5
27
485.1
205.9
87
540. 3 229. 4
48
320. 3
136.0
08
375. 6
159.4
68
430.8
182.9
28
486.0
206.3
88
541.2 229.8
49
321.3
136.4
09
376.5
159.8
69
431.7
183.3
29
486.9
206.7
89
542. 2 230. 2
50
322. 2
136.8
10
377. 4
160.2
70
432.6
183.7
30
487.8
207.1
90
543. 1 230. 6
351
323.1
137.2
411 378. 3
160.6
471
433.6
184.0
531
488.8
207.4
591 544.0 231.0
52 i 324.0
137.5
12
379.3
161.0
72
434.5
184.4
32
489.7
207.8
92 544. 9 231. 3
53
324.9
137.9
13
380.2
161.4
73
435.4
184.8
33
490.6
208.2
93 545. 8 231. 7
54
325.9
138.3
14
381.1
161.8
74
436.3
185.2
34
491.5
208.6
94
546. 8 232. 0
56
326.8
138. 7
15
382. 0
162.2
75
437.2
185.6
35
492.5
209.0
95
547.7 232.4
56
327.7
139.1
16
382.9
162.5
76
438.2
186.0
36
493.4
209.4
96
548.6 1 232.8
57
328.6
139.5
17
383.9
162.9
77
439.1
186.4
37
494.3
209.8
97
549. 5
233.2
58
329.5
139.9
18
384.8
163.3
78
440.0
186.8
38
495.2
210. 2
98
550. 4 233. 6
59
330. 5
140.3
19
385.7
163.7
79
440.9
187.2
39
496.1
210.6
99
551. 3 234. 0
60
331.4
140.7
20
386.6
164.1
80
441.8
187.6
40
497.1
211.0
600
552.3
234. 4
Dist,
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
67°(113°, 247°, 293°).
Page 578] TABLE 2.
Difference of Latitude and Departure for 24° ( 156°, 204°, 336° ) .
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.7
24.8
121
110.5
49.2
181
165.4
73.6
241
220.2
98.0
2
1.8
0.8
62
56.6
25.2
22
111.5
49.6
82
166. 3
74.0
42
221.1
98.4
3
2.7
1.2
63
57.6
25.6
23
112.4
50.0
83
167.2
74.4
43
222.0
98.8
4
3.7
1.6
64
58.5
26.0
24
113. 3
50.4
84
168.1
74.8
44
222.9
99.2
5
4.6
2.0
65
59.4
26.4
25
114.2
50.8
85
169.0
75.2
45
223.8
99.7
6
5.5
2.4
66
60.3
26.8
26
115.1
51.2
86
169. 9
75.7
46
224.7
100.1
7
6.4
2.8
67
61.2
27.3
27
116.0
51.7
87
170.8
76.1
47
225.6
100.5
8
7.3
3.3
68
62.1
27.7
28
116.9
52.1
88
171.7
76.5
48
226.6
100.9
9
8.2
3.7
69
63.0
28.1
29
117.8
52.5
89
172.7
76.9
49
227.5
101.3
10
9.1
4.1
70
63.9
28.5
30
118.8
52.9
90
173.6
77.3
50
228.4
101.7
11
10.0
4.5
71
64.9
28.9
131
119.7
53.3
191
174.5
77.7
251
229.3
102.1
12
11.0
4.9
72
65.8
29.3
32
120.6
53.7
92
175.4
78.1
52
230.2
102.5
13
11.9
5.3
73
66.7
29.7
33
121. 5
54.1
93
176. 3
78.5
53
231.1
102.9
14
12.8
5.7
74
67.6
30.1
34
122.4
54.5
94
177.2
78.9
54
232.0
103.3
15
13.7
6.1
75
68.5
30.5
35
123.3
54.9
95
178.1
79.3
55
233.0
103.7
16
14.6
6.5
76
69.4
30.9
36
124.2
55.3
96
179.1
79.7
56
233.9
104.1
17
15.5
6.9
77
70.3
31.3
37
125.2
55.7
97
180.0
80.1
57
234.8
104.5
18
16.4-
7.3
78
71.3
31.7
38
126.1
56.1
98 180. 9
80.5
58
235. 7
104.9
19 17. 4
7.7
79
72.2
32.1
39
127.0
56.5
99 181. 8
80.9
59
236.6
105.3
20 ! 18.3
8.1
80
73.1
32.5
40
127.9
56.9
200 182. 7
81.3
60
237. 5
105.8
21
19.2
8.5
81
74.0
32.9
141
128.8
57.3
201
183. 6
81.8
261
238.4
106.2
22
20.1
8.9
82
74.9
33.4
42
129.7
57.8
02
184.5
82.2
62
239.3
106.6
23
21.0
9.4
83
75.8
33.8
43
130.6
58.2
03
185.4
82.6
63
240.3
107.0
24
21.9
9.8
84
76.7
34.2
44
131.6
58.6
04
186.4
83.0
64
241.2
107.4
25
22.8
10.2
85
77.7
34.6
45
132.5
59.0
05
187.3
83.4
65
242.1
107.8
26
23.8
10.6
86
78.6
35.0
46
133.4
59.4
06
188. 2
83.8
66
243.0
108.2
27
24.7
11.0
87
79.5
35.4
47
134.3
59.8
07
189. 1
84.2
67
243.9
108.6
28
25.6
11.4
88
80.4
35.8
48
135. 2
60.2
08
190.0
84.6
68
244.8
109.0
29
26.5
11.8
89
81.3
36.2
49
136. 1
60.6
09
190.9
85.0
69
245.7
109.4
30
27.4
12.2
90
82.2
36.6
50
137.0
61.0
10
191.8
85.4
70
246.7
109.8
31
28.3
12.6
91
83.1
37.0
151
137.9
61.4
211
192.8
85.8
271
247.6
110.2
32
29.2
13.0
92
84.0
37.4
52
138.9
61.8
12
193. 7
86.2
7-2
248.5
110.6
33
30.1
13.4
93
85.0
37.8
53
139. 8
62.2
13
194. 6
86.6
73
249.4
111.0
34
31.1
13.8
94
85.9
38.2
54
140.7
62.6
14
195. 5
87.0
74
250.3
111.4
35
32.0
14.2
95
86.8
38.6
55
141.6
63.0
15
196.4
87.4
75
251.2
111.9
36
32.9
14.6
96
87.7
39.0
56
142.5
63.5
16
197.3
87.9
76
252.1
112.3
37
33.8
15.0
97
88.6
39.5
57
143.4
63.9
17
198. 2
88.3
77
253. 1
112.7
38
34.7
15.5
98
89.5
39.9
58
144.3
64.3
18
199.2
88.7
78
254.0
113.1
39
35.6
15.9
99
90.4
40.3
59
145.3
64.7
19
200.1
89.1
79
254.9
113.5
40
36.5
16.3
100
91.4
40.7
60
146.2
65.1
20
201.0
89.5
80
255. 8
113.9
41
37.5
16.7
101
92.3
41.1
161
147.1
65.5
221
201.9
89.9
281
256. 7
114.3
42
38.4
17.1
02
93.2
41.5
62
148. 0
65.9
22
202.8
90.3
82
257. 6
114. 7-
43
39.3
17.5
03
94.1
41.9
63
148.9
66.3
23
203.7
90.7
83
258. 5
115. 1
44
40.2
17.9
04
95.0
42.3
64
149. 8
66.7
24
204.6
91.1
84
259. 4
115.5
45
41.1
18.3
05
95.9
42.7
65
150.7
67.1
25
205.5
91.5
85
260.4
115.9
46
42.0
18.7
06
96.8
43.1
66
151.6
67.5
26
'206.5
91.9
86
261.3
116.3
47
42.9
19.1
07
97.7
43.5
67
152.6
67.9
27
207. 4
92.3
87
262.2
116.7
48
43.9
19.5
08
98.7
43.9
68
153.5
68.3
28
208.3
92.7
88
263.1
117.1
49
44.8
19.9
09
99.6
44.3
69
154.4
68.7
29
209.2
93.1
89
264. 0
117.5
50
45.7
20.3
10
100.5
44.7
70
155.3
69.1
30
210.1
93.5
90
264.9
118. 0
51
46.6
20.7
111
101.4
45.1
171
156.2
69.6
231
211.0
94.0
291
265. 8
1 18. 4
52
47.5
21.2
12
102.3
45.6
72
157. 1
70.0
32
211*9
94,4
92
266. 8
118. 8
53
48.4
21.6
13
103.2
46.0
73
158.0
70.4
33
212.9
94.8
93
267.7
119.2
54
49.3
22.0
14
104.1
46.4
74
159.0
70.8
34
213.8
95.2
94
268.6
119.6
55
50.2
22.4
15
105.1
46.8
75
159.9
71,2
35
214.7
95.6
95
269. 5
120.0
56
51.2
22.8
16
106.0
47.2
76
160.8
7176
36
215.6
96.0
96
270.4
120.4
57
52.1
23.2
17
106.9
47.6
77
16X.7
72.0
37
216.5
96.4
97
271.3
120.8
58
53.0
23.6
18
107.8
48.0
78
162.6
72.4
38
217.4
96.8
98
272. 2
121.2
59
53.9
24.0
19
108.7
48.4
79
163. 5
72.8
38
218.3
97.2
99
273.2
121. 6
60
54.8
24.4
20
109.6
48.8
80-
164.4
73.2
40
219. 3
97.6
300
274.1
122.0
Dist. | Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
66° (114°, 246°, 294°).
TABLE 2. [Page
579
Difference of Latitude and Departure for 24° (156°, 204°, 336°).
Dist. Lat. i Dep.
Dist.
Lat. | Dep.
Dist. Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
275.0 122.4
361
329.8
146.8
421
384.6
171.2
481
439.4
195.6
541
494.2
220.0
02
275. 9 i 122. 8
62
330.7
147.2
22
385.5
171.6
82
440.3 196.0
42
495.1
220.4
03
276.8
123.2
63
331.6
147.6
23
386.4
172. 1
83
441.2 196.5
43
496.0
220. 9
04
277.7
123.7
64
332.5
148.1
24
387.3
172.5
84
442. 1 196. 9
44
496.9
221.3
05
278.6
124.1
65
333.4
148.5
25 388. 2
172.9
85
443.0
197.3
45
497.8
221.7
06
279.5
124.5
66
334.3
148.9
26 389. 2
173.3
86
444.0
197.7
46
498.8
222.1
07
280.4
124.9
67
335.3
149.3
27 390. 1
173.7
87
444.9
198.1
47
499.7
222.5
08
281.4
125.3
68
336.2
149.7
28
391.0
174. 1
88
445.8
198.5
48
500.6
222.9
09
282.3
125.7
69
337.1
150.1
29
391.9
174.5
89
446.7
198.9
49
501.5
223.3
10
283.2
126.1
70
338.0
150.5
30
392.8
174.9
90
447.6
199.3
50
502.4
223.7
311
284.1
126.5
371
338.9
150.9
431 ! 393.7
175.3
491
448.6
199.7
551
503.4
224.1
12
285.0
126.9
72
339.8 1151.3
32 394. 6
175.7
92
449.5 200.1
52
504.3
224.5
13
285.9
127.3
73
340.7
151.7
33 395.6
176.1
93
450.4 200.5
53
505.2
224.9
14
286.8
127.7
74
341.7
152.1
34 i 396. 5
176.5
94
451.3 200.9
54
506.1
225.3
15
287. 8
128.1
75
342.6
152.5
35 j 397. 4
176.9
95
452.2 201.3
55
507.0
225. 7
16
288.7
128.5
76
343.5
152.9
36 i 398.3
177.3
96
453.1 1201.7
56
507.9
226.1
17
289.6
128.9
77
344.4
153.3
37 399. 2
177.7
97
454.0 202.2
57
508.8
226.6
18
290.5
129.3
78
345.3
153.7
38 ! 400.1
178.2
98
454.9 !202.6
58
509.7
227.0
19
291.4
129.8
79
346.2
154.2
39 401.0
178.6
99
455.8 203.0
59
510.6
227.4
20
292.3
130.2
80
347.1
154.6
40 402.0
179.0
500
456.8 i203.4
60
511.6
227.8
321
293.2 130.6
381
348. 1 155. 0
441 402. 9 179. 4
501
457.7 ,203.8
561
512.5
228. 2
22
294.2
131.0
82
349.0 155.4
42 1 403.8 179.8
02
458.6 204.2
62
513.4
228.6
23
295.1
131.4
83
349.9 155.8
43 | 404. 7
180.2
03
459.5 ^204.6
63
514.3
229.0
24
296.0
131.8
84
350. 8 i 156. 2
44 405.6
180.6
04
460.4 205.0
64
515.2
229.4
25
296.9
132.2
85
351.7 156.6
45 ! 406.5
181.0
05
461.3 205.4
65
516.1
229. 8
26
297.8
132.6
86
352. 6 157. 0
46 407. 4
181.4
06
462. 2 205. 8
66
517.0
230.2
27
298.7
133.0
87
353.5 157.4
47 408. 3
181.8
07
463. 2 206. 2
67
518.0
230.6
28
299.6
133.4
88 354.4 1157.8
48 ! 409.3 182.2
08 464. 1 i 206. 6
68
518.9
231.0
29
300.5
133.8
89 355. 4 ! 158. 2
49 1 410.2 182.6
09 1 465. 0 ! 207. 0
69
519.8
231.4
30 301. 5
134.2
90 356.3 158.6
50 411.1 i 183.0
10 465.9 ^207.4
70
520.7
231.8
331 i 302.4
134.6
391 357. 2 1 159. 0
451 412. 0 183. 4
511
466.8 207.8
571
521.6
232.2
32 303.3
135. 0
92 358.1 J159.4
52 412. 9
183.8
12
467.7 208.2
72
522.5
232.7
33 ! 304.2
135.4
93 359.0 159.8
53 413. 8
184.3
13
468.6 208.7
73
523. 4
233.1
34
305. 1 1 135. 9
94 359. 9 ; 160. 3
54 I 414. 7
184.7
14
469.5
209.1
74
524.3
233. 5
35
306.0 136.3
95 360. 8 160. 7
55 415. 7
185.1
15
470.5
209.5
75
525.3
233. 9
36
306.9 136.7
96 361.8 161.1
56 i 416.6
185.5
16
471.4
209.9
76
526.2
234.3
37
307.9 137.1
97 362. 7
161.5
57 417. 5
185.9
17
472.3
210.3
77
527.1
234.7
38
308.8 137.5
98 363. 6
161.9
58
418.4
186.3
18
473.2
210.7
78
528.0
235. 1
39
309.7 137.9
99 i 364.5 162.3
59
419. 3 j 186. 7
19
474.1
211.1
79
528. 9
235.5
40
310.6 138.3
400 365.4 162.7
60 i 420. 2 i 187. 1
20
475.0
211.5
80
529.8
235.9
341
311.5 138.7
401 366. 3 163. 1
461
421.1 ,187.5
521
475.9 211.9
581
530.8
236.3
42
312. 4 139. 1
02 I 367.2 163.5
62
422. 0 1 187. 9
22
476.8
212.3
82
531.7
236.7
43
313.3 139.5
03 368.2 163.9
63
423.0 188.3
23
477.8
212.7
83
532.6
237.1
44
314.3 139.9
04 369.1 164.3
64
423.9 188.7
24
478.7
213.1
84
533.5
237. 5
45
315.2 140.3
05 370.0 164.7
65
424.8 189.1
25
479.6
213.5
85
534.4
237.9
46
316.1 1140.7
06 370.9
165.1
66
425. 7 ! 189. 5
26
480.5
213.9
86
535.3
238.3
47
317.0
141.1
07 I 371.8
165.5
67
426. 6 i 189. 9
27
481.4
214.4
87
536.2
238.8
48
317.9
141.5
08 372. 7
165.9
68
427.5 1190.4
28
482.3
214.8
88
537.1
239.2
49
318.8
142.0
09 373. 6
166.4
69
428.4 190.8
29
483.2
215.2
89
538.0
239.6
50
319.7 142.4
10 374. 5
166.8
70
429.4
191.2
30
484.2
215.6
90
539.0
240.0
351
320.6 142.8
411 375. 5
167.2
471 i 430.3
191.6
531
485.1
216.0
591
539.9
240.4
52
321.6
143.2
12 376«4
167.6
72 431. 2
192.0
32
486.0
216.4
92
540.8
240.8
53
322.5
143.6
13 377. 3
168.0
73
432.1
192.4
33
486.9
216.8
93
541.7
241.2
54
323.4
144.0
14
378.2
168.4
74
433.0
192.8
34
487.8
217.2
94
542.6
241.6
55
324.3
144.4
15
379.1
168.8
75
433.9
193.2
35
488.7
217.6
95
543.5
242.0
56
325.2
144.8
16
380.0
169.2
76
434.8
193.6
36
489.6
218.0
96
544.4
242.4
57
326.1
145. 2
17
380.9
169.6
77
435.8
194.0
37
490.6
218.4
97
545.4
242.8
58
327.0
145.6
18
381.9
170.0
78
436.7
194.4
38
491.5
218.8
98
546.3
243.2
59
328.0
146.0
19
382.8
170.4
79
437.6
194.8
39
492.4
219.2
99
547.2
243.6
60
.
328.9
146.4
20
383.7
170.8
80
438.5
195.2
40
493.3
219.6
600
548.1
244.0
JDist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
66° (114°, 246°, 294°).
Page 580] TABLE 2.
Difference of Latitude and Departure for 25° (155°, 205°, 335°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.3
25.8
121
109.7
51.1
181
164.0
76.5
241
218.4
101.9
2
1.8
0.8
62
56.2
26.2
22
110.6
51.6
82
164.9
76.9
42
219.3
102.3
3
2.7
1.3
63
57.1
26.6
23
111.5
52.0
83
165. 9
77.3
43
220.2
102.7
4
3.6
1.7
64
58.0
27.0
24
112.4
52.4
84
166. 8
77.8
44
221.1
103.1
5
4.5
2.1
65
58.9
27.5
25
113.3
52.8
85
167.7
78.2
45
222.0
103.5
6
5.4
2.5
66
59.8
27.9
26
114.2
53.2
86
168.6
78.6
46
223.0
104.0
7
6.3
3.0
67
60.7
28.3
27
115.1
53.7
87
169.5
79.0
47
223.9
104.4
8
7.3
3.4
68
61.6
28.7
28
116.0
54.1
88
170.4
79.5
48
224.8
104.8
9
8.2
3.8
69
62.5
29.2
29
116.9
54.5
89
171.3
79.9
49
225. 7
105.2
10
9.1
4.2
70
63.4
29.6
30
117.8
54.9
90
172.2
80.3
50
226.6
105.7
11
10.0
4.6
71
64.3
30.0
131
118.7
55.4
191
173.1
80.7
251
227.5
106.1
12
10.9
5.1
72
65.3
30.4
32
119.6
55.8
92
174.0
81.1
52
228.4
106.5
13
11.8
5.5
73
66.2
30.9
33
120.5
56.2
93
174.9
81.6
53
229.3
106.9
14
12.7
5.9
74
67.1
31.3
34
121. 4
56.6
94
175.8
82.0
54
230.2
107.3
15
13.6
6.3
75
68.0
31.7
35
122.4
57.1
95
176.7
82.4
55
231.1
107.8
16
14.5
6.8
76
68.9
32.1
36
123.3
57.5
96
177.6
82.8
56
232.0
108.2
17
15.4
7.2
77
69.8
32.5
37
124.2
57.9
97
178.5
83.3
57
232.9
108.6
18
16.3
7.6
78
70.7
33.0
38
125.1
58.3
98
179.4
83.7
58-
233. 8
109.0
19
17.2
8.0
79
71.6
33.4
39
126.0
58.7
99
180.4
84.1
59
234.7
109.5
20
18.1
8.5
80
72.5
33.8
40
126.9
59.2
200
181.3
84.5
60
235.6
109.9
21
19.0
8.9
81
73.4
34.2
141
127.8
59.6
201
182.2
84.9
261
236.5
110.3
22
19.9
9.3
82
74.3
34.7
42
128.7
60.0
02
183.1
85.4
62
237.5
110.7
23
20.8
9.7
83
75.2
35.1
43
129.6
60.4
03
184.0
85.8
63
238.4
111.1
24
21.8
10.1
84
76.1
35.5
44
130.5
60.9
04
184.9
86.2
64
239.3
111.6
25
22.7
10.6
85
77.0
35.9
45
131.4
61.3
05
185.8
86.6
65
240.2
112.0
26
23.6
11.0
86
77.9
36.3
46
132.3
61.7
06
186.7
87.1
66
241.1
112.4
27
24.5
11.4
87
78.8
36.8
47
133.2
62.1
07
187.6
87.5
67
242.0
112.8
28
25.4
11.8
88
79.8
37.2
48
134. 1
62.5
08
188.5
87.9
68
242.9
113.3
29
26.3
12.3
89
80.7
37.6
49
135.0
63.0
09
189.4
88.3
69
243.8
113.7
30
27.2
12.7
90
81.6
38.0
50
135.9
63.4
10
190. 3
88-7
70
244.7
114.1
31
28.1
13.1
91
82.5
38.5
151
136.9
63.8
211
191.2
89.2
271
245.6
114.5
32
29.0
13.5
92
83.4
38.9
52
137.8
64.2
12
192.1
89.6
72
246.5
115.0
33
29.9
13.9
93
84.3
39.3
53
138.7
64.7
13
193.0
90.0
73
247.4
115.4
34
30.8
14.4
94
85.2
39.7
54
139.6
65.1
14
193.9
90.4
74
248.3
115.8
35
31.7
14.8
95
86.1
40.1
55
140.5
65.5
15
194.9
90.9
75
249.2
116.2
36
32.6
15.2
96
87.0
40.6
56
141.4
65.9
16
195.8
91.3
76
250.1
116.6
37
33.5
15.6
97
87.9
41.0
57
142. 3
66.4
17
196.7
91.7
77
251.0
117.1
38
34.4
16.1
98
88.8
41.4
58
143.2
66.8
18
197.6
92.1
78
252.0
117.5
39
35.3
16.5
99
89.7
41.8
59
144.1
67.2
19
198.5
92.6
79
252.9
117.9
40
36.3
16.9
100
90.6
42.3
60
145.0
67.6
20
199.4
93.0
80
253.8
118.3
41
37.2
17.3
101
91.5
42.7
161
145.9
68.0
221
200.3
93.4
281
254.7
118.8
42
38.1
17.7
02
92.4
43.1
62
146.8
68.5
22
201.2
93.8
82
255.6
119.2
43
39.0
18.2
03
93.3
43.5
63
147.7
68.9
23
202.1
94.2
83
256.5
119.6
44
39.9
18.6
04
94.3
44.0
64
148.6
69.3
24
203.0
94.7
84
257.4
120.0
45
40.8
19.0
05
95.2
44.4
65
149.5
69.7
25
203.9
95.1
85
258.3
120.4
46
41.7
19.4
06
96.1
44.8
66
150.4
70.2
26
204.8
95.5
86
259.2
120.9
47
42.6
19.9
07
97.0
45.2
67
151.4
70.6
27
205.7
95.9
87
260.1
121.3
48
43.5
20.3
08
97.9
45.6
68
152. 3
71.0
28
206.6
96.4
88
261.0
121.7
49
44.4
20.7
09
98.8
46.1
69
153.2
71.4
29
207.5
96.8
89
261.9
122.1
50
45.3
21.1
10
99.7
46.5
70
154.1
71.8
30
208.5
97.2
90
262.8
122.6
51
46.2
21.6
111
100.6
46.9
171
155.0
72.3
231
209.4
97.6
291
263.7
123.0
52
47.1
22.0
12
101.5
47.3
72
155.9
72.7
32'
210.3
98.0
92
264.6
123.4
53
48.0
22.4
13
102.4
47.8
73
156. 8
73.1
33
211.2
98.5
93
265.5
123.8
54
48.9
22.8
14
103.3
48.2
74
157. 7
73.5
34
212.1
98.9
94
266.5
124.2
55
49.8
23.2
15
104.2
48.6
75
158.6
74.0
35
213.0
99.3
95
267.4
124.7
56
50.8
23.7
16
105.1
49.0
76
159.5
74.4
36
213.9
99.7
96
268.3
125.1
57
51.7
24.1
17
106.0
49.4
77
160.4
74.8
37
214.8
100.2
97
269.2
125.5
58
52.6
24.5
18
106.9
49.9
78
161.3
75.2
38
215.7
100.6
98
270.1
125.9
59
53.5
24.9
19
107.9
50.3
79
162.2
75.6
39
216. 6
101.0
99
271.0
126.4
60
54.4
25.4
20
108.8
50.7
80
163.1
76.1
40
217.5
101.4
300
271.9
126.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat."
65° (115°, 245°, 295°).
TABLE 2. [Page 581
Difference of Latitude and Departure for 25° (155°, 205°, 335°).
Dist. 1 Lat. ! Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
272.8 127.2
361
327.1
152. 5
421
381.5
177.9
481
435.9
203.3
541
490.3
228.6
02
273. 7 ! 127. 6
62
328.0
153.0
22
382.4
178. 3
82
436.8
203.7
42
491.2
229.0
03
274. 6 1 128. 0
63
329.0
153.4
23
383.3
178.7
83
437.7
204.1
43
492.1
229.4
04
275. 5
128.4
64
329.9
153.8
24
384.2
179.2
84
438.6
204.5
44
493.0
229.9
05
276.4
128.9
65
330.8
154. 2
25
385.1
179.6
85
439.5
204.9
45
493.9
230.3
06
277.3
129.3
66
331.7
154.6
26
386.0
180.0
86
440.4
205.4
46
494.8
230.7
07
278.2
129.7
67
332.6
155.1
27
387.0
180.4
87
441.3
205.8
47
495.7
231.1
08
279.1
130.1
68
333.5
155.5
28
387.9
180.9
88
442.2
206.2
48
496.6
231.6
09
280.0
130.6
69
334.4
155.9
29
388.8
181.3
89
443.1
206.6
49
497.5
232.0
10
280.9
131.0
70
335.3
156.3
30
389.7
181.7
90
444.0
207.1
50
498.4
232.4
311
281.8
131.4
371
336.2
156.8
431
390.6
182.1
491
444.9 J207.5
551
499.3
232.8
12
282.7
131.8
72
337.1
157.2
32
391.5
182.5
92
445.9
207.9
52
500.2
233.2
13
283.6
132.2
73
338.0
157.6
33
392.4
183.0
93
446.8
208.3
53
501.1
233.7
14
284.5
132.7
74
338.9
158.0
34
393.3
183.4
94
447. 7 | 208. 7
54
502.0
234.1
15
285.4
133.1
75
339.8
158.5
35
394.2
183.8
95
448.6
209.1
55
503.0
234.5
16
286.4 133.5
76
340.7
158.9
36
395. 1 1 184. 2
96
449.5
209.6
56
503.9
235.0
17
287.3 133.9
77
341.6
159.3
37
396. 0 184. 7
97
450.4
210.0
57
504.8
235.4
18
288.2 134.4
78
342.5
159.7
38
396. 9 185. 1
98
451.3 J210.4
58
505.7
235.8
19
289.1 134.8
79
343.5
160.1
39
397.8 |185.5
99
452.2 210.9
59
506.6
236.2
20
290.0 135.2
80
344.4
160.6
40
398. 7 i 185. 9
500
453.1 211.3
60
507.5
236.6
321
290.9 135.6
381
345.3
161.0
441
399.6
186.3
501
454.0
211.7
561
508.4
237.1
22
291.8
136.1
82
346.2
161.4
42
400.6
186.8
02
454.9
212.1
62
509.3
237.5
23
292.7
136.5
83
347.1
161.8
43
401.5
187.2
03
455.8
212.5
63
510.2
237.9
24
293.6 136.9
84
348.0
162.3
44
402.4
187.6
04
456.7
213.0
64
511.1
238.3
25
294.5 137.3
85
348.9
162.7
45
403.3
188.0
05
457.7
213.4
65
512.0
238.7
26
295.4
137.7
86
349.8
163.1
46
404.2
188.5
06
458.6
213.8
66
512.9
239.2
27
296.3
138.2
87
350.7
163.5
47
405.1
188.9
07
459.5
214.2
67
513.8
239.6
28
297.2
138.6
88
351.6
163.9
48
406.0
189.3
08
460.4
214.7
68
514.8
240.1
29
298.1
139.0
89
352.5
164.4
49
406. 9 1 189. 7
09
461.3
215.1
69
515.7
240.5
30
299.0
139.4
90
353.4
164.8
50
407. 8 ( 190. 1
10
462.2
215.5
70
516.6
240.9
331
300.0
139.9
391
354.3
165.2
451
408.7
190.6
511
463.1
215.9
571
517.5
241.3
32
300.9
140.3
92
355.2
165.6
52
409.6
191.0
12
464.0
216.4
72
518.4
241.7
33
301.8
140.7
93
356.1
166.1
53
410.5
191.4
13
464.9
216.8
73
519.3
242.1
34
302.7
141.1
94
357.0
166.5
54
411.4
191.8
14
465.8
217.2
74
520.2
242.6
35
303.6
141.5
95
358.0
166.9
55
412.3
192.3
15
466.7
217.7
75
521.1
243.0
36
304.5
142.0
96
358.9
167.3
56
413.2
192.7
16
467.6
218.1
76
522.0
243.4
37
305.4
142.4
97
359.8
167.7
57
414.1
193.1
17
468.5
218.5
77
522.9
243.8
38
306.3
142.8
98
360.7
168.2
58
415.1
193.5
18
469.4
218.9
78
523.8
244.3
39
307.2
143.2
99
361.6
168.6
59
416.0
194.0
19
470.3
219.3
79
524.7
244.7
40
308.1
143.7
400
362.5
169.0
60
416.9
194.4
20
471.2
219.8
80
525.6
245.1
341
309.0
144.1
401
363.4
169.4
461
417.8
194.8
521
472.2
220.2
581
526.5
245.5
42
309.9
144.5
02
364.3
169.9
62
418.7
195.2
22
473.1
220.6
82
527.4
246.0
43
310.8
144.9
03
365.2
170.3
63
419.6
195.6
23
474.0
221.0
83
528.3
246.4
44
311.7
145.4
04
366.1
170.7
64
420.5
196.1
24
474.9
221.4
84
529.3
246.8
45
312.6
145.8
05
367.0
171.1
65
421.4
196.5
25
475.8
221.9
85
530.2
247.2
46 I 313. 5
146.2
06
367.9
171.6
66
422.3
196.9
26
476.7
222.3
86
531.1
247.7
47 314.5
146.6
07
368.8
172.0
67
423.2
197.3
27
477.6
222.7
87
532.0
248.1
48 315. 4
147.0
08
369.7
172.4
68
424.1
197.8
28
478.5
223.2
88
532.9
248.5
49 316. 3
147.5
09
370.6
172.8
69
425.0
198.2
29
479.4
223.6
89
533.8
248.9
50 317. 2
147.9
10
371.5
173.2
70
425.9
198.6
30
480.3
224.0
90
534.7
249.4
351 318. 1
148.3
411
372.5
173.7
471
426.8
199.0
531
481.2
224.4
591
535.6
249.8
52 319. 0
148.7
12
373.4
174.1
72
427.7
199.4
32
482.1
224.8
92
536.5
250.2
53 319.9
149.2
13
374.3
174.5
73
428.6
199.9
33
483.0
225.3
93
537.4
250.6
54 320. 8
149.6
14
375.2
174.9
74
429.6
200.3
34
483.9
225.7
94
538.3
251.1
55
321.7
150.0
15
376.1
175.4
75
430.5
200.7
35
484.8
226.1
95
539.2
251.5
56
322.6
150.4
16
377. 0
175.8
76
431.4
201.1
36
485.7
226.5
96
540.1
251. 9
57 323. 5
150.8
17
377.9
176.2
77
432.3
201.6
37
486.7
226.9
97
541.0
252.3
58 324. 4
151.3
18
378.8
176.6
78
433.2
202.0
38
487.6
227.4
98
541.9
252.7
59 325. 3
151.7
19
379.7
177.0
79
434.1
202.4
39
488.5
227.8
99
542.8
253.1
60 | 326. 2
152.1
20
380.6
177.5
80
435.0
202.8
40
489.4
228.2
600
543.8
253.6
Dist. j Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
65° (115°, 245°, 295°).
Page 582] TABLE 2.
Difference of Latitude and Departure for 26° (154°, 206°, 334°) .
Dist.
Lat,
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
54.8
26.7
121
108.8
53.0
181
162.7
79.3
241
216.6
105.6
2
1.8
0.9
62
55.7
27.2
22
109.7
53.5
82
163.6
79.8
42
217.5
106.1
3
2.7
1.3
63
56.6
27.6
23
110.6
53.9
83
164.5
80.2
43
218.4
106.5
4
3.6
1.8
64
57.5
28.1
24
111.5
54.4
84
165.4
80.7
44
219.3
107.0
5
4.5
2.2
65
58.4
28.5
25
112.3
54.8
85
166.3
81.1
45
220.2
107.4
6
5.4
2.6
66
59.3
28.9
26
113.2
55.2
86
167.2
81.5
46
221.1
107.8
7
6.3
3.1
67
60.2
29.4
27
114. 1
55.7
87
168.1
82.0
47
222.0
108.3
8
7.2
3.5
68
61.1
29.8
28
115.0
56.1
88
169.0
82.4
48
222.9
108.7
9
8.1
3.9
69
62.0
30.2
29
115.9
56.5
89
169.9
82.9
49
223.8
109.2
10
9.0
4.4
70
62.9
30.7
30
116.8
57.0
90
170.8
83.3
50
224.7
109.6
11
9.9
4.8
71
63.8
31.1
131
117.7
57.4
191
171.7
83.7
251
225.6
110.0
12
10.8
5.3
72
64.7
31.6
32
118.6
57.9
92
172.6
84.2
52
226.5
110.5
13
11.7
5.7
73
65.6
32.0
33
119.5
58.3
93
173.5
84.6
53
227.4
110.9
14
12.61
- 6.1
74
66.5
32.4
34
120.4
58.7
94
174.4
85.0
54
228.3
111.3
15
13. 5'
6.6
75
67.4
32.9
35
121.3
59.2
95
175.3
85.5
55
229.2
111.8
16
14.4
7.0
76
68.3
33.3
36
122.2
59.6
96
176.2
85.9
56
230.1
112.2
17
15.3
7.5
77
69.2
33.8
37
123.1
60.1
97
177.1
86.4
57
231.0
112.7
18
16.2
7.9
78
70.1
34.2
38
124.0
60.5
98
178.0
86.8
58
231.9
113.1
19
17.1
8.3
79
71.0
34.6
39
124.9
60.9
99
178.9
87.2
59
232.8
113.5
20
18.0
8.8
80
71.9
35.1
40
125.8
61.4
200
179.8
87.7
60
233.7
114.0
21
18.9
9.2
81
72.8
35.5
141
126.7
61.8
201
180.7
88.1
261
234.6
114.4
22
19.8
9.6
82
73.7
35.9
42
127.6
62.2
02
181.6
88.6
62
235.5
114.9
23
20.7
10.1
83
74.6
36.4
43
128.5
62.7
03
182.5
89.6
63
236.4
115. 3
24
21.6
10.5
84
75.5
36.8
44
129.4
63.1
04
183.4
89.4
64
237.3
115.7
25
22.5
11.0
85
76.4
37.3
45
130.3
63.6
05
184.3
89.9
65
238.2
116.2
26
23.4
11.4
86
77.3
37.7
46
131.2
64.0
06
185.2
90.3
66
239.1
116.6
27
24.3
11.8
87
78.2
38.1
47
132.1
64.4
07
186.1
90.7
67
240.0
117.0
28
25.2
12.3
88
79.1
38.6
48
133.0
64.9
08
186.9
91.2
68
240.9
117.5
29
26.1
12.7
89
80.0
39.0
49
133.9
65.3
09
187.8
91.6
69
241.8
117.9
30
27.0
13.2
90
80.9
39.5
50
134.8
65.8
10
188.7
92.1
70
242.7
118.4
31
27.9
13.6
91
81.8
39.9
151
135.7
66.2
211
189.6
92.5
271
243.6
118.8
32
28.8
14.0
92
82.7
40.3
52
136. 6
66.6
12
190.5
92.9
72
244.5
119.2
33
29.7
14.5
93
83.6
40.8
53
137.5
67.1
13
191.4
93.4
73
245.4
119.7
34
30.6
14.9
94
84.5
41.2
54
138.4
67.5
14
192.3
93.8
74
246.3
120.1
35
31.5
15.3
95
85.4
41.6
55
139.3
67.9
15
193.2
94.2
75
247.2
120.6
36
32.4
15.8
96
86.3
42.1
56
140.2
68.4
16
194.1
94.7
76
248.1
121.0
37
33.3
16.2
97
87.2
42.5
57
141.1
68.8
17
195.0
95.1
77
249.0
121.4
38
34.2
16.7
98
88.1
43.0
58
142.0
69.3
18
195.9
95.6
78
249.9
121.9
39
35.1
17.1
99
89.0
43.4
59
142.9
69.7
19
196.8
96.0
79
250.8
122.3
40
36.0
17.5
100
89.9
43.8
60
143.8
70.1
20
197.7
96.4
80
251.7
122.7
41
"36.9
18.0
101
90.8
44.3
161
144.7
70.6
221
198.6
96.9
281
252.6
123.2
42
37.7.
18.4
02
91.7
44.7
62
145.6
71.0
22
199.5
97.3
82
253.5
123.6
43
38,6
18.8
03
92.6
45.2
63
146.5
71.5
23
200.4
97.8
83
254.4
124.1
44
39.5
19.3
04
93.5
45.6
64
147.4
.71.9
24
201.3
98.2
84
255.3
124.5
45
40.4
19.7
05
94.4
46.0
65
148.3
72.3
25
202.2
98.6
85
256.2
124.9
46
41.3
20.2
06
95.3
46.5
66
149. 2
72.8
26
203.1
99.1
86
257.1
125.4
47
42.2
20.6
07
96.2
46.9
67
150.1
73.2
27
204.0
99.5
87
258.0
125.8
48
43.1
21.0
08
97.1
47.3
68
151.0
73.6
28
204.9
99.9
88
258.9
126.3
49
44.0
21.5
09
98.0
47.8
69
151.9
74.1
29
205.8
100.4
89
259.8
126.7
50
44.9
21.9
10
98.9
48.2
70
152.8
74.5
30
206.7
100.8
90
260.7
127.1
51
45.8
22.4
111
99.8
48.7
171
153.7
75.0
231
207.6
101.3
291
261.5
127.6
52
46.7
22.8
12
100.7
49.1
72
154.6
75.4
32
208.5
101.7
92
262.4
128.0
53
47.6
23.2
13
101.6
49.5
73
155.5
75.8
33
209.4
102.1
93
263.3
128.4
54
48.5
23.7
14
102.5
50.0
74
156.4
76.3
34
210.3
102.6
94
264.2
128.9
55
49.4
24.1
15
103.4
50.4
75
157.3
76.7
35
211.2
103.0
95
265. 1
129. 3
56
50.3
24.5
16
104.3
50.9
76
158.2
77.2
36
212.1
103.5
96
266.0
129.8
57
51.2
25.0
17
105.2
51.3
77
159.1
77.6
37
213.0
103.9
97
266.9
130.2
58
52.1
25.4
18
106.1
51.7
78
160.0
78.0
38
213.9
104.3
98
267.8
130.6
59
53.0
25.9
19
107.0
52.2
79
160.9
78.5
39
214. 8
104.8
99
268.7
131.1
60
53.9
26.3
20
107.9
52.6
80
161.8
78.9
40
215.7
105.2
300
269.6
131.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
64° (116°, 244°, 296°).
TABLE -2.
[Page
583
Difference of Latitude and Departure for 26° (154°, 206°, 334).
Dtat
Lat. Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
301
270.5 j 132.0
361 324. 5
158.3
421
378.4
184.6
481 432. 3
210.9
541
486.2
237.2
02
271.4 132.4
62
325.4
158.7
22
379.3
185.0
82
433.2
211.3
42
487.1
237.6
03
272.3 ;132.8
63
326.3
159.1
23 380. 2
185.4
83
434.1
211.7
43
488.0
238.0
04
273.2 J133.3
64
327. 2
159. 6
24 381. 1
185.9
84 435.0
212.2
44
488.9
238.5
05
274.1 ;133.7
65
328.1
160.0
25 382. 0
186.3
85 435.9
212.6
45
489.8
238.9
06
275. 0 i 134. 1
66
329.0
160.4
26 382. 9
186.7
86
436.8
213.0
46
490.7
239.3
07
275. 9 ! 134. 6
67
329.9
160.9
27 383. 8
1S7.2
87
437.7
213.5
47
491.6
239.8
08
276.8
135.0
68
330.8
161.3
28 384. 7
187.6
88
438.6
213.9
48
492. 5
240.2
09
277.7 135.5
69
331.7
161.8
29
385.6
188.1
89
439.5
214.4
49
493.4
240.7
10
278.6 135.9
70 332. 6
162.2
30
386.5
188.5
90
440.4
214.8
50
494.3
241.1
311
279. 5 136. 3
371 333. 5
162.6
431
387.4
188.9
491
441.3
215.2
551
495.2
241.5
12
280.4 136.8
72 334. 4
163.1
32 388. 3
189.4
92
442.2
215. 7
52
496.1
242.0
13
281. 3 i 137. 2
73 335.3 |163.5
33 389. 2
189.8
93
443.1
216.1
53
497.0
242.4
14
282. 2 i 137. 7
74 336. 2
164.0
34
390.1
190.3
94
444.0
216.6
54
497.9
242.9
15
283.1 138.1
75 337. 1
164.4
35
391.0
190.7
95
444.9
217.0
55
498.8
243.3
16
284. 0 138. 5
76 338. 0
164.8
36 391. 9
191.1
96
445.8
217.4
56
499.7
243.7
17
284. 9 139. 0
77 338.9
165.3
37
392. 8 1 191. 6
97
446.7
217.9
57
500.6
244.2
18
285.8 139.4
78 339. 8
165.7
38
393. 7 192. 0
98
447.6 J218.3
58
501.5
244.6
19
286.7 139.8
79 340. 7
166.2
39 394. 6 ! 192. 4
99
448.5
218.7
59
502.4
245.0
20 287. 6 140. 3
80 i 341.5
166.6
40 ! 395.5 192.9
500
449.4
219.2
60
503.3
245.5
321 288. 5 140. 7
381 . 342.4 167.0
441 396. 4 193. 3
501
450.3
219.6
561
504.2
245.9
22 1 289.4 141.2
82 i 343.3 167.5
42
397.3
193.8
02
451.2
220.1
62
505.1
246.4
23 ! 290.3 141.6
83 344.2 167.9
43
398.2
194.2
03
452. 1
220.5
63
506.0
246.8
24 ! 291. 2 ! 142. 0
84 i 345.1 168.3
44
399.1
194. 7
04
453.0
221.0
64
506.9
247. 3
25 292.1 i!42.5
85 • 346.0 168.8
45
400.0
195.1
05
453.9
221.4
65
507. 8
247.7
26
293.0
142.9
86
346.9
169.2
46
400.9 1195.5
06
454.8
221. 8
66
508.7
248.1
o-
293.9
143.4
87
347.8
169.7
47
401.8 1196.0
07
455. 7 1 222. 3
67
509.6
248.6
28
294.8
143.8
88
348.7
170. 1
48
402.7 ;i96.4
08
456. 6
222. 7
68
510.5
249.0
29 i 295. 7
144.2
89
349.6
170.5
49 403. 6 i 196. 8
09
457. 5
223! 1
69
511.4
249.4
30 296. 6
144.7
90
350.5
171.0
50 i 404. 5 1 197. 3
10
458. 4
223.6
70
512.3
249.9
331 297. 5
145. 1
391
351.4
171.4
451 405. 4 1 197. 7
511
459.3
224.0
571
513.2
250. 3
32 ! 298.4
145. 6
92
352. 3
171.8
52
406. 3 ! 198. 1
12
460.2 J224.4
72
514.1
250.8
33 299. 3
146.0
93
353. 2
172.3
53
407. 2 1 198. 6
13
461.1
224.9
73
515.0
251.2
34 300. 2
146.4
94
354. 1
172. 7
54
408. 1 199. 0
14
462.0
225. 3
74
515.9
251.6
35 • 301. 1
146.9
95
355.0
173.2
55
409.0
199.5
15
462.9
225.8
75
516.8
252. 1
36 302. 0
147.3
96
355. 9 173. 6
56 409.9
199.9
16
463.8
226.2
76
517. 7
252. 5
37 302. 9
147.7
97
356. 8 174. 0
57 410.8 200.3
17
464.7
226.6
77
518.6
252. 9
38 303. 8
148.2
98
357.7 174.5
58 411.7 200.8
18
465.6
227. 1
78
519.5
253. 4
39 304. 7
148.6
99
358.6 174.?-'
59 412.6 201.2
19
466.5
227. 5
79
520. 4
253. 8
40 305. 6
149.0
400
359.5 175.4
60 413.5 201.7
20
467.4
228.0
80
521.3
254. 3
341 306. 5
149.5
401
360.4 175.8
461 414.4 202.1
521
468.3
228.4
581
522.2
254. 7
42 307. 4
149.9
02
361.3
176.2
62 415. 2
202. 5
22
469.2
228. 8
82
523.1
255. 1
43 308. 3
150.4
03
362.2
176.7
63 416. 1 203. 0
23
470.1
229.3
83
524.0
255.6
44 309. 2
150. 8
04
363.1
177.1
64 417.0 203.4
24
471.0
229.7
84
524.9
256.0
45 310. 1
151. 2
05
364.0
177.5
65 417.9
203.8
25
471.9
230.1
85
525. 8
256.4
46 311.0
151.7
06
364.9 178.0
66 418. 8
204.3
26
472.8
230.6
86
526.7
256.9
47 311.9
152.1
07
365.8 178.4
67 419.7 204.7
27
473.7
231.0
87
527. 6
257. 3
48 312. 8
152.6
08
366. 7 178. 9
68 420. 6
205.2
28
474,6
231.5
88
528. 5
257. 8
49 313. 7
153.0
09
367. 6 179. 3
69 421.5 205.6
29
475.5
231.9
89
529.4
258. 2
50 314.-6
153.4
10
368.5 179.7
70 422. 4
206.0
30
476.4
232.3
90
530.3
258.6
351 315.5
153.9
411
369.4
180.2
471 423. 3
206.5
531
477.3
232.8
591
531.2
259. 1
52
316.4
154.3
12
370.3
180.6
72
424.2
206.9
32
478.2
233.2
92
532.1
259. 5
53 317. 3
154. 7
13
371.2 181.1
73 425.1 207.3
33
479.1
233.6
93
533.0
259.9
54
318.2
155.2
14
372.1 181.5
74 426.0 207.8
34
480.0
234.1
94
533.9
260. 4
55
319.1
155.6
15
373.0
181.9
75 i 426.9 208.2
35
480.9
234.5
95
534.8
260.8
56 320. 0
156.1
16
373.9
182.4
76 i 427.8 208.7
36
481.8
235.0
96
535.7
261.3
57 320. 9
156.5
17
374.8
182.8
77 i 428. 7 209. 1
37
482.7
23.5. 4
97
536.6
261.7
58 ! 321.8
156.9
18
375. 7
183.2
78 429. 6
209.5
38
483.6
235. 8
98
537.5
262.1
59 | 322. 7
157. 4
19
376.6
183.7
79 j 430.5
210.0
39
484.5
236.3
90
538.4
262.6
60 i 323.6 157.8
20
377.5
184.1
80 | 431.4
210.4
40
485.3
236.7
600
539.3
263.0
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
Dist. Dep. I Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
64° (116°, 244°, 296°).
Page 584] TABLE 2.
Difference of Latitude and Departure for 27° (153°, 207°, 333°) .
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
54.4
27.7
121
107.8
54.9
181
161.3
82.2
241
214.7
109.4
2
1.8
0.9
62
55.2
28.1
22
108.7
55.4
82
162.2
82.6
42
215.6
109.9
3
2.7
1.4
63
56.1
28.6
23
109.6
55.8
83
163.1
83.1
43
216.5
110.3
4
3.6
1.8
64
57.0
29.1
24
110.5
56.3
84
163. 9
83.5
44
217.4
110.8
5
4.5
2.3
65
57.9
29.5
25
111.4
56.7
85
164.8
84.0
45
218.3
111.2
6
5.3
2.7
66
58.8
30.0
26
112.3
57.2
86
165.7
84.4
46
219.2
111.7
7
6.2
3.2
67
59.7
30.4
27
113.2
57.7
87
166.6
84.9
47
220.1
112.1
8
7.1
3.6
68
60.6
30.9
28
114.0
58.1
88
167.5
85.4
48
221.0
112.6
9
8.0
4.1
69
61.5
31.3
29
114.9
58.6
89
168.4
85.8
49
221.9
113.0
10
8.9
4.5
70
62.4
31.8
30
115.8
59.0
90
169.3
86.3
50
222.8
113.5
11
9.8
5.0
71
63.3
32.2
131
116.7
59.5
191
170.2
86.7
251
223.6
114.0
12
10.7
5.4
72
64.2
32.7
32
117. 6
59.9
92
171.1
87.2
52
224.5
114.4
13
11.6
5.9
73
65.0
33.1
33
118.5
60.4
93
172.0
87.6
53
225.4
114.9
14
12.5
6.4
74
65.9
33.6
34
119.4
60.8
94
172.9
88.1
54
226.3
115.3
15
13.4
6.8
75
66.8
34.0
35
120.3
61.3
95
173.7
88.5
55
227.2
115.8
16
14.3
7.3
76
67.7
34.5
36
121.2
61.7
96
174.6
89.0
56
228.1
116.2
17
15.1
7.7
77
68.6
35.0
37
122.1
62.2
97
175.5
89.4
57
229.0
116.7
18
16.0
8.2
78
69.5
35.4
38
123.0
62.7
98
176.4
89.9
58
229.9
117.1
19
16.9
8.6
79
70.4
35.9
39
123.8
63.1
99
177.3
90.3
59
230.8
117.6
20
17.8
9.1
80
71.3
36.3
40
124.7
63.6
200
178.2
90.8
60
231.7
118.0
21
18.7
9.5
81
72.2
36.8
141
125.6
64.0
201
179.1
91.3
261
232.6
118.5
22
19.6
10.0
82
73.1
37.2
42
126.5
64.5
02
180.0
91.7
62
233.4
118.9
23
20.5
30.4
83
74.0
37.7
43
127.4
64.9
03
180.9
92.2
63
234.3
119.4
24
21.4
10.9
84
74.8
38.1
44
128.3
65.4
04
181.8
92.6
64
235.2
119.9
25
22.3
11.3
85
75.7
38.6
45
129.2
65.8
05
182.7
93.1
65
236.1
120.3
26
23.2
11.8
86
76.6
39.0
46
130.1
66.3
06
183. 5
93.5
66
237.0
120.8
27
24.1
12.3
87
77.5
39.5
47
131.0
66.7
07
184.4
94.0
67
237.9
121.2
28
24.9
12.7
88
78.4
40.0
48
131.9
67.2
08
185.3
94.4
68
238.8
121.7
29
25.8
13.2
89
79.3
40.4
49
132.8
67.6
09
186.2
94.9
69
239.7
122.1
30
26.7
13.6
90
80.2
40.9
50
133.7
68.1
10
187.1
95.3
70
240.6
122.6
31
27.6
14.1
91
81.1
41.3
151
134.5
68.6
211
188.0
95.8
271
241.5
123.0
32
28.5
14.5
92
82.0
41.8
52
135.4
69.0
12
188.9
96.2
72
242.4
123.5
33
29.4
15.0
93
82.9
42.2
53
136.3
69.5
13
189.8
96.7
73
243.2
123.9
34
30.3
15.4
94
83.8
42.7
54
137.2
69.9
14
190.7
97.2
74
244.1
124.4
35
31.2
15.9
95
84.6
43.1
55
138.1
70.4
15
191.6
97.6
75
245.0
124.8
36
32.1
16.3
96
85.5
43.6
56
139.0
70.8
16
192.5
98.1
76
245.9
125.3
37
33.0
16.8
97
86.4
44.0
57
139.9
71.3
17
193.3
98.5
77
246.8
125.8
38
33.9
17.3
98
87.3
44.5
58
140.8
71.7
IS
194.2
99.0
78
247.7
126.2
39
34.7
17.7
99
88.2
44.9
59
141.7
72.2
19
195.1
99.4
79
248.6
126.7
40
35.6
18.2
100
89.1
45.4
60
142.6
72.6
20
196.0
99.9
80
249.5
127.1
41
36.5
18.6
101
90.0
45.9
161
143.5
73.1
221
196.9
100.3
281
250.4
127.6
42
37.4
19.1
02
90.9
46.3
62
144.3
73.5
22
197.8
100.8
82
251.3
128.0
43
38.3
19.5
03
91.8
46.8
63
145.2
74.0
23
198.7
101.2
83
252.2
128.5
44
39.2
20.0
04
92.7
47.2
64
146.1
74.5
24
199.6
101.7
84
253.0
128.9
45
40.1
20.4
05
93.6
47.7
65
147.0
74.9
25
200.5
102.1
85
253.9
129.4
46
41.0
20.9
06
94.4
48.1
66
147.9
75.4
26
201.4
102.6
86
254.8
129.8
47
41.9
21.3
07
95.3
48.6
67
148.8
75.8
27
202.3
103.1
87
255.7
130.3
48
42.8
21.8
08
96.2
49.0
68
149.7
76.3
28
203.1
103.5
88
256.6
130.7
49
43.7
22.2
09
97.1
49.5
69
150. 6
76.7
29
204.0
104.0
89
257.5
131.2
50
44.6
22.7
10
98.0
49.9
70
151.5
77.2
30
204.9
104.4
90
258.4
131.7
51
45.4
23.2
111
98.9
50.4
171
152.4
77.6
231
205.8
104.9
291
259.3
132.1
52
46.3
23.6
12
99.8
50.8
72
153.3
78.1
32
206.7
105.3
92
260.2
132.6
53
47.2
24.1
13
100.7
51.3
73
154.1
78.5
33
207.6
105.8
93
261.1
133.0
54
-48.1
24.5
14
101.6
51.8
74
155.0
79.0
34
208.5
106.2
94
262.0
133.5
55
49.0
25.0
15
102.5
52.2
75
155.9
79.4
35
209.4
106.7
95
262.8
133.9
56
49.9
25.4
16
103.4
52.7
76
156.8
79.9
36
210.3
107.1
96
263.7
134.4
57
50.8
25.9
17
104.2
53.1
77
157.7
80.4
37
211.2
107.6
97
264.6
134.8
58
51.7
26.3
18
105.1
53.6
78
158.6
80.8
38
212.1
108.0
98
265.5
135.3
59
52.6
26.8
19
106.0
54.0
79
159.5
81.3
39
213.0
108.5
99
266.4
135.7
60
53.5
27.2
20
106.9
54.5
80
160.4
81.7
40
213.8
109.0
300
267.3
136.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
63° (117°, 243°, 297°).
TABLE 2. [Page 585
Difference of Latitude and Departure for 27° (153°, 207°, 333°).
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
268.2
136.7
361
321.7
163.9
421 375. 1
191.1
481
428.6
218.3
541
482.0
245.6
02
269.1
137.1
62
322.5
164.4
22 | 376.0
191.6
82
429.4
218.8
42
482.9
246.1
03
270.0
137.6
63
323.4
164.8
23 376. 9
192.0
83
430.3
219.2
43
483.8
246. 5
04
270. 9
138.0
64
324.3
165.3
24 377. 8
192.5
84
431.2
219.7
44
484.7
247.0
05
271.8
138.5
65
325.2
165. 7
25 378. 7
193.0
85
432.1
220.1
45
485.6
247.4
06
272.7
138.9
66
326.1
166.2
26 379. 6
193.4
86
433.0
220.6
46
486.4
247.9
07
273.5
139.4
67
327.0
166.6
27 380. 5
193.9
87
433.9
221.1
47
487.3
248.4
08
274.4
139.8
68
327.9
167.1
28
381.4
194.3
88
434.8
221.5
48
488.2
248.8
09
275. 3
140.3
69
328.8
167.5
29
382.2
194.8
89
435.7
222.0
49
489.1
249.2
10
276.2
140.7
70
329.7
168.0
30 383. 1
195.2
90
436.6
222. 4
50
490.0
249.7
311
277.1
141.2
371
330.6
168.4
431
384.0
195.7
491
437.5
222.9
551
490.9
250. 1
12
278.0
141.7
72
331.5
168.9
32
384.9
196.1
92
438.3
223.3
52
491.8
250.6
13
278.9
142.1
73
332.3
169.3
33
385.8
196.6
93
439.2
223.8
53
492.7
251.0
14
279.8
142.6
74
333.2
169.8
34
386.7
197.0
94
440.1
224.2
54
493.6
251.5
15
280.7
143.0
75
334.1
170.3
35
387.6 197.5
95
441.0
224.7
55
494.5
252.0
16
281.6
143. 5
76
335.0
170.7
36
388.5 197.9
96
441.9
225.2
56
495.4
252.4
17
282.5
143.9
77
335.9
171.2
37
389.4 198.4
97
442.8
225.6
57
496.3
252.9
18
283.3
144.4
78
336.8
171.6
38
390.3
198.9
98
443.7
226.1
58
497.2
253. 3
19
284.2
144.8
79
337.7
172.1
39
391.2
199.3
99
444.6
226.5
59
498.1
253.8
20
285.1
145.3
80
338.6
172.5
40
392.0
199.8
500
445.5
227.0
60
499.0
254.2
321
286.0
145.7
381 1 339.5
173.0
441
392. 9 j 200. 2
501 i 446. 4
227.5
561
499.8
254.7
22
286.9
146.2
82
340.4
173.4
42
393.8
200.7
02 447. 3
227.9
62
500.7
255. 1
23
287.8
146.6
83
341.3
173.9
43
'394. 7
201.1
03 | 448.2
228.4
63
501.6
255.6
24
288.7
147.1
84
342.1
174.3
44
395.6
201.6
04 449. 0
228.8
64
502.5
256.0
25
289.6
147.6
85
343.0
174.8
45
396.5
202.0
05 449. 9
229.3
65
503.4
256. 5
26
290.5
148.0
86
343.9
175.2
46
397.4
202.5
06
450.8
229.8
66
504.3
257.0
27
291.4
148.5
87
344.8
175.7
47
398.3
202.9
07
451.7
230.2
67
505.2
257. 4
28
292.3
148.9
88
345.7
176.2
48
399.2
203.4
08
452.6
230.6
68
506.1
257.9
29
293.2
149.4
89
346.6
176.6
49
400.1
203.8
09
453.5
231.0
69
507.0
258.3
30
294.0
149.8
90
347.5
177.1
50
401.0
204.3
10
454.4
231.5
70
507.9.
258.8
331 294. 9
150.3
391
348.4
177.5
451
401.8
204.7
511
455.3
231.9
571
508.7
259.2
32 295. 8
150.7
92
349.3
178.0
52
402.7
205.2
12
456.2
232.4
72
509.6
259.7
33
296.7
151.2
93
350.2
178. 4
53
403.6
205.7
13
457.1
232.9
73
510.5
260.1
34
297.6
151.6
94
351.1
178.9
54
404.5
206.1
14
458.0
233.3
74
511.4
260.6
35
298.5
152.1
95
352.0
179.3
55
405.4
206.6
15
458.8
233.8
75
512.3
261.1
36
299.4
152.5
96
352.8
179.8
56
406.3
207.0
16
459.7
234.2
76
513.2
261.5
37
300.3
153.0
97
353.7
180.2
57
407.2
207.5
17
460.6
234.7
77
514.1
262.0
38
301.2
153.5
98
354.6
180.7
58
408.1
207.9
18
461.5
235.2
78
515.0
262.4
39
302.1
153.9
99
355.5
181.2
59
409.0
208.4
19
462.4
235. 7
79
515.9
262.9
40
302.9
154.4
400
356.4
181.6
60
409.9
208.8
20
463.3
236.1
80
516.8
263.4
341
303.8
154.8
401
357.3
182.1
461
410.8
209.3
521
464.2
236.6
581
517.7
263.8
42
304.7
155.3
02
358.2
182. 5
62
411.6
209.8
22
465.1
237.0
82
518.5
264.3
43
305.6
155. 7
03
359. 1 1 183. 0
63
412.5
210.2
23
466.0
237.5
83
519.4
264.7
44
306.5
156.2
04
360. 0 1 183. 4
64
413.4
210.7
24
466.9
237.9
84
520.3
265.2
45
307.4
156.6
05
360. 9 i 183. 9
65
414.3
211.1
25
467.8
238.4
85
521.2
265.6
46
308.3
157.1
06
361. 8 ; 184. 3
66
415.2
211.6
26
468.7
238.8
86
522.1
266.0
47
309.2
157.5
07
362. 6 184. 8
67
416.1
212.0
27
469.5
239.3
87
523.0
266.5
48
310.1
158.0
08
363. 5 ! 185. 2
68
417.0
212.5
28
470.4
239.7
88
523.9
267.0
49
311.0
158.5
09
364. 4 ! 185. 7
69
417.9
212.9
29
471.3
240.2
89
524.8
267.4
50
311.9
158.9
10
365. 3 186. 1
70
418.8
213.4
30
472.2
240.6
90
525. 7
267.9
351
312.7
159.4
411
366.2
186.6
471
419.7
213.8
531
473.1
241.1
591
526.6
268.3
52
313.6
159.8
12
367.1
187.1
72
420.6
214.3
32
474.0
241.5
92
527.5
268.8
53
314.5
160.3
13
368.0
187.5
73
421.4
214.7
33
474.9
242.0
93
528.4
269.2
54
315.4
160.7
14
368.9
188.0
74
422.3
215.2
34
475.8
242.4
94
529.3
269.7
55
316.3
161.2
15
369.8
188.4
75
423.2
215.7
35
476.7
242.9
95
530. 1 270. 1
56
317.2
161.6
16
370.7
188.9
76
424.1
216.1
36
477.6
243.4
96
531.0 270.6
57
318.1
162.1
17
371.6
189.3
77
425.0
216.6
37
478.4
243.8
97
531.9
271.1
58
319.0
162.5
18
372.4
189.8
78
425.9
217.0
38
479.3
244.3
98
532.8
271.5
59
319.9
163.0
19
373.3
190.2
79
426.8
217.5
39
480.2
244.7
99
533.7
272.0
60
320.8
163.4
20
374.2
190.7
80
427.7
217.9
40
481.1
245.2
600
534.6
272.4
Dist.
Dep. | Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
63° (117°, 243°, 297° .
Page 586] , TABLE 2.
Difference of Latitude and Departure for 28° (152°, 208°, 332°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.9
28.6
121
106.8
56.8
181
159.8
85.0
241
212.8
113.1
2
1.8
0.9
62
54.7
29.1
22
107.7
57.3
82
160.7
85.4
42
213.7
113.6
3
2.6
1.4
63
55.6
29.6
23
108.6
57.7
83
161.6
85.9
43
214.6
114.1
4
3.5
1.9
64
56.5
30.0
24
109.5
58.2
84
162.5
86.4
44
215.4
114.6
5
4.4
2.3
65
57.4
30.5
25
110.4
58.7
85
163.3
86.9
45
216.3
115.0
6
5.3
2.8
66
58.3
31.0
26
111.3
59.2
86
164.2
87.3
46
217.2
115.5
7
6.2
3.3
67
59.2
31.5
27
112.1
59.6
87
165.1
87.8
47
218.1
116.0
8
7.1
3.8
68
60.0
31.9
28
113.0
60.1
88
166.0
88.3
48
219.0
116.4
9
7.9
4.2
69
60.9
32.4
29
113.9
60.6
89
166.9
88.7
49
219.9
116.9
10
8.8
4.7
70
61.8
32.9
30
114.8
61.0
90
167.8
89.2
50
220.7
117.4
11
9.7
5.2
71
62.7
33.3
131
115.7
61.5
191
168.6
89.7
251
221.6
117.8
12
10.6
5.6
72
63.6
33.8
32
116.5
62.0
92
169.5
90.1
52
222.5
118.3
13
11.5
6.1
73
64.5
34.3
33
117.4
62.4
93
170.4
90.6
53
223.4
118.8
14
12.4
6.6
74
65.3
34.7
34
118.3
62.9
94
171.3
91.1
54
224.3
119.2
15
13.2
7.0
75
66.2
35.2
35
119.2
63.4
95
172.2
91.5
55
225.2
119.7
16
14.1
7.5
76
67.1
35.7
36
120.1
63.8
96
173.1
92.0
56
226.0
120.2
17
15.0
8.0
77
68.0
36.1
37
121.0
64.3
97
173.9
92.5
57
226.9
120.7
18
15.9
8.5
78
68.9
36.6
38
121.8
64.8
98
174.8
93.0
58
227.8
121.1
19
16.8
8.9
79
69.8
37.1
39
122.7
65.3
99
175.7
93.4
59
228.7
121.6
20
17.7
9.4
80
70.6
37.6
40
123. 6
65.7
200
176.6
93.9
60
229.6
122.1
21
18.5
9.9
81
71.5
38.0
141
124.5
66.2
201
177.5
94.4
261
230.4
122.5
22
19.4
10.3
82
72.4
38.5
42
125.4
66.7
02
178.4
94.8
62
231.3
123.0
23
20.3
10.8
83
73.3
39.0
43
126.3
67.1
03
179.2
95.3
63
232.2
123.5
24
21.2
11.3
84
74.2
39.4
44
127.1
67.6
04
180.1
95.8
64
233.1
123.9
25
22.1
11.7
85
75.1
39.9
45
128.0
68.1
05
181.0
96.2
65
234.0
124.4
26
23.0
12.2
86
75.9
40.4
46
128.9
68.5
06
181.9
96.7
66
234. 9
124.9
27
23.8
12.7
87
76.8
40.8
47
129.8
69.0
07
182.8
97.2
67
235.7
125.3
28
24.7
13.1
88
77.7
41.3
48
130.7
69.5
08
183.7
97.7
68
236.6
125.8
29
25.6
13.6
89
78.6
41.8
49
131.6
70.0
09
184.5
98.1
69
237.5
126.3
30
26.5
14.1
90
79.5
42.3
50
132.4
70.4
10
185.4
98.6
70
238.4
126.8
31
27.4
14.6
91
80.3
42.7
151
133.3
70.9
211
186.3
99.1
271
239.3
127.2
32
28.3
15.0
92
81.2
43.2
52
134.2
71.4
12
187.2
99.5
72
240.2
127.7
33
29.1
15.5
93
82.1
43.7
53
135.1
71.8
13
188.1
100.0
73
241.0
128.2
34
30.0
16.0
94
83.0
44.1
54
136.0
72.3
14
189.0
100.5
74
241.9
128.6
35
30.9
16.4
95
83.9
44.6
55
136.9
72.8
15
189.8
100.9
75
242.8
129.1
36
31.8
16.9
96
84.8
45.1
56
137.7
73.2
16
190.7
101.4
76
243.7
129.6
37
32.7
17.4
97
85.6
45.5
57
138.6
73.7
17
191.6
101.9
77
244.6
130.0
38
33.6
17.8
98
86.5
46.0
58
139.5
74.2
18
192.5
102.3
78
245.5
130.5
39
34.4
18.3
99
87.4
46.5
59
140.4
74.6
19
193.4
102.8
79
246.3
131.0
40
35.3
18.8
100
88.3
46.9
60
141.3
75.1
20
194.2
103.3
80
247.2
131.5
41
36.2
19.2
101
89.2
47.4
161
142.2
75.6
221
195.1
103.8
281
248.1
131.9
42
37.1
19.7
02
90.1
47.9
62
143.0
76.1
22
196.0
104.2
82
249.0
132.4
43
38.0
20.2
03
90.9
48.4
63
143.9
76.5
23
196. 9 •
104.7
83
249.9
132.9
44
38.8
20.7
04
91.8
48.8
64
144.8
77.0
24
197.8
105.2
84
250.8
133.3
45
39.7
21.1
05
92.7
49.3
65
145.7
77.5
25
198.7
105.6
85
251.6
133.8
46
40.6
21.6
06
93.6
49.8
66
146.6
77.9
26
199.5
106.1
86
252.5
134.3
47
41.5
22.1
07
94.5
50.2
67
147.5
78.4
27
200.4
106.6
87
253.4
134.7
48
42.4
22.5
08
95.4
50.7
68
148.3
78.9
28
201.3
107.0
88
254.3
135.2
49
43.3
23.0
09
96.2
51.2
69
149.2
79.3
29
202.2
107.5
89
255.2
135.7
50
44.1
23.5
10
97.1
51.6
.70
150.1
79.8
30
203.1
108.0
90
256.1
136.1
51
45.0
23.9
111
98.0
52.1
m
151.0
80.3
231
204.0
108.4
291
256.9
136.6
52
45.9
24.4
12
98.9
52.6
72
151.9
80.7
32
204.8
108.9
92
257.8
137.1
53
46.8
24.9
13
99.8
53.1
73
152.7
81.2
33
205.7
109.4
93
258.7
137.6
54
47.7
25.4
14
100.7
53.5
74
153.6
81.7
34
206.6
109.9
94
259.6
138.0
55
48.6
25.8
15
101.5
54.0
75
154.5
82.2
35
207.5
110.3
95
260.5
138.5
56
49.4
26.3
16
102.4
54.5
76
155.4
82.6
36
208.4
110.8
96
261.4
139.0
57
50.3
26.8
17
103.3
54.9
77
156.3
83.1
37
209.3
111.3
97
262.2
139.4
58
51.2
27.2
18
104.2
55.4
78
157.2
83.6
38
210.1
111.7
98
263.1
139. 9
59
52.1
27.7
19
105.1
55.9
79
158.0
84.0
39
211.0
112.2
99
264.0
140.4
60
53.0
28.2
20
106.0
56.3
80
158.9
84.5
40
211.9
112.7
300
264.9
140.8
Diet.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
62° (118°, 242°, 298°).
TABLE 2. [Page 587
Difference of Latitude and Departure for 28° (152°, 208°, 332°).
Dist. Lat. Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
265. 7 141. 3
361
318.7
169.5
421
371.7
197.7
481
424.7
225.8
541
477.7
254.0
02
266.6 141.8
62
319.6
170.0
22
372.6
198.1
82
425.6
226.3
42
478.6
254. 5
03
267. 5 142. 3
63
320.5
170.4
23
373.5
198.6
83
426.5
226.8
43
479.4
255. 0
04
268. 4 142.7
64
321.4
170.9
24
374.3
199.1
84
427.4
227.3
44
480.3
255.5
05
269.3 143.2
65
322.2
171.4
25
375.2
199.5
85
428.3
227.7
45
481.1
255.9
06
270. 2 143. 7
66
323.1
171.8
26
376.1
200.0
86
429.2
228.2
46
482. 0
256.4
07
271.0 144.1
67
324.0
172.3
27
377.0
200.5
87
430.1
228.6
47
482.9
256.9
08
271.9 1144.6
68
324.9
172.8
28
377.9
200.9
88
430.9
229.1
48
483.8
257.3
09
272. 8 j 145. 1
69
325.8
173.2
29
378.8
201.4
89
431.8
229.6
49
484.7
257.8
10
273. 7 145. 5
70
326.7
173. 7
30
379.6
201.9
90
432.6
230.0
50
485.6
258.2
311
274.6
146.0
371
327.5
174.2
431
380.5
202.3
491
433.5
230.5
551
486.5
258. 7
12
275.5
146.5
72
328.4
174.6
32
381.4
202.8
92
434.4
231.0
52
487.4
259.1
13
276.3
146.9
73
329.3
175. 1
33
382.3
203.3
93
435.3
231.4
53
488.3
259. 6
14
277.2
147.4
74
330.2
175.6
34
383.2
203.8
94
436.2
231.9
54
489.2
260.1
15
278.1
147.9
75
331.1
176.1
35
384.1
204.2
95
437.1
232.4
55
490.1
260.6
16
279.0
148.4
76
332.0
176.5
36
384.9
204.7
96
437.9
232.9
56
490.9
261.0
17
279.9
148.8
77
332.8
177.0
37
385.8
205.2
97
438.8
233.4
57
491.8
261.5
18
280.7
149.3
78
333.7
177. 5
38
386.7
205.6
98
439.7
233.8
58
492.7
262.0
19
281. 6
149.8
79
334.6
177.9
39
387.6
206.1
99
440.6
234.3
59,
493.5
262.5
20
282.5
150.2
80
335.5
178.4
40
388.5
206.6
500
441.5
234.7
60
494.4
262.9
321
283.4
150.7
381 336. 4
178.9
441
389.4
207.0
501
442.3
235. 2
561
495. 3 263. 4
22
284.3
151.2
82 337. 3
179.3
42
390.2
207.5
02
443.2
235.6
62
496. 2 263. 8
23
285.2
151. 6
83 338. 1
179.8
43
391.1
208.0
03 444.1
236.1
63
497. 1 264. 3
24
286.0
152.1
84 339. 0
180.3
44
392.0
208.4
04 445. 0
236.6
64
498. 0 264. 7
25
286.9
152. 6
85 339. 9
180.8
45
392.9
208. 9
05
445.9
237.1
65
498. 9 265. 2
26
287.8
153. 1
86 340. 8
181.2
46
393. 8
209.4
06
446.8
237.5
66
499. 8 265. 7
27
288.7
153.5
87 341. 7
181.7
47
394.6
209.9
07
447.6
238.0
67
500.7 266.2
28
289.6
154. 0
88*1 342.6
182.2
48
395. 5
210.3
08
448. 5
238.5
68
501.6 266.6
29
290.5
154.5
89 343.4
182.6
49
396.4 210.8
09
449.4
239.0
69 502. 4 267. 1
30 291.3
154.9
90 344. 3
183.1
50
397.3
211.3
10
450.3
239.4
70 503.3 1 267.6
331 292. 2
155.4
391 345. 2
183.6
451
398.2
211.7
511 451.2
239.9
571 504.2 j 268.0
32 ! 293.1
155.9
92 346. 1
184.0
52
399.1
212.2
12
452.1
240.4
72 505. 1
268.5
33 294. 0
156.3
93
347.0
184.5
53
399.9
212.7
13
452. 9 240. 8
73 505. 9
269.0
34 294.9
156.8
94
347.9
185.0
54
400.8
213.1
14
453.8 i241.3
74 506. 8
269.4
35 ! 295. 8 ; 157. 3
95
348.7
185.4
55
401.7 213.6
15
454.7 241. S
75 507. 7
269.9
36 296. 6 157. 7
93 349. 6
185. 9
56
402.6 214.1
16
455.6 242.2
76 508. 6
270. 4
37 297. 5
158.2
97 350. 5
186.4
57
403.5 214.6
17
456.4 242.7
77 509. 4
270.9
38 298. 4
158.7
98
351. 4
186.9
58
404.4 j 215.0
18
457.3 243.2
78 510.3
271.3
39 299. 3 1 159. 2
99
352.3
187.3
59
405.2 215.5
19
458.2 243.7
79 511. 2
271.8
40 300.2 159.6
400 353. 1
187.8
60
406. 1 216. 0
20
459.1
244.1
80
512.1
272.3
341
301.0
160.1
401 354. 0
188.3
461
407.0
216.4
521
460.0
244.6
581
513.0
42
301.9
160.6
02
354.9
188. 7
62
407.9
216.9
22
460.9
245. 0
82
513.9
273.2
43
302.8
161.0
03
355. 8
189.2
63
408.8
217.4
23
461.8
245. 5
83
514.8
273.7
44
303.7
161.5
04
356. 7
189.7
64
409.7
217.8
24
462.7
246.0
84
515.7 | 274.2
45
304.6
162.0
05 357. 6
190.1
65
410.5
218.3
25
463.5
246.5
85
516.5
274. 7
46
305.5 162.4
06
358.4
190.6
66
411.4
218.8
26
464.4
246.9
86
517.4
275. 1
47 j 306.4 162.9
07
359.3
191.1
67
412.3
219.2
27
465.3
247.4
87
518.3
275.5
48 j 307. 2
163. 4
08
360.2
191.5
68
413.2
219.7
28
466.2
247.9
88
519.2
276.0
49
308.1
163.8
09 361. 1
192. 0
69
414. 1
220.2
29
467.1
248.3
89
520. 1 276. 5
50
309.0
164.3
10 ! 362. 0 192. 5
70
415.0
220.7
30
468.0
248.8
90
521.0 277.0
351 309. 9 164. 8
411
362. 9 193. 0
471
415.8
221.1
531
468.9
249.3
591
521.8 277.4
52 310.8 165.3
12
363.7
193.4
72
416.7
221.6
32
469.8
249.8
92
522.6
277.9
53 311. 7
165.7
13
364.6
193.9
73
417.6
222.1
33
470.7
250. -2
93
523.5
278. 4
54
312. 5
166.2
14
365.5
194.4
74
418.5
222.5
34
471.5
250.7
94
524.4
278.8
55
313.4
166.7
15
366.4
194. 8
75
419.4
223.0
35
472. 4
251.1
95
525.3
279.3
56
314.3
167.1
16
367.3
195.3
76
420.3
223.5
36
473.3
251.6
96
526.2
279.8
57
315.2
167.6
17
368.2
195.8
"77
421.1
223.9
37
474.2
252.1
97
527.1
280.3
58
316.1
168.1
18
369.0
196.2
78
422.0
224.4
38
475.1
252. 6
98
528.0
280.8
59
316.9
168.5
19
369.9
196.7
79
422.9
224.9
39
476.0
253.1
99
528.9
281.3
60
317.8
169.0
20
370.8
197.2
80
423.8
225.3
40
476.8
253.6
600
529.8
281.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
62° (118°, 242°, 298°).
Page 588] TABLE 2.
Difference of Latitude and Departure for 29° (151°, 209°, 331°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.4
29.6
121
105.8
58.7
181
158.3
87.8
241
210.8
116.8
2
1.7
1.0
62
54.2
30.1
22
106.7
59.1
82
159.2
88.2
42
211.7
117.3
3
2.6
1.5
63
55.1
30.5
23
107.6
59.6
83
160.1
88.7
43
212.5
117.8
4
3.5
1.9
64
56.0
31.0
24
108.5
60.1
84
160.9
89.2
44
213.4
118.3
5
4.4
2.4
65
56.9
31.5
25
109.3
60.6
85
161.8
89.7
45
214. 3
118.8
6
5.2
•2.9
66
57.7
32.0
26
110.2
61.1
86
162.7
90.2
46
215.2
119.3
7
6.1
3.4
67
58.6
32.5
27
111.1
61.6
87
163.6
90.7
47
216.0
119.7
8
7.0
3.9
68
59.5
33.0
28
112.0
62.1
88
164.4
91.1
48
216.9
120. 2
9
7.9
4.4
69
60.3
33.5
29
112.8
62.5
89
165.3
91.6
49
217.8
120.7
10
8.7
4.8
70
61.2
33.9
30
113.7
63.0
90
166.2
92.1
50
218.7
121.2
11
9.6
5.3
71
62.1
34.4
131
114.6
63.5
191
167.1
92.6
251
219.5
121.7
12
10.5
5.8
72
63.0
34.9
32
115.4
64.0
92
167.9
93.1
52
220.4
122. 2
13
11.4
6.3
73
63.8
35.4
33
116.3
64.5
93
168.8
93.6
53
221.3
122.7
14
12.2
6.8
74
64.7
35.9
34
117.2
65.0
94
169.7
94.1
54
222.2
123.1
15
13.1
7.3
75
65.6
36.4
35
118.1
65.4
95
170.6
94.5
55
223.0
123.6
16
14.0
7.8
76
66.5
36.8
36
118.9
65.9
96
171.4
95.0
56
223.9
124.1
17
14.9
8.2
77
67.3
37.3
37
119.8
66.4
97
172.3
95.5
57
224.8
124.6
18
15.7
8.7
78
68.2
37.8
38
120.7
66.9
98
173.2
96.0
58
225.7
125.1
19
16.6
9.2
79
69.1
38.3
39
121.6
67.4
99
174.0
96.5
59
226.5
125.6
20
17.5
9.7
80
70.0
38.8
40
122.4
67.9
200
174.9
97.0
'60
227.4
126.1
21
18.4
10.2
81
70.8
39.3
141
123.3
68.4
201
175.8
97.4
261
228.3
126.5
22
19.2
10.7
82
71.7
39.8
42
124.2
68.8
02
176.7
97.9
62
229. 2
127.0
23
20.1
11.2
83
72.6
40.2
43
125.1
69.3
03
177.5
98.4
63
230io
127.5
24
21.0
11.6
84
73.5
40.7
44
125.9
69.8
04
178.4
98.9
64
230.9
128.0
25
21.9
12.1
85
74.3
41.2
45
126.8
70.3
05
179.3
99.4
65
231.8
128.5
26
22.7
12.6
86
75.2
41.7
46
127.7
70.8
06
180.2
99.9
66
232.6
129.0
27
23.6
13.1
87
76.1
42.2
47
128.6
71.3
07
181.0
100.4
67
233.5
129.4
28
24.5
13.6
88
77.0
42.7
48
129.4
71.8
08
181.9
100.8
68
234.4
129.9
29
25.4
14.1
89
77.8
43.1
49
130.3
72.2
09
182.8
101.3
69
235.3
130.4
30
26.2
14.5
90
78.7
43.6
50
131.2
72.7
10
183.7
101.8
70
236.1
130.9
31
27.1
15.0
91
79.6
44.1
151
132.1
73.2
211
184.5
102.3
271
237.0
131.4
32
28.0
15.5
92
80.5
44.6
52
132.9
73.7
12
185.4
102.8
72
237.9
131.9
'33
28.9
16.0
93
81.3
45.1
53
133.8
74.2
13
186.3
103.3
73
238.8
132.4
34
29.7
16.5
94
82.2
45.6
54
134.7
74.7
14
187.2
103.7
74
239.6
132.8
35
30.6
17.0
95
83.1
46.1
55
135.6
75.1
15
188.0
104.2
75
240.5
133.3
36
31.5
17.5
96
84.0
46.5
56
136.4
75.6
16
188.9
104.7
76
241.4
133.8
37
32.4
17.9
97
84.8
47.0
57
137.3
76.1
17
189.8
105.2
77
242.3
134.3
38
33.2
18.4
98
85.7
47.5
58
138.2
76.6
18
190.7
105.7
78
243. 1
134.8
39
34.1
18.9
99
86.6
48.0
59
139.1
77.1
19
191.5
106.2
79
244.0
135.3
40
35.0
19.4
100
87.5
48.5
60
139.9
77.6
20
192.4
106.7
80
244.9
135.7
41
35.9
19.9
101
88.3
49.0
161
140.8
78.1
221
193.3
107.1
281
245.8
136.2
42
36.7
20.4
02
89.2
49.5
62
141.7
78.5
22
194.2
107.6
82
246.6
136.7
43
37.6
20.8
03
90.1
49.9
63
142.6
79.0
23
195.0
108.1
83
247.5
137.2
44
38.5
21.3
04
91.0
50.4
64
143.4
79:5
24
195.9
108.6
84
248.4
137.7
45
39.4
21.8
05
91.8
50.9
65
144.3
80.0
25
196.8
109. 1
85
249.3
138.2
46
40.2
22.3
06
92.7
51.4
66
145.2
80.5
26
197.7
109. 6
86
250. 1.
138.7
47
41.1
22.8
07
93.6
51.9
67
146.1
81.0
27
198.5
110. 1
87
251.0
139.1
48
42.0
23.3
08
94.5
52.4
68
146. 9
81.4
28
199.4
110.5
88
251. 9
139.6
49
42.9
23.8
09
95.3
52.8
69
147.8
81.9
29
200.3
111.0
89
252.8
140.1
50
43.7
24.2
10
96.2
53.3
70
148.7
82.4
30
201.2
111.5
90
253.6
140.6
51
44.6
24.7
111
97.1
53.8
171
149.6
82.9
231
202.0
112. 0
291
254. 5
141.1
52
45.5
25.2
12
98.0
54.3
72
150. 4
83.4
32
202.9
112.5
92
255.4
141.6
53
46.4
25.7
13
98.8
54.8
73
151.3
83.9
33
203.8
113.0
93
256.3
142.0
54
47.2
26.2
14
99.7
55.3
74
152.2
84.4
34
204.7
113. 4
94
257.1
142.5
55
48.1
26.7
15
100.6
55.8
75
153. 1
84.8
35
205.5
113. 9
95
258. 0
143.0
56
49.0
27.1
16
101.5
56.2
76
153.9
85.3
36
206.4
114.4
96
258. 9
143.5
57
49.9
27.6
17
102. 3
56.7
77
154.8
85.8
37
207.3
114.9
97
259.8
144.0
58
50.7
28.1
18
103.2
57.2
78
155.7
86.3
38
208.2
115.4
98
260.6
144.5
59
51.6
28.6
19
104.1
57.7
79
156.6
86.8
39
209.0
115.9
99
261.5
145.0
60
52.5
29.1
20
105.0
58.2
80
157.4
87.3
40
209.9
116.4
300
262.4
145.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
61° (119°, 241°, 299°).
TABLE 2. [Page 589
Difference of Latitude and Departure for 29° (151°, 209°, 331°).
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist. ' Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
.
i
301
263.2
145.9
361 315.7
175.0
421 368. 2
204.1
481
420.7
233.2
541
473.2
262.3
02
264. 1
146.4
62 316.6
175.5
22 369. 1
204.6
82
421.5
233.7
42
474.0
262.8
03
265. 0
146.9
63 j 317. 5
176.0
23 369. 9
205. 1
83
422.4
234.2
43
474.9
263.2
04
265.9
147.4
64 318. 3
176.5
24
370.8
205.6
84
423.3
234.6
44
475.8
263. 7
05
266.7
147.9
65 ! 319.2
177.0
25
371.7
206.0
85
424.2
235.1
45
476.6
264.2
06
267.6
148.4
66 320. 1
177.4
26 372. 6
206.5
86
425.0
235. 6
46
477. 5
264.7
07
268.5
148.8
67
321.0
177.9
27 373. 4
207.0
87 425. 9
236.1
47
478.4
265.2
08
269.4
149.3
68
321.8
178.4
28 j 374. 3
207.5
88 i 426. 8
236.6
48
479.3
265.7
09
270.2
149.8
69 322. 7
178.9
29 375. 2
208.0
89 1 427. 7
237.1
49
480.1
266.2
10
271.1
150.3
70 323- 6
179.4
30 i 376. 1
208.5
90 j 428. 5
237.6
50
481.0
266.6
311
272.0
150.8
371 324. 5
179.9
431 i 376. 9
209.0
491
429. 4
238.0
00 1
481.9
267.1
12
272.9
151.3
72 325. 3
180.4
32 ! 377.8
209.4
92
430.3
238.5
52
482. 8
267.6
13
273.7
151.7
73 326. 2
180.8
33 378.7
209.9
93
431.2
239.0
53
483.6
268.1
14
274.6
152.2
74 327. 1
181.3
34 379. 6
210.4
94
432.0
239.5
54
484.5
268. 6
15
275.5
152.7
75 328.0
181.8
35 380. 4
210.9
95
432.9
240.0
55
485.4
269.1
16
276.3
153.2
76 328. 8
182.3
36 I 381.3 211.4
96
433.8
240. 5
56
486.3
269.5
17
277.2
153.7
77 1 329. 7
182.8
37 382. 2 j 211. 9
97
434.7
240.9
57
437. 1
270.0
18
278.1
154.2
78
330.6
183.3
38 383.1 1212.3
98
435.5
241.4
58
488.0
270.5
19
279.0
154.7
79
331.4
183.7
39 383.9 1212.8
99
436.4
241.9
59
488.9
271.0
20
279.8
155.1
80
332.3
184. 2
40 384.8 213.3
500
437.3
242.4
60
489.8
271.5
321
280.7
155.6
381
333.2
184. 7
441 385.7 213.8
501
438. 2
242. 9
561
490.6
272.0
22
281.6
156.1
82
334.1
185.2
42 386.6 214.3
02
439.0
243.4
62
491.5
272.5
23
282.5
156.6
83 ! 334. 9
185. 7
43 387.4 214.8
03
439.9
243.9
63
492. 4 272. 9
24
283.3
157.1
84 335. 8
186.2
44 388.3 '215.3
04
440.8
244.3
64
493. 2 273. 4
25
284.2
157.6
85 336. 7
1S6. 7
45 389.2 215.7
05
441.6
244. 8
65
494.1
273.9
26
2S5. 1
158.1
86 1 337.6
187.1
46 390.0 216.2
06
442.5
245.3
66
495.0
274.4
27
286.0
158.5
87 338. 4
1S7.6
47 i 390.9 218.7
07
443.4 245.8
67
495.9
274.9
28
286.8
159.0
88 339. 3
188.1
48 391.8 217.2
08
444.3 246.3
68
496. 8 275. 4
29
287.7
159.5
89 340. 2
188.6
49
392.7 217.7
09
445.2 246.8
69
497. 7 275. 9
30
288.6
160.0
90 341. 1
189.1
50
393.5
218.2
10
446. 1 1 247. 3
70
498.5 ! 276.3
S31
289.5
160.5
391 341. 9
189.6
451 394. 4
218.7
511
447.0
247.8
571
499.4
276.8
32
290.3
161.0
92
342.8
190.0
52 395. 3
219.1
12
447.8
248.2
72
500.3
277.3
33
291.2
161.4
93
343. 7 i 190. 5
53
396.2
219.6
13
448.6
248.7
73
501.1
277.8
34
292.1
161.9
94
344.6
191.0
54
397.0
220. 1
14
449.5
249. ^
74
502.0
278.3
35
293.0
162.4
95
345.4
191.5
55
397.9
220.6
15
450.4
249.7
75
502.9
278.8
36
293.8
162.9
96
346.3
192.0
56
398.8
221.1
16
451.3
250. 2
76
503. 7
279.2
37
294.7
163.4
97
347.2 192.5
57 399. 7
221. "6
17
452.2
250.6
77
504. 6 279. 7
38
295.6
163.9
98
348.1
193.0
58 400. 5
222.0
18
453.1
251.1
78
505.5
280.2
39
296.5
164.4
99
348.9
193.4
59
401.4
222. 5
19
453.9
251.6
79
506.4
280.7
40
297.3
164.8
400
349.8
193.9
60
402.3
223.0
20
454.8
252. 1
80
507.2
281.2
341
298.2
165.3
401
350.7
194.4
461 403.2 (223.5
521
455.6
252.6
581
508.1
281.7
42
299.1
165.8
02
351.6
194.9
62 i 404.0 224.0
22
456.5
253.1
82
509.0
282.2
43
300.0
166.3
03
352.4
195.4
63
404.9
224. 5
23
457. 4
253.6
83
509.9
282.7
44
300.8
166.8
04
353. 3
195.9
64
405.8
225.0
24
458.3
254.0
84
510. 7
283.2
45
301.7
167.3
05
354.2
196.3
65
406.7
225.4
25
459.1 254.5
85
511.6
283.6
46
302.6 167.7
06
355.1
196.8
66
407.5
225.9
26
460.0 255.0
86
512.5
284.1
47
303.5 168.2
07
355.9
197.3
67
408.4
226. 4
27
460.9 255.5
87
513.4
284.6
48
304.3 168.7
08
356.8
197.8
68
409.3
226.9
28
461.8 256.0
88
514.3
285.0
49
305. 2 ; 169. 2
09
357.7
198.3
69 410. 2
227. 4
29
462.6 256.5
89
515.1
285.5
50
306. 1 169. 7
10
358. 6
198.8
70 i 411.0
227.9
30
463.5 ;256.9
90
516. 0
286.0
351
307.0 .170.2
411 359.4
199. 3
471 411.9
228.3
531
464.4 1257.4
591
516.9
286.5
52
307.8
170.7
12 1 360.3
199.7
72 412. 8
228. 8
32
465.3 257.9
92
517.7 287.0
53
308.7
171.1
13 361.2
200.2
73
413.7
229.3
33
466.1 258.4
93
518. 6 287. 5
54
309.6
171.6
14
362.1
200.7
74
414.5
229.8
34
467.0
258.9
94
519.5
288. 0
55
310.5
172.1
15
362.9
201.2
75
415.4
230.3
35
467.9
259.4
95
520. 4
288. 5
56
311.3
172.6
16
363.8
201. 7
76
416.3
230.8
36
468.8
259.9
96
521. 2
288. 9
57
312.2
173.1
17
364.7
202.2
77
417.2
231.3
37
469.6
260.3
97
522. 1
2S9. 4
58
313.1
173. 6
18
365.6
202. 7
78
418.0
231.7
38
470.5
260.8
98
523.0
2S9.9
59
314.0
174.0
19
366.4
203.1
79
418.9
232.2
39
471.4
261.3
99
523.9
290.4
60
314.8
174.5
20
367.3
203.6
80
419.8
232.7
40
472.3
261.8
600
524.8
290.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
61° (119°, 241°, 299°).
Page 590] TABLE 2.
Difference of Latitude and Departure for '30° (150°, 210°, 330°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
52.8
30.5
121
104.8
60.5
181
156.8
90.5
241
208.7
120.5
2
1.7
1.0
62
53.7
31.0
22
105.7
61.0
82
157.6
91.0
42
209.6
121.0
3
2.6
1.5
63
54.6
31.5
23
106.5
61.5
83
158.5
91.5
43
210.4
121.5
4
3.5
2.0
64
55.4
32.0
24
107.4
62.0
84
159.3
92.0
44
211.3
122.0
5
4.3
2.5
65
56.3
32.5
25
108.3
62.5
85
160.2
92.5
45
212.2
122.5
6
5.2
3.0
66
57.2
33.0
26
109.1
63.0
86
161.1
93.0
46
213.0
123.0
7
6.1
3.5
67
58.0
33.5
27
110.0
63.5
87
161.9
93.5
47
213.9
123.5
8
6.9
4.0
68
58.9
34.0
28
110.9
64.0
88
162.8'
94.0
48
214.8
124.0
9
7.8
4.5
69
59.8
34.5
29
111.7
64.5
89
163. 7
94.5
49
215.6
124.5
10
8.7
5.0
70
60.6
35.0
30
112.6
65.0
90
164.5
95.0
50
216.5
125.0
11
9.5
5.5
71
61.5
35.5
131
113.4
65.5
191
165.4
95.5
251
217.4
125.5
12
10.4
6.0
72
62.4
36.0
32
114.3
66.0
92
166.3
98.0
52
218.2
126.0
13
11.3
6.5
73
63.2
36.5
33
115.2
66.5
93
167.1
96.5
53
219.1
126.5
14
12.1
7.0
74
64.1
37.0
34
116.0
67.0
94
168.0
97.0
54
220.0
127.0
15
13.0
7.5
75
65.0
37.5
35
116.9
67.5
95
168.9
97.5
55
220.8
127.5
16
13.9
8.0
76
65.8
38.0
36
117.8
68.0
96
169.7
98.0
56
221.7
128.0
17
14.7
8.5
77
66.7
38.5
37
118.6
68.5
97
170.6
98.5
57
222.6
128.5
18
15.6
9.0
78
67.5
39.0
38
119.5
69.0
98
171.5
99.0
58
223.4
129.0
19
16.5
9.5
79
68.4
39.5
39
120.4
69.5
99
172.3
99.5
59
224.3
129.5
20
17.3
10.0
80
69.3
40.0
40
121.2
70.0
200
173.2
100.0
60
225.2
130.0
21
18.2
10.5
81
70.1
40.5
141
122.1
70.5
201
174.1
100.5
261
226.0
130.5
22
19.1
11.0
82
71.0
41.0
42
123.0
71.0
02
174.9
101.0
62
226.9
131.0
23
19.9
11.5
83
71.9
41.5
43
123.8
71.5
03
175.8
101.5
63
227.8
131.5
24
20.8
12.0
84
72.7
42.0
44
124.7
72.0
04
176.7
102.0
64
228.6
132.0
25
21.7
12.5
85
73.6
42.5
45
125. 6
72.5
05
177.5
102.5
65
229.5
132.5
26
22.5
13.0
86
74.5
43.0
46
126.4
73.0
06
178.4
103.0
66
230.4
133.0
27
23.4
13.5
87
75.3
43.5
47
127.3
73.5
07
179.3
103.5
67
231.2
133.5
28
24.2
14.0
88
76.2
44.0
48
128.2
74.0
08
180.1
104.0
68
232.1
134.0
29
25.1
14.5
89
77.1
44.5
49
129.0
74.5
09
181.0
104.5
69
233.0
134.5
30
26.0
15.0
90
77.9
45.0
50
129.9
75.0
10
181.9
105.0
70
233.8
135.0
31
26.8
15.5
91
78.8
45.5
151
130.8
75.5
211
182.7
105. 5
271
234.7
135.5
32
27.7
16.0
92
79.7
46.0
52
131.6
76.0
12
183.6
106.0
72
235.6
136.0
33
28.6
16.5
93
80.5
46.5
53
132.5
76.5
13
184.5
106.5
73
236.4
136.5
34
29.4
17.0
94
81.4
47.0
54
133.4
77.0
14
185.3
107.0
74
237.3
137.0
35
30.3
17.5
95
82.3
47.5
55
134.2
77.5
15
186. 2
107.5
75
238.2
137.5
36
31.2
18.0
96
83.1
48.0
56
13-5.1
78.0
16
187.1
108.0
76
239.0
138.0
37
32.0
18.5
97
84.0
48.5
57
136.0
78.5
17
187.9
108.5
77
239. 9 138. 5
38
32.9
19.0
98
84.9
49.0
58
136.8
79.0
18
188.8
109. 0
78
240.8
139.0
39
33.8
19.5
99
85.7
49.5
59
137.7
79.5
19
189.7
109.5
79
241.6
139.5
40
34.6
20.0
100
86.6
50.0
60
138.6
80.0
20
190.5
110. 0
80
242.5 | 140.0
41
35.5
20.5
101
87.5
50.5
161
139.4
80.5
221
191.4
110.5
281
243.4 i 140.5
42
36.4
21.0
02
88.3
51.0
62
140. 3
81.0
22
192.3
111.0
82
244.2 ! 141.0
43
37.2
21.5
03
89.2
51.5
63
141.2
81.5
23
193.1
111.5
83
245.1 i 141.5
44
38.1
22.0
04
90.1
52.0
64
142.0
82.0
24
194.0
112.0
84
246.0 j 142.0
45
39.0
22.5,
05
90.9
52.5
65
142.9
82.5
25
194.9
112.5
85
246.8
142. 5
46
39.8
23.0
06
91.8
53.0
66
143.8
83.0
26
195.7
113.0
86
247.7
143.0
47
40.7
23.5
07
92.7
53.5
67
144.6
83.5
27
196.6
113.5
87
248.5
143.5
48
41.6
24.0
08
93.5
54.0
68
145. 5
84.0
28
197.5
114.0
88
249.4
144. 0
49
42.4
24.5
09
94.4
54.5
69
146.4
84.5
29
198.3
114.5
89
250.3
144.5
50
43.3
25.0
10
95.3
55.0
70
147.2
85.0
30
199.2
115.0
90
251.1
145.0
51
44.2
25.5
111
96.1
55.5
171
148.1
85.5
231
200.1
115.5
291
252.0
14o. 5
52
45.0
26.0
12
97.0
56.0
72
149.0
86.0
32
200.9
116.0
92
252.9
146.0
53
45.9
26.5
13
97.9
56.5
73
149.8
86.5
33
201.8
116.5
93
253.7
146. 5
54
46.8
27.0
14
98.7
57.0
74
150.7
87.0
34
202.6
117.0
94
254.6
147.0
55
47.6
27.5
15
99.6
57.5
75
151.6
87.5
35
203.5
117.5
95
255.5
147.5
56
48.5
28.0
16
100.5
58.0
76
152. 4
88.0
36
204.4
118.0
96
256.3
148.0
57
49.4
28.5
17
101.3
58.5
77
153.3
88.5
37
205.2
118.5
97
257.2
148.5
58
50.2
29.0
18
102.2
59.0
78
154.2
89.0
38
206.1
119.0
98
258. 1
149.0
59
51.1
29.5
19
103.1
59.5
79
155.0
89.5
39
207. 0
119.5
99
258.9
149. 5
60
52.0
30.0
20
103.9
60.0
80
155. 9
90.0
40
207.8
120.0
300
259.8
150.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
60° (120°, 240°, 300°).
TABLE 2. [Page 591
Difference of Latitude and Departure for 30° (150°, 210°, 330°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
260.7
150.5
361
312.6
180.5
421
364.6
210.5
481
416.6
240.5
541
468.5
270.5
02
261.5
151.0
62
313.5
181.0
22
365.5
211.0
82
417.4
241.0
42
469.4
271.0
03
262.4
151.5
63
314.4
181.5
23
366.3
211.5
83
418.3
241.5
43
47.0.3
271.5
04
263.3
152.0
64
315.2
182.0
24
367.2
212.0
84
419.2
242.0
44
471.1
272.0
05
264.1
152. 5
65
316.1
182. 5
25
368.1
212.5
85
420.0
242.5
45
472.0
272.5
06
265.0
153.0
66
317.0
183.0
26
368.9
213.0
86
420.9
243.0
46
472.9
273.0
07
265.9
153.5
67
317.8
183.5
27
369.8
213.5
87
421.8
243.5
47
473.7
273.5
08
266. 7
154.0
68
318.7
184.0
28
370.7
214.0
88
422.6
244.0
48
474.6
274.0
09
267.6
154.5
69
319.6
184.5
29
371.5
214.5
89
423.5
244.5
49
475.5
274.5
10
268.5
155.0
70
320.4
185.0
30
372.4
215.0
90
424.4
245.0
50
476.3
275.0
311
269.3
155.5
371
321.3
185.5
431
373.3
215.5
491
425.2
245.5
551
477.2
275.5
12
270.2
156.0
72
322.2
186.0
32
374.1
216.0
92
426.1
246.0
52
478.1
276.0
13
271.1
156.5
73
323.0
186.5
33
375.0
216.5
93
426.9
246.5
53
478.9
276.5
14
271.9
157.0
74
323.9
187.0
34
375.9
217.0
94
427.8
247.0
54
479.8
277.0
15
272.8
157.5
75
324.8
187.5
35
376.7
217.5
95
428.7
247.5
55
480.7
277.5
16
273.7
158.0
76
325.6
188.0
36
377.6
218.0
96
429.6
248.0
56
481.5
278.0
17
274.5
158.5
77
326.5
188.5
37
378.5
218.5
97
430.4
248.5
57
482.4
278.5
18
275. 4
159.0
78
327.4
189.0
38
379.3
219.0
98
431.3
249.0
58
483.3
279.0
19
276.3
159.5
79
328.2
189.5
39
380.2
219.5
99
432.2
249.5
59
484.1
279.5
20
277.1
160.0
80
329.1
190.0
40
381.1
220.0
500
433.0
250.0
60
485.0
280.0
321
278.0
160.5
381
330.0
190.5
441
381.9
220.5
501
433.9
250.5
561
485.9
280.5
22
278.9
161.0
82
330.8
191.0
42
382.8
221.0
02
434.8
251.0
62.
486.7
281.0
23
279.7
161.5
83
331.7
191.5
43
383.7
221.5
03
435.6
251.5
63
487.6
281.5
24
280.6
162.0
84
332.6
192.0
44
384.5
222.0
04
436.5
252.0
64
488.5
282.0
25
281.5
162.5
85
333.4
192.5
45
385.4
222.5
05
437.4
252.5
65
489.3
282.5
26
282.3
163.0
86
334.3
193.0
46 386.3
223.0
06
438.2
253. 0
66
490.2
283.0
27
283.2
163.5
87
335.2
193.5
47 387. 1
223.5
07
439.1
253.5
67
491.1
283.5
28
284.1
164.0
88
336.0
194.0
48 388. 0
224.0
08
440.0
254.0
68
491.9
284.0
29
284.9
164.5
89
336.9
194.5
49 ! 388. 9
224.5
09
440.8
254. 5
69
492.8
284.5
30
285.8
165.0
90
337.8
195.0
50 389. 7
225.0
10
441.7
255.0
70
493.6
285.0
331
286.7
165.5
391
338.6
195.5
451 390.6
225. 5
511
442.6
255. 5
571
494.5
285.5
32
287.5
166.0
92
339.5
196.0
52 391.5
226.0
12
443.4
256.0
72
495.4
286.0
33
288.4
166.5
93
340.4
196.5
53 392. 3
226.5
13
444.3
256.5
73
496.3
286.5
34
289.3
167.0
94
341.2
197.0
54 393. 2
227. 0
14
445.2
257.0
74
497.1
287.0
35
290.1
167.5
95
342.1
197.5
55 394.0
227.5
15
446.0
257.5
75
497.9
287.5
36
291.0
168.0
96
343.0
198.0
56 | 394.9
228.0
16
446.9
258.0
76
498.8
288.0
37
291.9
168.5
97
343.8
198.5
57 395.8
228.5
17
447.8
258.5
77
499.7
288.5
38
292.7
169.0
98
344.7
199.0
58
396.6
229.0
18
448.6
259.0
78
500.5
289.0
39
293.6
169.5
99
345.6
199.5
59
397.5
229.5
19
449.4
259.5
79
501.3
289.5
40
294.5
170.0
400
346.4
200.0
60
398.4
230.0
20
450.3
260.0
80
502.2
290.0
341 295. 3
170.5
401
347.3
200.5
461
399.2
230.5
521
451.2
260.5
581
503.1
290.5
42 296.2
171.0
02
348.1
201.0
62
400.1
231.0
22
452. 1
261.0
82
504.0
291.0
43 I 297.1
171.5
03
349.0
201.5
63
401.0
231.5
23
452.9
261.5
83
504.9
291.5
44 | 297.9
172.0
04
349.9
202.0
64
401.8
232.0
24
453.8
262.0
84
505.8
292.0
45 298. 8
172.5
05
350. 7
202.5
65
402.7
232.5
25
454.7
262.5
85
506.6
292.5
46 - 299. 7
173.0
06
351.6
203.0
66
403.6
233.0
26
455.5
263.0
86
507.5
293.0
47 1 300. 5
173.5
07
352.5
203.5
67
404.4
233.5
27
456.4
263.5
87
508.4
293.5
48 : 301.4
"174.0
08
353.3
204.0
68
405.3
234.0
28
457.3
264.0
88
509.2
294.0
49 302. 3
174.5
09
354.2
204.5
69
406.2
234.5
29
458.1
264.5
89
510.1
294.5
50 ; 303.1
175.0
10
355.1
205.0
70
407.0
235.0
30
459.0
265.0
90
511.0
295.0
351
304.0
175. 5
411
355.9
205.5
471
407.9
235.5
531
459.9
265.5
591
511.8
295.5
52
304.8
176.0
12
356.8
206.0
72
408.8
236.0
32
460.7
266.0
92
512.7
296.0
53
305.7
176.5
13
357.7
206.5
73
409.6
236.5
33
461.6
266.5
93
513.6
296.5
54
306.6
177.0
14
358.5 207.0
74
410.5
237.0
34
462.5
267.0
94
514.4
297.0
55
307.4
177. 5
15
359.4 |207.5
75
411.4
237.5
35
463.3
267.5
95
515.3
297.5
56
308.3
178.0
16
360.3 1208.0
76
412.2
238.0
36
464.2
268.0
96
516.2
298.0
57
309.2
178.5
17
361.1
208.5
77
413.1
238.5
37
465.1
268.5
97
517.0
298.5
58
310.0
179.0
18
362.0
209.0
78
414.0
239.0
38
465.9
269.0
98
517.9
299.0
59
310.9
179.5
19
362.9
209.5
79
414.8
239.5
39
466.8
269.5
99
518.8
299.5
60
311.8
180.0
20
363.7
210.0
80
415.7
240.0
40
467.7
270.0
600
519.6
300.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
Dist.
Dep.
Lat.
60° (120°, 240°, 300°).
61828°— 16-
Page 592] TABLE 2.
Difference of Latitude and Departure for 31° (149°, 211°, 329°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
52.3
31.4
121
103.7
62.3
181
155.1
93.2
241
206.6
124.1
2
1.7
1.0
62
53.1
31.9
22
104.6
62.8
82
156.0
93.7
42
207.4
124.6
3
2.6
1.5
63
54 0
32.4
23
105.4
63.3
83
156.9
94.3
43
208.3
125.2
4
3.4
2.1
64
54.9
33.0
24
106.3
63.9
84
157.7
94.8
44
209.1
125.7
5
4.8
2.6
65
55.7
33.5
25
107.1
64.4
85
158.6
95.3
45
210.0
126.2
6
5.1
3.1
66
56.6
34.0
26
108.0
64.9
86
159.4
95.8
46
210.9
126.7
7
6.0
3.6
67
57.4
34.5
27
108.9
65.4
87
160.3
96.3
47
211.7
127.2
8
6.9
4.1
68
58.3
35.0
28
109.7
65.9
88
161.1
96.8
48
212.6
127.7
9
7.7
4.6
69
59.1
35.5
29
110.6
66.4
89
162.0
97.3
^9
213.4
128.2
10
8.6
5.2
70
60.0
36.1
30
111.4
67.0
90
162.9
97.9
50
214.3
128.8
11
9.4
5.7
71
60.9
36.6
131
112.3
67.5
191
163.7
98.4
251
215.1
129.3
12
10.3
6.2
72
61.7
37.1
32
113.1
68.0
92
164.6
98.9
52
216.0
129.8
13
11.1
6.7
73
62.6
37.6
33
114.0
68.5
93
165.4
99.4
53
216.9
130.3
14
12.0
7.2
74
63.4
38.1
34
114.9
69.0
94
166.3
99.9
54
217.7
130.8
15
12.9
7.7
75
64.3
38.6
35
115.7
69.5
95
167.1
100.4
55
218.6
131.3
16
13.7
8.2
76
65.1
39.1
36
116.6
70.0
96
168.0
100.9
56
219.4
131.8
17
14.6
8.8
77
66.0
39.7
37
117.4
70.6
97
168.9
101.5
57
220.3
132.4
18
15.4
9.3
78
66.9
40.2
38
118.3
71.1
98
169.7
102.0
58
221.1
132.9
19
16.3
9.8
79
67.7
40.7
39
119.1
71.6
99
170.6
102.5
59
222.0
133.4
20
17.1
10.3
80
68.6
41.2
40
120.0
72.1
200
171.4
103.0
60
222.9
133.9
21
18.0
10.8
81
69.4
41.7
141
120.9
72.6
201
172.3
103.5
261
223.7
134.4
22
18.9
11.3
82
70.3
42.2
42
121.7
73.1
02
173.1
104.0
62
224.6
134.9
23
19.7
11.8
83
71.1
42.7
43
122.6
73.7
03
174.0
104.6
63
225.4
135. 5
24
20.6
12.4
84
72.0
43.3
44
123.4
74.2
04
174.9
105.1
64
22(3.3
136.0
25
21.4
12.9
85
72.9
43.8
45
124.3
74.7
05
175.7
105.6
65
227.1
136.5
26
22.3
13.4
86
73.7
44.3
46
125.1
75.2
06
176.6
106.1
66
228.0
137.0
27
23.1
13.9
87
74.6
44.8
47
126.0
75.7
07
177.4
106.6
67
228.9
137.5
28
24.0
14.4
88
75.4
45.3
48
126.9
76.2
08
178.3
107.1
68
229.7
138.0
29
24.9
14.9
89
76.3
45.8
49
127.7
76.7
09
179.1
107.6
69
230.6
138.5
30
25.7
15.5
90
77.1
46.4
50
128.6
77.3
10
180.0
108.2
70
231.4
139.1
31
26.6
16.0
91
78.0
46.9
151
129.4
77.8
211
180.9
108.7
271
232.3
139.6
32
27.4
16.5
92
78.9
47.4
52
130.3
78.3
12
181.7
109.2
72
233.1
140.1
33
28.3
17.0
93
79.7
47.9
53
131.1
78.8
13
182.6
109.7
73
234,0
140.6
34
29.1
17.5
94
80.6
48.4
54
132.0
79.3
14
183.4
110.2
74
234.9
141.1
35
30.0
18.0
95
81.4
48.9
55
132.9
79.8
15
184.3
110.7
75
235.7
141.6
36
30.9
18.5
96
82.3
49.4
56
133.7
80.3
16
185.1
111.2
76
236.6
142.2
37
31.7
19.1
97
83.1
50.0
57
134.6
80.9
17
186.0
111.8
77
237.4
142.7
38
32.6
19.6
98
84.0
50.5
58
135.4
81.4
18
186.9
112.3
78
238.3
143.2
39
33.4
20.1
99
84.9
51.0
59
136.3
81.9
19
187.7
112.8
79
239.1
143. 7
40
34.3
20.6
100
85.7
51.5
60
137.1
82.4
20
188.6
113.3
80
240.0
144.2
41
35.1
21.1
101
86.6
52.0
161
138.0
82.9
221
189.4
113.8
281
240.9
144.7
42
36.0
21.6
02
87.4
52.5
62
138.9
83.4
22
190.3
114.3
82
241.7
145.2
43
36.9
22.1
03
88.3
53.0
63
139.7
84.0
23
191.1
114.9
83
242.6
145.8
44
37.7
22.7
04
89.1
53.6
64
140.6
84.5
24
192.0
115.4
84
243.4
146.3
45
38.6
23.2
05
90.0
54.1
65
141.4
85.0
25
192.9
115.9
85
244.3
146.8
46
39.4
23.7
06
90.9
54.6
66
142.3
85.5
26
193.7
116.4
86
245.1
147.3
47
40.3
24.2
07
91.7
55.1
67
143.1
86.0
27
194.6
116.9
87
. 246. 0
147.8
48
41.1
24.7
08
92.6
55.6
68
144.0
86.5
28
195.4
117.4
88
246.9
148.3
49
42.0
25.2
09
93.4
56.1
69
144.9
87.0
29
196.3
117.9
89
247.7
148.8
50
42.9
25.8
10
94.3
56.7
70
145.7
87.6
30
197.1
118.5
90
248.6
149.4
51
43.7
26.3
111
95.1
57.2
171
146.6
88.1
231
198.0
119.0
291
249.4
149.9
52
44.6
26.8
12
96.0
57.7
72
147.4
88.6
32
198.9
119.5
92
250.3
150.4
53
45.4
27.3
13
96.9
58.2
73
148.3
89.1
33
199.7
120.0
93
251.2
150.9
54
46.3
27.8
14
97.7
58.7
74
149.1
89.6
34
200.6
120.5
94
252.0
151.4
56
47.1
28.3
15
98.6
59.2
75
150.0
90.1
35
201.4
121.0
95
252.9
151.9
56
48.0
28.8
16
99.4
59.7
76
150.9
90.6
36
202.3
121.5
96
253.7
152.5
57
48.9
29.4
17
100.3
60.3
77
151.7
91.2
37
203.1
122.1
97
254.6
153.0
58
49.7
29.9
18
101.1
60.8
78
152.6
91.7
38
204.0
122.6
98
255.4
153.5
59
50.6
30.4
19
102.0
61.3
79
153.4
92.2
39
204.9
123.1
99
256.3
154.0
60
51.4
30.9
20
102.9
61.8
80
154.3
92.7
40
205.7
123.6
300
257.1
154.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
59° (121°, 239°, 301°).
TABLE 2. [Page 593
Difference of Latitude and Departure for 31° (149°, 211°, 329°).
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
258.0
155.0
361
309.4
185.9
421
360.9
216.8
481
412.3
247.7
541
463.7
278.6
02
258.9
155.5
62
310.3
186.4
22
361.7
217.3
82
413.2
248.2
42
464.6
279.1
03
259. 7
156.1
63
311.2
187.0
23
362.6
217.9
83
414.0
248.8
43
465.4
279.7
04
260.6
156.6
64
312.0
187.5
24
363.4
218.4
84
414.9
249. 3
44
466.3 i 280.2
05
261.4
157.1
65
312.9
188.0
25
364.3
218.9
85 415. 7
249.8
45
467. 2 1 280. 7
06
262.3
157.6
66
313.7
188.5
26
365. 2
219.4
86
416.6
250. 3
46
468. 0 ! 281. 2
07
263.2
158.1
67
314.6
189.0
27
366.0
219.9
87
417.4
250.8
47
468.9 : 281.7
08
264.0
158.6
68
315. 4
189.5
28
366.9
220.4
88
418.3
251.3
48
469. 7 ! 282. 3
09
264.9
159.2
69
316.3
190.1
29
367.7
221.0
89
419.2
251.9
49
470. 6 282. 8
10
265. 7
159. 7
70
317.2
190.6
30
368.6
221.5
90
420.0
252.4
50
471. 4 283. 3
311
266.6
160.2
371
318.0
191.1
431
369.4
222.0
491
420.9
252.9
551
472. 3 ! 283. 8
12
267.4
160. 7
72
318.9
191.6
32
370.3
222.5
92
421.7
253.4
52
473.2
284.3
13
268.3
161.2
73
319.7
192.1
33
371.2
223.0
93
422.6
253.9
53
474.0
284.8
14
269.2
161.7
74
320.6
192.6
34
372.0
223.5
94
423.4
254.4
54
474.9
285.3
15
270.0
162.2
75
321.4
193. 1
35
372.9
224.0
95
424. 3
254.9
55
475.7
285.8
16
270.9
162.8
76
322.3
193.7
36
373. 7
224.6
96
425.2
255.5
56
476.6
286.4
17
271.7
163.3
77
323.2
194.2
37
374.6
225.1
97
426.0
256.0
57
477.4
286.9
18
272.6
163.8
78
324.0
194.7
38
375.4
225.6
98
426.9
256.5
58
478.3
287.4
19
273.4
164.3
79
324.9
195.2
39
376.3
226.1
99
427.7
257.0
59
479. 2
287.9
20
274.3
164.8
80
325.7
195.7
40
377.2
226.6
500
428.6
257.5
60
480.0
288.4
321
275.2
165.3
381
326. 6
196.2
441
378.0
227.1
501
429.4
258.0
561
480.9
288.9
22
276.0
165.8
82
327.4
196.7
42
378.9
227.7
02
430.3
258.6
62
481.7
289.5
23
276.9
166.4
83
328.3
197.3
43
379.7
238.2
03
431.2
259.1
63
482.6
290.0
24
277.7
166.9
84
329.2
197.8
44
380.6
228.7
04
432.0
259.6
64
483.4
290.5
25
278.6
167.4
85
330.0
198.3
45
381.4
229.2
05
432.9
260.1
65
484.3
291.0
26
279.4
167.9
86
330.9
198.8
46
382.3
229.7
06
433.7
260.6
66
485.2
291.5
27
280.3
168.4
87
331.7
199.3
47
383.2
230.2
07
434.6
261.1
67
486.0 | 292.0
28
281.2
168.9
88
332.6
199.8
48
384.0
230.7
08
435.4
261.6
68
486.9 1 292.5
29
282.0
169.5
89
333.4
200.4
49
384.9
231.3
09
436.3
262.2
69
487.7 i 293.1
30
282 9
170.0
90
334.3
200.9
50
385. 7
231.8
10
437.2
262.7
70
488. 6 j 293. 6
331
283.7
170.5
391
335.2
201.4
451
386.6
232.3
511
438.0
263.2
571 ! 489.4
294. 1
32
284.6
171.0
92
336.0
201.9
52
387.4
232.8
12
438.9
263.7
72 490. 3
294.6
33
285.4
171.5
93
336.9
202.4
53
388.3
233.3
13
439.7
264.2
73
491.2
295. 1
34
286.3
172.0
94
337.7
202.9
54
389.2
233.8
14
440.6
264.7
74
492.0
295.6
35
287.2
172. 5
95
338.6
203.4
55
390.0
234.3
15
441.4
265.2
75
492.9
296.1
36
288.0
173.1
96
339.4
204.0
56
390.9
234.9
16
442.3
265.8
76
493.7
296.7
37
288.9
173.6
97
340.3
204.5
57
391.7
235.4
17
443.2
266.3
77
494.6
297.2
38
289.7
174.1
98
341.2
205. 0
58
392.6
235.9
18
444.0
266.8
78
495.4
297.7
39
290.6
174.6
99
342.0
205. 5
59
393.4
236.4
19
444.9
267.3
79
496.3
298.2
40
291.4
175.1
400
342.9
206.0
60
394.3
236.9
20
445.7
267.8
80
497.2
298.7
341
292.3
175.6
401
343.7
206. 5
461
395.2
237.4
521
446.6
268. 3
581
498.0
299.2
42
293.2
176.1
02
344.6
207.0
62
396.0
238.0
22
447.4
268.9
82
498. 9 ! 299. 8
43
294.0
176.7
03
345. 4
207.6
63
396.9
238.5
23
448.3
269.4
83
499. 7 300. 3
44
294.9
177.2
04
346.3
208.1
64
397.7
239.0
24
449.2
269.9
84
500. 6 j 300. 8
45
295.7
177.7
05
347.2
208.6
65
398.6
239.5
25
450.0
270.4
85
501. 4 1 301. 3
46
296.6
178.2
06
348.0
209.1
66
399.4
240.0
26
450.9
270.9
86
502.3
301.8
47
297.4
178. 7
07
348.9
209.6
67
400.3
240.5
27
451.7
271.4
87
503.2
302.3
48
298.3
179.2
08
349.7
210.1
68
401.2
241.0
28
452.6
271.9
88
504.0
302.8
49
299.2
179.8
09
350.6
210.7
69
402.0
241.5
29
453.4
272.4
89
504.9
303.3
50
300.0
180.3
10
351.4
211.2
70
402.9
242.1
30
454.3
273.0
90
505.7
303.9
351
300.9
180.8
411
352.3
211.7
471
403.7
242.6
531
455.2
273. 5
591
506.6
304.4
52
301.7
181.3
12
353.2
212.2
72
404.6
243.1
32
456.0
274.0
92
507.4
304.9
53
302.6
181.8
13
354. 0
212.7
73
405.4
243.6
33
456.9
274.5
93
508.3
305.4
54
303.4
182.3
14
354.9
213.2
74
406.3
244.1
34
457.7
275.0
94
509.2
305.9
55
304.3
182.8
15
355.7
213.7
75
407.2
244.6
35
458.6
275.5
95
510.0
306.4
56
305.2
183.4
16
356.6
214.3
76
408.0
245.2
36
459.4
276.1
96
510.9
307.0
57
306.0
183.9
17
357.4
214.8
77
408.9
245.7
37
460.3
276.6
97
511.7
307.5
58
306.9
184.4
18
358.3
215.3
78
409.7
246.2
38
461.2
277.1
98
512.6
308.0
59
307.7
184.9
19
359.2
215.8
79
410.6
246.7
39
462.0
277.6
99
513.4
308.5
60
308.6
185.4
20
360.0
216.3
80
411.4
247.2
40
462.9
278.1
600
514.3
309.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
59° (121°, 239°, 301°).
Page 594] TABLE 2.
Difference of Latitude and Departure for 32° (148°, 212°, 328°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. I Lat.
Dep.
1
0.8
0.5
61
51.7
32.3
121
102.6
64.1
181
153.5
95.9
241
204.4
127.7
2
1.7
1.1
'62
52.6
32.9
22
103.5
64.7
82
154.3
96.4
42
205.2
128.2
3
2.5
1.6
63
53.4
33.4
23
104.3
65.2
83
155.2
97.0
43
206.1
128.8
4
3.4
2.1
64
54.3
33.9
24
105.2
65.7
84
156.0
97.5
44
206.9
129.3
5
4.2
2.6
65
55.1
34.4
25
106.0
66.2
85
156. 9
98.0
45
207.8
129.8
6
5.1
3.2
66
56.0
35.0
26
106.9
66.8
86
157.7
98.6
46
208.6
130.4
7
5.9
3.7
67
56.8
35.5
27
107. 7
67.3
87
158.6
99.1
47
209.5
130.9
8.
6.8
4.2
68
57.7
36.0
28
108.6
67.8
88
159.4
99.6
48
210.3
131.4
9
7.6
4.8
69
58.5
36.6
29
109. 4
68.4
89
160.3
100. 2
49
211.2
131.9
10
8.5
5.3
70
59.4
37.1
30
110.2
68.9
90
161.1
100.7
50
212.0
132.5
11
9.3
5.8
71
60.2
37.6
131
111.1
69.4
191
162.0
101.2
251
212.9
133.0
12
10.2
6.4
72
61.1
38.2
32
111.9
69.9
92
162.8
101.7
52
213.7
133.5
13
11.0
6.9
73
61.9
38.7
33
112.8
70.5
93
163.7
102.3
53
214.6
134.1
14
11.9
7.4
74
62.8
39.2
34
113.6
71.0
94
164.5
102.8
54
215.4
134.6
15
12.7
7.9
75
63.6
39.7
35
114.5
71.5
95
165.4
103.3
55
216.3
135.1
16
13.6
8.5
76
64.5
40.3
36
115.3
72.1
96
166.2
103.9
56
217.1
135.7
17
14.4
9.0
77
65.3
40.8
37
116.2
72.6
97
167.1
104.4
57
217.9
136.2
18
15.3
9.5
78
66.1
41.3
38
117.0
73.1
98
167.9
104.9
58
218.8
136.7
19
16.1
10.1
79
67.0
41.9
39
117.9
73.7
99
168.8
105.5
59
219.6
137.2
20
17.0
10.6
80
67.8
42.4
40
118.7
74.2
200
169.6
106.0
60
220.5
137. 8
21
17.8
11.1
81
68.7
42.9
141
119.6
74.7
201
170.5
106.5
261
221.3
138.3
22
18.7
11.7
82
69.5
43.5
42
120.4
75.2
02
171.3
107.0
62
222.2
138.8
23
19.5
12.2
83
70.4
44.0
4&
121.3
75.8
03
172.2
107.6
63
223.0
139.4
24
20.4
12.7
84
71.2
44.5
44
122.1
76.3
04
173. 0
108.1
64
223.9
139.9
25
21.2
13.2
85
72.1
45.0
45
123.0
76.8
05
173.8
108.6
65
224.7
140.4
26
22.0
13.8
86
72.9
45.6
46
123.8
77.4
06
174.7
109.2
66
225.6
141.0
27
22.9
14.3
87
73.8
46.1
47
124.7
77.9
07
175.5
109.7
67
226.4
141.5
28
23.7
14.8
88
74.6
46.6
48
125.5
78.4
08
176.4
110.2
68
227.3
142.0
29
24.6
15.4
89
75.5
47.2
49
126.4
79.0
09
177.2
110.8
69
228.1
142.5
30
25.4
15.9
90
76.3
47.7
50 | 127.2
79.5
10
178.1
111.3
70
229.0
143.1
31
26.3
16.4
91
77.2
48.2
151
128.1
80.0
211
178.9
111.8
271
229.8
143.6
32
27.1
17.0
92
78.0
48.8
52
128.9
80.5
12
179.8
112.3
72
230.7
144.1
33
28.0
17.5
93
78.9
49.3
53
129.8
81.1
13
180.6
112.9
73
231.5
144.7
34
28.8
18.0
94
79.7
49.8
54
130.6
81.6
14
181.5
113.4
74
232.4
145.2
35
29.7
18.5
95
80.6
50.3
55
131.4
82.1
15
182.3
113.9
75
233.2
145.7
36
30.5
19.1
96
81.4
50.9
56
132.3
82.7
16
183.2
114; 5
76
234.1
146.3
37
31.4
19.6
97
82.3
51.4
57
133.1
83.2
17
184.0
115.0
77
234.9
146.8
38
32.2
20.1
98
83.1
51.9
58
134.0
83.7
18
184.9
115.5
78
235.8
147.3
39
33.1
20.7
99
84.0
52.5
59
134.8
84.3
19
185.7
116.1
79
236.6
147.8
40
33.9
21.2
100
84.8
53.0
60
135.7
84.8
20
186.6
116.6
80
237.5
148.4
41
34.8
21.7
101
85.7
53.5
161
136.5
85.3
221
187.4
117.1
281
238.3
148.9
42
35.6
22.3
02
86.5
54.1
62
137.4
85.8
22
188.3
117.6
82
239.1
149.4
43
36.5
22.8
03
87.3
54.6
63
138.2
86.4
23
189.1
118.2
83
240.0
150.0
44
37.3
23.3
04
88.2
55.1
64
139.1
86.9
24
190.0
118.7
84
240. 8
150.5
45
38.2
23.8
05
89.0
55.6-
65
139.9
87.4
25
190.8
119.2
85
241.7
151.0
46
39.0
24.4
06
89.9
56.2
66
140.8
88.0
26
191.7
119.8
86
242.5
151. 6
47
39.9
24.9
07
90.7
56.7
67
141.6
88.5
27
192.5
120.3
87
243.4
152.1
48
40.7
25.4
08
91.6
57.2
68
142.5
89.0
28
193.4
120. 8
88
244.2
152.6
49
41.6
26.0
09
92.4
57.8
69
143.3
89.6
29
194.2
121.4
89
245. 1
153.1
50
42.4
26.5
10
93.3
58.3
70
144.2
90.1
30
195.1
121.9
90
245.9
153. 7
51
43.3
27.0
111
94.1
58.8
171
145.0
90.6
231
195.9
122.4
291
246.8
154.2
52
44.1
27.6
12
95.0
59.4
72
145.9
91.1
32
196.7
122.9
92
247.6
154.7
53
44.9
28.1
13
95.8
59.9
73
146.7
91.7
33
197.6
123.5
93
248.5
155.3
54
45.8
28.6
14
96.7
60.4
74
147.6
92.2
34
198.4
124.0
94
249.3
155.8
55
46.6
29.1
15
97.5
60.9
75
148.4
92.7
35
199.3
124.5
95
250.2
156.3
56
47.5
29.7
16
98.4
61.5
76
149.3
93.3
36
200.1
125.1
96
251.0
156.9
57
48.3
30.2
17
99.2
62.0
77
150.1
93.8
37
201.0
125.6
97
251.9
157. 4
58
49.2
30.7
18
100.1
62.5
78
151. 0
94.3
38
201.8
126. 1
98
252.7
157.9
59
50.0
31.3
19
100.9
63.1
79
151.8
94.9
39
202.7
126.7
99
253.6
158.4
60
50.9
31.8
20
101.8
63.6
80
152.6
95.4
40
203.5
127.2
300
254.4
159.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
58° (122°, 238°, 302°).
j TABLE 2. [Page 595
j Difference of Latitude and Departure for 32° (148°, 212°, 328°).
JlDist.
Lat
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1301
255.3
159.5
361
306.2
191.3
421
357.0
223.1
481
407.9
254.9
541
458.8
286.7
I 02
256.1
160.0
62
307.0
191.8
22
357.9
223.6
82
408.8
255.4
42
459.6
287.2
I 03
257.0
160.5
63
307.9
192.3
23
358.7
224.1
83
409.6
255.9
43
460.5
287.7
1 04
257.8
161.1
64
308.7
192.9
24
359.6
224. 7
84
410.5
256.5
44
461.3
288.3
1 05
258.7
161.6
65
309.5
193.4
25
360.4
225.2
85
411.3
257.0
45
462.2
288.8
06
259.5
162.1
66
310.4
193. 9
26
361.3
225. 7
86
412.2
257.5
46
463.0
289.3
07
260.4
162.7
67
311.2
194.5
27
362.1 226.3
87
413.0
258.1
47
463.9
289.9
08
261.2
163.2
68
312.1
195.0
28
363.0
226.8
88
413.9
258.6
48
464.7
290.4
1 09 262.1
163. 7
69
312.9
195. 5
29
363. 8
227.3
89
414.7
259.1
49
465.6
290.9
10 262.9
164.3
70
313.8
196.0
30
364.7
227.8
90
415.6
259.6
50
466.4
291.5
1311
263. 8
164.8
3/1
314.6
196.6
431
365.5
228. 4
491
416.4
260.2
boi
467. 3
292.0
12
264.6
165.3
72
315.5
197.1
32
366.4
228.9
92
417.3
260.7
52
468.1
292.5
13
265.4
165.8
73
316.3
197.6
33
367. 2
229.4
93
418.1
261.2
53
469.0
293.0
14
266.3
166.4
74
317.2
198. 2
34
368.1
230.0
94
419.0
261.8
54
469.8
293.6
15
267. 1
166.9
75
318.0
198.7
35
368.9
230.5
95
419.8
262. 3
55
470. 7
294.1
16
268.0
167.4
76
318.9
199.2
36
369.8
231.0
96
420.6
262.8
56
471.5
294.6
17
268.8
168.0
77
319.7
199.8
37
370.6
231.6
97
421.5
263.4
57
472.4
295.2
18
269.7
168.5
78
320.6
200.3
38
371.5
232.1
98
422.3
263.9
58
473.2
295.7
1 19
270.5
169.0
79
321.4
200.8
39
372.3
232. 6
99
423.2
264.4
59
474.1
296.2
20
271.4
169.6
80
322.3
201.3
40
373.2
233.1
500
424.0
265.0
60 i 474. 9
296.7
|32T
272.2
170.1
381
323.1
201.9
441
374.0
233.7
501
424.9
265. 5
561
475. S
297.3
22 273.1
170.6
82
324.0
202.4
42
374.8
234.2
02
425.7
266.0
62
476.6
297.8
23
273.9
171.1
83
324.8
202.9
43
375. 7
234.7
03
426.6
266.5
63
477. 5
298.3
24
274.8
171.7
84
325.7
203.5
44
376.5
235. 3
04
427.4
267. 1
64
478. 3 298. 9
25
275.6
172.2
85
326.5
204.0
45
377.4
235.8
05
428.3
267.6
65
479.2
299.4
26
276.5 172.7
86
327.4
204.5
46
378.2
236.3
06
429.1
268.1
66
480.0
299.9
27
277.3 173.3
87
328.2
205. 1
47 379. 1
236.9
07
430.0
268.7
67
480. 9 300. 5
28
278.2 J173.8
88
329.1
205. 6
48
379.9
237.4
08
430.8
269.2
68
481. 7 ; 301. 0
29
279.0 (174.3
89
329.9
206.1
49
380. 8
237.9
09
431.7
269.7
69
482.6 i 301.5
30
279.9 174.9
90
330.8
206.6
50
381.6 238.4
10
432.5
270.3
70
483. 4 i 302. 1
331
280.7 175.4
391
331.6 207.2
451
382.5 239.0
511 433. 4
270.8
571 484. 3 302. 6
32
281. 6 i 175. 9
92
332.5 207.7
52
383.3
239.5
12
434.2
271.4
72
485. 1 303. 2
33
282. 4 176. 4
93
333.3 1208.2
53
384.2
240.0
13
435.1
271.9
73
486. 0 ! 303. 7
34
283.3
177.0
94
334.2
208.8
54 j 385.0
240.6
14
435.9
272. 4
74
486. 8 304. 2
35
284.1
177. 5
95
335.0
209.3
55 385. 9
241.1
15
436.8
272.9
75
487. 7 304. 7
1 36 285.0
178.0
96
335.8
209.8
56 386. 7
241.6
16
437.6
273.5
76
488. 5 305. 3
1 37 285.8
178.6
97
336. 7
210.4
57 387. 6
242. 2
17
438.5
274.0
77
489. 4 305. 8
38
286.7 179.1
98 337. 5
210.9
58 388. 4
242. 7
18
439.3
274. 5
78
490. 2 j 306. 3
39
287.5
179.6
99 338. 4
211.4
59 389. 3
243.2
19
440.2
275.0
79
491.1
306.8
40
288. 3 ! 180. 2
400 339. 2
211.9
60 390.1 243.8
20
441.0
275.6
80
491.9
307.4
1 341
289.2
ISO. 7
401 340. 1
212.5
461 391. 0
244.3
521 i 441.9
276.1
581
492. 8
307.9
42
290.0
181.2
02
340.9
213.0
62 391. 8
244.8
22 442. 7
276.6
82
493.6
308.4
43
290.9
181. 7
03
341.8
213.5
63 392. 7
245.4
23
443.6
277.2
83
494.5
309.0
44
291.7
182.3
04
342.6
214.1
64 393.5 245.9
24
444.4
277. 7
84
495.3
309.5
45
292.6
182.8
05
343.5
214.6
65
394.4 246.4
25 445. 3
278.2
85
496.2 j 310.0
46
293.4
183.3
06
344.3
215. 1
66
395.2 246.9
26
446.1
278. 7
86
497. 0
310.5
47
294.3
183.9
07
345.2
215.7
67
396.0
247.5
27
446.9
279.3
87
497.8
311.1
48
295.1
184.4
08
346.0
216.2
68
396.9
248.0
28
447.8
279.8
88
498.7
311.6
49
296.0
184.9
09
346.9
216.7
69
397.7
248.5
29 448.6
280.3
89
499.5
312.1
| 50
296.8
185.4
10
347.7
217.2
70
398.6
249.0
30 i 449.5
280.9
90
500.3
312.6
poT
297.7
186.0
411
348.6
217.8
471
399.4 24i». 6
531 450. 3
281.4
591
501.2
313.2
1 52
298.5
186.5
12
349.4
218.3
72
400.3
250.1
32 451. 1
281.9
92
502.0
313.7
1 53
299.4
187.0
13
350.3
218.8
73
401.1
250.6
33
452.0
282.4
93
502.9
314.2
54
300,2
187.6
14
351.1
219.4
74
402.0
251.2
34
452.8
283.0
94
503.7
314.8
1 55
301.1
188.1
15
352.0
219.9
75
402.8
251. 7
35
453.7
283.5
95
504.6
315. 3
I 56
301.9
188.6
16
352.8
220.4
76
403.7
252.2
36
454.5
284.0
96
505.4
315.8
57
302.8
189.2
17
353. 6
221.0
77
404.5
252.8
37
455.4
284.6
97
506.2
316.4
1 58
303.6
189.7
18
354. 5
221.5
78
405.4
253.3
38
456.2
285.1
98
507.1
316.9
1 59
304.5
190.2
19
355.3
222. 0
79
406.2
253.8
39
457.1
285.6
99
508.0
317.4
1 60
305.3
190.8
20
356.2 222.5
80
407.1
254.3
40
457.9
286.2
600
508.8
318.0
Dist.
Dep.
Dist.
Dep. j Lat.
Dist. | Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
58° (122°, 238°, 302°).
Page 596] TABLE 2.
Difference of Latitude and Departure for 33° (147°, 213°, 327°).
Dist,
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. ; Lat.
Dep.
Dist. 1 Lat. Dep.
Dist.
Lat.
Dep.
1
0.8
0.5
61
51.2
33.2
121
101. 5 65. 9
181 151. 8 98. 6
241
202.1
131.3
2
L7
1.1
62
52.0
33.8
22
102.3 ! 66.4
82 152.6 ! 99.1
42
203.0
131.8
3
2.5
1.6
63
52.8
34.3
23 103. 2 67. 0
83 ; 153.5 i 99.7
43 203. 8
132.3
4
3.4
2.2
64
53.7
34.9
24 104. 0 67. 5
84 154.3 1100.2
44
204.6
132.9
5
4.2
2.7
65
54.5
35.4
25 104. 8 ' 68. 1
85 155.2 |100.8
45
205.5
133.4
6
5.0
3.3
66
55.4
35.9
26 105. 7 i 68. 6
86
156. 0 i 101. 3
46
206.3
134.0
7
5.9
3.8
67
56.2
36.5
27 106. 5
69.2
87
156. 8 ! 101. 8
47
207.2
134.5
8
6.7
4.4
68
57.0
37.0
28 107. 3
69.7
88
157. 7 i 102. 4
48
208.0
135.1
9
7.5
4.9
69
57.9
37.6
29 108. 2
70.3
89
158.5 |102.9
49
208.8
135. 6
10
8.4
5.4
70
58.7
38.1
30
109.0
70.8
90
159.3 103.5
50
209.7
136. 2
11
9.2
6.0
71
59.5
38.7
131
109.9
71.3
191
160.2
104.0
251
210.5
136.7
12
10.1
6.5
72
60.4
39.2
32
110.7
71.9
92
161.0
104. 6
52
211.3
137.2
13
10.9
7.1
73
61.2
39.8
33
111.5"
"72.4
93
161. 9 i 105. 1
53
212.2
137.8
14
11.7
7.6
74
62.1
40.3
34
112.4
73.0
94
162.7 1105.7
54
213.0
138.3
15
12.6
8.2
75
62.9
40.8
35
113.2 i 73.5
95
163. 5 1 106. 2
55
213.9
138.9
16
13.4
8.7
76
63.7
41.4
36
114. 1 ! 74. 1
96
164. 4 j 106. 7
56
214.7
139.4
17
14.3
9.3
77
64.6
41.9
37
114. 9
74.6
97
165. 2 107. 3
57
215. 5
140.0
18
15.1
9.8
78
65.4
42.5
38
115.7
75.2
98
166.1 107.8
58
216.4
140.5
19
15.9
10.3
79
66.3
43.0
39
116.6
75.7
99
166.9 108.4
59
217.2
141.1
20
16.8
10.9
80
67.1
43.6
40
117.4
76.2
200
167.7 108.9
60
218.1
141.6
21
17.6
11.4
81
67.9
44.1
141
118.3
76.8
201
168.6
109.5
261
218.9
142.2
22
18.5
12.0
82
68.8
44.7
42
119.1
77.3
02
169.4
110.0
62
219.7
142.7
23
19.3
12.5
83
69.6
45.2
43
119.9
77.9.
03
170.3
110.6
63
220.6
143.2
24
20.1
13.1
84
70.4
45.7
44
120.8
78.4
04
171.1
111.1
64
221.4
143.8
25
21.0
13.6
85
71.3
46.3
45
121.6
79.0
05
171.9
111.7
65
222.2
144.3
26
21.8
14.2
86
72.1
46.8
46
122.4
79.5
06
172.8
112.2
66
223.1
144.9
27
22.6
14.7
87
73.0
47.4
47
123.3
80.1
07
173.6
112.7
67
223.9
145.4
28
23.5
15.2
88
73.8
47.9
48
124.1
80.6
08
174.4
113.3
68
224.8
146.0
29
24.3
15.8
89
74.6
48.5
49
125.0
81.2
09
175. 3 1 113. 8
69
225. 6
146.5
30
25.2
16.3
90
75.5
49.0
50
125.8
81.7
10
176.1 |114.4
70
226.4
147.1
31
26.0
16.9
91
76.3
49.6
151
126.6
82.2
211
177. 0
114.9
271
227.3
147.6
32
26.8
17.4
92
77.2
50.1
52
127.5
82.8
12 177. 8
115.5
72
228.1
148.1
33
27.7
18.0
93
78.0
50.7
53
128. 3
83.3
13
178.6 116.0
73
229.0
148.7
34
28.5
18.5
94
78.8
51.2
54 129.2
83.9
14
179.5 116.6
74
229.8
149.2
35
29.4
19.1
95
79.7
51.7
55 130. 0
84.4
15
180.3 1117.1
75
230.6
149.8
36
30.2
19.6
96
80.5
52.3
56
130.8
85.0
16
181.2 117.6
76
231.5
150.3
37
31.0
20.2
97
81.4 52.8
57 131. 7
85.5
17 182. 0! 118. 2
77
232.3
150.9
38
31.9
20.7
98
82.2 i 53.4
58 ' 132.5
86.1
18 182.8
118.7
78
233.2
151.4
39
32.7
21.2
99
83.0""
53. 9
59 i 133.3
86.6
19 j 183. 7
119.3
79
234.0
152. 0
40
33.5
21.8
100
83.9
54.5
60 ! 134.2
87.1
20 184. 5
119.8
80
234.8
152.5
41
34.4
22.3
101
84.7
55.0
161 135. 0
87.7
221 i 185.3
120.4
281
235. 7
153.0
42
35.2
22.9
02
85.5
55.6
62 135. 9
88.2
22 186.2
120.9
82
236.5
153. 6
43
36.1
23.4
03
86.4
56.1
63 1 136. 7
88.8
23 187. 0
121.5
83 ! 237. 3
154.1
44
36.9
24.0
04
87.2
56.6
64 i 137. 5
89.3
24 187. 9
122.0
84
238.2
154.7
45
37.7
24.5
05
88.1
57.2
65
138.4
89.9
25 i 188.7
122.5
85
239.0
155.2
46
38.6
25.1
06
88.9
57.7
66
139.2
90.4
26
189.5 123.1
86
239.9
155.8
47
39.4
25.6
07
89.7
58.3
67 140. 1
91.0
27
190.4
123.6
87
240.7
156.3
48
40.3
26.1
08
90.6
58.8
68
140.9
91.5
28
191.2
124.2
88
241.5
156.9
49
41.1
26.7
09
91.4
59.4
69
141.7
92.0
29
192.1
124.7
89
242.4
157.4
50
41.9
27.2
10
92.3
59.9
70 142. 6
92.6
30
192.9
125.3
90
243. 2
157. 9
51
42.8
27.8
111
93.1 i 60.5
171 143.4
93.1
231
193.7
125.8
291
244.1
158.5
52
43.6
28.3
12
93.9
61.0
72
144.3
93.7
32
194.6
126.4
92
244.9
159.0
53
44.4
28.9
13
94.8
61.5
73
145. 1
94.2
33
195.4
126.9
93
245.7
159.6
54
45.3
29.4
14
95.6
62.1
74 145. 9
94.8
34
196.2
127.4
94
246.6
160.1
55
46.1
30.0
15
96.4
62.6
75 ! 146. 8
95.3
35
197.1
128.0
95
247.4
160.7
56
47.0
30.5
16
97.3
63.2
76
147.6
95.9
36 1 197. 9
128. 5
96
248.2
161.2
57
47.8
31.0
17
98.1
63.7
77
148.4
96.4
37 198. 8
129.1
97
249.1
161.8
58
48.6
31.6
18
99.0
64.3
78
149.3
96.9
38 199. 6
129.6
98
249.9
162.3
59
49.5
32.1
19
99.8
64.8
79
150.1
97.5
39 200.4
130. 2
99
250. 8
162.8
60
50.3
32.7
20
100.6
65.4
80
151.0
98.0
40
201.3
130.7
300
251.6
163. 4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
57° (123°, 237°, 303°).
TABLE 2. [Page 597
Difference of Latitude and Departure for 33° (147°, 213°, 327°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
252.4
163.9
361
302.8
196.6
421
353.1
229.3
481
403.4
262.0
541
453.7
294.6
02
253.3
164.4
62
303.6
197.1
22
353.9
229.8
82
404.2
262.5
42
454.6
295.2
03
254. 1
165. 0
63
304.4
197.7
23
354.7
230.4
83
405.1
263.1
43
455.4
295.7
04
255.0
165. 5
64
305. 3
198.2
24
355.6
230.9
84
405. 9
263.6
44
456. 2
296.2
05
255.8
166.1
65
306.1
198.8
25
356.4
231.4
85
406.7
264.1
45
457. 1
296.8
06
256.6
166.6
66
307.0
199.3
26
357.3
232.0
86
407.6
264.7
46
457.9
297.3
07
257. 5
167.2
67
307.8
199.8
27
358.1
232.5
87
408.4
265.2
47
458.8
297.9
08
258.3
167.7
68
308.6
200.4
28
359.0
233.1
88
409.3
265.8
48
459.6
298.4
09
259.2
168.3
69
309.5
200.9
29
359.8
233.6
89
410.1
266.3
49
460.4
299.0
10
260.0
168.8
70
310.3
201.5
30
360.6
234.2
90
411.0
266.8
50
461.3
299.5
311
260.8
169.3
371
311.2
202.0
431
361.5
234.7
491
411.8
267.4
551
462.1
300.1
12
261.7
169.9
72
312.0
202.6
32
362.3
235. 2
92
412.6
267.9
52
463.0
300.6
13
262.5
170.4
73
312.8
203.1
33
363.1
235.8
93
413.5
268.5
53
463.8
301.2
14
263.3
171.0
74
313.7
203.7
34
364.0
236.3
94
414.3 269.0
54
464.6
301.7
15
264.2
171.5
75
314.5
204.2
35
364.8
236.9
95
415. 1 269. 6
55
465. 5
302.3
16
265.0
172.1
76
315.3
204. 7
36
365.7
237.4
96
416.0
270.1
56
466.3
302.9
17
265. 9
172.6
77
316.2
205.3
37
366.5
238.0
97
416.8
270.7
57
467.2
303.4
18
266.7
173.2
78
317.0
205.8
38
367.3
238.5
98
417.6
271.2
58
468.0
303.9
19
267.5
173.7
79
317.9
206.4
39
368.2
239.1
99
418. 5 i 271. 8
59
468.8
304.5
20
268.4
174.2
80
318.7
206.9
40
369.0
239.6
500
419.3 272.3
60
469. 7 305. 0
321
269.2
174.8
381
319.5
207. 5
441
369.9
240.1
501
420. 2 272. 8
561
470. 5
305. 5
22
270.1
175.3
82
320.4
208.0
42
370.7
240.7
02
421.0 1273.4
62
471.3
306.1
23
270.9
175.9
83
321.2
208.6
43
371.5
241.2
03
421.9 J273.9
63
472.2
306.6
24
271.7
176.4
84
322.1
209.1
44
372. 4
241.8
04
422.7
274.5
64
473.0
307.2
25
272.6
177. 0
85
322.9
209.6
45
373.2
242.3
05
423.5
275.0
65
473.8
307.7
26 j
273.4
177.5
86
323.7
210.2
46
374.1
242. 9
06
424.4
275.6
66
474.7
308.3
27
274.2
178.1
87
324.6
210.7
47
374.9
243.4
07
425. 2
276.1
67
475. 5
308.8
28 !
275.1
178.6
88
325.4
211.3
48
375.7
244.0
08
426.0
276.7
68
476.4
309.4
29 i
275.9
179.1
89
326.2
211.8
49
376.6
244.5
09
426.9
277.2
69
477.2
309.9
30 !
276.8
179.7
90
327.1
212.4
50
377. 4
245.1
10
427.7
277.8
70
478.0
310.4
.331
277. 6 180. 2
391
327.9 212.9
451
378.2
245. 6
511
428.5
278.3
571
478.9
311.0
32
278. 4
180.8
92
328.8
213.5
52
379.1
246.1
12
429.4
278.8
72
479.7
311.5
33
279.3
181.3
93
329.6
214.0
53
379.9
246.7
13
430.2
279.4
73
480.6
312.0
34
280.1
181.9
94
330.4
214.6
54
380.8
247.2
14
431.1
279.9
74
481.4
312.6
35
281.0
182.4
95
331.3
215.1
55
381.6
247.8
15
431.9
280.4
75
482.2
313.1
36 !
281. 8
183.0
96
332. 1 215. 6
56
382.4
248.3
16
432. 7
281.0
76
483.1
313.7
37
282.6
183.5
97
333.0
216.2
57
383.3
248.9
17
433.6
281.5
77
483.9
314.2
38 i
283.5
184.1
98
333.8
216.7
58
384.1
249.4
18
434.4
282.1
78
484.7
314.8
39
284.3
184.6
99
334.6
217. 3
59
385.0
250.0
19
435.3
282.6
79
485.6
315.3
40
285. 2
185. 1
400
335.5
217.8
60
385.8
250. 5
20
436.1
283.2
80
486.4
315. 9
~34T
286.0
185. 7
401
336. 3
218.4
461
386.6
251. 0
521
436.9
283.7
581
487.2
316.4
42
286.8
186.2
02
337. 1
218.9
62
387.5
251.6
22
437.8
284.3
82
488.1
317.0
43
287.7
186.8
03
338.0
219.5
63
388.3
252. 1
23
438.6
284.8
83
488.9
317.5
44
288.5
187.3
04
338.8
220.0
64
389.1
252. 7
24
439.4
285. 4
84
489.8
318.1
45
289.3
187.9
05
339.7
220.5
65
390.0
253.2
25
440. 3
285. 9
85
490.6
318.6
46 i
290.2
188.4
06
340.5 221.1
66
390.8
253.8
26
441.1
286.5
86
491.5
319.2
47
291.0
189.0
07
341.3 221.6
67
391.7
254.3
27
442. 0
287.0
87
492.3
319.7
48
291.9
189.5
08
34°. 2 '>0° °
68 392. 5 | 254. 9
28
442.8
287.5
88
493. 1
320. 2
49 |
292.7
190.0
09
343] 0 22i\ 7
69 393. 3
255.4
29
443.6
288.1
89
494.0
320.8
50
293.5 190.6
10 1 343.9 1223.3
70
394.2
255.9
30
444.5
288.6
90
494.8
321.3
351
294.4
191.1
411
344. 7 223. 8
471
395. 0
256.5
o31
445.3
289.2
591
495.7
321.9
52
295.2
191.7
12
345.5 224.4
72
395.8
257. 0
32
446.1
289.7
92
496.5
322. 4
53
296.1
192.2
13
346.4 224.9
73
396.7
257.6
33
447.0
290.3
93
497.3
322. 9
54
296.9
192.8
14
347.2
225. 4
74
397. 5
258.1
34
447.8
290.8
94
498.1
323.5
55
297.7
193.3
15
348.1
226.0
75
398.3
25 S. 7
35
448.7
291.4
95
499.0
324.1
56
298.6
193.9
16
348.9
226. 5
76
399.2
259.2
36
449.5
291.9
96
499.8
324.6
57
299.4
194.4
17
349.7
227.1
77
400.0
259.8
37
450.3
292.5
97
500. 6
325.1
58 ;
300.2
194.9
18
350.6
227.6
78
400.9
260.3
38
451. 2
293.0
98
501. 5 i 325. 7
59
301.1
195.5
19
351.4
228. 2
79
401.7
260.9
39
452. 0
293.6
99
502. 3 326. 2
60
301.9
196.0
20
352.2
228.7
80
402.6
261. 4
40
452.9 294.1
600
503.2
326.8
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep,
Lat
57° (123°, 237°, 303°) .
Page 598] TABLE 2.
Difference of Latitude and Departure for 34° (146°, 214°, 326°).
Dink
Laf
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
50.6
34.1
121
100.3
67.7
181
150.1
101.2
241
199.8
134.8
2
1.7
1.1
62
51.4
34.7
22
101.1
68.2
82
150.9
101.8
42
200.6
135.3
3
2.5
1.7
63
52.2
35.2
23
102.0
68.8
83
151.7
102.3
43
201.5
135.9
4
3.3
2.2
64
53.1
35.8
24
102. 8
69.3
84
152. 5
102.9
44
202.3
136.4
5
4.1
2.8
65
53.9
36.3
25
103.6
69.9
85
153.4
103. 5
45
203.1
137.0
6
5.0
3.4
66
54.7
36.9
26
104.5
70.5
86
154.2
104.0
46
203.9
137.6
7
5.8
3.9
67
55.5
37.5
27
105.3
71.0
87
155.0
104.6
47
204.8
138.1
8
6.6
4.5
68
56.4
38.0
28
106.1
71.6
88
155.9
105. 1
48
205.6
138.7
9
7.5
5.0
69
57.2
38.6
29
106.9
72.1
89
156.7
105.7
49
206.4
139.2
10
8.3
5.6
70
58.0
39.1
30
107.8
72.7
90
157.5
106.2
50
207.3
139.8
11
9.1
6.2
71
58.9
39.7
131
108. 6
73.3
191
158.3
106.8
251
208.1
140.4
12
9.9
6.7
72
59.7
40.3
32
109.4
73.8
92
159.2
107.4
52
208.9
140.9
13
10.8
7.3
73
60.5
40.8
33
110. 3
74.4
93
160.0
107.9
53
209.7
141. 5
14
11.6
7.8
74
61.3
41.4
34
111.1
74.9
94
160.8
108. 5"
' 54
210.6
142.0
15
12.4
8.4
75
62.2
41.9
35
111.9
75.5
95
161.7
109.0
55
211.4
142.6
16
13.3
8.9
76
63.0
42.5
36
112.7
76.1
96
162.5
109.6
56
212.2
143. 2
17
14.1
9.5
77
63.8
43.1
37
113.6
76.6
97
163.3
110.2
57
213.1
143.7
18
14.9
10.1
78
64.7
43.6
38
114.4
77.2
98
164.1
110.7
58
213.9
144.3
19
15.8
10.6
79
65.5
44.2
39
115.2
77.7
99
165.0
111. 3
59
214.7
144.8
20
16.6
11.2
80
66.3
44.7
40
116.1
78.3
200
165.8
111.8
60
215.5
145.4
21
17.4
11.7
81
67.2
45.3
141
116.9
78.8
201
166.6
112.4
261
216.4
145.9
22
18.2
12.3
82
68.0
45.9
42
117.7
79.4
02
167.5
113.0
62
217.2
146.5
23
19.1
12.9
83
68.8
46.4
43
118.6
80.0
03
168.3
113.5
63
218.0
147.1
24
19.9
13.4
84
69.6
47.0
44
119.4
80.5
04
169.1
114.1
64
218.9
147.6
25
20.7
14.0
85
70.5
47.5
45
120.2
81.1
05
170.0
114.6
65
219.7
148.2
26
21.6
14.5
86
71.3
48.1
46
121.0
81.6
06
170.8
115.2
66
220.5
148.7
27
22.4
15.1
87
72.1
48.6
47
121.9
82.2
07
171.6
115.8
67
221.4
149.3
28
23.2
15.7
88
73.0
49.2
48
122.7
82.8
08
172.4
116.3
68
222.2
149.9
29
24.0
16.2
89
73.8
49.8
49
123.5
83.3
09
173.3
116.9
39
223.0
150.4
30
24.9
16.8
90
74.6
50.3
50
124.4
83.9
10
174.1
117.4
70
223.8
151.0
31
25.7
17.3
91
75.4
50.9
151
125. 2
84.4
211
174.9
118.0
271
224.7
151.5
32
26.5
17.9
92
76.3
51.4
52
126.0
85.0
12
175.8
118.5
72
225.5
152.1
33
27.4
18.5
93
77.1
52.0
53
126. 8
85.6
13
176.6
119.1
73
226.3
152.7
34
28.2
19.0
94
77.9
52.6
54
127.7
86.1
14
177.4
119.7
74
227.2
153.2
35
29.0
19.6
95
78.8
53.1
55
128.5
86.7
15
178.2
120.2
75
228.0
153.8
36
29.8
20.1
96
79.6
53.7
56
129.3
87.2
16
179.1
120.8
76
228.8
154.3
37
30.7
20.7
97
80.4
54.2
57
130.2
87.8
17
179.9
121.3
77
229.6
154.9
38
31.5
21.2
98
81.2
54.8
58
131.0
88.4
18
180.7
121.9
78
230.5
155.5
39
32.3
21.8
99
82.1
55.4
59
131.8
88.9
19
181.6
122.5
79
231.3
156.0
40
33.2
22.4
100
82.9
55.9
60
132.6
89.5
20
182.4
123.0
80
232.1
156.6
41
34.0
22.9
101
83.7
56.5
161
133.5
90.0
221
183.2
123. B
281
233.0
157.1
42
34.8
23.5
02
84.6
57.0
62
134.3
90.6
22
184.0
124.1
82
233.8
157.7
43
35.6
24.0
03
85.4
57.6
63
135.1
91.1
23
184.9
124.7
83
234.6
158.3
44
36.5
24.6
04
86.2
58.2
64
136. 0
91.7
24
185.7
125. 3
84
235.4
158.8
45
37.3
25.2
05
87.0
58.7
65
136.8
92.3
25
186.5
125.8
85
236.3
159.4
46
38.1
25.7
06
87.9
59.3
66
137.6
92.8
26
187.4
126.4
86
237.1
159.9
47
39.0
26.3
07
88.7
59.8
67
138.4
93.4
27
188.2
126.9
87
237.9
160.5
48
39.8
26.8
08
89.5
60.4
68
139.3
93.9
28
189.0
127.5
88
238.8
161.0
49
40.6
27.4
09
90.4
61.0
.69
140.1
94.5
29
189.8
128.1
89
239.6
161.6
50
41.5
28.0
10
91.2
61.5
70
140.9
95.1
30
190.7
128.6
90
240.4
162.2
51
42.3
28.5
111
92.0
62.1
171
141.8
95.6
231
191. 5
129.2
291
241.2
162.7
52
43.1
29.1
12
92.9
62.6
72
142.6
96.2
32
192.3
129.7
92
242.1
163.3
53
43.9
29.6
13
93.7
63.2
73
143.4
96.7
33
193.2
130.3
93
242.9
163.8
54
44.8
30.2
14
94.5
63.7
74
144.3
97.3
34
194.0
130.9
94
243.7
164.4
55
45.6
30.8
15
95.3
64.3
75
145.1
97.9
35
194.8
131.4
95
244.6
165.0
56
46.4
31.3
16
96.2
64.9
76
145.9
98.4
36
195. 7
132.0
96
245.4
165.5
57
47.3
31.9
17
97.0
65.4
77
146.7
99.0
37
196.5
132.5
97
246.2
166.1
58
48.1
32.4
18
97.8
66.0
78
147.6
99.5
38
197.3
133.1
98
247.1
166.6
59
48.9
33.0
19
98.7
66.5
79
148.4
100.1
39
198.1
133.6
99
247.9
167.2
60
49.7
33.6
20
99.5
67.1
80
149.2
100.7
40
199.0
134.2
300
248.7
167.8
JDist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
56° (124°, 236°, 304°).
TABLE 2. [Page 599
Difference of Latitude and Departure for 34° (146°, 214°, 326°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
DLst.
Lat. Dep.
Dist.
Lat. Dep.
301
249. 5 168. 3
361
299.3
201.9
421
349.0 235.4
481
398.8
269.0
541
448.5
302. 5
02
250.4 J168.9
62
300.1
202.4
22
349.9
236.0
82
399.6
269.5
42
449.4
303. 1
03
251.2 ;169.4
63
300.9
203. 0
23
350.7
236.5
83
400.4
270. 1
43
450.2
303.6
04
252.0 170.0
64
301.8
203.5
24
351.5
237.1
84 401.3
270.6
44
451.0
304. 2
05
252.9
170.6
65
302.6
204.1
25
352.3
237.7
85
402.1
271.2
45
451.8
304.8
06
253. 7
171.1
66
303.4
204.7
26 353. 2
238.2
86
402.9
271.8
46
452.6
305. 3
07
254. 5
171.7
67
304.3
205.2
27 354. 0
238.8
87
403.8
272.3
47
453. 5
305. 9
08
255.3 172.2
68
305.1
205.8
28 354. 8
239.3
88
404.6
272.8
48
454. 3
306.4
09
256. 2 1 1-1. 8
69
305. 9
206.3
29 355.7
239.9
89
405.4
273.4
49
455. 2 307. 0
10
257. 0
70
306.7 206.9
30 356. 5
240.4
90
406.2
274.0
50
456.0 I 307.5
311
257.8
371
307.6
207.5
431 357. 3
241.0
491
407.1
274.6
551
456.8
308.1
12
258. 7 ! 74. 5
72
308.4
208.0
32
358.1
241.6
92
407.9
275.1
52
457.6
308.7
13
259.5 175.0
73
S09.2 208.6
33
359.0
242.1
93
408.7
275. 7
53
458. 4
309.2
14
260.3 175.6
74
310.1 209.1
34
359.8
242.7
94
409.5
276.2
54
459. 3
309.8
15
261.2
176.1
75
310.9 J209.7
35
360.6
243.2
95
410.4
276.8
55
460.1
310.3
16
262.0
176.7
76
311.7 1210.3
36
361.5
243.8
96
411.2
277.4
56
460.9
310.9
17
262.8
177.3
77 312.6 1210.8
37
362.3
244.4
97
412.0 277.9
57
461.7
311.5
18
263.7
177.8
78 313.4 211.4
38
363.1
244.9
98
412.8
278.4
58
462.6
312.0
19
264.5
178.4
79 314.2 1211.9
39
364.0
245.5
99
413.7
279.0
59
463.4
312.6
20
265.3
178.9
80 315. 0 i 212. 5
40
364.8
246.0
500
414.5 279.6
60
464.2
313.1
321
266.1
179.5
381 315.9 1213.0
441 365.6
246.6
501
415.3 280.1
561
465.1
313.7
22
267.0
180.1
82 316.7 J213.6
42 366. 4
247.2
02
416.2 280.7
62
465.9
314. 3
23
267.8
180.6
83 317.5 214.2
43
367.3
247. 7
03
417.0
281.3
63
466.8
314.8
24
268.6
181.2
84 318.4
214.7
44
368.1
248.3
04
417.8
281.8
64
467.6
315.4
25
269.5
181.7
85 319.2
215.3
45
368.9
248.8
05
418.6
282.4
65
468.4
315.9
26
270.3
182.3
86 320. 0
215.8
46
369.8
249.4
06
419.4
282.9
66
469.2
316.5
27
271.1
182.9
87 320. 8
216.4
47
370.6
250.0
07
420.3
283.5
67
470.1
317.1
28 271. 9
183.4
88 321. 7
217.0
48
371.4
250. 5
08
421.1
284.1
68
470.9
317.6
29 272. 8
184.0
89 322. 5
217.5
49
372.2
251.1
09
421.9
284.6
69
471.7
318.2
30 ; 273. 6
184.5
90 323. 3
218.1
50
373.1
251.6
10
422.8
285.2
70
472. 6 318. 7
331 274.4 j 185.1
391 324. 2
218.6
451 373.9 252.2
511
423.6
285. 8
571
473. 4
319.3
32 275. 2 185. 6
92
325.0
219.2
52 374.7 252.8
12
424.4
286.3
72
474.2
319.9
33 i 276. 1 186. 2
93
325. 8
219.8
53 375.6 253.3
13
425.3
286.9
73
475. 0
320.4
34 i 276. 9 186. 8
94
326.6
220.3
54 376.4 253.9
14
426.1
287.4
74
475.9
321.0
35
277.7
187.3
95
327.5
220.9
55 3f7.2 254.4
15
426.9
288.0
75
476.7
321.5
36
278.6
187.9
96 328. 3
221.4
56 378. 0
255.0
16
427.8
288.5
76
477. 5
322.1
37
279.4
188.4
97 329.1
222.0
57 378. 9
255.5
17
428.6
289.1
77
478.3
322.7
38
280.2
189.0
98
330.0
222.6
58 379. 7
256.1
18 i 429.4
289.6
78
479.2
323. 2
39 281. 0 189. 6
99
330.8
223.1
59 380. 5
256.7
19
430.3
290.2
79
480.0
323.8
40 281. 9 ! 190. 1
400
331. 6
223.7
60
381.3
257.2
20
431.1
290.8
80
480.8
324.3
341 282. 7 190. 7
401
332.4
224.2
461
382.2
257.8
521
431.9
291.3
581
481.6
324.9
42
283. 5 191. 2
02
333.3
224.8
62
383.0
258.3
22
432.8
291.9
82
482. 5
325. 4
43
284.4
191.8
03
334.1
225.4
63
383.8
258.9
23
433.6
292.5
83
483.3
326.0
44
285.2
192.4
04
334.9
225.9
64
384.7
259.5
24
434.4
293.0
84
484.1
326.6
45
286.0 192.9
05
335. 8
226.5
65
385.5
260.0
25
435.3
293.6
85
485.0
327.2
46
286.9 193.5
06
336.6
227.0
66
386.3
260.6
26
436.1
294.1
86
485.8
327.7
47
287.7
194.0
07
337.4
227.6
67
387.2
261.1
27
436.9
294.7
87
486.6
328.2
48
288.5
194.6
08
338.3
228.1
68
388.0
261.7
28
437.8
295.3
88
328.8
49
289. 3 195. 2
09
339.1
228.7
69
388.8
262.3
29
438.6
295.8
89
488. 3
329.4
50
290.2 195.7
10
339.9
229. 3
70
389.7
262.8
30
439. 4
296.4
90
489.2
329.9
351
291.0 196.3
411
340.7
229.8
471
390.5
263.4
531
440.3
296.9
591
490.0 > 330.5
52
291.8
196.8
12
341.6
230.4
72
391.3
263.9
32
441.1
297.4
92
490. 8 331. 0
53
292.7
197.4
13
342.4
230.9
73
392.1
264.5
33
441.9
298.0
93
491.6 331.6
54
293.5
198.0
14
343.2
231.5
74
393.0
265.0
34
442.7
298.6
94
492. 5 332. 2
65
294.3
198. 5
15
344.1
232. 1
75
393.8
265.6
35
443.6
299.1
95
493. 3 332. 7
56
295.1
199.1
16
344.9
232.6
76
394.6
266.2
36
444.4
299.7
96
494. 1 333. 3
57
296.0
199.6
17
345.7
233.2
77
395. 5
266.7
37
445.3
300.2
97
494. 9 333. 8
58
296.8
200.2
18
346.5
233.7
78
396.3
267.3
38
446.1
300.8
98
495. S 334. 4
59
297.6 J200. 7
19
347.4
234.3
79
397.1
267.9
39
446.9
301.4
99
14.9
60
298.5
201.3
20
348.2
234.9
80
397.9
268.4
40
447.7
302.0
600
497. 4 335. 5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. ; L;it.
56° (124°, 236°, 304°).
Page 600] TABLE 2.
Difference of Latitude and Departure for 35° (145°, 215°, 325°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
50.0
35.0
121
99.1
69.4
181
148.3
103.8
241
197.4
138.2
2
1.6
1.1
62
50.8
35.6
22
99.9
70.0
82
149.1
104.4
42
198.2
138.8
3
2.5
1.7
63
51.6
36.1
23
100.8
70.5
83
149. 9
105.0
43
199. 1
139.4
4
3.3
2.3
64
52.4
36.7
24
101.6
71.1
84
150.7
105. 5
44
199.9
140.0
5
4.1
2.9
65
53.2
37.3
25
102. 4
71.7
85 ' 151.5
106.1
45
200.7
140.5
6
4.9
3.4
66
54.1
37.9
26
103.2
72.3
86
152.4
106.7
46
201.5
141.1
7
5.7
4.0
67
54.9
38.4
27
104.0
72.8
87
153. 2
107.3
47
202.3
141.7
8
6.6
4.6
68
55.7
39.0
28
104.9
73.4
88
154. 0 j 107. 8
48
2Q3.1
142.2
9
7.4
5.2
69
56.5
39.6
29
105.7
74.0
89
154.8
108.4
49
204.0
142.8
10
8.2
5.7
70
57.3
40.2
30
106.5
74.6
90
155.6
109.0
50
204.8
143.4
11
9.0
6.3
71
58.2
40.7
131
107.3
75.1
191
156. 5
109.6
251
205.6
144.0
12
9.8
6.9
72
59.0
41.3
32
108.1
75.7
92
157. 3
110.1
52
206.4
144.5
13
10.6
7.5
73
59.8
41.9
33
108.9
76.3
93
158. 1
110.7
53
207.2
145.1
14
11.5
8.0
74
60.6
42.4
34
109.8
76.9
94
158.9
111.3
54
208.1
145.7
15
12.3
8.6
75
61.4
43.0
35
110.6
77.4
95
159.7
111.8
55
208.9
146.3
16
13.1
9.2
76
62.3
43.6
36
111.4
78.0
96
160. 6
112.4"
56
209.7
146.8
17
13.9
9.8
77
63.1
44.2
37
112.2
78.6
97
161.4
113.0
57
210.5
147.4
18
14.7
10.3
78
63.9
44.7
38
113.0
79.2
98
162.2
113.6
58
211.3
148.0
19
15.6
10.9
79
64.7
45.3
39
113.9
79.7
99
163.0
114.1
59
212.2
148.6
20
16.4
11.5
80
65.5
45.9
40
114.7
80.3
200
163.8
114.7
60
213.0
149.1
21
17.2
12.0
81
66.4
46.5
141
115.5
so. y
201
164.6
115.3
261
213.8
149.7
22
18.0
12.6
82
67.2
47.0
42
116.3
81.4
02
165.5
115.9
62
214.6
150.3
23
18.8
13.2
83
68.0
47.6
43
117.1
82.0
03
166.3
116.4
63
215.4
150.9
24
19.7
13.8
84
68.8
48.2
44
118.0
82.6
04
167.1
117.0
64
216.3
151.4
25
20.5
14.3
85
69.6
48.8
45
118.8
83.2
05
167.9
117.6
65
217.1
152.0
26
21.3
14.9
86
70.4
49.3
46
119.6
83.7
06
168.7
118.2
66
217.9
152.6
27
22.1
15.5
87
71.3
49.9
47
120.4
84.3
07
169.6
118.7
67
218. 7
153.1
28
22.9
16.1
88
72.1
50.5
48
121.2
84.9
08
170.4
119.3
68
219.5
153.7
29
23.8
16.6
89
72.9
51.0
49
122.1
85.5
09
171.2
119.9
69
220.4
154. 3
30
24.6
17.2
90
73.7
51.6
50
122.9
86.0
10
172.0
120.5
70
221.2
154.9
31
25.4
17.8
91
74.5
52.2
151
123.7
86.6
211
172.8
121.0
271
222.0
155. 4
32
26.2
18.4
92
75.4
52.8
52
124.5
87.2
12
173.7
121.6
72
222.8
156.0
33
27.0
18.9
93
76.2
53.3
53
125.3
87.8
13
174.5
122.2
73
223.6
156.6
34
27.9
19.5
94
77.0
53.9
54
126.1
88.3
14
175.3
122.7
74
224.4
157.2
35
28.7
20.1
95
77.8
54.5
55
127.0
88.9
15
176.1
123.3
75
225. 3
157.7
36
29.5
20.6
96
78.6
55.1
56
127.8
89.5
16
176.9
123.9
76
226.1
158.3
37
30.3
21.2
97
79.5
55.6
57
128.6
90.1
17
177.8
124.5
77
226.9
158.9
38
31.1
21.8
98
80.3
56.2
58
129.4
90.6
18
178.6
125.0
78
227.7
159. 5
39
31.9
22.4
99
81.1
56.8
59
130.2
91.2
19
179.4
125.6
79
228.5
160.0
40
32.8
22.9-
100
81.9
57.4
60
131.1
91.8
20
180.2
126.2
80
229.4
160.6
41
33.6
23.5
101
82.7
57.9
161
131.9
92.3
221
181.0
126.8
281
230.2
161. 2
42
34.4
24.1
02
83.6
58.5
62
132.7
92.9
22
181.9
127.3
82
231. 0
161.7
43
35.2
24.7
03
84.4
59.1
63
133.5
93.5
23
182.7
127.9
83
231.8
162.3
44
36.0
25.2
04
85.2
59.7
64
134.3
94.1
24
183.5
128.5
84
232. 6
162.9
45
36.9
25.8
05
86.0
60.2
65
135.2
94.6
25
184.3
129.1
85
233.5
163.5
46
37.7
26.4
06
86.8
60.8
66
136.0
95.2
26
185.1
129.6
86
234. 3
164.0
47
38.5
27.0
07
87.6
61.4
67
136. 8
95.8
27
185.9
130. 2
87
235.1
164.6
48
39.3
27.5
08
88.5
61.9
68
137.6
96.4
28
186. 8
130.8
88
235. 9
165.2
49
40.1
28.1
09
89.3
62.5
69
138.4
96.9
29
187.6
131.3
89
236. 7
165.8
50
41.0
28.7
10
90.1
63.1
70
139.3
97.5
30
188.4
131.9
90
237.6
166.3
51
41.8
29.3
111
90.9
63.7
171
140.1
98.1
231
189.2
132.5
291
238. 4
166. 9"
52
42.6
29.8
12
91.7
64.2
72
140.9
98.7
32
190.0
133.1
92
239.2
167.5
53
43.4
30.4
13
92.6
64.8
73
141.7
99.2
33
190.9
133. 6
93
240.0
168.1
54
44.2
31.0
14
93.4
65.4
74
142.5
99.8
34
191.7
134.2
94
240.8
168.6
55
45.1
31.5
15
94.2
66.0
75
143.4
100.4
35
192.5
134.8
95
241.6
169.2
56
45.9
32.1
16
95.0
66.5
76
144.2
100.9
36
193.3
135. 4
96
242.5
169.8
57
46.7
32.7
17
95.8
67.1
77
145. 0
101.5
37
194.1
135.9
97
243. 3
170.4
58
47.5
33.3
18
96.7
67.7
78
145.8
102.1
38
195.0
136.5
98
244.1
170.9
59
48.3
33.8
19
97.5
68.3
79
146.6
102.7
39
195.8
137.1
99
244.9
171.5
60
49.1
34.4
20
98.3
68.8
80
147.4
103.2
40 196. 6
137.7
300
245.7
172.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. | Dep.
Lat.
Dist.
Dep.
Lat.
55° (125°, 235°, 305°).
TABLE 2. [Page 601
Difference of Latitude and Departure for 35° (145°, 215°, 325°).
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
i
301
246.6
172.6
361
295.7
207.0
421
344.9
241.5
481
394.0
275.9
541
443.2
310.3
02
247. 4
173.2
62
296.5
207.6
22
345. 7
242.0
82
394.8
276.4
42
444.0
310.9
03
248.2
173.8
63
297.4
20S. 2
23
346.5
242.6
83
395.7
277. 0
43
444.8
311.4
04 I 249.0
174.3
64
298.2
208.8
24
347.3
243.2
84
396.5
277.6
44
445. 6 312. 0
05 ! 249. 9
174.9
65
299.0
209.3
25
348.1
243.8
85
397.3
278.2
45
446.4
312.6
O'i 250. 7
175. 5
66
299.8
209.9
26
349.0 J244.3
86
398.1
278.7
46
447.3
313.2
07 i 251.5
176.1
67
300.6
210.5
27
349.8
244.9
87
398.9
279.3
47
448.1
313. 7
08
252. 3
176.6
68
301.5
211.1
28
350.6
245. 5
88
399.8
279.9
48
448.9
314.3
09
253. 1
177.2
69
302.3
211.6
29
351.4
246.0
89
400.6
280.5
49
449.7
314.9
10
253. 9
177.8
70
303.1
212.2
30
352. 2
246.6
90
401.4
281.0
50
450.5
315.4
311
254. 8
178.4
371
303.9
212.8
431
353. i
247.2
491
402.2
281.6
551
451.4
316.0
12
255. 6
178.9
72
304. 7
213.4
32
353.9
247.8
92
403.0
282. 2
52
452. 2
316.6
13
256. 4
179.5
73
305. 6
213.9
33
354.7
248.3
93
403.9
282! 8
53
453.0
317.2
14
257. 2
180.1
74
306.4
214.5
34
355.5
248.9
94
404.7
283.3
54
453. 8
317.7
15
258. 0
180.7
75
307. 2
215.1
35
356.3
249.5
95
405. 5
283.9
55
454. 6
318.3
16
258. 9
181.2
76
308.0
215. 6
36
357.2
250. 1
96
406.3
284.5
56
455. 5
318. 9
17
259. 7
181.8
77
308.8
216.2
37
358.0
250. 6
97
407.1
285.1
57
456. 3
319.5
18
260.5
182.4
78
309.6
216.8
38
358.8
251. 2
98
408.0
285.6
58
457.1
320.0
19
261.3
183.0
79
310.5
217.4
39
359. 6
251.8
99
408.8
286.2
59
457. 9
320.6
20
262.1
183.5
80
311.3
217.9
40
360.4
252. 4
500
409.6
286.8
60
458.7
321.2
321
263.0
184.1
381
312.1
218.5
441
361.3
252. 9
501
410.4
287.4
561 459. 6
321.8
22
263.8
184.7
82
312.9
219.1
42
362.1
253. 5
02
411.2
287.9
62
460.4
322.3
23
264.6
185.2
83
313. 7
219.7
43
362.9
254. 1
03
412.1
288.5
63
461.2
322.9
24
265. 4
185.8
84
314.6
220. 2
44
363.7
254.7
04
412.9
289.1
64
462.0
323.5
25
266.2
186.4
85
315.4
220.8
45
364. 5
255.2
05
413.7
289.7
65
462.8
324.1
26
267.1
187.0
86
316.2
221.4
46
365.4
255.8
06
414.5
290.2
66
463. 7
324.6
27
267.9
187.5
87
317.0
222.0
47
366.2
256. 4
07
415.3
290.8
67
464. 5
325. 2
28
268.7
188.1
88
317. 8
222. 5
48
367.0
256. 9
08
416.1
291.4
68
465. 3
325.8
29
269.5
188.7
89
318. 7
223.1
49
367.8
257. 5
09
417.0
291.9
69
466.1
326.4
30
270.3
189.3
90
319.5
223.7
50
368. 6 | 258. 1
10
417.8
292.5
70
466.9
326.9
331
271.1
189.8
391
320.3
224.3
451
369.4
258. 7
511
418.6
293.1
571
467.8
327.5
32'
272.0
190.4
92
321.1
224.8
52
370.3
259.2
12
419.4
293.7
72
468.6
328.1
33
272.8
191.0
93
321.9
225. 4
53
371.1
259. 8
13
420. 2
294.2
73
469.4
328.7
34
273.6
191.6
94
322.8
226.0
54
371.9
260.4
14
421.1
294.8
74
470.2
329.2
35
274.4
192.1
95
323. 6
226.5
55
372.7
261.0
15
421.9 295.4
75
471.0
329.8
36
275. 2
192.7
96
324.4
227.1
56
373.5
261.5
16
422.7 296.0
76
471.9
330.4
37
276. 1
193.3
97
325. 2
227. 7
57
374.4
262. 1
17
423.5 1296. 5
1 1
472.7
331.0
38
276.9
193.9
98
326.0
228.3
58
375. 2
262. 7
18
424.3
297.1
78
473.5
331.5
39
277.7
194.4
99
326.9
228.8
59
376.0
263.3
19
425. 2
297.7
79
474.3
332.1
40
278.5
195.0
400
327.7
229.4
60
37*.8
263.8
20
426.0 1298.3
80
475.1
332. 7
341
279.3
195. 6
401
328.5 230.0
461
377.6
264.4
521
426.8 |298.8
581
476.0
333.3
42
2SO. 2
196.1
02
329.3
230.6
62
378.5
265.0
22
42". 6 299.4
82
476.8
333.8
43
281.0
196.7
03
330.1
231.1
63
379.3
265.5
23
428. 4 300. 0
83
477. 6 334. 4
44
281.8
197.3
04
330.9
231.7
&4
380.1
266.1
24
429. 3 1 300. 5
84
47S. 4 335. 0
45
282.6
197.9
05
331.8
232.3
65
380.9
266.7
25
430.1 1 301.1
85
479. 2
335.6
46
283. 4
198.4
06
332. 6
232.9
66
381.7
267.3
26
430.9
301.7
86
480. 1
336. 1
47 284. 3
199.0
07
333.4
233.4
67
382.6
267.8
27
431. 7
302.3
87
480.9
336.7
48
285.1
199.6
08
334.2
234.0
68
383.4
268.4
28
432. 5
302.8
88
481. 7 337. 3
49
285.9
200.2
09
335.0
234.6
69
384.2
269.0
29
433. 4
303.4
89
4S2. 5 337. 9
50 286. 7
200.7
10
335.9
235.1
70
385. 0
269.6
30
434.2
304.0
90
483.3
338. 4
351 287. 5
201.3
411
336.7
235.7
471
385.8
270. 1
531
435.0
304.5
591
484.2
339. 0
52 288. 3
201.9
12
337.5
236:3
72
386.6
270. 7
32
435. 8
305.1
92
485. 0
339.6
53 2s9. 2
202.5
13
338.3
236.9
73
387.5
271.3
33
436. 6
305. 7
93
485. 8
340.2
54 290. 0
203.0
14
339. 1
237.4
74
388.3
271.9
34
437. 5
306.3
94
486.6
340.7
55 290. 8
203.6
15
340.0
238.0
75
389.1
272. 4
35
438.3
306. 8
95
487. 4
341.3
56 291.6
204.2
16
310.8
238.6
76
389.9
273.0
36
439 1
307.4
96
488. 3
341.9
57 292. 4
204. 7
17
341.6
239.2
77
390. 7
273.6
37
439.9
308.0
97
489.1
342.5
58 i 293.3
205. 3
18
342.4
239.7
78
391.6
274.2
38
440.7
308.6
98
489.9
343.0
59 ! 294.1 205.9
19
343.2
240.3
79
392.4
274.7
39
441.5
309.1
99
490. 7
343.6
60 294.9 206.5
20
344.1
240.9
80
393.2
275. 3
40
442. 3
309. 7
600
491. 5 344. 1
Dist. I-n. Lat.
D:-t. Dep.
Lat.
Dist,
Dep.
Lat.
Dist.
Dep. Lat.
DL-t. Dep. Lat.
55° (125°, 235°, 305°).
Page 602] TABLE 2.
Difference of Latitude and Departure for 36° (144°, 216°, 324°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
49.4
35.9
121
97.9
71.1
181
146.4
106.4
241
195.0
141.7
2
1.6
1.2
62
50.2
36.4
22
98.7
71.7
82
147.2
107.0
42
195.8
142.2
3
2.4
1.8
63
51.0
37.0
23
99.5
72.3
83
148.1
107.6
43
196.6
142.8
4
3.2
2.4
64
51.8
37.6
24
100.3
72.9
84
148.9
108.2
44
197.4
143.4
5
4.0
2.9
65
52.6
38.2
25
101.1
73.5
85
149.7
108.7
45
198.2
144.0
6
4.9
3.5
66
53.4
38.8
26
101.9
74.1
86
150.5
109.3
46
199.0
144.6
7
5.7
4.1
67
54.2
39.4
27
102.7
74.6
87
151.3
109.9
47
199.8
145.2
8
6.5
4.7
68
55.0
40.0
28
103.6
75.2
88
152.1
110.5
48
200.6
145.8
9
7.3
5.3
69
55.8
40.6
29
104.4
75.8
89
152.9
111.1
49
201.4
146.4
10
8.1
5.9
70
56.6
41.1
30
105.2
76.4
90
153.7
111.7
50
202.3
146.9
11
8.9
6.5
71
57.4
41.7
131
106.0
77.0
191
154.5
112.3
251
203.1
147.5
12
9.7
7.1
72
58.2
42.3
32
106.8
77.6
92
155.3
112.9
52
203.9
148. 1
13
10.5
7.6
73
59.1
42.9
33
107.6
78.2
93
156.1
113.4
53
204.7
148.7
14
11.3
8.2
74
59.9
43.5
34
108.4
78.8
94
156.9
114.0
54
205.5
149.3
15
12.1
8.8
75
60.7
44.1
35
109.2
79.4
95
157.8
114.6
55
206.3
149.9
16
12.9
9.4
76
61.5
44.7
36
110.0
79.9
96
158.6
115.2
56
207. 1
150.5
17
13.8
10.0
77
62.3
45.3
37
110.8
80.5
97
159.4
115.8
57
207.9
151.1
18
14.6
10.6
78
63.1
45.8
38
111.6
81.1
98
160.2
116.4
58
208.7
151.6
19
15.4
11.2
79
63.9
46.4
39
112.5
81.7
99
161.0
117.0
59
209.5
152.2
20
16.2
11.8
80
64.7
47.0
40
113.3
82.3
200
161.8
117.6
60
210. 3
152.8
21
17.0
12.3
81
65.5
47.6
141
114.1
82.9
201
162.6
118.1
261
211.2
153.4
22
17.8
12.9
82
66.3
48.2
42
114.9
83.5
02
163.4
118.7
62
212.0
154.0
23
18.6
13.5
83
67.1
48.8
43
115.7
84.1
03
164.2
119.3
63
212.8
154.6
24
19.4
14.1
84
68.0
49.4
44
116. 5
84.6
04
165.0
119.9
64
213.6
155.2
25
20.2
14.7
85
68.8
50.0
45
117.3
85.2
05
165.8
120.5
65
214.4
155.8
26
21.0
15.3
86
69.6
50.5
46
118.1
85.8
06
166.7
121.1
66
215.2
156. 4
27
21.8
15.9
87
70.4
51.1
47
118. 9
86.4
07 167. 5
121.7
67
216.0
156.9
28
22.7
16.5
88
71.2
51.7
48
119.7
87.0
08
168.3
122.3
68
216.8
157.5
29
23.5
17.0
89
72.0
52.3
49
120.5
87.6
09
169.1
122.8
69
217.6
158.1
30
24.3
17.6
90
72.8
52.9
50
121.4
88.2
10
169.9
123.4
70
218.4
158.7
31
25.1
18.2
91
7S.6
53.5
151
122.2
88.8
211
170.7
124.0
271
219.2
159.3
32
25.9
18.8
92
74.4
54.1
52
123.0
89.3
12
171.5
124.6
72
220.1
159.9
33
26.7
19.4
93
75.2
54.7
53
123.8
89.9
13
172.3
125.2
73
220.9
160.5
34
27.5
20.0
94
76.0
55.3
54
124.6
90.5
14
173.1
125.8
74
221.7
161.1
35
28.3
20.6
95
76.9
55.8
55
125.4
91.1
15
173.9
126.4
75
222.5
161.6
36
29.1
21.2
96
77.7
56.4
56
126.2
91.7
16
174.7
127.0
76
223.3
162.2
37
29.9
21.7
97
78.5
57.0
57
127.0
92.3
17
175.6
127.5
77
224.1
162.8
38
30.7
22.3
98
79.3
57.6
58
127.8
92.9
18
176.4
128. 1
78
224.9
163.4
39
31.6
22.9
99
80.1
58.2
59
128.6
93.5
19
177.2
128.7
79
225.7
164.0
40
32.4
23.5
100
80.9
58.8
60
129.4
94.0
20
178.0
129.3
80
226.5
164.6
41
33.2
24.1
101
81.7
59.4
161
130.3
94.6
221
178.8
129.9
281
227.3
165.2
42
34.0
24.7
02
82.5
60.0
62
131.1
95.2
22
179.6
130.5
82
228.1
165.8
43
34.8
25.3
03
83.3
60.5
63
131.9
95.8
23
180.4
131.1
83
229.0
166.3
44
35.6
25.9
04
84.1
61.1
64
132.7
96.4
24
181 2
131.7
84
229.8
166.9
45
36.4
26.5
05
84.9
61.7
65
133.5
97.0
25
182.0
132.3
85
230.6
167.5
46
37.2
27.0
06
85.8
62.3
66
134.3
97.6
26
182.8
132.8
86
231.4
168.1
47
38.0
27.6
07
86.6
62.9
.67
135.1
98.2
27
183.6
133.4
87
232.2
168.7
48
38.8
28.2
08
87.4
63.5
68
135. 9
98.7
28
184.5
134.0
88
233.0
169.3
49
39.6 J
28.8
09
88.2
64.1
69
136.7
99.3
29
185.3
134.6
89
233.8
169.9
50
40.5 ,
29.4
10
89.0
64.7
70
137.5
99.9
30
186.1
135.2
90
234.6
170.5
51
41.3
30.0
111
89.8
65.2
171
138.3
100.5
231
186.9
135.8
291
235. 4
171.0
52
42.1
30.6
12
90.6
65.8
72
139.2
101.1
32
187.7
136.4
92
236.2
171.6
53
42.9
31.2
13
91.4
66.4
73
140.0
101.7
33
188.5
137.0
93
237.0
172.2
54
43.7
31.7
14
92.2
67.0
74
140.8
102.3
34
189.3
137.5
94
237.9
172.8
55
44.5
32.3
15
93.0
67.6
75
141.6
102.9
35
190.1
138.1
95
238.7
173.4
56
45.3
32.9
16
93.8
68.2
76
142.4
103.5
36
190.9
138.7
96
239.5
174. 0
57
46.1
33.5
17
94.7
68.8
77
143.2
104.0
37
191.7
139.3
97
240.3
174.6
58
46.9
34.1
18
95.5
69.4
78
144.0
104.6
38
192.5
139.9
98
241.1
175.2
59
47.7
34.7
19
96.3
69.9
79
144.8
105.2
39
193.4
140.5
99
241.9
175.7
60
48.5
35.3
20
97.1
70.5
80
145.6
105.8
40
194.2
141.1
300
242.7
176.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. | Lat.
54° (126°, 234°, 306° .
TABLE 2. [Page 603
Difference of Latitude and Departure for 36° (144°, 216°, 324°).
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. | Dep.
301
243.5
176.9
361
292.1
212.2
421
340.6
247.5
481
389.1
282.7
541
437.7
318.0
02
244.3
177.5
62
292.9
212.8
22
341.4
248.1
82
390.0
283.3
42
438.5
318.6
03
245.1
178.1
63
293.7
213.4
23
342.2
248.6
83
390.8
283.9
43
439.3
319.1
04
246.0
178.7
64
294.5
214.0
24
343.0
249.2
84
391.6
284.5
44
440.2
319.7
05
246.8
179.3
65
295.3
214.6
25
343.8
249.8
85
392.4
285.1
45
441.0
320.3
06
247.6
179.9
66
296.1
215.1
26
344.7
250. 4
86
393.2
285.6
46
441.8
320.9
07
248.4
180.5
67
296.9
215.7
27
345.5
251.0
87
394.0
286.2
47
442.6
321.5
08
249.2
181.1
68
297.7
216.3
28
346.3
251.6
88
394.8
286.8
48
443.4
322.1
09
250.0
181.6
69
298.5
216.9
29
347.1
252.2
89
395.6
287.4
49
444.2
322.7
10
250.8
182.2
70
299.3
217.5
30
347.9
252. 8
90
396.4
288.0
50
445.0
323.3
311
251.6
182.8
371
300.2
218.1
431
348.7
253.3
491
397.3
288.6
551
445.8
323.8
12
252. 4
183.4
72
301.0
218.7
32
349.5
253.9
92
398.1
289.2
52
446.6
324.4
13
253.2
184.0
73
301.8
219.3
33
350.3
254. 5
93
398.9
289. 8
53
447.4
325.0
14
2-54.0
184.6
74
302.6
219.8
34
351.1
255.1
94
399.7
290.3
54
448.2
325.6
15
254.9
185.2
75
303.4
220.4
35
351.9
255.7
95
400.5
290.9
55
449.0
326.2
16
255.7
185.8
76
304.2
221.0
36
352.7
256.3
96
401.3
291.5
56
449.8
326.8
17 256. 5
186.4
77
305.0
221.6
37
353.6
256.9
97
402.1
292.1
57
450.7
327.4
18 257.3
186.9
78
305.8
222.2
38
354.4
257.5
98
402.9
292.7
58
451.5
328.0
19 j 258.1
187.5
79
306.6
222.8
39
355.2
258.0
99
403.7
293.3
59
452.3
328.5
20 i 258.9
188.1
80
307.4
223.4
40
356.0
258.6
500
404.5
293.9
60
453.1
329.1
321 259. 7
188.7
381
308.2
224.0
441
356.8
259.2
501
405.3
294.5
561
453.9
329.7
22 260. 5
189.3
82
309.1
224.5
42
357.6
259.8
02
406.1
295.0
62
454. 7
330.3
23 261. 3
189.9
83
309.9
225.1
43
358.4
260.4
03
407.0
295.6
63
455. 5
330.9
24
262.1
190.5
84
310.7
225.7
44
359.2
261.0
04
407.8
296.2
64
456. 3
331.5
25
262.9
191.0
85
311.5
226.3
45
360.0
261.6
05
408.6
296.8
65
457.1
332.1
26
263.7
191.6
86
312.3
226.9
46
360.8
262.2
06
409.4
297.4
66
457.9
332.7
27
264.6
192.2
87
313.1
227.5
47
361.6
262.8
07
410.2
298.0
67
458. 7
333.3
28
265.4
192.8
88
313. 9
228.1
48
362.4
263.3
08
411.0
298.6
68
459.5
333.8
29
266.2
193.4
89
314.7
228.7
49
363.3
263.9
09
411.8
299.2
69
460.3
334.4
30
267.0
194.0
90
315.5
229.2
50
364.1
264.5
10
412.6
299.8
70
461.1
335.0
331
267.8
194.6
391
316.3
229.8
451
364.9
265.1
511
413.4
300.3
571
462.0
335.6
32
268.6
195.2
92
317.1
230.4
52
365.7
265.7
12
414.2
300.9
72
462.8
336.2
33
269.4
195.7
93
318.0
231.0
53
366.5
266.3
13
415.1
301.5
73
463.6
336.8
34
270.2
196.3
94
318.8
231.6
54
367.3
266.9
14
415.9
302.1
74
464.4
337.4
35
271.0
196.9
95
319.6
232.2
55
368.1
267.5
15
416.7
302.7
75
465.2
338.0
36
271.8
197.5
96
320.4
232.8
56
368.9
268.0
16
417.5
303.3
76
466.0
338.5
37
272.6
198.1
97
321.2
233.4
57
369.7
268.6
17
418.3
303.9
77
466.8
339.1
38
273.5
198.7
98
322.0
233.9
58
370.5
269.2
18
419.1
304.4
78
467.6
339.7
39
274.3
199.3
99
322.8
234.5
59
371.3
269.8
19
419.9
305.0
79
468.4
340.3
40
275.1
199.9
400
323.6
235.1
60
372.2
270.4
20
420.7
305.6
80
469.3
340.9
341
275.9
200.4
401
324.4
235. 7
461
373.0
271.0
521
421.5
306.2
581
470.1
341.5
42
276.7
201.0
02
325.2
236.3
62
373.8
271.6
22
422.3
306.8
82
470.9
342.1
43
277.5
201.6
03
326.0
236.9
63
374.6
272.2
23
423.1
307.4
83
471.7
342.7
44
278.3
202. 2
04
326.9
237.5
64
375.4
272.7
24
423.9
308.0
84
472. 5
343.2
45
279.1
202.8
05
327.7
238.1
65
376.2
273.3
25
424.7
308.6
85
473.3
343.8
46.
279.9
203.4
06
328.5
238.7
66
377.0
273.9
26
425.5
309.2
86
474.1
344.4
47
280.7
204.0
07
329.3
239.2
67
377.8
274.5
27
426.4
309.7
87
474.9
345.0
48
281.5
204.6
08
330.1
239.8
68
378.6
275.1
28
427.2
310.3
88
475. 7
345.6
49
282.4
205.1
09
330.9
240. 4
69
379.4
275.7
29
428.0
310.9
89
476.5
346.2
50
283.2
205.7
10
331.7
241.0
70
380.2
276.3
30
428.8
311.5
90
477.3
346.8
351
284.0
206.3
411
332.5
241.6
471
381.1
276.9
531
429.6
312.1
591
478.2
347.4
52
284.8
206.9
12
333.3
242.2
72
381.9
277.4
32
430.4
312.7
92
479.0
347.9
53
285.6
207.5
13
334.1
242.8
73
382.7
278.0
33
431.2
313.3
93
479.8
348.5
54
286.4
208.1
14
334.9
243.4
74
383.5
278.6
34
432.0
313.9
94
480.6
349.1
55
287. 2
208.7
15
335.8
243.9
75
384.3
279.2
35
432.9
314.4
95
481.4
349.7
56
288.0
209.3
16
336.6
244.5
76
385.1
279.8
36
433.7
315.0
96
482.2
350.3
57
288.8
209.8
17
337.4
245.1
77
385.9
280.4
37
434.5
315. 6
97
483.0
350.9
58
289.6
210.4
18
338.2
245.7
78
386.7
281.0
38
435.3
316.2
98
483.8
351.5
59
290.4
211.0
19
339.0
246.3
79
387.5
281.6
39
436.1
316.8
99
484.6
352.1
60
291.3
211.6
20
339.8
246.9
80
388.3
282.1
40
436.9
317.4
600
485.4
352.7
Dirt.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. •
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
54° (126°, 234°, 306°). •»
1 Page 604] TABLE 2.
Difference of Latitude and Departure for 37° (143°, 217°, 323°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
48.7
36.7
121
96.6
72.8
181
144.6
108.9
241
192.5
145.0
2
1.6
1.2
62
49.5
37.3
22
97.4
73.4
82
145.4
109.5
42
193.3
145.6
3
2.4
1.8
63
50.3
37.9
23
98.2
74.0
83
146.2
110.1
43
194.1
146.2
4
3.2
2.4
64
51.1
38.5
24
99.0
74.6
84
146.9
110.7
44
194.9
146.8
5
4.0
3.0
65
51.9
39.1
25
99.8
75.2
85
147.7
111.3
45
195.7
147.4
6
'4.8
3.6
66
52.7
39.7
26
100.6
75.8
86
148.5
111.9
46
196.5
148.0
7
5.6
4.2
67
53.5
40.3
27
101.4
76.4
87
149.3
112.5
47
197.3
148.6
8
6.4
4.8
68
54.3
40.9
28
102.2
77.0
88
150.1
113.1
48
198.1
149.3
9
7.2
5.4
69
55.1
41.5
29
103.0
77.6
89
150.9
113.7
49
198.9
149.9
10
8.0
6.0
70
55.9
42.1
30
103.8
78.2
90
151.7
114.3
50
199.7
150.5
11
8.8
6.6
71
56.7
42.7
131
104.6
78.8
191
152.5
114.9
251
200.5
151.1
12
9.6
7.2
72
57.5
43.3
32
105.4
79.4
92
153.3
115.5
52
201.3
151.7
13
10.4
7.8
73
58.3
43.9
33
106.2
80.0
93
154.1
116.2
53
202.1
152.3
14
11.2
8.4
74
59.1
44.5
34
107.0
80.6
94
154.9
116.8
54
202.9
152.9
15
12.0
9.0
75
59.9
45.1
35
107.8
81.2
95
155.7
117.4
55
203.7
153.5
16
12.8
9.6
76
60.7
45.7
36
108.6
81.8
96
156.5
118.0
56
204.5
154.1
17
13.6
10.2
77
61.5
46.3
37
109.4
82.4
97
157.3
118.6
57
205.2
154.7
18
14.4
10.8
78
62.3
46.9
38
110.2
83.1
98
158.1
119.2
58
206.0
155.3
19
15.2
11.4
79
63.1
47.5
39
111.0
83.7
99
158.9
119.8
59
206.8
155.9
20
16.0
12.0
80
63.9
48.1
40
111.8
84.3
200
159.7
120.4
60
207.6
156.5
21
16.8
12.6
81
64.7
48.7
141
112.6
84.9
201
160.5
121.0
261
208.4
157.1
22
17.6
13.2
82
65.5
49.3
42
113.4
85.5
02
161.3
121.6
62
209.2
157.7
23
18.4
13.8
83
66.3
50.0
43
114.2
86.1
03
162.1
122.2
63
210.0
158. 3
24
19.2
14.4
84
67.1
50.6
44
115.0
86.7
04
162.9
122.8
64
210.8
158.9
25
20.0
15.0
85
67.9
51.2
45
115.8
87.3
05
163.7
123.4
65
211.6
159.5
26
20.8
15.6
86
68.7
51.8
46
116.6
87.9
06
164.5
124.0
66
212.4
160.1
27
21.6
16.2
87
69.5
52.4
47
117.4
88.5
07
165.3
124.6
67
213.2
160.7
28
22.4
16.9
88
70.3
53.0
48
118.2
89.1
08
166.1
125.2
68
214.0
161.3
29
23.2
17.5
89
71.1
53.6
49
119.0
89.7
09
166.9
125.8
69
214.8
161.9
30
24.0
18.1
90
71.9
54.2
50
119.8
90.3
10
167.7
126. 4
70
215. 6
162.5
31
24.8
18.7
91
72.7
54.8
151
120.6
90.9
211
168.5
127.0
271
216.4
163.1
32
25.6
19.3
92
73.5
55.4
52
121.4
91.5
12
169. 3
127.6
72
217.2
163.7
33
26.4
19.9
93
74.3
56.0
53
122.2
92.1
13
170.1
128.2
73
218.0
164.3
34
27.2
20.5
94
75.1
56.6
54
123.0
92.7
14
170.9
128.8
74
218.8
164.9
35
28.0
21.1
95
75.9
57.2
55
123.8
93.3
15
171.7
129.4
75
219.6
165.5
36
28.8
21.7
96
76.7
57.8
56
124.6
93.9
16
172.5
130.0
76
220.4
166.1
37
29.5
22.3
97
77.5
58.4
57
125.4
94.5
17
173.3
130.6
77
221.2
166.7
38
30.3
22.9
98
78.3
59.0
58
126.2
95.1
18
174.1
131.2
78
222.0
167.3
39
31.1
23.5
99
79.1
59.6
59
127.0
95.7
19
174.9
131.8
79
222.8
167.9
40
31.9
24.1
100
79.9
60.2
60
127.8
96.3
20
175.7
132.4
80
223. 6
168.5
41
32.7
24.7
101
80.7
60.8
161
128.6
96.9
221
176.5
133.0
281
224.4
169.1
42
33.5
25.3
02
81.5
61.4
62
129.4
97.5
22
177.3
133,6
82
225.2
169.7
43
34.3
25.9
03
82.3
62.0
63
130.2
98.1
23
178. 1
134.2
83
226.0
170.3
44
35.1
26.5
04
83.1
62.6
64
131.0
98.7
24
178.9
134.8
84
226.8
170.9
45
35.9
27.1
05
83.9
63.2
65
131.8
99.3
25
179.7
135.4
85
227.6
171.5
46
36.7
27.7
06
84.7
63.8
66
132.6
99.9
26
180.5
136.0
86
228.4
172.1
47
37.5
28.3
07
85.5
64.4
67
133.4
100.5
27
181.3
136.6
87
229.2
172.7
48
38.3
28.9
08
86.3
65.0
68
134.2
101.1
28
182.1
137.2
88 .
230. 0
173.3
49
39.1
29.5
09
87.1
65.6
69
135.0
101.7
29
182.9
137.8
89
230.8
173.9
50
39.9
30.1
10
87.8
66.2
70
135.8
102.3
30
183.7
138.4
90
231.6
174.5
51
40.7
30.7
111
88.6
68.8
171
136.6
102:9
231
184.5
139.0
291
232.4
175.1
52
41.5
31.3
12
89.4
67.4
72
137.4
103.5
32
185.3
139.6
92
233.2
175.7
53
42.3
31.9
13
90.2
68.0
73
138.2
104.1
33
186.1
140.2
93
234.0
176.3
54
43.1
32.5
14
91.0
68.6
74
139.0
104.7
34
186.9
140.8
94
234.8
176.9
55
43.9
33.1
15
91.8
69.2
75
139.8
105.3
35
187.7
141.4
95
235.6
177.5
56
44.7
33.7
16
92.6
69.8
76
140.6
105.9
36
188.5
142.0
96
236.4
178.1
57
45.5
34.3
17
93.4
70.4
77
141.4
106.5
37
189. 3
142.6
97
237.2
.178. 7
58
46.3
34.9
18
94.2
71.0
78
142.2
107.1
38
190.1
143.2
98
238.0
179.3
59
47.1
35.5
19
95.0
71.6
79
143.0
107.7
39
190.9
143.8
99
238.8
179.9
60
47.9
36.1
20
95.8
72.2
80
143.8
108.3
40
191.7
144.4
300
239.6
180.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
53° (127°, 233°, 307°).
TABLE 2. [Page
605
Difference of Latitude and Departure for 37° (143°, 217°, 323°).
Dist. Lat. | Dep.
Dist. Lat. Dep.
Dist. ! Lat. i Dep.
Dist. Lat. j Dep.
Dist. Lat.
Dep.
1
i
301
240.4
181.1
361
288.3
217.3
421
336.2
253.4
481
384.1
289.5
541
432.0
325.6
02
241.2
181.7
62
289.1
217.9
22
337.0
254.0
82
384.9
290.0
42
432.8
326.2
03
242.0
182.4
63
289.9
218.5
23
337.8
254. 6
83
385.7
290.6
43
433.6
326.8
04
242. 7
183.0
64
290.7
219.1
24
338.6
255. 2
84
386.5
291.2
44
434.4
327.3
05
243.5
183.6
65
291.5
219.7
25
339.4
255. 8
85
387.3
291.8
45
435. 2
327.9
06
244.3
184.2
66
292.3
220.3
26
340. 2
256.4
86
388.1
292. 4
46
436.0
328.5
07
245.1
184.8
67
293.1
220.9
27
341.0
257.0
87
388.9
293.0
47
436.8
329.1
08
245.9
185.4
68
293.9
221.5
28
341.8
257.6
88
389.7
293.6
48
437.6
329.7
09
246. 7
186.0
69
294.7
222. 1
29
342.6
258.2
89 390. 5
294.2
49
438.4
330.3
10
247.5
186.6
70
295.5
222. 7
30
343.4
258.8
90 391.3
294.8
50
439.2
330.9
311
248.3
187.2
371
296.3
223. 3
431
344.2
259.4
491 i 392.1 i 295. 4
551 440. 0
331.5
12
249.1
187.8
72
297.1
223.9
32
345.0
260.0
92 392.9 ' 296.0
52 440. 8
332. 1
13
249.9
188.4
73
297.9
224.5
38
345. 8
260.6
93 i 393.7 i2961 6
53 441.6
332.7
14
250.7
189.0
74
298.7
225.1
34
346.6
261.2
94 394.5 1297.2
54 442.4
333.3
15
251.5
189.6
75
299.5
225. 7
35
347.4
261.8
95
395.3 297.8
55
443.2
333.9
16
252.3
190.2
76
300.3
226.3
36
348.2
262.4
96 396.1 298.5
56
444.0
334.6
17
253.1
190.8
77
301.1
226.9
37
349.0
263.0
97
396.9 .299.1
57
444.8
235.2
18
253.9
191.4
78
301.8
227.5
38
349.8
263.6
98
397.7 209.7
58
445. 6
335.8
19
254. 7
192.0
79
302. 6
228. 1
39
350.6
264.2
99 398.5 1300.3
59 446. 4
336.4
20 255. 5
192.6
80
303. 4 ! 228. 7
40 351. 4
264.8
500 399.3 .300.9
60 447. 2
337.0
321 | 256.3
193.2
381
304.2
229. 3
441 352.2
265.4
501 i 400. 1 1 301. 5
561 448. 0
337.6
22 257. 1
193.8
82
305.0
229.9
42 353.0
266.0
02 400. 9 | 302. 1
62 448. 8
338.2
23 257.9
194.4
83
305.8
230.5
43 353. 8
266.6
03
401.7 302.7
63
449.6
338.8
24 258.7
195.0
84
306.6
231.1
44 354. 6
267. 2
04
402.5 303.3
64
450. 4
339.4
25 i 259.5
195.6
85
307.4
231.7
45 355. 4
267.8
05
403.3 303.9
65 451. 2
340.0
26 260. 3
196.2
86
308.2
232.3
46 356. 2
2£8.4
06
404. 1 304. 5
66
452. 0
340.6
27 261. 1
196.8
87
309.0
232.9
47 357. 0
269.0
07 404.9 1305.1
67
452. 8
341.2
28 261. 9
197.4
88
309.8
233.5
48 357. 8
269.6
08 405.7 305.7
68
453.6
341. 8
29 262. 7
198.0
89
310.6
234.1
49 358.6 270.2
09 406. 5
306.3
69 454. 4
342.4
30 263. 5
198.6
90
311.4
234.7
50 359.4 270.8
10 407. 3
306.9
70 455. 2
343.0
331 264.3
199.2
391
312.2
235.3
451
360.1 271.4
511 408. 1
307.5
571 456. 0
343.6
32 265. 1
199.8
92
313.0
235.9
52 360.9 272.0
12 408. 9
308.2
72 456. 8
344.3
33
265. 9
200.4
93
313.8
236.5
53 ! 361.7 272.6
13
409.7 308.8
73
457.6
344.9
34 266. 7
201.0
94
314.6
237.1
54 ' 362.5
273. 2
14
410.5 309.4
74
458.4
345.5
35 267. 5
201.6
95
315.4
237.7
55 363. 3
273. S
15
411.3 310.0
75
459.2
346.1
36
268.3
202.2
96
316.2
238.3
56 .364.1
274.4
16
412.1 310.6
76
460. 0
346.7
37
269.1
202. 8
97
317. 0 ! 238. 9
57 364. 9
275.0
17
412.9 311.2
77
460.8
347.3
269. 9
203.4
98
317.8
239. 5
58 365. 7
275. 6
18
413.7 311.8
78
461.6
347.9
270. 7
204.0
99
318. 6
240. 1
59 i 366.5
276. 2
19
414.5
312.4
79
462. 4
348.5
40 271. 5
204.6
400
319.4
240.7
60 367. 3
276. 8
20
415.3
313.0
80
463.2
349.1
341 272. 3
205.2
401
320. 2
241.3
461 368. 1
277.4
521 416. 1
313.6
581
464.0
349.7
4"
273. 1
205.8
02
321.0
241.9
62 368. 9
278. 0
22
416.9
314.2
82
464.8
350.3
43
273.9
206. 4
03
321.8
242.5
63 369. 7
278. 6
23
417.7
314.8
83
465.6
350. 9
44
274.7
207.0
> 4
322. 6
243.1
64 370. 5
279. 2
24
418.5
315.4
84
466.4
351. 5
45
275.5
207.6
05
323.4
243.7
65 371.3
279.8
25
419.3
316.0
85
467.2
352.1
46
276.3
208.2
06
324. 2
244.3
66
372. 1
280.4
26
420.1
316.6
86
468.0
352.7
47
277.1
208.8
07
325. 0
244.9
67
372.9
281.0
27
420.9
317.2
87
468.8
353.3
48
277.9
209.4
08
325.8
245.5
68
373.7
281.6
28
421.7
317. 8
88
469.6
353. 9
49
278.7
210.0
09
326.6
246.1
69
374.5
282.3
29
422.5
318.4
89
470.4
354.5
50
279.5
210. 6
10
327.4
246.7
70
375.3
282.9
30
423.3
319.0
90
471.2
355.1
351
280.3
211.2
411
328.2
247.3
471
376.1
283.5
531
424.1
319.6
591
472.0
355. 7
52
281.1
211.8
12
329.0
247.9
72
376.9
284.1
32
424.9
320.2
92
472. 8
356.3
53
281.9
212.4
13
329.8
248.5
73
377. 7
284.7
33
425.7
320.8
93
473.6
356.9
54
282.7
213.0
14
330.6
249.2
74
378.5
285.3
34
426. 5
321.4
94
474.4
357. 5
55
283.5
213.6
15
331.4
249.8
75
379.3
285.9
35
427.3
322. 0
95
475. 2
358. 1
56
284.3
214.2
16
332.2
250.4
76
380.1
286.5
36
428.1
322.6
96
476.0
358. 7
57
285.1
214.8
17
333.0
251.0
77
380.9
287.1
37
428.9
323.2
97
476.8
359.3
58
285.9
215.4
18
333.8
251.6
78
381.7
287.7
38
429.7
323.8
98
477.6
359.9
59
286.7
216.1
19
334.6
252.2
79
382.5
288.3
39
430.5
324.4
99
478.4
360.5
60
287.5
216.7
20
335.4
252.8
80
383.3
288.9
40
431.3
325.0
600
479.2
361,1
Dist.
Dep.
Lat.
Dist."
Dep.
Lat.
Dist. Dep.
Lat.
Dist,
Dep.
Lat.
Dist. I Dep.
Lat.
53° (127°, 233°, 307°).
Page 606] TABLE 2.
Difference of Latitude and Departure for 38° (142°, 218°, 322° .
Disk
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
48.1
37.6
121
95.3
74.5
181
142.6
111.4
241
189.9
148.4
2
1.6
1.2
62
48.9
38.2
22
96.1
75.1
82
143.4
112.1
42
190.7
149.0
3
2.4
1.8
63
49.6
38.8
23
96.9
75.7
83
144.2
112.7
43
191.5
149.6
4
3.2
2.5
64
50.4
39.4
24
97.7
76.3
84
145.0
113.3
44
192.3
150.2
5
3.9
3.1
65
51.2
40.0
25
98.5
77.0
85
145.8
113.9
45
193.1
150.8
6
4.7
3.7
66
52.0
40.6
26
99.3
77.6
86
146.6
114.5
46
193.9
151.5
7
5.5
4.3
67
52.8
41.2
27
100.1
78.2
87
147.4
115.1
47
194.6
152.1
8
6.3
4.9
68
53.6
41.9
28
100. .9
78.8
88
148.1
115.7
48
195.4
152.7
9
7.1
5.5
69
54.4
42.5
29
101.7
79.4
89
148.9
116.4
49
196.2
153.3
10
7.9
6.2
70
55.2
43.1
30
102. 4
80.0
90
149.7
117.0
50
197.0
153.9
11
8.7
6.8
71
55.9
43.7
131
103.2
80.7
191
150. 5
117.6
251
197.8
154.5
12
9.5
7.4
72
56.7
44.3
32
104.0
81.3
92
151.3
118.2
52
198. 6
155.1
13
10.2
8.0
73
57.5
44.9
33
104.8
81.9
93
152.1
118.8
53
199.4
155.8
14
11.0
8.6
74
58.3
45.6
34
105.6
82.5
94
152.9
119.4
54
200.2
156.4
15
11.8
9.2
75
59.1
46.2
35
106.4
83.1
95
153.7
120.1
55
200.9
157.0
16
12.6
9.9
76
59.9
46.8
36
107.2
83.7
96
154.5
120.7
56
201.7
157.6
17
13.4
10.5
77
60.7
47.4
37
108.0
84.3
97
155.2
121.3
57
202.5
158.2
18
14.2
11.1
78
61.5
48.0
38
108.7
85.0
98
156.0
121.9
58
203.3
158.8
19
15.0
11.7
79
62.3
48.6
39
109.5
85.6
99
156.8
122.5
59
204.1
159.5
20
15.8
12.3
80
63.0
49.3
40
110.3
86.2
200
157.6
123.1
60
204.9
160.1
21
16.5
12.9
81
63.8
49.9
141
111.1
86.8
201
158.4
123.7
261
205.7
160.7
22
17.3
13.5
82
64.6
50.5
42
111.9
87.4
02
159.2
124.4
62
206.5
161.3
23
18.1
14.2
83
65.4
51.1
43
112.7
88.0
03
160.0
125.0
63
207.2
161.9
24
18.9
14.8
84
66.2
51.7
44
113.5
88.7
, 04
160.8
125.6
64
208.0
162.5
25
19.7
15.4
85
67.0
52.3
45
114.3
89.3
05
161.5
126.2
65
208.8
163. 2
26
20.5
16.0
86
67.8
52.9
46
115.0
89.9
06
162.3
126.8
66
209.6
163.8
27
21.3
16.6
87
68.6
53.6
47
115.8
90.5
07
163.1
127.4
67
210.4
164.4
28
22.1
17.2
88
69.3
54.2
48
116.6
91.1
08
163.9
128.1
68
211.2
165.0
29
22.9
17.9
89
70.1
54.8
49
117.4
91.7
09
164.7
128.7
69
212.0
165.6
30
23.6
18.5
90
70.9
55.4
50
118.2
92.3
10
165.5
129.3
70
212.8
166.2
31
24.4
19.1
91
71.7
56.0
151
119.0
93.0
211
166.3
129.9
271
213.6
166.8
32
25.2
19.7
92
72.5
56.6
52
119.8
93.6
12
167.1
130.5
72
214.3
167.5
33
26.0
20.3
93
73.3
57.3
53
120.6
94.2
13
167.8
131.1
73
215.1
168.1
34
26.8
20.9
94
74.1
57.9
54
121.4
94.8
14
168.6
131.8
74
215.9
168.7
35
27.6
21.5
95
74.9
58.5
55
122.1
95.4
15
169.4
132.4
75
216.7
169.3
36
28.4
22.2
96
75.6
59.1
56
122.9
• 96.0
16
170.2
133.0
76
217.5
169.9
37
29.2
22.8
97
76.4
59.7
57
123.7
96.7
17
171.0
133.6
77
218.3
170.5
38
29.9
23.4
98
77.2
60.3
58
124.5
97.3
18
171.8
134.2
78
219.1
171.2
39
30.7
24.0
99
78.0
61.0
59
125.3
97.9
19
172.6
134.8
79
219.9
171.8
40
31.5
24.6
100
78.8
61.6
60
126.1
98.5
20
173.4
135.4
80
220.6
172.4
41
32.3
25.2
101
79.6
62.2
161
126.9
99.1
221
174.2
136.1
281
221.4
173.0
42
33.1
25.9
02
'80.4
62.8
62
127.7
99.7
22
174.9
136.7
82
222.2
173.6
43
33.9
26.5
03
81.2
63.4
63
128.4
100.4
23
175.7
137.3
83
223.0
174.2
44
34.7
27.1
04
82.0
64.0
64
129.2
101.0
24
176.5
137. 9
84
223.8
174.8
45
35.5
27.7
05
82.7
64.6
65
130.0
101.6
25
177.3
138.5
85
224.6
175.5
46
36.2
28.3
06
83.5
65.3
66
130.8
102.2
26
178.1
139.1
86
225.4
176.1
47
37.0
28.9
07
84.3
65.9
67
131.6
102.8
27
178.9
139.8
87
226.2
176.7
48
37.8
29.6
08
85.1
66.5
68
132.4
103.4
28
179.7
140.4
88
226.9
177.3
49
38.6
30.2
09
85.9
67.1
69
133.2
104.0
29
180.5
141.0
89
227.7
177.9
50
39.4
30.8
10
86.7
67.7
70
134.0
104.7
30
181.2
141.6
90
228.5
178.5
51
40.2
31.4
111
87.5
68.3
171
134.7
105.3
231
182.0
142.2
291
229.3
179.2
52
41.0
32.0
12
88.3
69.0
72
135.5
105.9
32
182.8
142.8
92
230.1
179.8
53
41.8
32.6
13
89.0
69.6
73
136.3
106.5
33
183.6
143.4
93
230.9
180.4
54
42.6
33.2
14
89.8
70.2
74
137.1
107.1
34
184.4
144.1
94
231.7
181.0
55
43.3
33.9
15
90.6
70.8
75
137.9
107.7
35
185.2
144.7
95
232.5
181.6
56
44.1
34.5
16
91.4
71.4
76
138.7
108.4
36
186.0
145.3
96
233.3
182.2
57
44.9
35.1
17
92.2
72.0
77
139.5
109.0
37
186.8
145.9
97
234.0
182.9
58
45.7
35.7
18
93.0
72.6
78
140.3
109.6
38
187.5
146.5
98
234. 8
183.5
59
46.5
36.3
19
93.8
73.3
79
141.1
110.2
39
188.3
147.1
99
235.6
184.1
60
47.3
36.9
20
94.6
73.9
80
141.8
110.8
40
189.1
147.8
300
236.4
184.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
52° (128°, 232°, 308°).
! TABLE 2. [Page
607
Difference of Latitude and Departure for 38° (142°, 218°, 322°).
JDist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist 1 Lat.
Dep.
Dist.
Lat.
Dep.
301
237.2 185.3
361
284.5
222.3
421
331.8
259.2
481
379.0
296.2
541
426.3
333.1
02
231.0 185.9
62
285.3
222.9
22
332.5
259. 8
82
379.8
296.8
42
427.1
333.7
03
23S.8 1186.6
63
286.0
223.5
23
333.3
260.4
83
380.6
297.4
43
427.9
334.3
04
239. 6 i 187. 2
64
286.8
224.1
24
334.1
261.0
84
381.4
298.0
44
428.7
335. 0
05
240.3
187.8
65
287.6
224.7
25
334.9
261. 7
85
382.2
298.6
45
429.5
335.6
06
241.1
188.4
66
288.4
225.3
26
335.7
262.3
86
383.0
299.2
46
430.3
336.2
07
241.9
189.0
67
289.2
226.0
27
336.5
262.9
87
383.8
299.8
47
431.0
336.8
08
242.7
189.6
68
290.0
226.6
28
337.3
263.5
88
384. 5
300.4
48
431.8
337.4
09
243.5
190.2
69
290.8
227.2
29
338.1
264.1
89
385.3
301.1
49
432.6
338.0
10
244.3
190.9
70
291.6
227.8
30
338.8
264.7
90
386.1
301.7
50
433.4
338.6
311
245.1
191.5
371
292.4
228.4
431
339.6
265. 4
491
386.9 302.3
551
434.2
339.3
12
245.9
192.1
72
293.1
229.0
32
340.4
266.0
92
387.7 302.9
52
435.0
339.9
13
246.6
192.7
73
293.9
229.6
33
341.2
266.6
93
388.5
303.5
53
435.8
340.5
14
247.4
193.3
74
294.7
230.3
34
342. 0
267.2
94
389.3
304.2
54
436.6
341.1
15
248.2
193.9
75
295.5
230.9
35
342.8
267.8
95
390.1
304.8
55
437.4
341.7
16
249.0
194.6
76
296.3
231.5
36
343.6
268.4
96
390.9
305.4
56
438.1
342.3
17
249.8
195.2
77
297.1
232.1
37
344.4
269.1
97
391.6
306.0
57
438.9
343.0
18
250. 6
195.8
78
297.9
232.7
38
345. 2
269.7
98
392.4 306.6
58
439.7
343.6
19
251.4
196.4
79
298.7
233.3
39
345.9
270.3
99
393.2 307.2
59
440.5
344.2
20
252. 2
197.0
80
299.4
234.0
40
346.7
270.9
500
394. 0 l 307. 8
60
441.3
344.8
321
253.0
197.6
381
300.2
234.6
441
347.5
271.5
501
394.8 j308.4
561
442.1
345. 4
22
253.7
198.2
82
301.0
235.2
42
348.3
272.1
02
395.6 309.1
62
442.9
346.0
23
254.5
198.9
83
301.8
235.8
43
349.1
272.7
03
396,4 309.7
63
443.7
346.6
24
255.3
199.5
84
302.6
236.4
44
349.9 1273.4
04
397. 2 ! 310. 3
64
444.4
347.2
25
256.1
200.1
85
303.4
237.0
45
350. 7
274.0
05
397. 9 310. 9
65
445.2
347.8
26
256.9
200.7
86
304.2
237.7
46
351.5
274.6
06
398. 7 311. 6
66
446.0
348.5
27
257.7
201.3
87
305. 0
238. 3
47
352.2
275.2
07
399. 5 312. 2
67
446.8
349.1
28
258.5
201.9
88
305.7
238.9
48 353. 0
275.8
08
400.3 312.8
68
447.6
349.7
29
259.3
202.6
89
306.5
239.5
49 353. 8
276.4
09
401.1
313.4
69
448.4
350.3
30
260.0
203.2
90
307.3
240.1
50 354. 6
277.1
10
401.9 314.0
70
449.2
350.9
331
260.8
203.8
391
308.1
240.7
451 355. 4
277.7
511
402.7 314.6
571
450. 0
351.6
32
261.6
204.4
92
308.9
241.3
52 356. 2
278.3
12
403.5 315.2
72
450.7
352.2
33
262.4
205.0
93
309.7
242.0
53 357. 0
278.9
13
404. 2 ! 315. 8
73
451.5
352.8
34
263.2
205.6
94
310.5
242.6
54 357. 8
279. 5
14
405. 0 i 316. 4
74
452.3
353.4
35
264.0
206.3
95
311.3
243.2
55 358. 5
280.1
15
405.8 1317.1
75
453.1
354.0
36
264.8
206.9
96
312.1
243.8
56 359. 3
280.7
16
406.6 317.7
76
453.9
354.6
37
265. 6
207.5
97
312.8
244.4
57
360.1
281.4
17
407.4 318.3
77
454.7
355.2
38
266.3
208.1
98
313.6
245.0
58
360.9
282.0
18
408. 2 i 318. 9
78
455. 5
355.8
39
267. 1 | 208. 7
99
314.4
245.7
59
361.7
282.6
19
409.0 319.5
79
456.3
356.4
40
267.9 1209.3
400
315.2
246.3
60
362.5
283. 2
20
409.8 320.2
80
457.1
357.1
341
268.7 209.9
401
316.0
246.9
461
363.3
283.8
521
410. 6 320. S
581
457.8
357.7
42
269.5 210.6
02
316.8
, 247. 5
62 364. 1
284.4
22
411.3
321.4
82
458.6
358.3
43
270.3
211.2
03
317.6
248.1
63 364. 9
285.1
23
412.1 322.0
83
459.4
358.9
44
271.1
211.8
04
318.4
248.7
64
365.6
285.7
24
412.9 322.6
84
460.2
359.5
45
271.9
212.4
05
319.1
249.3
65 366. 4
286.3
25
413.7
323.2
85
461.0
360.2
46
272.7
213.0
06
319.9
; 250. 0
66
367.2
286.9
26
414.5
323.8
86
461.8
360.8
47
273.4
213.6
07
320.7
i 250. 6
67
368.0
287.5
27
415.3 324.5
87
462.6
361.4
48
274.2 214.3
08
321.5
i 251. 2
68
368.8
288.1
28
416.1
325. 1
88
463.3
362.0
49
275.0 214.9
09 322. 3
i 251. 8
69 369. 6
288.7
29
416. 9 325. 7
89
464.1
362.6
_50_
275.8 ;215.5
10 1 323. 1
i 252. 4
70 370. 4
289.3
30
417. 6 ; 326. 3
90
464.9
363.2
|3oT
276.6 216.1
411
323.9
253.0
471
371.2
290.0
531
418. 4 326. 9
591
465.7
363.8
52
277. 4 ' 216. 7
12
324.7
253. 7
72
371.9
290.6
32
419.2 327.5
92
466.5
364.4
53
278.2 i217.3
13 325. 5
254. 3
73
372.7
291.2
33
420.0
328.2
93
467.3
365.1
54
279.0 218.0
14
326.2
254. 9
74
373.5
291.8
34
420. 8 1 328. 8
94
468.1
365.7
55
279.7
218.6
15
327.0
255. 5
75
374.3
292.4
35
421.6 329.4
95
468.9
366.3
56
280.5
219.2
16
327. 8
' 256. 1
76
375.1
293.1
36
422. 4
330.0
96
469. 7
366.9
57
£81.3
219.8
17
328.6
1 256. 7
1 7
375.9
293.7
37
423.2
330.6
97
470.5
367.5
58
282.1
220.4
18
329.4
1 257. 4
78
376.7
294.3
38
424.0
331.2
98
471.2
368.1
59
282.9
221.0
19
330.2
258.0
79
377.5
294.9
39
424.7
331.8
99
472. 0
368.7
60
283.7
221.6
20
331.0
258. 6
80
378.2
295.5
40
425. 5
332.5
600
472.8
369.4
Dist.
Dep.
Lat.
Dist.
Dep.
| Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. i Dep.
Lat.
52° (128°, 232°, 308°).
61828°— 16 32
Page 608] TABLE 2.
Difference of Latitude and Departure for 39° (141°, 219°, 321°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
47.4
38.4
121
94.0
76.1
181
140.7
113.9
241
187.3
151.7
2
1.6
1.3
62
48.2
39.0
22
94.8
76.8
82
141.4
114.5
42
188.1
152.3
3
2.3
1.9
63
49.0
39.6
23
95.6
77.4
83
142.2
115. 2
43
188.8
152.9
4
3.1
2.5
64
49.7
40.3
24
96.4
78.0
84
143.0
115.8
44
189.6
153. 6
5
3.9
3.1
65
50.5
40.9
25
97.1
78.7
85
143.8
116.4
45
190.4
154.2
6
4.7
3.8
66
51.3
41.5
26
97.9
79.3
86
144.5
117.1
46
191.2
154.8
7
5.4
4.4
67
52.1
42.2
27
98.7
79.9
87
145.3
117.7
47
192.0
155.4
8
6.2
5.0
68
52.8
42.8
28
99.5
80.6
88
146.1
118.3
48
192.7
156.1
9
7.0
5.7
69
53.6
43.4
29
100.3
81.2
89
146.9
118.9
49
193.5
156.7
10
7.8
6.3
70
54.4
44.1
30
101. 0
81.8
90
147.7
119.6
50
194.3
157.3
11
8.5
6.9
71
55.2
44.7
131
101.8
82.4
191
148.4
120.2
251
195.1
158.0
12
9.3
7.6
72
56.0
45.3
32
102. 6
83.1
92
149.2
120.8
52
195.8
158.6
13
10.1
8.2
73
56.7
45.9
33
103.4
83.7
93
150.0
121.5
53
196.6
159.2
14
10.9
8.8
74
57.5
46.6
34
104.1
84.3
94
150.8
122.1
54
197.4
159.8
15
11.7
9.4
75
58.3
47.2
35
104.9
85.0
95
151.5
122.7
55
198.2
160.5
16
12.4
10.1
76
59.1
47.8
36
105. 7
85.6
96
152.3
123.3
56
198.9
161.1
17
13.2
10.7
77
59.8
48.5
37
106.5
86.2
97
153.1
124.0
57
199.7
161.7
18
14.0
11.3
78
60.6
49.1
38
107.2
86.8
98'
153.9
124.6
58
200.5
162.4
19
14.8
12.0
79
61.4
49.7
39
108.0
87.5
99
154.7
125.2
59
201.3
163.0
20
15.5
12.6
80
62.2
50.3
40
108.8
88.1
200
155.4
125.9
60
202.1
163.6
21
16.3
13.2
81
62.9
51.0
141
109.6
88.7
201
156.2
126.5
261
202.8
164.3
22
17.1
13.8
82
63.7
51.6
42
110.4
89.4
02
157.0
127.1
62
203.6
164.9
23
17.9
14.5
83
64.5
52.2
43
111.1
90.0
03
157.8
127.8
63
204.4
165.5
24
18.7
15.1
84
65.3
52.9
44
111.9
90.6
04
158.5
128.4
64
205.2
166.1
25
19.4
15.7
85
66.1
53.5
45
112.7
91.3
05
159.3
129.0
65
205.9
166.8
26
20.2
16.4
86
66.8
54.1
46
113.5
91. ft
06
160. 1 '
129.6
66
206. 7
167.4
27
21.0
17.0
87
67.6
54.8
47
114.2
92.5
07
160.9
130.3
67
207.5
168.0
28
21.8
17.6
88
68.4
55.4
48
115.0
93.1
08
161.6
130.9
68
208.3
168.7
29
22.5
18.3
89
69.2
56.0
49
115.8
93.8
09
162.4
131.5
69
209.1
169.3
30
23.3
18.9
90
69.9
56.6
50
116.6
94.4
10
163.2
132.2
70
209.8
169.9
31
24.1
19.5
91
70.7
57.3
151
117.3
95.0
211
164.0
132.8
271
210.6
170.5
32
24.9
20.1
92
71.5
57.9
52
118.1
95.7
12
164.8
133.4
72
211.4
171.2
33
25.6
20.8
93
72.3
58.5
53
118.9
96.3
13
165.5
134.0
73
212.2
171.8
34
26.4
21.4
94
73.1
59.2
54
119.7
96.9
14
166.3
134.7
74
212.9
172.4
35
27.2
22.0
95
73.8
59.8
55
120.5
97.5
15
167.1
135.3
75
213.7
173.1
36
2&0
22.7
96
74.6
60.4
56
121.2
98.2
16
167.9
135.9
76
214.5
173.7
37
28.8
23.3
97
75.4
61.0
57
122.0
98.8
17
168.6
136.6
77
215.3
174.3
38
29.5
23.9
98
76.2
61.7
58
122.8
99.4
18
169.4
137.2
78
216.0
175.0
39
30.3
24.5
99
76.9
62.3
59
123.6
100.1
19
170.2
137.8
79
216.8
175.6
40
31.1
25.2
100
77.7
62.9
60
124.3
100.7
20
171.0
138. 5
80
217.6
176.2
41
31.9
25.8
101
78.5
63.6
161
125.1
101.3
221
171.7
139.1
281
218.4
176.8
42
32.6
26.4
02
79.3
64.2
62
125.9
101.9
22
172.5
139.7
82
219.2
177.5
43
33.4
27.1
03
80.0
64.8
63
126.7
102.6
23
173.3
140.3
83
219.9
178.1
44
34.2
27.7
04
80.8
65.4
64
127.5
103.2
24
174.1
141.0
84
220.7
178.7
45
35.0
28.3
05
81.6
66.1
65
128.2
103.8
25
174.9
141.6
85
221.5
179.4
46
35.7
28.9
06
82.4
66.7
66
129.0
104.5
26
175.6
142.2
86
222.3
180.0
47
36.5
29.6
07
83.2
67.3
67
129.8
105.1
27
176.4
142.9
87
223. 0
180.6
48
37.3
30.2
08
83.9
68.0
68
130.6
105.7
28
177.2
143.5
88
223.8
181.2
49
38.1
30.8
09
84.7
68.6
69
131.3
106.4
29
178.0
144.1
89
224.6
181.9
50
38.9
31.5
10
85.5
69.2
70
132.1
107.0
30
178.7
144.7
90
225.4
182.5
51
39.6
32.1
111
86.3
69.9
171
132.9
107.6
231
179.5
145.4
291
226.1
183. 1
52
40.4
32.7
12
87.0
70.5
72
133.7
108.2
32
180.3
146.0
92
226.9
183.8
53
41.2
'33.4
13
87.8
71.1
73
134.4
108.9
33
181.1
146.6
93
227.7
184.4
54
42.0
34.0
14
88.6
71.7
74
135.2
109.5
34
181.9
147.3
94
228.5
185. 0
55
42.7
34.6
15
89.4
72.4
75
136.0
110.1
35
182.6
147.9
95
229.3
185.6
56
43.5
35.2
16
90.1
73.0
76
136.8
110.8
36
183.4
148.5
96
230.0
186.3
57
44.3
35.9
17
90.9
73.6
77
137.6
111.4
37
184.2
149.1
97
230.8
186.9
58
45.1
36.5
18
91.7
74.3
78
138.3
112.0
38
185.0
149.8
98
231.6
187.5
59
45.9
37.1
19
92.5
74.9
79
139.1
112.6
39
185.7
150.4
99
232.4
188.2
60
46.6
37.8
20
93.3
75.5
80
139.9
113.3
40
186.5
151.0
300
233.1
188.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
51° (129°, 231°, 309°).
r "TABLE 2. [Page 609
! Difference of Latitude and Departure for 39° (141°, 219°, 321°).
IDist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
'1 301
233.9
189.4
361
280.6
227.1
421
327.2
264.9
481
373.8
302.6
541
420.4
340.4
1 02
234. 7
190.0
62
281.3
227.8
22
328.0
265.5
82
374.6
303.3
42
421.2
341.0
1 03
235.5
190.6
63
282.1
228.4
23 328. 7
266.2
83
375.4
303.9
43
422.0
341.7
I 04
236.3
191.3
64
282.9
229.0
24 329. 5
266.8
84
376.1
304.5
44
422.7
342.3
1 05
237.0
191.9
65
283.7
229.7
25 330. 3
267.4
85
376.9
305.2
45
423.5
342.9
1 06
237.8
192.5
66
284.4
230.3
26
331.1
268.0
86
377.7
305.8
46
424.3
343.6
I 07 238.6
193.2
67
285.2
230.9
27
331.9
268.7
87
378.5
306.4
47
425.1
344.2
1 08
239.4
193.8
68
286.0
231.5
28 332. 6
269.3
88
379.3
307.1
48
425.9
344.8
09
240.1
194.4
69
286.8
232.2
29 333. 4
269.9
89
380.0
307.7
49
426.6
345.5
1 10
240.9
195.0
70
287.6
232.8
30 334. 2
270.6
90
380.8
308.3
50
427.4
346.1
|311 ; 241.7
195.7
371
288.3 1233.4
431 335. 0
271.2
491
381.6
308.9
551
428.2
346.7
I 12 242.5
196.3
72
289.1 ; 234.1
32
335.7
271.8
92
382.4
309.6
52
429.0
347.4
I 13 243.3
196.9
73
289.9 234.7
33
336.5
272.5
93
383.1
310.2
53
429.7
348.0
14 244.0 197.6
74
290.7 235.3
34
337.3
273.1
94
383.9
310.8
54
430.5
348.6
j 15 244.8 198.2
75
291.4
236.0
35
338.1
273.7
95
384.7
311.5
55
431.3
349.2
I 16 245. 6 i 198. 8
76
292.2
236.6
36
338.8
274.3
96
385.5
312.1
56
432.1
349.9
1 17 246. 4 i 199. 5
77
293.0
237.2
37
339.6
275. 0
97
386.2
312.7
57
432.8
350.5
1 18 247. 1 200. 1
78
293.8
237. 8
38
340.4
275.6
98
387.0
313.3
58
433.6
351.1
j 19 247. 9 200. 7
79
294.5
238.5
39
341.2
276.2
99
387.8
314.0
59
434.4
351.7
20 248.7 1201.3
80
295.3
239.1
40
342.0
276.9
500
388.6
314.7
60
435.2
352.4
1 321 249. 5
202.0
381
296.1
239.7
441
342.7
277.5
501
389.4
315.3
561
435.9
353.0
1 22 250.3
202.6
82
296.9
240.4
42
343.5
278.1
02
390.1
315.9
62
436.7
353.6
1 23 ! 251.0
203.2
83
297.7
241.0
43
344.3
278.7
03
390.9
316.5
63
437.5
354.3
24 ; 251.8 203.9
84
298.4
241.6
44
345.1
279.4
04
391.7
317.1
64
438.3
354.9
25
252.6 204.5
85
299.2
242.2
45
345.8
280.0
05
392.5
317.8
65
439.1
355.5
26
253.4 205.1
86
300.0
242.9
46
346.6
280.6
06
393.2
318.4
66
439.8
356.2
27
254.1
205.7
87
300.8
243.5
47
347.4
281.3
07
394.0
319.0
67
440.6
356.8
28
254.9
206.4
88
301.5
244.1
48
348.2
281.9
08
394.8
319.6
68
441.4
357.4
29
255.7
207.0
89
302.3
244.8
49
349.0
282.5
09
395.6
320.3
69
442.2
358.1
30
256.5
207.6
90
303. 1 245. 4
50
349.7
283.2
10
396.3
320.9
70
443.0
358.7
II 331
257.2
208.3
391
303.9
246.0
451
350.5
283.8
511
397.1
321.6
571
443.7
359.3
32
258.0
208.9
92
304.7
246.7
52
351.3
284.4
12
397.9
322.2
72
444.5
359.9
33
258.8
209.5
93
305.4
247.3
53
352.1
285.0
13
398.7
322.8
73
445. 3
360.6
34
259.6
210.2
94
306.2
247.9
54
352.8
285.7
14
399.4
323.4
74
446.1
361.2
35
260.4
210.8
95
307.0
248.5
55
353.6
286.3
15
400.2
324.1
75
446.9
361.8
1 36
261.1
211.4
96
307.8
249.2
56
354.4
286.9
16
401.0
324.7
76
447.6
362.4
37
261.9
212.0
97
308.5
249.8
57
355.2
287.6
17
401.8
325.3
77
448.4
363.1
38
262.7
212.7
98
309.3
250.4
58
355.9
288.2
18
402.5
325.9
78
449.2
363.7
39
263.5
213.3
99
310.1
251.1
59
356.7
288.8
19
403.3
326.6
79
450.0
364.3
40
264.2
213.9
400
310.9
251.7
60
357. 5
289.4
20
404.1
327.2
80
450.7
365.0
341
265.0
214.6
401
311.6
252.3
461
358.3
290.1
521
404.9
327.8
581
451.5
365.6
1 42
265.8
215.2
02
312.4
252.9
62
359.1
290.7
22
405.7
328.5
82
452.3
366.2
43
266.6
215.8
03
313.2
253.6
63
359.8
291.3
23
406.4
329.1
83
453.1
366.9
44
267.3
216.4
04
314.0
254.2
64
360.6
292.0
24
407.2
329.7
84
453.9
367.5
45
268.1
217.1
05
314.8
254.8
65
361.4
292.6
25
408.0
330.4
85
454.6
368.1
j 46
268.9
217.7
06
315.5
255.5
66
362.2
293.2
26
408.8
331.0
86
455.4
368.8
j 47
269.7
218.3
07
316.3
256.1
67
362.9
293.8
27
409.5
331. 6
87
456.2
369.4
48
270. 5
219.0
08
317.1
256.7
68
363.7
294.5
28
410.3
332.3
88
457.0
370.0
49
271.2
219.6
09
317.9
257.3
69
364.5
295.1
29
411.1
332.9
89
457.8
370.6
50
272.0
220.2
10
318.6
258.0
70
365.3
295.7
30
411.9
333.5
90
458.5
371.3
1 351
272.8
220.8
411
319.4
258.6
471
366.0
296.4
531
412.6
334.1
591
459.3
371.9
1 52
273.6
221.5
12
320.2
259.2
72
366.8
297.0
32
413.4
334.8
92
460.1
372.5
J 53
274.3
222.1
13
321.0
259.9
73
367.6
297.6
33
414.2
335.4
93
460.9
373.2
54
275. 1
222.7
14
321.8
260.5
74
368.4
298.3
34
415.0
336.1
94
461.6
373.8
1 55
275.9
223.4
15
322.5
261.1
75
369.2
298.9
35
415.8
336.7
95
462.4
374.4
1 56
276.7
224.0
16
323.3
261.8
76
369.9
299.5
36
416.5
337.3
96
463.2
375.1
1 57
277.5
224.6
17
324.1
262.4
77
370.7
300.1
37
417.3
337.9
97
464.0
375.7
58
278.2
225.3
18
324.9
263.0
78
371.5
300.8
38
418.1
338.5
98
464.8
376.3
59
279.0
225. 9
19
325.6
263.6
79
372.3
301.4
39
418.9
339.1
99
465.5
376.9
60
279.8
226.5
20
326.4
264.3
80
373.0
302.0
40
419.6
339.8
600
466.3
377.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
51° (129°, 231°, 309°).
Page 610] TABLE 2.
Difference of Latitude and Departure for 40° (140°, 220°, 320°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
46.7
39.2
121
92.7
77.8
181
138.7
116.3
241
184.6
154.9
2
1.5
1.3
62
47.5
39.9
22
93.5
78.4
82
139.4
117.0
42
185.4
155.6
3
2.3
1.9
63
48.3
40.5
23
94.2
79.1
83
140.2
117.6
43
186.1
156.2
4
3.1
2.6
64
49.0
41.1
24
95.0
79.7
84
141.0
118.3
44
186.9
156.8
5
3.8
3.2
65
49.8
41.8
25
95.8
80.3
85
141.7
118.9
45
187.7
157.5
6
4.6
3.9
66
50.6
42.4
26
967F
81.0
86
142.5
119.6
46
188.4
158.1
7
5.4
4.5
67
51.3
43.1
27
97.3
81.6
87
143.3
120.2
47
189.2
158.8
8
6.1
5.1
68
52.1
43.7
28
98.1
82.3
88
144.0
120.8
48
190.0
159.4
9
6.9
5.8
69
52.9
44.4
29
98.8
82.9
89
144.8
121. 5
49
190.7
160.1
10
7.7
6.4
70
53.6
45.0
30
99.6
83.6
. 90
145.5
122.1
50
191.5
160.7
11
8.4
7.1
71
54.4
45.6
131
100.4
84.2
191
146.3
122.8
251
192.3
161.3
12
9.2
7.7
72
55.2
46.3
32
101.1
84.8
92
147.1
123.4
52
193.0
162.0
13
10.0
8.4
73
55.9
46.9
33
101.9
85.5
93
147.8
124.1
53
193.8
162.6
14
10.7
9.0
74
56.7
47.6
34
102.6
86.1
94
148.6
124.7
54
194.6
163.3
15
11.5
9.6
75
57.5
48.2
35
103.4
86.8
95
149.4
125.3
55
195.3
163.9
16
12.3
10.3
76
58.2
48.9
36
104.2
87.4
96
150.1
126.0
56
196.1
164.6
17
13.0
10.9
77
59.0
49.5
37
104.9
88.1
97
150.9
126.6
57
196.9
165.2
18
13.8
11.6
78
59.8
50.1
38
105.7
88.7
98
151.7
127.3
58
197.6
165.8
19
14.6
12.2
79
60.5
50.8
39
106.5
89.3
99
152.4
127.9
59
198.4
166.5
20
15.3
12.9
80
61.3
51.4
40
107.2
90.0
200
153.2
128.6
60
199.2
167.1
21
16.1
13.5
81
62.0
52.1
141
108.0
90.6
201
154.0
129.2
261
199.9
167.8
22
16.9
14.1
82
62.8
52.7
42
108.8
91.3
02
154.7
129.8
62
200.7
168.4
23
17.6
14.8
83
63.6
53.4
43
109.5
91.9
03
155.5
130.5
63
201.5
169.1
24
18.4
15.4
84
64.3
54.0
44
110.3
92.6
04
156.3
131.1
64
202.2
169.7
25
19.2
16.1
85
65.1
54.6
45
111.1
93.2
05
157.0
131.8
65
203.0
170.3
26
19.9
16.7
86
65.9
55.3
46
111.8
93.8
06
157.8
132.4
66
203.8
171.0
27
20.7
17.4
87
66.6
55.9
47
112.6
94.5
07
158.6
133.1
67
204.5
171.6
28
21.4
18.0
88
67.4
56.6
48
113.4
95.1
08
159.3
133.7
68
205.3
172.3
29
22.2
18.6
89
68.2
57.2
49
114.1
95.8
09
160.1
134.3
69
206.1
172.9
30
23.0
19.3
90
68.9
57.9
50
114.9
96.4
10
160.9
135.0
70
206.8
173.6
31
23.7
19.9
91
69.7
58.5
151
115.7
97.1
211
161.6
135.6
271
207.6
174.2
32
24.5
20.6
92
70.5
59.1
52
116.4
97.7
12
162.4
136.3
72
208.4
174.8
33
25.3
21.2
93
71.2
59.8
53
117.2
98.3
13
163.2
136.9
73
209.1
175.5
34
26.0
21.9
94
72.0
60.4
54
118.0
99.0
14
163.9
137.6
74
209.9
176.1
35
26.8
22.5
95
72.8
61.1
55
118.7
99.6
15
164.7
138.2
75
210.7
176.8
36
27.6
23.1
96
73.5
61.7
56
119.5
100.3
16
165.5
138.8
76
211.4
177.4
37
28.3
23.8
97
74.3
62.4
57
120.3
100.9
17
166.2
139.5
77
212.2
178.1
38
29.1
24.4
98
75.1
63.0
58
121.0
101.6
18
167^0
140.1
78
213.0
178.7
39
29.9
25.1
99
75.8
63.6
59
121.8
102.2
19
167.8
140.8
79
213.7
179.3
40
30.6
25.7
100
76.6
64.3
60
122.6
102.8
20
168.5
141.4
80
214.5
180.0
41
31.4
26.4
101
77.4
64.9
161
123.3
103.5
221
169.3
142.1
281
215.3
180.6
42
32.2
27.0
02
78.1
65.6
62
124.1
104.1
22
170.1
142.7
82
216.0
181.3
43
32.9
27.6
03
78.9
66.2
63
124.9
104.8
23
170.8
143.3
83
216.8
181.9
44
33.7
28.3
04
79.7
66.8
64
125.6
105.4
24
171.6
144.0
84
217. a
182.6
45
34.5
28.9
05
80.4
67.5
65
126.4
106.1
25
172.4
144.6
85
218.3
183.2
46
35.2
29.6
06
81.2
68.1
66
127.2
106.7
26
173.1
145. 3
86
219.1
183.8
47
36.0
30.2
07
82.0
68.8
67
127.9
107.3
27
173.9
145.9
87
219.9
184.5
48
36.8
30.9
08
82.7
69.4
68
128.7
108.0
28
174.7
146.6
88
220.6
185.1
49
37.5
31.5
09
83.5
70.1
69
129.5
108.6
29
175.4
147.2
89
221.4
185.8
50
38.3
32.1
10
84.3
70.7
70
130.2
109.3
30
176.2
147.8
90
222.2
186.4
51
39.1
32.8
111
85.0
71.3
171
131.0
109.9
231
177.0
148.5
291
222.9
187.1
52
39.8
33.4
12
85.8
72.0
72
131.8
110.6
32
177.7
149.1
92
223.7
187.7
53
40.6
34.1
13
86.6
72.6
73
132.5
111.2
33
178.5
149.8
93
224.5
188.3
54
41.4
34.7
14
87.3
73. 3
74
133.3
111.8
34
179.3
150.4
94
225.2
189.0
55
42.1
35.4
15
88.1
73.9
75
134.1
112.5
35
180.0
151.1
95
226.0
189.6
56
42.9
36.0
16
88.9
74.6
76
134.8
113.1
36
180.8
151.7
96
226.7
190.3
57
43.7
36.6
17
89.6
75.2
77
135.6
113.8
37
181.6
152.3
97
227.5
190.9
58
44.4
37.3
18
90.4
75.8
78
136.4
114.4
38
182.3
153.0
98
228.3
191.6
59
45.2
37.9
19
91.2
76.5
79
137.1
115.1
39
183.1
153.6
99
229.0
192.2
60
46.0
38.6
20
91.9
77.1
80
137.9
115.7
40
183.9
154.3
300
229.8
192.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
50° (130°, 230°, 310°).
TABLE 2. [Page 611
Difference of Latitude and Departure for 40° (140°, 220°, 320°).
Dist.
Lat.
Dep.
Dist. Lat. Dep.
Dist.
Lat.
Dep.
Dist. I Lat.
Dep.
Dist.
Lat.
Dep.
301
230.6
193.5
361
276.5
232.1
421
322.5
270.6
481
368.5
309.2
541
414.4
347.7
02
231.3
194.1
62
277.3
232.7
22
323.3
271.3
82
369.2
309.8
42
415.2
348.4
03
232.1
194.8
63
278.1
233.3
23
324.0
271.9
83
370.0
310.5
43
416.0
349.0
04 | 232.9
195.4
64
278.8
234.0
24
324.8
272.6
84
370.8
311.1
44
416.7
349.7
05
233.6
196.1
65
279.6
234.6
25
325.6
273.2
85
371.5
311.7
45
417.5
350.3
06
234.4
196.7
66
280.4
235.3
26
326.3
273.8
86
372.3
312.4
46
418.3
351.0
07
235.2
197.3
67
281.1
235.9
27
327.1
274.5
87
373.1
313.0
47
419.0
351.6
08
235.9
198.0
68
281.9
236.6
28
327.9
275.1
88
373.8
313.6
48
419.8
352.2
09
236.7
198.6
69
282.7
237.2
29
328.6
275.8
89
374.6
314.3
49
420.6
352.9
10
237.5
199.3
70 283. 4
237.8
30
329.4
276.4
90
375.4
314.9
50
421.3
353.5
311
238.2
199.9
371 284.2
238.5
431
330.2
277.1
491
376.1
315.6
551
422.1
354.2
12 239. 0
200.6
72
285.0
239.1
32
330.9
277.7
92
376.9
316.2
52
422.9
354.8
13 239. 8
201.2
73
285.7
239.7
33
331.7
278.3
93
377.7
316.9
53
423.6
355.5
14 240.5
201.8
74
286.5
240.4
34
332.5
279.0
94
378.4
317.5
54
424.4
356.1
15
241.3
202.5
75
287.3
241.0
35
333.2
279.6
95
379.2
318.2
55
425.2
356.8
16
242. 1 203. 1
76
288.0
241.7
36
334.0
280.3
96
380.0
318.8
56
425.9
357.4
17
242.8 203.8
77
288.8
242.3
37
334.8
280.9
97
380.7
319.5
57
426.7
358.0
18
243.6
204.4
78
289.6
243.0
38
335.5
281.6
98
381.5
320.1
58
427.5
358.7
19
244.4
205.1
79
290.3
243.6
39
336.3
282.2
99
382. 3 320. 8
59
428.2
359.3
20 245. 1
205. 7
80
291. 1 244. 3
40 337. 1
282.8
500
383.0 I321.4
60
429.0
360.0
321 245. 9
206. 3
381
291.9
244.9
441 337. 8
283.5
501
383.8 322.0
561
429.8
360.6
22 246. 7
207.0
82
292.6
245.6
42
338.6
284.1
02
384.6 322.7
62
430.5
361.2
23 247. 4
207.6
83
293.4
246.2
43
339.4
284.8
03
385.3
323.3
63
431.3
361.9
24 ' 248.2
208.3
84
294.2
246.8
44
340.1
285.4
04
386.1
324.0
64
432.1
362.5
25 j 249.0
208.9
85
294.9
247.5
45
340.9
286.0
05
386.8
324.6
65
432.8
363.2
26 | 249. 7
209.6
86 295. 7
248.1
46
341r7
286.7
06
387.6
325.2
66
433.6
363.8
27 ! 250.5
210.2
87 296. 5
248.8
47
342. 4
287.3
07
388.4
325.9
67
434.3
364.5
28 ! 251.3
210.8
88 297. 2
249.4
48
343.2
288.0
08
389.2
326.5
68
435.1
365.1
29 ! 252.0 1211.5
89 i 298.0
250.1
49
344.0
288.6
09
389.9 327.1
69
435.9
365.8
30 252. 8
212.1
90 298. 8
250.7
50
344.7
289.3
10
390.7 327.8
70
436.6
366.4
331 253.6
212. 8
391 299. 5
251.3
451
345.5
289.9
511
391.5 i328.4
571
437.4
367. 0
32 i 254.3
213.4
92 300. 3 *
252.0
52 346.3 290.5
12
392. 2 i 329. 1
72
438.2
367.7
33 255. 1
214.1
93 301. 1
252.6
53 £47.0 1291.2
13
393. 0 329. 7
73
438.9
368.3
34 : 255.9
214.7
94 301.8
253.3
54 347. 8
291.8
14
393.8
330.4
74
439.7
369.0
35 256. 6
215.3
95 302. 6
253.9
55 348. 6
292.5
15
394.5
331.0
75
440.5
369.6
36 257. 4
216.0
96
303.4
254.6
56 349. 3
293.1
16
395.3 331.6
76
441.2
370.2
37 258. 2
216.6
97
304.1
255. 2
57 350. 1
293.8
17 396.1 332.3
77
442.0
370.9
38 258.9 217.3
98 304. 9
255.8
58
350.8
294.4
18
396.8 332.9
78
442.8
371.5
39 259. 7
217.9
99 305. 7
256.5
59 i 351. 6
295.0
19
397.6 333.6
79
443.5
372.2
40 260. 5
218.6
400 ! 306.4
257.1
60 352.4 295.7
20
398, 3 334. 2
80
444.3
372.8
341 261. 2
219.2
401 ! 307.2 257.8
461 i 353.1 1296.3
521
399. 1 i 334. 9
581
445.1
373.5
42 262. 0
219.8
02 i 308. 0 258. 4
62 353.9 297.0
22
399.9 335.5
82
445.8
374.1
43 262. 8
220.5
03 308. 7 259. 1
63 354. 7 ! 297. 6
23
400.6 336.1
83
446.6
374.8
44 263. 5
221.1
04 309.5 259.7
64 ! 355.4 1298.3
24
401. 4 336. 8
84
447.4
375.4
45 264.3
221.8
05 310.2 260.3
65 i 356.2 J298.9
25
402.2 1337.4
85
448.1
376.0
46
265.1
222. 4
06 311.0
261.0
66 i 357.0 |299.5
26
402.9 338.1
86
448.9
376.7
47
265.8
223! 1
07 ! 311.8 261.6
67 j 357.7 300.2
27
403.7 J338.7
87 449. 7
377.3
48
266.6
223. 7
08 ! 312.5 262.3
68 358. 5 1 300. 8
28
404.5 J339.4
88
450.4
378.0
49
267.4
224.3
09 313. 3
262.9
69 359.3 301.5
29
405.2 1340.0
89
451.2
378.6
50
268.1
225. 0
10 i 314.1
263.6
70 360.0 :302. 1
30
406.0 340.6
90 452. 0
379.2
351 268.9
225.6
411 I 314.8 ;264.2
471 360.8 302.8
531
406.8 341.3
591 452. 7
379.9
52 269. 6
226.3
12 315.6 264.8
72 361.6 303.4
32
407.5 341.9
92 453. 5
380.5
53 270. 4
226.9
13 316.4
265.5
73 i 362.3 304.0
33
408.3 342.6
93
454.3
381.2
54
271.2 1227.6
14 317. 1
266.1
74 i 363.1 304.7
34
409.1 343.2
94
455.0
381.8
55
271.9
228.2
15 317.9 266.8
75 j 363.9 305.3
35
409.8 -343.9
95
455.8
382. 4
56
272. 7
228.8
16 318.7 267.4
76 ! 364. 6 306. 0
36
410.6
344.5
96
456.6
383.1
57
273.5
229.5
17 319.4 268.1
77
365.4
306.6
37
411.4
345.2
97
457.3
383.7
58
274.2
230.1
18
320.2
268.7
78
366.2
307.3
38
412.1
345.8
98
458.1
384.4
59
275.0
230.8
19 321. 0
269.3
79
366.9
307.9
39
412.9 346.4
99
458.9
385.0
60
275.8
231.4
20 321. 7
270.0
80
367.7
308.5
40
413.7
347.1
600
459.6
385.7
Dist.
Dep.
Lat.
Dist. Dep. | Lat.
Dist. Dep.
Lat.
Dist. Dep. Lat.
Dist. Dep. Lat.
50° (130°, 230°, 310°).
Page 612] TABLE 2.
Difference of Latitude and Departure for 41° (139°, 221°, 319°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.7
61
46.0
40.0
121
91.3
79.4
181
136.6
118.7
241
181.9
158.1
2
1.5
1.3
62
46.8
40.7
22
92.1
80.0
82
137.4
119.4
42
182. 6
158.8
3
2.3
2.0
63
47.5
41.3
23
92.8
80.7
83
138.1
120.1
43
183.4
159.4
4
3.0
2.6
64
48.3
42.0
24
93.6
81.4
84
138.9
120.7
44
184.1
160.1
5
3.8
3.3
65
49.1
42.6
25
94.3
82.0
85
139.6
121.4
45
184.9
160.7
6
4.5
3.9
66
49.8
43.3
26
95.1
82.7
86
140.4
122.0
46
185.7
161.4
7
5.3
4.6
67
50.6
44.0
27
95.8
83.3
87
141.1
122.7
47
186.4
162.0
8
6.0
5.2
68
51.3
44.6
28
96.6
84.0
88
141.9
123.3
48
187.2
162.7
9
6.8
5.9
69
52.1
45.3
29
97.4
84.6
89
142.6
124.0
49
187.9
163. 4 1
10
7.5
6.6
70
52.8
45.9
30
98.1
85.3
90
143.4
124.7
50
188.7
164. 0 1
11
8.3
7.2
71
53.6
46.6
131
98.9
85.9
191
144.1
125.3
251
189.4
164. 7 1
12
9.1
7.9
72
54.3
47.2
32
99.6
86.6
92
144.9
126.0
52
190.2
165. 3 1
13
9.8
8.5
73
55.1
47.9
33
100.4
87.3
93
145.7
126.6
53
190.9
166.0
14
10.6
9.2
74
55.8
48.5
34
101.1
87.9
94
146.4
127.3
.54
191.7
166.6
15
11.3
9.8
75
56.6
49.2
35
101.9
88.6
95
147.2
127.9
55
192.5
167. 3 1
16
12.1
10.5
76
57.4
49.9
36
102.6
89.2
96
147.9
128.6
56
193.2
168. 0 1
17
12.8
11.2
77
58.1
50.5
37
103.4
89.9
97
148.7
129.2
57
194.0
168.6
18
13.6
11.8
78
58.9
51.2
38
104.1
90.5
98
149.4
129.9
58
194.7
169.3
19
14.3
12.5
79
59.6
51.8
39
104.9
91.2
99
150.2
130.6
59
195.5
169.9
20
15.1
13.1
80
60.4
52.5
40
105.7
91.8
200
150.9
131.2
60
196.2
170. 6
21
15.8
13.&
81
61.1
53.1
141
106.4
92.5
201
151.7
131.9
261
197.0
171.2
22
16.6
14.4
82
61.9
53.8
42
107.2
93.2
02
152.5
132.5
62
197.7
171.9
23
17.4
15.1
83
62.6
54.5
43
107.9
93.8
03
153.2
133.2
63
198.5
172.5
24
18.1
15.7
84
63.4
55.1
44
108.7
94.5
04
154.0
133.8
64
199.2
173. 2 I
25
18.9
16.4
85
64.2
55.8
45
109.4
95.1
05
154.7
134.5
65
200.0
173. 9
26
19.6
17.1
86
64.9
56.4
46
110.2
95.8
06
155.5
135.1
66
200.8
174.5
27
20.4
17.7
87
65.7
57.1
47
110.9
96.4
07
156.2
135.8
67
201.5
175.2
28
21.1
18.4
88
66.4
57.7
48
111.7
97.1
08
157.0
136.5
68
202.3
175.8
29
21.9
19.0
89
67.2
58.4
49
112.5
97.8
09
157.7
137.1
69
203.0
176.5
30
22.6
19.7
90
67.9
59.0
50
113.2
98.4
10
158.5
137.8
70
203.8
177.1
31
23.4
20.3
91
68.7
59.7
151
114.0
99.1
211
159.2
138.4
271
204.5
177.8
32
24.2
21.0
92
69.4
60.4
52
114.7
99.7
12
160.0
139.1
72
205.3
178.4
33
24.9
21.6
93
70.2
61.0
53
115.5
100.4
13
160.8
139.7
73
206.0
179.1
34
25.7
22.3
94
70.9
61.7
54
116.2
101.0
14
161.5
140.4
74
206.8
179.8
35
26.4
23.0
95
71.7
62.3
55
117.0
101.7
15
162.3
141.1
75
207.5
180.4
36
27.2
23.6
96
72.5
63.0
56
117.7
102. 3
16
163.0
141.7
76
208.3
181.1
37
27.9
24.3
97
73.2
63.6
57
118.5
103.0
17
163.8
142.4
77
209.1
181.7
38
28.7
24.9
98
74.0
64.3
58
119.2
103.7
18
164.5
143.0
78
209.8
182.4
39
29.4
25.6
99
74.7
64.9
59
120.0
104.3
19
165.3
143.7
79
210.6
183.0
40
30.2
26.2
100
75.5
65.6
60
120.8
105.0
20
166.0
144.3
80 211. 3
183.7
41
30.9
26.9
101
76.2
66.3
161
121.5
105.6
221
166.8
145.0
281 212. 1
184.4
42
31.7
27.6
02
77.0
66.9
62
122.3
106.3
22
167.5
145.6
82 | 212.8
185.0
43
32.5
28.2
03
77.7
67.6
63
123.0
106.9
23
168.3
146.3
83
213.6
185.7
44
33.2
28.9
04
78.5
68.2
64
123.8
107.6
24
169.1
147.0
84
214.3
186.3
45
34.0
29.5
05
79.2
68.9
65
124.5
108.2
25
169.8
147.6
85
215.1
187.0
46
34.7
30.2
06
80.0
69.5
66
125.3
108.9
26
170.6
148.3
86
215.8
187.6
47
35.5
30.8
07
80.8
70.2
67
126.0
109.6
27
171.3
148.9
87
216.6
188.3
48
36.2
31.5
08
81.5
70.9
68
126.8
110.2
28
172.1
149.6
88
217.4
188.9
49
37.0
32.1
09
82.3
71.5
69
127.5
110.9
29
172.8
150.2
89
218.1
189.6
50
37.7
32.8
10
83.0
72.2
70
128.3
111.5
30
173.6
150.9
90
218.9
190.3
51
38.5
33.5
111
83.8
72.8
171
129.1
112.2
231
174.3
151.5
291
219.6
190.9
52
39.2
34.1
12
84.5
73.5
72
129.8
112.8
32
175.1
152.2
92
220.4
191.6
53
40.0
34.8
13
85.3
74.1
73
130.6
113.5
33
175.8
152.9
93
221.1
192.2
54
40.8
35.4
14
86.0
74.8
74
131.3
114.2
34
176.6
153.5
94
221.9
.192. 9
55
41.5
36.1
15
86.8
75.4
75
132.1
114.8
35
177.4
154.2
95
222.6
193.5
56
42.3
36.7
16
87.5
76.1
76
132.8
115.5
36
178.1
154.8
96
223.4
194.2
57
43.0
37.4
17
88.3
76.8
77
133.6
116.1
37
178.9
155.5
97
224.1
194.8
58
43.8
38.1
18
89.1
77.4
78
134.3
116.8
38
179.6
156.1
98
224.9
195.5
59
44.5
38.7
19
89.8
78.1
79
135.1
117.4
39
180.4
156.8
99
225.7
196.2
60
45.3
39.4
20
90.6
78.7
80
135.8
118.1
40
181.1
157.5
300
226.4
196.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
49° (131°, 229°, 311°).
TABLE 2.
[Page 613
Difference of Latitude and Departure for 41° (139°, 221
°, 319°).
Dist.
Lat.
Dep.
Dist.
Lat | Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist
Lat.
Dep.
301 227. 2
197.5
361
272.5
236.9
421 317. 7
276. 2
481 363. 0
315.6
541
408. 3 354. 9
02 227. 9 ! 198. 1
62
273.2
237.5
22 318. 5
276. 9
82 363. 8
316.2
42
409. 0 355. 6
03 228.7 1198.8
63
274.0
238.2
23
319.2
277. 5
83 364. 5
316.9
43
409. 8 356. 2
04 229. 4 199. 4
64
274.7
238.8
24
320.0
278.2
84
365.3
317.5
44
410.6 > 356.9
05 230.2 200.1
65
275.5
239.5
25
320.8
278.8
85
366.0
318.2
45
411.3
357.5
06 | 230. 9 ! 200. 8
66
276.2
240.1
26
321.5
i 279. 5
86
366.8
318.8
46
412.1
358.2
07 ! 231. 7 1 201. 4
67
277.0
240.8
27
322.3
! 280. 1
87
367.5
319.5
47
412.8
358.8
08 | 232. 5 ! 202. 1
68
277.7
241.4
28
323.0
1280.8
88 368.3
320.1
48
413.6
359.5
09 ! 233.2 '202. 7
69
278.5
242.1
29 323. 8
281.5
89 369. 0
320.8
49
414. 3 360. 2
10 i 234. 0 ; 203. 4
70
279.2
242.7
30 324. 5
! 282. 1
90 369. 8
1321.5
50 i 415.1 360.8
311 234.7 204.0
3V 1
280.0
243.4
431 325. 3
: 282. 8
491
370.6
322.1
551 415. 8 361. 5
12 235.5 1204.7
72
280.8
244.1
32
326.0
1 283. 4
92
371.3
322.8
52
416. 6 362. 1
13 ! 236.2 ;205.4
73
281.5
244.7
33 326. 8
284. 1
93
372.1
323.4
53
417. 3 362. 8
14 1 237.0 206.0
74
282.3
245.4
34 327. 5
i 284. 7
94
372.8
324.1
54
418.1 i 363.4
15 237.7 ;206. 7
75
283.0
246.0
35 328. 3
;285.4
95
373.6
324.7
55
418. 9 364. 1
16 238.5 J207.3
76
283.8
246.7
36
329.1
286.0
96
374.3
325. 4
56
419. 6 364. 8
17 239. 2 j 208. 0
77
284.5
247.3
37
329.8
; 286. 7
97
375.1
326.0
57
420. 4 365. 4
18 240. 0 208. 6
78
285.3
248.0
38
330.6
! 287. 4
98
375. 8
326.7
58
421. 1 366. 1
19 240. 8 ! 209. 3
79
286.0
248.7
39
331.3
1 288. 0
99
376.6
327.4
59
421.9 366.7
20 241.5 1209.9
80
286.8
249.3
40
332.1
288.7
500
377.3
328.0
60 ! 422.6 367.4
321 242.3 210.6
381
287.5
250.0
441 332. 8
289.3
501
378.1
328.7
561 423. 4 368. 0
22 243.0 211.3
82
288.3
250.6
42 ! 333.6
290.0
02
378.9
329.3
62 424.1 368.7
23 243.8 211.9
83
289.1
251.3
43
334.3
290.6
03
379.6
330.0
63 424.9 369.4
24 244.5 |212.6
84
289.8
251.9
44
335.1
291.3
04
380.4
330.6
64
425.7 370.0
25
245.3
213.2
85
290.6
252. 6
45
335.8
292.0
05
381.1
331.3
65
426.4 370.7
26
246.0
213.9
86
291.3
253. 2
46
336.6
292.6
06
381.9
332. 0
66
427.2
371.3
27 246. 8
214.5
87
292.1
253. 9
47
337.4
293.3
07 382.6
332.6
67
427.9
372.0
28 247. 5
215. 2
88
292.8
254. 6
48
338.1
293.9
08
383.4
333.3
68
428. 7 372. 6
29
248.3
215.9
89
293.6
255. 2
49
338.9
294.6
09 384. 1
333.9
69
429.4
373.3
30
249.1
216.5
90
294.3
255.9
50
339.6
295.2
10 384. 9
334.6
70
430.2
374.0
331
249.8
217.2
391
295.1
256.5
451
340.4
295.9
511 385. 7
335.2
571
430.9
374.6
32
250. 6
217.8
92
295.8
257.2
52
341.1
296.5
12 386.4
335.9
72
431.7
375.3
33
251. 3
218.5
93
296.6
257. 8
53
341.9
297.2
13 387.2
336.5
73
432.4
375.9
34
252.1
219.1
94
297.4
258.5
54
342. 6
297.9
14
387. 9
337.2
74
433.2
376.6
35
252.8
219.8
95
298.1
259.2
55
343.4
298. 5
15
388.7
337.9
75
434.0
377.2
36
253.6
220.4
96
298.9
259.8
56
344.1
299.2
16
389.4
338.5
76
434.7
377.9
37
254.3
221.1
97
299.6
260.5
57
344.9
299.8
17
390.2
339.2
i 1
435.5
378.5
38
255.1
221.8
98
300.4
261.1
58
345.7
300.5
18
390.9
339.8
78
436.2
379.2
39
255.8
222.4
99
301.1
261.8
59
346.4
301.1
19
391.7
340.5
79
437. 0
379.8
40
256.6
223.1
400
301.9
262.4
60
347.2
301.8
20
392.4
341.1
80
437.7
380.5
341
257.4
223.7
401
302.6
263.1
461
347.9
302.5
521
393.2
341.8
581
438.5
3S1.2
42
258. 1
224.4
02
303.4
263.7
62
348.7
303.1
22
394.0
342. 5
82
439.2
381.8
43
258. 9
225. 0
03
304.2
264.4
63
349.4
303.8
23
394.7
343.1
83
440.0
382.5
44
259.6
225.7
04
304.9
265.1
64
350.2
304.4
24
395. 5
343.8
84
440.7
383.2
45
260.4
226.3
05
305. 7
265.7
65
350.9
305.1
25
396.2
344.4
85
441.5
383.8
46
261.1
227.0
06
306.4
266.4
66
351.7
305.7
26
397.0
345.1
86
442.3
384.5
47
261.9
227.7
07
307.2
267.0
67
352.5
306.4
27
397.7
345.7
87
443.0
385.1
48
262.6
228.3
08
307.9
267.7
68
353.2
307.0
28
398.5
346.4
88
443.8
385.8
49
263.4
229.0
09
308.7
268.3
69
354.0
307.7
29
399.2
347.0
89
444.5
386.4
50
264.2
229.6
10
309.4
269.0
70
354.7
308.4
30
400.0
347.7
90
445.3
387.1
351
264.9
230.3
411
310.2
269.6
471
355.5
309.0
531
400.7
348.4
591
446.0
387.7
52
265.7
230.9
12
310. 9
270.3
72
356.2
309.7
32
401.5
349.0
92
446.8
388.4
53
266.4
231.6
13
311.7
271.0
73
357.0
310.3
33
402.2
349.7
93
447.5
389.1
54
267.2
232.3
14
312.5
271.6
74
357.7
311.0
34
403.0
350.3
94
448.3
389.7
55
267.9
232.9
15
313.2
272.3
75
358.5 1311.6
35
403.8
351.0
95
449.1
390.4
56
268.7
233.6
16
314.0
272.9
76
359.2
312.3
36
404.5
351.6
96
449.8
391.0
57
269.4
234.2
17
314.7
273.6
77
360.0
312.9
37
405.3
352.3
97
450.6
391.7
58
270.2
234.9
18
315.5
274.2
78
360.8
313. 6
38
406.0
352.9
98
451.3
392.3
59
270.9
235.5
19
316.2
274.9
79
361.5
314.3
39 406.8
353.6
99
452.1
393.0
60
271.7
236.2
20
317.0
275.6
80
362.3
314.9
40 407. 5
354.3
600
452.8
393.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
49° (131°, 229
°, 311°).
Page 614] TABLE 2.
Difference of Latitude and Departure for 42° (138°, 222°, 318° .
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
45.3
40.8
121
89.9
81.0
181
134.5
121.1
241
179.1
161.3
2
1.5
1.3
62
46.1
41.5
22
90.7
81.6
82
135.3
121.8
42
179.8
161.9
3
2.2
2.0
63
46.8
42.2
23
91.4
82.3
83
136.0
122.5
43
180.6
162.6
4
3.0
2.7
64
47.6
42.8
24
92.1
83.0
84
136.7
123.1
44
181.3
163.3
5
3.7
3.3
65
48.3
43.5
25
92.9
83.6
85
137.5
123.8
45
182.1
163.9
6
4.5
4.0
66
49.0
44.2
26
93.6
84.3
86
138.2
124.5
46
182.8
164.6
7
5.2
4.7
67
49.8
44.8
27
94.4
85.0
87
139.0
125.1
47
183.6
165.3
8
5.9
5.4
68
50.5
45.5
28
95.1
85.6
88
139.7
125.8
48
184.3
165.9
9
6.7
6.0
69
51.3
46.2
29
95.9
86.3
89
140.5
126.5
49
185.0
166.6
10
7.4
6.7
70
52.0
46.8
30
96.6
87.0
90
141.2
127.1
50
185.8
167.3
11
8.2
7.4
71
52.8
47.5
131
97.4
87.7
191
141.9
127.8
251
186.5
168.0
12
8.9
8.0
72
53.5
48.2
32
98.1
88.3
92
142.7
128.5
52
187.3
168.6
13
9.7
8.7
73
54.2
48.8
33
98.8
89.0
93
143.4
129.1
53
188.0
169.3
14
10.4
9.4
74
55.0
49.5
34
99.6
89.7
94
144.2
129.8
54
188.8
170.0
15
11.1
10.0
75
55.7
50.2
35
100.3
90.3
95
144.9
130.5
55
189.5
170.6
16
11.9
10.7
76
56.5
50.9
36
101.1
91.0
96
145.7
131.1
56
190.2
171.3
17
12.6
11.4
77
57.2
51.5
37
101.8
91.7
97
146.4
131.8
57
191.0
172.0
18
13.4
12.0
78
58.0
52.2
38
102.6
92.3
98
147.1
132.5
58
191.7
172.6
19
14.1
12.7
79
58.7
52.9
39
103.3
93.0
99
147.9
133.2
59
192.5
173.3
20
14.9
13.4
80
59.5
53.5
40
104.0
93.7
200
148.6
133.8
60
193.2
174.0
21
15.6
14.1
81
60.2
54.2
141
104.8
94.3
201
149.4
134.5
261
194.0
174.6
22
16.3
14.7
82
60.9
54.9
42
105.5
95.0
02
150.1
135.2
62
194.7
175.3
23
17.1
15.4
83
61.7
55.5
43
106.3
95.7
03
150.9
135.8
63
195.4
176.0
24
17.8
16.1
84
62.4
56.2
44
107.0
96.4
04
151.6
136.5
64
196.2
176.7
25
18.6
16.7
85
63.2
56.9
45
107.8
97.0
05
152.3
137.2
65
196.9
177.3
26
19.3
17.4
86
63.9
57.5
46
108.5
97.7
06
153.1
137.8
66
197.7
178.0
27
20.1
18.1
87
64.7
58.2
47
109.2
^98.4
07
153.8
138.5
67
198:4
178.7
28
20.8
18.7
88
65.4
58.9
48
110.0
99.0
08
154.6
139.2
68
199.2
179.3
29
21.6
19.4
89
66.1
59.6
49
110.7
99.7
09
155.3
139.8
69
199.9
180.0
i§0
22.3
20.1
90
66.9
60.2
50
111.5
100.4
10
156.1
140.5
70
200.6
180.7
31
23.0
20.7
91
67.6
60.9
151
112.2 i 101.0
211
156.8
141.2
271
201.4
181.3
32
23.8
21.4
92
68.4
61.6
52
113.0
101.7
12
157.5
141.9
72
202.1
182.0
33-
24.5
22.1
93
69.1
62.2
53
113.7
102.4
13
158.3
142.5
73
202.9
182.7
34
25.3
22.8
94
69.9
62.9
54
114.4
103.0
14
159.0
143.2
74
203.6
183. 3
35
26.0
23.4
95
70.6
63.6
55
115.2
103.7
15
159.8
143.9
75
204.4
184.0
36
26.8
24.1
96
71.3
64.2
56
115.9
104.4
16
160.5
144. 5
76
205.1
184.7
37
27.5
24.8
97
72.1
64.9
57
116.7
105.1
17
161.3
145.2
77
205.9
185.3
38
28.2
25.4
98
72.8
65.6
58
117.4
105. 7
18
162.0
145.9
78
206.6
186.0
39
29.0
26.1
99
73.6
66.2
59
118.2
106.4
19
162.7
146.5
79
207.3
186.7
40
29.7
26.8
100
74.3
66.9
60
118.9
107.1
20
163.5
147.2
80
208.1
187.4
41
30.5
27.4
101
75.1
67.6
161
119.6
107.7
221
164.2
147.9
281
208.8
188.0
42
31.2
28.1
02
75.8
68.3
62
120.4
108.4
22
165.0
148.5
82
209.6
188.7
43
32.0
28.8.
03
76.5
68.9
63
121.1
109.1
23
165.7
-149.2
83
210.3
189.4
44
32.7
29.4
04
77.3
69.6
64
121.9
109.7
24
166.5
149.9
84
211.1
190.0
45
33.4
30.1
05
78.0
70.3
65
122.6
110.4
25
167.2
150.6
85
211.8
190.7
46
34.2
30.8
06
78.8
70.9
66
123.4
111.1
26
168.0
151.2
86
212.5
191.4
47
34.9
31.4
07
79.5
71.6
67
124.1
111.7
27
168.7
151.9
87
213.3
192.0
48
35.7
32.1
08
80.3
72.3
68
124.8
112.4
28
169.4
152.6
88
214.0
192.7
49
36.4
32.8
09
81.0
72.9
69
125.6
113.1
29
170.2
153.2
89
214.8
193.4
50
37.2
•33.5
10
81.7
73.6
70
126. 3
113.8
30
170.9
153.9
90
215.5
194.0
51
37.9
34.1
111
82.5
74.3
171
127.1
114.4
231
171.7
154.6
291
216.3
194.7
52
38.6
34.8
12
83.2
74.9
72
127.8
115.1
32
172.4
155.2
92
217.0
195.4
53
39.4
35.5
13
84.0
75.6
73
128.6
115.8
33
173.2
155.9
93
217.7
196.1
54
40.1
36.1
14
84.7
76.3
74
129.3
116.4
34
173.9
156. 6
94
218.5
196.7
55
40.9
36.8
15
85.5
77.0
75
130.1
117.1
35
174.6
15^.2
95
219.2
197.4
56
41.6
37.5
16
86.2
77.6
76
130.8
117.8
36
175.4
157. 9
96
220.0
198.1
57
42.4
38.1
17
86.9
78.3
77
131.5
118.4
37
176.1
158.6
97
220.7
198.7
58
43.1
38.8
18
87.7
79.0
78
132.3
119.1
38
176.9
159.3
98
221.5
199.4
59
43.8'
39.5
19
88.4
79.6
79
133.0
119.8
39
177.6
159.9
99
222.2
200.1
60
44.6
40.1
20
89.2
80.3
80
133.8
120.4
40
178.4
160.6
300
222.9
200.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
48° (132°, 228°, 312). .
TABLE 2. [Page 615
' ,
Difference of Latitude and Departure for 42° (138°, 222°, 318°).
Dist.
Lat. | Dep.
Dist
Lat.
Dep.
Dist
Lat. j Dep.
Dist. | Lat. Dep.
Dist. Lat. Dep.
301
223.7
201.4
361
268.3
241.6
421
312.9
281. 7
481
357.5 1321.9
541
402. 1 362. 0
02
224.4
202.1
62
269.0
242.2
2g
313.6
282.4
82
358.2
322.5
42
402.8
362.7
03
225.2
202.8
65
269.8
242.9
23
314.4
283.0
83
358.9
323.2
43
403. 5 363. 3
04
225.9
203.4
64
270.5
243.6
24
315.1
283.7
84
359.7
323.9
44
404.3
364.0
05
226.6
204.1
65
271.2
244.2
25
315.8
284.4
85
360.4
324.6
45
405.0
364.7
06
227.4
204.8
66
272.0
244.9
26
316.6
285.1
86
361.2
325.2
46
405.8
365.4
07
228.1
205. 4
67
272.7
245.6
27
317.3
285.7
87
361.9
325.9
47
406.5
366.0
08
228.9
206.1
68
273.5
246.2
28
318.1
286.4
88
362.7
326.6
48
407.2
366.7
09
229.6
206.8
69
274.2
246.9
29
318.8
287.1
89 363. 4 i 327. 2
49 408. 0
367.4
10
230.4
207.4
70
275.0
247.6
30
319.6
287.7
90 364. 1 1 327. 9
50 • 408. 7
368.0
311
231. 1
208.1
371
275. 7
248.3
431
320.3 1288.4
491
364.9 1328.6
551 409. 5
368.7
12
231.9
208.8
72
276.5
248.9
32
321.0
289. 1
92
365.6
329.2
52
410.2
369.4
13
232.6
209.4
73
277. 2
249.6
33
321.8
289. 7
93
366.4
329.9
53
411.0
370.0
14
233.3
210.1
74
277.9
250.3
34
322.5
290.4
94
367.1
330.6
54
411.7
370.7
15
234.1
210.8
75
278.7
250.9
35
323.3
291.1
95
367.9
331.3
55
412.4
371.4
16
234.8
211.5
76
279.4
251.6
36
324.0
291.7
96
368.6
331.9
56
413.2
372.0
17
235.6
212.1
77
280.2
252.3
37
324.8
292.4
97
369.3
332.6
57
413.9
372.7
18
236.3
212.8
78
280.9
252.9
38
325.5
293.1
98
370.1
333.3
58
414.7
373.4
19
237.1
213.5
79
281.7
253.6
39
326.2
293.8
99
370.8
333.9
59
415.4
374.1
20
237.8
214.1
80 282. 4
254. 3
40
327.0 1294.4
500
371.6 334.6
60
416.2
374.7
321
238.6 214.8
381 | 283. 1
254.9
441
327.7 295.1
501
372.3 335.3
561
416.9
375. 4
22
239.3 215.5
82 283.9
255.6
42
328. 5 : 295. 8
02
373.1
335.9
62
417.6
376.1
23
240.0 216.1
83 1 284.6
256.3
43
329.2
296.4
03
373.8
336.6
63
418.4
376.7
24
240.8 216.8
84 285.4
257.0
44
330.0
297.1
04
374.5
337.2
64
419.1
377.4
25
241.5 217.5
85
286.1
257. 6,
45
330.7
297.8
05
375.3
337.9
65
419.9
378.1
26
242.3 218.1
86
286.9
258.3
46
331.4
298.4
06
376.0
338.6
66
420.6
378.7
27
243.0 218.8
87
287.6
259.0
47
332. 2
299.1
07
376.8
339.3
67
421.4
379.4
28
243.8 1219.5
88 288. 3
259.6
48
332.9
299.8
08
377.5
339.9
68
422.1
380.1
29
244.5 220.1
89 i 289. 1 260. 3
49
333.7
300.4
09
378.3
340.6
69
422.8
380.7
30
245.2 220. S
90 289.8 261.0
50
334.4 301.1
10
379.0 341.3
70
423.6
381.4
331
246.0 j221.5
391 290. 6 i 261. 6
451
335.2 1301.8
511
379.7
341.9
571
424.3
382.1
32
246.7 1222.2
92 291. 3
262.3
52
335.9 302.5
12
380.5
342.6
72
425.1
382.8
33
247.5 222.8
93 292. 1
263.0
53
336.6
303.1
13
381.2
343.3
73
425.8
383.4
34
248.2
223.5
94 : 292.8
263.6
54
337.4
303.8
14
382.0
343.9
74
426.6
384.1
35
249.0
004 o
95 j 293. 5
264.3
55
338.1
304.5
15 382. 7
344.6
75
427.3
384.8
36
249.7
224! 8
96 i 294.3
265.0
56
338.9
305.1
16 383. 5
345. 3
76
428.0
385.4
37
250. 4
225.5
97 | 295. 0
265.7
57
339.6
305.8
17 384.2
346.0
77
428.8
386.1
38
251. 2
226.2
98 295. 8
266.3
58
340.4
306.5
18 1 384. 9
346.6
78
429.5
386.8
39
251.9
226.8
99 j 296. 5 267. 0
59 341. 1
307.1
19 j 385. 7
347.3
79
430.3
387. 4
40
252.7
227.5
400 297.3 267.7
60 341. S
307.8
20 386. 4
348.0
80
431.0
388.1
341
253.4
228.2
401 298.0 268.3
461 342.6 ,308.5
521
387.2
348.6
581
431.8
388.8
42
254.2 1228.8
02 I 298.7 269.0
62 343.3 309.1
22
387.9
349.3
82
432.5
389.4
43
254.9
229.5
03 | 299. 5
269.7
63 i 344.1 309.8
23
388.7
350.0
83
433.2
390.1
44
255.6
230.2
04 300.2
270.3
64 344.8 310.5
24
389.4
350.6
84
434.0
390.8
45
256.4
230.9
05 301.0
271. 0
65 i 345.6 311.2
25
390.1
351.3
85
434.7
391.4
46
257.1
231.5
06 ; 301. 7
271.7
66 346.3 311.8
26
390.9
352.0
86
435.5
392.1
47
257. 9
232.2
07 ! 302. 5
272.3
67 347.0 1312.5
27
391.6
352.6
87
436.2
392.8
48
258.6
232.9
OS 303. 2
273.0
68 347. 8 i 313. 2
28
392.4
353.3
88
437.0
393.4
49
259. 4
233.5
09 303. 9
273.7
69
348.5
313.8
29 i 393. 1
354.0
89
437.7
394.1
50
260.1
234.2
10 ' 304.7 1274.3
70
349.3
314.5
30 393. 9
354.6
90
438.4
394.8
351
260.8 234.9
411 , 305.4 275.0
471
350.0
315.2
531 394. 6
355.3
591
439.2
395.4
52
261.6 235.5
12 306. 2 275. 7
72 350. 8
315.8
32 i 395. 3
356.0
92
440.0
396.1
53
262.3
236.2
13 306. 9
276.4
73
351.5
316.5
33 1 396. 1
356.6
93
440.7
396.8
54
263.1
236.9
14 307. 7
277. 0
74
352.3
317.2
34 396.8
357.3
94
441.4
397.5
55
263.8
237.5
15
308.4
277.7
75
353.0
317.8
35 i 397.6
358.0
95
442.2
398.1
56
264.6
238.2
16
309.1
278.4
76
353.7
318.5
36 398.3 358.6
96
442.9
398.8
57
265.3
238.9
17 309. 9
279.0
77 354. 5 1 319. 2
37 399.1 359.3
97
443.7
399.5
58
266.0 239.6
18 310. 6
279.7
78 355.2 (319.9
38 399. 8 i 360. 0
98
444.4
400.1
59
266.8
240.2
19 1 311.4
280.4
79 356.0 320.5
39
400.6 360.6
99
445.2
400.8
60
267. 5
240.9
20
312.1
281.0
80 i 356. 7 321. 2
40
401.3 361.3
600
445.9
401.5
Dist.
Dep. Lat.
Dist. Dep.
Lat.
Dist. Dep. ! Lat.
Dist. Dep. Lat
Dist Dep.
Lat
48° (132°, 228°, 312°).
Page 616] TABLE 2.
Difference of Latitude and Departure for 43° (137°, 223°, 317°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
44.6
41.6
121
88.5
82.5
181
132.4
123.4
241
176.3
164.4
2
1.5
1.4
62
45.3
42.3
22
89.2
83.2
82
133.1
124.1
42
177.0
165.0
3
2.2
2.0
63
46.1
43.0
23
90.0
83.9
83
133.8
124.8
43
177.7
165.7
4
2.9
2.7
64
46.8
43.6
24
90.7
84.6
84
134.6
125.5
44
178.5
166.4
5
3.7
3.4
65
47.5
44.3
25
91.4
85.2
85
135.3
126.2
45
179.2
167.1
6
4.4
4.1
66
48.3
45.0
26
92.2
85.9
86
136.0
126.9
46
179.9
167.8
7
5.1
4.8
67
49.0
45.7
27
92.9
86.6
87
136.8
127.5
47
180.6
168.5
8
5.9
5.5
68
49.7
46.4
28
93.6
87.3
88
137.5
128.2
48
181.4
169.1
9
6.6
6.1
69
50.5
47.1
29
94.3
88.0
89
138.2
128. 9
49
182.1
169.8
10
7.3
6.8
70
51.2
47.7
30
95.1
88.7
90
139.0
129.6
50
182.8
170.5
11
8.0
7.5
71
51.9
48.4
131
95.8
89.3
191
139.7
130.3
251
183.6
171.2
12
8.8
8.2
72
52.7
49.1
32
96.5
90.0
92
140.4
130.9
52
184. 3
171.9
13
9.5
8.9
73
53.4
49.8
33
97.3
90.7
93
141.2
131.6
53
185.0
172.5
14
10.2
9.5
74
54.1
50.5
34
98.0
91.4
94
141.9
132.3
54
185. 8
173.2
15
11.0
10.2
75
54.9
51.1
35
98.7
92.1
95
142.6
133.0
55
186.5
173.9
16
11.7
10.9
76
55.6
51.8
36
99.5
92.8
96
143.3
133.7
56
187.2
174.6
17
12.4
11.6
77
56.3
52.5
37
100.2
93.4
97
144.1
134.4
57
188.0
175.3
18
13.2
12.3
78
57.0
53.2
38
100.9
94.1
98
144.8
135.0
58
188.7
176.0
19
13.9
13.0
79
57.8
53.9
39
101.7
94.8
99
145.5
135.7
59
189.4
176.6
20
14.6
13.6
80
58.5
54.6
40
102.4
95.5
200
146.3
136.4
60
190.2
177.3
21
15.4
14.3
81
59.2
55.2
141
103.1
96.2
201
147.0
137.1
261
190.9
178.0
22
16.1
15.0
82
60.0
55.9
42
103. 9
96.8
02
147.7
137.8
62
191.6
178.7
23
16.8
15.7
83
60.7
56.6
43
104.6
97.5
03
148.5
138.4
63
192.3
179.4
24
17.6
16.4
84
61.4
57.3
44
105.3
98.2
04
149.2
139.1
64
193.1
180.0
25
18.3
17.0
85
62.2
58.0
45
106.0
98.9
05
149.9
139.8
65
193.8
180.7
26
19.0
17.7
86
62.9
58.7
46
106.8
99.6
06
150.7
140.5
66
194. 5 .
181.4
27
19.7
18.4
87
63.6
59.3
47
107.5
100.3
07
151.4
141.2
67
195.3
182. 1
28
20.5
19.1
88
64.4
60.0
48
108.2
100.9
08
152.1
141.9
68
196.0
182.8
29
21.2
19.8
89
65.1
60.7
49
109.0
101.6
09
152.9
142.5
69
196.7
183.5
30
21.9
20.5
90
65.8
61.4
50
109.7
102.3
10
153.6
143.2
70
197.5
184.1
31
22.7
21.1
91
66.6
62.1
151
110.4
103.0
211
154.3
143.9
271
198.2
184.8
32
23.4
21.8
92
67.3
62.7
52
111.2
103.7
12
155.0
144.6
72
198.9
185.5
33
24.1
22.5
93
68.0
63.4
53
111.9
104.3
13
155.8
145. 3
73
199.7
186.2
34
24.9
23.2
94
68.7
64.1
54
112.6
105.0
14
156.5
145.9
74
200.4
186.9
35
25.6
23.9
95
69.5
64.8
55
113.4
105.7
15
157.2
146.6
' 75
201.1
187.5
36
26.3
24.6
96
70.2
65.5
56
114.1
106.4
16
158.0
147.3
76
201.9
188.2
37
27.1
25.2
97
70.9
66.2
57
114.8
107.1
17
158.7
148.0
77
202.6
188.9
38
27.8
25.9
98
71.7
66.8
58
115.6
107.8
18
159.4
148.7
. 78
203.3
189.6
39
28.5
26.6
99
72.4
67.5
59
116.3
108.4
19
160.2
149.4
79
204.0
190.3
40
29.3
27.3
100
73.1
68.2
60
117.0
109.1
20
160.9
150.0
80
204.8
191.0
41
30.0
28.0
101
73.9
68.9
161
117.7
109.8
221
161.6
150.7
281
205.5
191.6
42
30.7
28.6
02
74.6
69.6
62
118.5
110.5
22
162.4
151.4
82
206.2
192.3
43
31.4
29.3
03
75.3
70.2
63
119.2
111.2
23
163.1
152.1
83
207.0
193.0
44
32.2
30.0
04
76.1
70.9
64
119.9
111.8
24
163.8
152.8
84
207.7
193.7
45
32.9
30.7
05
76.8
71.6
65
120.7
112.5
25
164.6
153.4
85
208.4
194.4
46
33.6
31.4
06
77.5
72.3
66
121.4
113.2
26
165.3
154.1
86
209.2
195.1
47
34.4
32.1
07
78.3
73.0
67
122.1
113.9
27
166.0
154.8
87
209.9
195.7
48
35.1
32.7
08
79.0
73.7
68
122.9
114.6
28
166.7
155.5
88
210.6
196.4
49
35.8
33.4
09
79.7
74.3
69
123.6
115.3
29
167.5
156.2
89
211.4
197.1
50
36.6
34.1
10
80.4
75.0
70
124.3
115.9
30
168.2
156.9
90
212.1
197.8
51
37.3
34.8
111
81.2
75.7
171
125.1
116.6
231
168.9
157.5
291
212.8
198.5
52
38.0
35.5
12
81.9
76.4
72
125.8
117.3
32
169.7
158.2
92
213.6
199.1
53
38.8
36.1
13
82.6
77.1
73
126.5
118.0
33
170.4
158.9
93
214.3
199.8
54
39.5
36.8
14
83.4
77.7
74
127.3
118.7
34
171.1
159.6
94
215.0
200.5
55
40.2
37.5
15
84.1
78.4
75
128.0
119.3
35
171.9
160.3
95
215.7
201.2
56
41.0
38.2
16
84.8
79.1
76
128.7
120.0
36
172.6
161.0
96
216.5
201.9
57
41.7
38.9
17
85.6
79.8
77
129.4
120.7
37
173.3
161.6
97
217.2
202.6
58
42.4
39.6
18
86.3
80.5
78
130.2
121.4
38
174.1
162.3
98
217.9
203.2
59
43.1
40.2
19
87.0
81.2
79
130.9
122.1
39
174.8
163.0
99
218.7
203.9
60
43.9
40.9
20
87.8
81.8
80
131.6
122.8
40
175.5
163.7
300
219.4
204.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
47° (133°, 227°, 313°).
TABLE 2.
[Page 617
Difference of Latitude and
Departure for 43° (137°, 223°, 317°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat
Dep.
Dist.
Lat.
Dep.
301
220.1
205.3
361
264.0
246.2
421
307.9
287.1
481 351. 8
328.1
541
395. 7 ! 369. 0
02
220 9
206.0
62
264.8
246.9
22
308.6
287.8
82
352.5
328.7
42
396.4
369.7
03
221.6
206.7
63
265.5
247.6
23
309.4
288.5
83
353. 2
329.4
43
397.1
370.3
04
222.3
207.3
64
266.2
248.3
24
310.1
289.2
84
354.0
330.1
44
397.9
371.0
05
223.1
208.0
65
267.0
248.9
25
310.8
289.9
85
354.7
330.8
45
398.6
371.7
06
223.8
208.7
66
267.7
249.6
26
311.6
290.5
86
355.4
331.4
46
399.3
372.4
07
224.5
209.4
67
268.4
250.3
27
312.3
291.2
87
356.2
332.1
47
400.1
373.1
08
225.3
210.1
68
269.1
251.0
28
313.0
291.9
88
356.9
332.8
48
400.8
373.7
09
226. C
210.7
69
269.9
251.7
29
313.8
292.6
89
357.7
333.5
49
401.5
374.4
10
226.7
211.4
70
270.6
252.3
30
314.5
293.3
90
358.4
334.2
50
402.2
375.1
311
227.5
212.1
371
271.3
253.0
431
315.2
293.9
491
359.1
334.9
551 403. 0
375.8
12
228.2
212.8
72
272.1
253.7
32
316.0
294.6
92
359.8
335.5
52
403.7
376.5
13
228.9
213.5
73
272.8
254.4
33
316.7
295.3
93
360.6
336.2
53
404.4
377.1
14
229.7
214.2
74
273.5
255. 1
34
317.4
296.0
94
361.3
336.9
54
405.2
377.8
15
230.4
214.8
75
274.3
255.8
35
318.1
296.7
95
362.0
337.6
55
405.9
378.5
16
231.1
215.5
76
275. 0
256.4
36
318.9
297.4
96
362.8
338.3
56
406.6
379.2
17
231.8
216.2
77
275.7
257. 1
37
319.6
298.0
97
363.5
338.9
57
407.4
379.9
18
232.6
216.9
78
276.5
257.8
38
320.3
298.7
98
364.2
339.6
58
408.1
380.6
19
233.3
217.6
79
277.2
258.5
39
321.1
299.4
99 364. 9
340.3
59
408.8
381.2
20
234.0
218.2
80
277.9
259.2
40
321.8
300.1
500 365. 7
341.0
60
409.6
381.9
321
234.8
218.9
381
278.7
259.8
441
322. 5
300.8
501
366.4
341.7
561
410.3 1 382.6
22
235.5
219.6
82
279.4
260.5
42
323.3
301.4
02
367.1
342.4
62
411.0 383.3
23
236.2
220.3
83
280.1
261.2
43
324.0
302.1
03
367.8
343.0
63
411.8 384.0
24
237.0
221.0
84
280.8
261.9
44
324.7
302.8
04
368.6
343.7
64
412.5 ! 384.6
25
237.7
221.7
85
281.6
262.6
45
325. 5
303.5
05
369.3
344.4
65
413.2 385.3
26
238.4
222.3
86
282.3
263.3
46
326.2
304.2
06
370.0
345. 1
66
414.0 386.0
27
239.2
223.0
87
283.0
263.9
47
326.9
304.9
07
370.8
345.8
67
414.7 i 386.7
28
239.9
223. 7
88
283.7
264.6
48
327. 7
305. 5
08 371.5
346.5
68
415.4 i 387.4
29
240.6
224. 4
89
284.5
265.3
.49
328.4
306.2
09 372. 3
347.1
69
416. 2 ; 388. 1
30
241.4
225.1
90
285.2
266.0
50
329.1
306.9
10 ! 373. 0
347.8
70
416. 9 j 388. 7
331
242.1
225.7
391
286.0
266.7
451
329.9
307.6
511 373. 8
348.5
571
417.6 i 389.4
32
242. 8
226.4
92
286.7
267.3
52
330.6
308.3
12 | 374. 5
349.2
72
418. 3 390. 1
33
243. 5
227.1
93
287.4
268.0
53
331.3
309.0
13
375.2
349.9
73
419. 1 390. 8
34
244.3
227.8
94
288. 2
268.7
54
332.1
309.6
14
376.0
350.5
74
419. 8 391. 5
35
245.0
228.5
95
288.9
269.4
55
332.8
310.3
15
376.6
351.2
75
420.5
392.2
36
245.7
229.2
96
289.6
270.1
56
333.5
311.0
16
377.4
351.9
76
421.3
392.8
37
246.5
229.8
97
290.4
270.8
57
334.3
311.7
17
378.2
352.6
77 422. 0 393. 5
38
247.2
230. 5
98
291.1
271.4
58
335.0
312.4
18 378. 9
353. 3
78 422.7 394.2
39
247.9
231.2
99
291.8
272. 1
59
335.7
313.0
19 379. 6
3.54.0
79 i 423.5 394.9
40
248.7
231.9
400
292.6
272.8
60
336.5
313.7
20 380. 3
354.6
80 424. 2 395. 6
341
249.4
232.6
401
293.3
273.5
461
337.2
314.4
521 i 381.1
355.3
581 424. 9 396. 2
42
250.1
233.2
02
294.0
274.2
62
337.9
315.1
22 ! 381.8
356.0
82 425. 7 396. 9
43
250.9
233.9
03
294.7
274.9
63
338.7
315.8
23 382.6
356.7
83 * 426.4
397.6
44
251.6
234.6
04
295. 5
275.5
64
339.4
316.5
24
383.3
357.4
84 427. 1
398.3
45
252. 3
235.3
05
296.2
276.2
65
340.1
317.1
25
384.0
358.1
85 427. 9
399.0
46
253. 1
236.0
06
296.9
276.9
66
340.8
317.8
26
384.7
358.7
86 428. 6
399.6
47
253.8
236.7
07
297.7
277.6
67
341.6
318.5
27 385. 5
359. 4
87
429.3
400.3
48
254.5
237.3
08
298.4
278.3
68
342.3
319.2
28 386.2 360.1
88 430. 1
401.0
49
255.3
238.0
09
299.1
278.9
69
343.0
319.9
29 386.9
360.8
89 i 430. 8 401. 7
50
256.0
238.7
10
299.9
279.6
70
343.7
320. 5
30 387.6
361.5
90 431.5 : 402.4
351
256.7
239.4
411
300.6
280.3
471
344.5
321.2
531 : 388.4
362.1
591 432. 3
403.1
52
257.4
240.1
12
301.3
281.0
72
345. 2
321.9
32 389. 1
362.8
92 I 433.0
403.7
53
258.2
240.8
13
302.1
281.7
73
345.9
322.6
33 389. 9
363.5
93
433.7
404.4
54
258.9
241.4
14
302.8
282.4
74
346.7
323.3
34
390.6
364.2
94
434.5
405.1
55
259.6
242.1
15
303.5
283.0
75
347.4
324.0
35
391.3
364.9
95
435.2
405.8
56
260. 4
242.8
16
304.3
283.7
76
348.1
324.6
36
392.0
365.5
96
435.9
406.5
57
261.1
243.5
17
305.0
284.4
77
348.9
325.3
37
392.8
366.2
97
436.7
407.2
58
261.8
244.2
18
305.7
285.1
78
349.6
326.0
38
393.5
366.9
98
437.4
407.8
59
262.6
244.8
19
306.4
285.8
79
350.3
326.7
39
394.2
367.6
99
438.1
408.5
60
263.3
245.5
20
307.2
286.4
80
351.1
327.4
40
394.9
368.3
600
438.8
409.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist. Dep.
Lat.
47° (133°, 227°, 313° .
Page 618] TABLE 2.
Difference of Latitude and Departure for 44° (136°, 224°, 316°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.9
42.4
121
87.0
84.1
181
130.2
125.7
241
173.4
167.4
2
1.4
1.4
62
44.6
43.1
22
87.8
84.7
82
130.9
126.4
42
174.1
168.1
3
2.2
2.1
63
45.3
43.8
23
88.5
85.4
83
131.6
127.1
43
174.8
168.8
4
2.9
2.8
64
46.0
44.5
24
89.2
86.1
84
132.4
127.8
44
175.5
169.5
5
3.6
3.5
65
46.8
45.2
25
89.9
86.8
85
133.1
128.5
45
176.2
170.2
6
4.3
4.2
66
47.5
45.8
26
90.6
87.5
86
133.8
129.2
46
177.0
170.9
7
5.0
4.9
67
48.2
46.5
27
91.4
88.2
87
134.5
129.9
47
177.7
171.6
8
5.8
5.6
68
48.9
47.2
28
92.1
88.9
88
135.2
130.6
48
178.4
172.3
9
6.5
6.3
69
49.6
47.9
29
92.8
89.6
89
136.0
131.3
49
179.1
173.0
10
7.2
6.9
70
50.4
48.6
30
93.5
90.3
90
136.7
132.0
50
179.8
173.7
11
7.9
7.6
71
51.1
49.3
131
94.2
91.0
191
137.4
132.7
251
180.6
174.4
12
8.6
8.3
72
51.8
50.0
32
95.0
91.7
92
138.1
133.4
52
181.3
175.1
13
9.4
9.0
73
52.5
50.7
33
95.7
92.4
93
138.8
134.1
53
182.0
175.7
14
10.1
9.7
74
53.2
51.4
34
96.4
93.1
94
139.6
134.8
54
182.7
176.4
15
10.8
10.4
75
54.0
52.1
35
97.1
93.8
95
140.3
135.5
55
183.4
177.1
16
11.5
11.1
76
54.7
52.8
36
97.8
94.5
96
141.0
136.2
56
184.2
177.8
17
12.2
11.8
77
55.4
53.5
37
98.5
95.2
97
141.7
136.8
57
184.9
178.5
18
12.9
12.5
78
56.1
54.2
38
99.3
95.9
98
142.4
137.5
58
185.6
179.2
19
13.7
13.2
79
56.8
54.9
39
100.0
96.6
99
143.1
138.2
59
186.3
179.9
20
14.4
13.9
80
57.5
55.6
40
100.7
97.3
200
143.9
138.9
60
187.0
180.6
21
15.1
14.6
81
58.3
56.3
141
101.4
97.9
201
144.6
139.6
261
187.7
181.3
22
15.8
15.3
82
59.0
57.0
42
102.1
98.6
02
145.3
140,3
62
188.5
182.0
23
16.5
16.0
83
59.7
57.7
43
102.9
99.3
03
146.0
141.0
63
189.2
182.7
24
17.3
16.7
84
60.4
58.4
44
103.6
100.0
04
146.7
141.7
64
189.9
183.4
25
18.0
17.4
85
61.1
59.0
45
104.3
100.7
05
147.5
142.4
65
190.6
184.1
26
18.7
18.1
86
61.9
59.7
46
105.0
101.4
06
148.2
143.1
66
191.3
184.8
27
19.4
18.8
87
62.6
60.4
47
105.7
102.1
07
148.9
143.8
67
192.1
185.5
28
20.1
19.5
88
63.3
61.1
48
106.5
102.8
08
149.6
144.5
68
192.8
186.2
29
20.9
20.1
89
64.0
61.8
49
107.2
103.5
09
150.3
145.2
69
193.5
186.9
30
21.6
20.8
90
64.7
62.5
50
107.9
104.2
10
151.1
145. 9
70
194.2
187.6
31
22.3
21.5
91
65.5
63.2
151
108.6
104.9
211
151.8
146.6
271
194.9
188.3
32
23.0
22.2
92
66.2
63.9
52
109.3
105.6
12
152.5
147.3
72
195.7
188.9
33
23.7
22.9
93
66.9
64.6
53
110.1
106.3
13
153.2
148.0
73
196.4
189.6
34
24.5
23.6
94
67.6
65.3
54
110.8
107.0
14
153.9
148.7
74
197.1
190.3
35
25.2
24.3
95
68.3
66.0
55
111.5
107.7
15
154.7
149.4
75
197.8
191.0
36
25.9
25.0
96
69.1
66.7
56
112.2
108.4
16
155.4
150.0
76
198.5
191.7
37
26.6
25.7
97
69.8
67.4
57
112.9
109.1
17
156.1
150.7
77
199.3
192.4
38
27.3
26.4
98
70.5
68.1
58
113.7
109.8
18
156.8
151.4
78
200.0
193.1
39
28.1
27.1
99
71.2
68.8
59
114.4
110.5
19
157.5
152.1
79
200.7
193.8
40
28.8
27.8
100
71.9
69.5
60
115.1
111.1
20
158.3
152.8
80
201.4
194.5
41
29.5
28.5
101
72.7
70.2
161
115.8
111.8
221
159.0
153.5
281
202. 1
195.2
42
30.2
29.2
02
73.4
70.9
62
116.5
112.5
22
159.7
154.2
82
202.9
195.9
43
30.9
29.9
03
74.1
71.5
63
117.3
113.2
23
160.4
154.9
83
203.6
196.6
44
31.7
30.6
04
74.8
72.2
64
118.0
113.9
24
161.1
155.6
84
204.3
197.3
45
32.4
31.3
05
75.5
72.9
65
118.7
114.6
25
161.9
156.3
85
205.0
198.0
46
33.1
32.0
06
76.3
73.6
66
119.4
115.3
26
162.6
157. 0
86
205.7
198.7
47
33.8
32.6
07
77.0
74.3
67
120.1
116.0
27
163.3
157.7
87
206.5
199.4
48
34.5
33.3
08
77.7
75.0
68
120.8
116.7
28
164.0
158.4
88
207.2
200.1
49
35.2
34.0
09
78.4
75.7
69
121.6
117.4
29
164.7
159.1
89
207.9
200.8
50
36.0
34.7
10
79.1
76.4
70
122.3
118.1
30
165.4
159.8
90
208.6
201.5
51
36.7
35.4
111
79.8
77.1
171
123.0
118.8
231
166.2
160.5
291
209.3
202.1
52
37.4
36.1
12
80.6
77.8
72
123.7
119.5
32
166.9
161.2
92
210.0
202.8
53
38.1
36.8
13
81.3
78.5
73
124.4
120.2
33
167.6
161.9
93
210.8
203.5
54
38.8
37.5
14
82.0
79.2
74
125.2
120.9
34
168.3
162.6
94
211.5
204.2
55
39.6
38.2
15
82.7
79.9
75
125.9
121.6
35
169.0
163.2
95
212.2
204.9
56
40.3
38.9
16
83.4
80.6
76
126.6
122.3
36
169.8
163.9
96
212.9
205.6
57
41.0
39.6
17
84.2
81.3
77
127.3
123.0
37
170.5
164.6
97
213.6
206.3
58
41.7
40.3
18
84.9
82.0
78
128.0
123.6
38
171.2
165.3
98
214.4
207.0
59
42.4
41.0
19
85.6
82.7
79
128.8
124.3
39
171.9
166.0
99
215.1
207.7
60
43.2
41.7
20
86.3
83.4
80
129.5
125.0
40
172.6
166.7
300
215.8
208.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
46° (134°, 226°, 314°).
r
IMBMM^MHBHHiHH^^MHM^H^H^aKMHI^HMI^W^KMMaMlM^^^B^^^^^^^H^^^^^^^HH^^^^^^^^^^^^^Hl^^^H^MBBHHHHHBBH^B^HM^^^^ .,<,•-.. -. -fc.-«
TABLE 2. [Page 619
Difference of Latitude and Departure for 44° (136°, 224°, 316°).
joist.
Lat.
Dep.
Dist.
Lat.
DeP.
Dist. | Lat.
Dep.
Dist. Lat.
Dep.
Dist. Lat.
Dep.
1301
216.5
209.1
361
259.7
250.8
421
302.8
292.5
481
346.0
334.1
541
389.2
375.8
02
217.2
209.8
62
260.4
251.5
22
303.6
293.2
82
346.7
334.8
42
389.9
376.5
03
218.0
210.5
63
261.1
252. 2
23
304.3
293.8
83
347.4
335.5
43
390.6
377.2
04
218.7
211.2
64
261.8
252. 9
24
305.0
294.5
84
348.2
336.2
44
391.3
377.9
05
219.4
211.9
65
262.6
253. 6
25
305. 7
295.2
85
348.9
336.9
45
392.0
378.6
06
220.1
212.6
66
263. 3 I 254. 3
26
306.4
295. 9
86
349. 6
337. 6
46
392.8
379.3
07
220.8
213.3
67
264.0
254. 9
27
307.2
296.6
87
350.3
338. 3
47
393.5
380.0
08
221.6
214.0
68
264.7
255.6
28
307.9
297.3
88
351.0
339.0
48
394.2
380.7
09
222.3
214.7
69
265.4
256.3
29
308.6
298.0
89
351.7
339.7
49
394.9
381.4
10
223.0
215.4
70
266.2
257.0
30
309.3
298.7
90
352.5
340.4
50
395.6
382.1
311
223.7
216.0
3/1
266.9
257. 7
431
310.0
299.4
491
353.2
341.1
551 396. 4
382.7
12
224.4
216.7
72
267.6
258.4
32
310.8
300.1
92
353.9
341.8
52
397.1
383.4
13
225. 2
217.4
73
268.3
259.1
33
311.5
300.8
93
354.6
342.5
53 397. 8
384.1
14
225.9
218.1
74
269.0
259.8
34
312.2
301.5
94
355.3
343.2
54
398.5
384.8
15
226.6
218.8
75
269.8
260.5
35
312.9
302.2
95 356. 1
343.9
55
399.2
385.5
16
227.3
219.5
76
270.5
261.2
36
313.6
302.9
96
356.8
344.6
56
400.0
386.2
17
228.0
220.2
77 271. 2
261.9
37
314.4 303.6
97
357.5
345.2
57
400.7
386.9
18
228.8
220.9
78 271. 9
262.6
38
315.1 304.3
98
358.2
345.9
58
401.4
387.6
19 !
229.5
221.6
79 272. 6
263.3
39
315.8 305.0
99
358.9
346. 6
59
402.1
388.3
20
230.2 222.3
80 273. 4
264.0
40
316.5
305.7
500
359. 7
347.3
60
402.8
389.0
321
230.9
223.0
381 ! 274. 1 264. 7
441
317.2
306.4
501
360.4 348.0
561
403.6
389. 7
22 1
231.6
223.7
82 274.8 265.4
42
318.0
307.0
02
361.1 348.7
62 i 404.3
390.4
23 j
232.3 224.4
83
275.5 266.1
43
318.7
307.7
03
361.8 349.4
63 ! 405.0
391.1
24
233. 1 1 225. 1
84
276.2 266.8
44 319. 4
308.4
04
362.5 350.1
64 405. 7
391.8
25
233. 8 : 225. 8
85
276.9 267.5
45 320. 1
309.1
05
363. 3 i 350. 8
65 406.4
392.5
26 !
234.5 ;226.5
86
277.7 268.1
46 320.8 309.8
06
364.0 351.5
66 i 407. 2
393.2
27 j
235.2 1227.2
87
278.4 268.8
47 321.5
310.5
07
364.7 352.2
67 407. 9
393.9
28 i
235.9 ;227.9
88
279.1 269.5
48 322.3 311.2
08
365.4 352.9
68
408.6
394.6
29 :
236. 7 228. 6
89 I 279. 8 270. 2
49 1 323.0 311.9
09 1 366.1 353.6
69
409.3
395.3
30
237. 4 ; 229. 2
90 ' 280. 5 270. 9
50 ! 323. 7 312. 6
10 I 366.9 '354.3
70 410. 0 ! 396. 0
331
238.1 ;229.9
391 281.3 :271.6
451 ! 324. 4 : 313. 3
511 i 367. 6 355. 0
571 i 410. 7
396.7
32 !
238.8 230.6
92 ! 282.0 i272.3
52 325. 2 314. 0
12 ! 368. 3 355. 7
72 411. 5
397.3
33
239.5 231.3
93 ! 282. 7 273. 0
53 325. 9
314.7
13 j 369. 0 356. 4
73
412. 2 i 398. 0
34
240.3 232.0
94 ! 283. 4 1 273. 7
54 326. 6
315.4
14 1 369.7 357.1
74
412. 9 398. 7
35 i
241. 0 232. 7
95 ' 284. 1 i 274. 4
55 327. 3
316.1
15
370. 5 357. 8
75 413. 6 399. 4
36
241.7 1233.4
96 1 284. 9 275. 1
56 328. 0
316.8
16
371.2 1358.4
76 414. 3 i 400. 1
37 !
242.4 1234.1
97 285.6 275.8
57 328. 7
317.5
17 ! 371. 9 ' 359. 1
77 415. 1 400. 8
38 !
243.1 '234.8
98 286.3 |276.5
58 i 329.5
318.2
18
372. 6 | 359. 8
78 415. 8 401. 5
39 i
243. 9 i 235. 5
99 I 287.0 277.2
59 330.2 318.9
19 373.3 J360.5
79
416. 5 402. 2
40
244.6 236.2
400 ' 287. 7 277. 9
60
330.9 1319.6
20 : 374. 1 361. 2
80
417. 2 402. 9
f34T
245.3 236.9
401 288.5 1278.6
461 ! 331. 6 i 320. 2
521 374. 8 i 361. 9
581
417.9
403.6
42
246. 0 I 237. 6
02 289.2 279.3
62 332. 3 | 320. 9
22 375. 5 362. 6
82
418.7
404.3
43 i
246.7 1238.3
03 ! 289. 9 280. 0
63
333.1 321.6
23 376. 2
363.3
83
419.4
405.0
44
247.5 1239.0
04
290.6 280.7
64
333.8 322.3
24 376. 9
364.0
84
420.1
405.7
45
248. 2 i 239. 7
05
291.3
281.3
65
334.5 i 323.0
25
377.7
364.7
85
420.8
406.4
46 i
248. 9 240. 4
06
292.1
282.0
66
335. 2 i 323. 7
26
378.4
365. 4
86
421.5
407.1
47]
249.6
241.1
07
292.8
282.7
67
335.9 j 324. 4
27
379.1
366.1
87
422.3
407.8
48
250.3
241.7
08
293.5
283.4
68
336. 7 ! 325. 1
28
379.8
366.8
88
423.0
408.5
49
251.1 1242.4
09
294.2 284.1
69
337. 4 ; 325. 8
29
380.5
367.5
89 423. 7
409.1
50
251.8 | 243.1
10 294. 9 ! 284. 8
70
338.1 '326.5
30 381. 2
368.2
90 424. 4
409.9
351
252. 5 ! 243. 8
411 295.7 ;285.5
471
338.8 ;327.2
531 382.0 368.9
591
425.1
410.5
52
253.2 244.5
12 296.4 1286.2
72
339.5 327.9
32
382.7
369.6
92
425. 9
411.2
53
253.9 245.2
13 297.1 1286.9
73
340.3 328.6
33
383.4 370.3
93
426.6
411.9
54
254.6 245.9
14 297.8 1287.6
74
341.0 329.3
34 i 384. 1 i 371. 0
94
427.3
412.6
55
255.4 246.6
15 298.5 288.3
75 341.7 330.0
35 384.8
371.7
95
428.0
413.3
56 !
256. 1 247. 3
16 299. 2 ! 289. 0
76 342.4 330.7
36 385. 6
372.4
96
428.7
414.0
57 |
256.8 248.0
17 300. 0 ! 289. 7
77 343. 1 331. 4
37
386.3
373.1
97
429.5
414.7
58
257. 5 248. 7
18
300.7 290.4
78
343. 8 i 332. 1
38
387.0
373.7
98
430.2
415.4
59
258.2 249.4
19
301.4
291.1
79
344.6 1332.7
39 387. 7
374.4
99
430.9
416.1
60
259. 0 ! 250. 1
20
302.1
291.8
80
345.3
333.4
40 388. 4
375.1
600
431.6
416.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist. Dep.
Lat.
Dist. Dep.
Lat.
46° (134°, 226°, 314°).
Pagre 620] TABLE 2.
Difference of Latitude and Departure for 45° (135°, 225°, 315°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.1
43.1
121
85.6
85.6
181
128.0
128.0
241
170.4
170.4
2
1.4
1.4
62
43.8
43.8
22
86.3
86.3
82
128.7
128.7
42
171.1
171.1
3
2.1
2.1
63
44.5
44.5
23
87.0
87.0
83
129.4
129.4
43
171.8
171.8
4
2.8
2.8
64
45.3
45.3
24
87.7
87.7
84
130.1
130.1
44
172.5
172.5
5
3.5
3.5
65
46.0
46.0
25
88.4
88.4
85
130.8
130.8
45
173.2
173.2
6
4.2
4.2
66
46.7
46.7
26
89.1
89.1
86
131.5
131.5
46
173.9
173.9
7
4.9
4.9
67
47.4
47.4
27
89.8
89.8
87
132.2
132.2
47
174.7
174.7
8
5.7
5.7
68
48.1
48.1
28
90.5
90.5
88
132.9
132.9
48
175.4
175.4
9
6.4
6.4
69
48.8
48.8
29
91.2
91.2
89
133.6
133. 6
49
176.1
176. 1
10
7.1
7.1
70
49.5
49.5
30
91.9
91.9
90
134.4
134.4
50
176.8
176.8
11
7.8
7.8
71
50.2
50.2
131
92.6
92.6
191
135.1
135.1
251
177.5
177.5
12
8.5
8.5
72
50.9
50.9
32
93.3
93.3
92
135.8
135.8
52
178.2
178.2
13
9.2
9.2
73
51.6
51.6
33
94.0
94.0
93
136.5
136.5
53
178.9
178.9
14
9.9
9.9
74
52.3
52.3
34
94.8
94.8
94
137.2
137.2
54
179.6
179.6
15
10.6
10.6
75
53.0
53.0
35
95.5
95.5
95
137.9
137.9
55
180.3
180.3
16
11.3
11.3
76
53.7
53.7
36
96.2
96.2
96
138. 6
138.6
56
181.0
181.0
17
12.0
12.0
77
54.4
54.4
37
96.9
96.9
97
139.3
139.3
57
181.7
181.7
18
12.7
12.7
78
55.2
55.2
38
97.6
97.6
98
140.0
140.0
58
182.4
182.4
19
13.4
13.4
79
55.9
55.9
39
98.3
98.3
99
140.7
140.7
59
183.1
183.1
20
14.1
14.1
80
56.6
56.6
40
99.0
99.0
200
141.4
141.4
60
183.8
183.8
21
14.8
14.8
81
57.3
57.3
141
99.7
99.7
201
142.1
142.1
261
184.6
184.6
22
15.6
15.6
82
58.0
58.0
42
100.4
100.4
02
142.8
142.8
62
185.3
185.3
23
16.3
16.3
83
58.7
58.7
43
101.1
101.1
03
143.5
143.5
63
186.0
186.0
24
17.0
17.0
84
59.4
59.4
44
101.8
101.8
04
144.2
144.2
64
186.7
186.7
25
17.7
17.7
85
60.1
60.1
45
102.5
102.5
05
145.0
145.0
65
187.4
187.4
26
18.4
18.4
86
60.8
60.8
46
103.2
103.2
06
145.7
145.7
66
188.1
188.1
27
19.1
19.1
87
61.5
61.5
47
103.9
103.9
07
146.4
146.4
67
188.8
188.8
28
19.8
19.8
88
62.2
62.2
48
104.7
104.7
08
147.1
147.1
68
189.5
189.5
29
20.5
20.5
89
62.9
62.9
49
105.4
105.4
09
147.8
147.8
69
190.2
190.2
30
21.2
21.2
90
63.6
63.6
50
1064
106.1
10
148.5
148.5
70
190.9
190.9
31
21.9
21.9
91
64.3
64.3
151
106.8
106.8
211
, 149. 2
149.2
271
191.6
191.6
32
22.6
22.6
92
65.1
65.1
52
107.5
107.5
12
149.9
149.9
72
192.3
192.3
33
23.3
23.3
93
65.8
65.8
53
108.2
108.2
13
150.6
150.6
73
193.0
193.0
34
24.0
24.0
94
66.5
66.5
54
108.9
108.9
14
151.3
151.3
74
193.7
193.7
35
• 24.7
24.7
95
67.2
67.2
55
109.6
109.6
15
152.0
152.0
75
194.5
194.5
36
25.5
25.5
96
67.9
67.9
56
110.3
110.3
16
152.7
152.7
76
195.2
195.2
37
26.2
26.2
97
68.6
68.6
57
111.0
111.0
17
153.4
153.4
77
195.9
195.9
38
26.9
26.9
98
69.3
69.3
58
111.7
111.7
18
154.1
154.1
78
196.6
196.6
39
27.6
27.6
99
70.0
70.0
59
112.4
112.4
19
154.9
154.9
79
197.3
197.3
40
28.3
28.3
100
70.7
70.7
60
113.1
113.1
20
155.6
155.6
80
198.0
198.0
41
29.0
29.0
101
71.4
71.4
161
113.8
113.8
221
156.3
156.3
281
198.7
198.7
42
29.7
29.7
02
72.1
72.1
62
114.6
114.6
22
157.0
157.0
82
199.4
199.4
43
30.4
30.4
03
72.8
72.8
63
115.3
115.3
23
157.7
157.7
83
200.1
200.1
44
31.1
31.1
04
73.5
73.5
64
116.0
116.0
24
158.4
158.4
84
200.8
200.8
45
31.8
31.8
05
74.2
74.2
65
116.7
116.7
25
159.1
159.1
85
201.5
201.5
46
32.5
32.5
06
75.0
75.0
66
117.4
117.4
26
159.8
159.8
86
202.2
202.2
47
33.2
33.2
07
75.7
75.7
67
118.1
118.1
27
160.5
160.5
87
202.9
202.9
48
33.9
33.9
08
76.4
76.4
68
118.8
118.8
28
161.2
161.2
88
203.6
203.6
49
34.6
34.6
09
77.1
77.1
69
119.5
119.5
29
161.9
161.9
89
204.4
204.4
50
35.4
35.4
10
77.8
77.8
70
120.2
120.2
30
162.6
162.6
90
205.1
205.1
51
36.1
36.1
111
78.5
78.5
171
120.9
120.9
231
163.3
163.3
291
205.8
205.^
52
36.8
36.8
12
79.2
79.2
72
121.6
121.6
32
164.0
164.0
92
206.5
206.5
53
37.5
37.5
13
79.9
79.9
73
122.3
122.3
33
164.8
164.8
93
207.2
207.2
54
38.2
38.2
14
80.6
80.6
74
123.0
123.0
34
165.5
165.5
94
207.9
207. f
55
38.9
38.9
15
81.3
81.3
75
123.7
123.7
35
166.2
166.2
95
208.6
208.6
56
39.6
39.6
16
82.0
82.0
76
124.5
124.5
36
166.9
166.9
96
209.3
209.3
57
40.3
40.3
17
82.7
82.7
77
125.2
125.2
37
167.6
167.6
97
210.0
210.0
58
41.0
41.0
18
83.4
83.4
78
125. 9
125.9
38
168.3
168.3
98
210.7
210.7
59
41.7
41.7
19
84.1
84.1
79
126.6
126.6
39
169.0
169.0
99
211.4
211.4
60
42.4
42.4
20
84.9
84.9
80
127.3
127.3
40
169.7
169.7
300
212.1
212.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
45° (135°, 225°, 315°).
TABLE 2.
[Page 620a
Difference of Latitude and Departure for 45° (135°, 225°, 315°).
Dist.
Lat. Dep.
Dist.
Lat. :
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
212.8
212.8
361
255.3
255.3
421
297.7 297.7
481
340.1
340.1
541 382. 5
382.5
02
213.5
213.5
62
256.0
256.0
22
298.4
298.4
82
340.8
340.8
42 383.2
383.2
03
214.3
214.3
63
256. 7
256.7
23
299.1
299.1
83
341.5
341.5
43 383. 9
383.9
04
215.0
215.0
64
257. 4 :
257.4
24
299.8
299.8
84
342.2
342.2
44 384. 7
384.7
05
215.7
215.7
65
258.1 '
258.1
25
300.5
300.5
85
342.9
342.9
45 385. 4
385.4
06
216.4
216.4
66
258.8 !
258.8
26
301.2
301.2
86
343.6
343.6
46 ! 386. 1
386.1
07
217.1
217.1
67
259.5
259.5
27
301.9
301.9
87
344.3
344.3
47
386.8
386.8
08
217.8
217.8
68
260.2
260.2
28
302.6
302.6
88
345.1
345. 1
48 387. 5
387.5
09
218.5
218.5
69
260.9 i
260.9
29
303.4
303.4
89
345.8
345.8
49 388. 2
388.2
10 219.2 219.2
70
261.6
261.6
30
304.1
304.1
90
346.5
346.5
50 388. 9
388.9
311 219.9 219.9
371
262.3 i
262.3
431
304.8
304.8
491
347.2
347.2
551
389.6
389.6
12
220.6
220.6
72
263.0
263.0
32
305. 5
305. 5
92
347.9
347.9
52 390. 3
390.3
13
221.3
221.3
73
263.8 :
263.8
33
306.2
306.2
93
348.6
348.6
53 391. 0
391.0
14
222.0
222.0
74
264.5
264.5
34
306.9
306.9
94
349.3
349.3
54
391.7
391.7
15
222.7
222.7
75
265.2
265.2
35
307.6
307.6
95
350.0
350.0
55
392.4
392.4
16
223.4
223.4
76
265.9 i
265.9
36
308.3
308.3
96
350.7
350.7
56 393. 1
393.1
17
224.2 !224.2
77
266.6 ;
266.6
37
309.0
309.0
97
351.4
351.4
57 393. 9
393.9
18
224.9 224.9
78
267.3 I
267.3
38
309.7
309.7
98
352.1
352.1
58
394.6
394.6
19
225.6 225.6
79
268.0 !
268.0
39
310.4
310.4
99
352.8
352.8
59
395.3
395.3
20
226.3 226.3
80
268.7
268.7
40
311.1
311.1
500
353.5
353.5
60 396. 0
396.0
321
227. 0 i 227. 0
381
269.4
269. 4
441
311.8
311.8
501
354. 3 i 354. 3
561 396. 7
396.7
22
227.7
227.7
82
270.1
270.1
42
312.5
312.5
02
355.0
355.0
62 397. 4
397.4
23
228.4
228.4
83
270.8
270.8
43
313.3 J313.3
03
355.7
355.7
63 398. 1
398.1
24
229.1
229.1
84
271.5
271.5
44
314.0
314.0
04
356.4
356.4
64
398.8
398.8
25
229.8
229.8
85
272.2
272.2
45
314.7
314.7
05
357.1
357.1
65 399. 5
399.5
26
230.5
230.5
86
272. 9
272.9
46
315.4
315.4
06
357.8 357.8
66
400.2
400.2
27
231.2
231.2
87
273. 7 j
273.7
47
316.1
316.1
07
358.5 358.5
67 400. 9
400.9
28
231.9
231.9
88
274.4 1
274.4
48
316.8
316.8
08
359.2
359.2
68 401. 6
401.6
29
232.6
232.6
89
275.1 275.1
49
317.5
317.5
09
359.9
359.9
69 402. 3
402.3
30 233.3 J233.3
90
275.8 i
275.8
50
318.2 318.2
10
360.6
360.6
70 403. 0
403.0
331
234.1 234.1
391
276. 5 I
276.5
451
318.9
318.9
511
361.3
361.3
571 403. 8
403.8
32
234.8 234.8
92
277.2 |
277.2
52
319.6
319.6
12
362.0 1362.0
72 404.5
404.5
33 235. 5
235.5
93
277.9 i
277.9
53
320.3
320.3
13
362.7
362.7
73 405.2
405.2
34 I 236.2
236.2
94
278.6 !
278.6
54
321.0
321.0
14
363.5
363.5
74 405. 9
405.9
35 236. 9 i 236. 9
95
279.3 i
279.3
55
321.7
321.7
15
364.2
364.2
75 406. 6
406.6
36 237. 6 I 237. 6
96
280.0 ;
280.0
56
322.4
322.4
16
364.9
364.9
76 407. 3
407.3
37 238. 3 i 238. 3
97
280. 7
280.7
57
323.2
323.2
17
365.6
365.6
77
408.0
408.0
38 239.0 i 239.0
98
281.4 i
281.4
58
323.9
323.9
18
366.3 1366.3
78 408. 7
408.7
39 239.7 1239.7
99
282.1
282.1
59
324.6
324.6
19
367.0
367.0
79 409. 4
409.4
40 240.4 240.4
400
282.8 ;
282.8
60
325.3
325.3
20
367.7
367.7
80 410. 1
410.1
341
241. 1 241. 1
401
283. 6 ;
283.6
461
326.0
326.0
521
368.4
368.4
581 410.8
410.8
42
241.8 241.8
02
284.3 1
284.3
62
326.7
326.7
22
369.1
369.1
82
411.5
411.5
43
242.5
242.5
03
285.0 !
285.0
63
327.4 1327.4
23
369. 8 | 369. 8
83
412.2
412.2
44
243.2
243.2
04
285.7
285.7
64
328.1
328.1
24
370.5 370.5
84
412.9
412.9
45
244.0
244.0
05
286. 4 i
286.4
65
328.8
328.8
25
371.2
371.2
85
413.7
413.7
46
244.7 244.7
06
287.1 i
287.1
66
329.5
329. 5
26
371.9 1371.9
86
414.4
414.4
47
245.4
245.4
07
287. 8 !
287.8
67
330.2
330.2
27
372.6
372.6
87
415.1
415.1
48
246. 1 246. 1
08
288.5
288.5
68
330. 9
330.9
28
373.4
373.4
88
415.8
415.8
49
246.8 246.8
09
289.2
289.2
69
331.6
331.6
29
374.1
374.1
89
416.5
416.5
50
247.5 1247.5
10
289.9
289.9
70
332.3
332.3
30
374.8
374.8
90
417.2
417.2
351
248.2 1248.2
411
290.6
290.6
471
333.1
333.1
531
375.5
375.5
591
417.9
417.9
52
248.9 248.9
12
291.3
291.3
72
333.8
333.8
32
376.2
376.2
92
418.6
418.6
53
249.6 249.6
13
292.0
292.0
73
334.5
334.5
33
376.9
376.9
93
419.3
419.3
54
250.3 250.3
14
292.7
292.7
74
335.2
335.2
34
377.6
377.6
94
420.0
420.0
55
251.0 251.0
15
293.5
293.5
75
335.9
335.9
35
378.3
378.3
95
420.7
420.7
56
251.7 251.7
16
294.2
294.2
76
336.6
336.6
36
379.0
379.0
96
421.4
421.4
57
252.4
252.4
17
294.9
294.9
77
337. 3
337.3
37
379.7
379.7
97
422.1
422. 1
58
253.1
253.1
18
295.6
295.6
78
338.0
338.0
38
380.4
380.4
98
422.8
422.8
59
253.9
253.9
19
296.3
296.3
79
338.7
338.7
39
381.1
381.1
99
423. 6
423.6
60
254.6
254.6
20
297.0
297.0
80
339.4
339.4
40
381.8
381.8
600
424.3
424.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
45° (135°, 225°, 315°).
TAB]
Meridional Parts, or
Comp
jE 3. [Page 621
Increased Latitudes,
i
' 293.465
M.
0°
1°
go 30
4° 5°
6° 7° 8°
9°
M.
0
1
2
3
4
0.0
1.0
2.0
3.0
4.0
59.6
60.6
61.6
62.6
63.6
119.2
20.2
21.2
22.2
23.2
178.9
79.9
80.8
81.8
82.8
238.6
39.6
40.6
41.6
42.5
298.3
99.3
300.3
01.3
02.3
358.2
59.2
60.2
61.2
62.2
418.2
19.2
20.2
21.2
22.2
478.3
79.3
80.3
81.3
82.3
538.6
39.6
40.6
41.6
42.6
0
1
2
3
4
5
6
7
8
9
5.0
6.0
7.0
7.9
8.9
64.6
65.6
66.5
67.5
68.5
124.2
25.2
26.2
27.2
28.2
183.8
84.8
85.8
86.8
87.8
1 243. 5
44.5
45. 5
46.5
47.5
303.3
04.3
05.3
06.3
07.3
363.2
64.2
65.2
66.2
67.2
423.2 - 483.3
24.2 i 84.3
25. 2 85. 3
26. 2 86. 3
27. 2 87. 3
543.6
44.6
45.6
46.6
47.6
5
6
7
8
9
10
11
12
13
14
9.9
10.9
11.9
12.9
13.9
69.5
70.5
71.5
72.5
73.5
129.1
30.
31.
32.
33.
188.8
89.8
90.8
91.8
92.8
248.5
49.5
50.5
51.5
52.5
308.3
09.3
10.3
11.3
12.3
368.2
69.2
70.2
71.2
T2.2
428.2 i 488.3
29. 2 89. 3
30.2 i 90.4
31.2 91.4
32. 2 92. 4
548.6
49.6
50.6
51.7
52.7
10
11
12
13
14
15
16
17
18
19
14.9
15.9
16.9
17.9
18.9
74.5
75. 5
76.5
77.5
78.5
134.
35.1
36.1
37.1
38.1
193.8
94.8
95.8
96.8
97.8
253. 5
54.5
55. 5
56.5
57. 5
313.3
14.3
15.3
16.3
17.3
373.2
74.2
75.2
76.2
77.2
433. 2 : 493. 4
34. 2 94. 4
35.2 i 95.4
36. 2 96. 4
37.2 97.4
553.7
54.7
55.7
56.7
57.7
15
16
17
18
19
20
21
22
23
24
19.9
20.9
21.9
22.8
23.8
79.5
80.5
81.5
82.4
83.4
139. 1 198. 8
40. 1 99. 7
41. 1 200. 7
42.1 01.7
43. 1 02. 7
258.5
59.5
60.5
61.5
62.5
318.3
19.3
20.3
21.3
22.3
378.2
79.2
80.2
81.2
82.2
438. 2 j 498. 4
39. 2 99. 4
40.2 ! 500.4
41.2 01.4
42.2 02.4
558.7
59.7
60.7
61.7
62.7
20
21
22
23
24
25
26
27
28
29
24.8
25.8
26.8
27.8
28.8
84.4 144.1 203.7
85.4 45.1 04.7
86. 4 1 46. 0 05. 7
87.4 47.0 06.7
88. 4 48. 0 07. 7
263.5
64.5
65.5
66.5
67.4
323.3
24.3
25.3
26.3
27.3
383.2
84.2
85.2
86.2
87.2
443. 2 503. 4
44. 2 01. 4
45. 2 05. 4
46. 2 06. 4
47. 2 07. 4
563.7
64.7
65.7
66.8
67.8
25
26
27
28
29
30
31
32
33
34
29.8
30.8
31.8
32.8
33.8
89. 4 149. 0 208. 7
90. 4 ; 50. 0 i 09. 7
91.4 51.0 10.7
92.4 52.0 11.7
93. 4 ! 53. 0 12. 7
268.4
69.4
70.4
71.4
72.4
328.3
29.3
30.3
31.3
32.3
388.2
89.2
90.2
91.2
92.2
448.2
49.2
50.2
51.2
52.2
508.4
09.4
10.4
11.4
12.4
568.8
69.8
70.8
71.8
72.8
30
31
32
33
34
35
36
37
38
39
34.8
35.8
36.7
37.7
38.7
94. 4 ; 154. 0 j 213. 7
95. 41 55. 0 • 14. 7
96. 4 i 56. 0 15. 7
97. 3 57. 0 16. 7
98.3 ! 58.0 17.7
273,4
74.4
75.4
76.4
77.4
333.3
34.3
35.3
36.2
37.2
393.2
94.2
95.2
96.2
97.2
453.2
54.3
55.3
56.3
57.3
513.4
14.5
15.5
16.5
17.5
573.8
74.8
75.8
76.8
77.8
35
36
37
38
39
40
41
42
43
44
39.7
40.7
41.7
42.7
43.7
99.3
100.3
01.3
02.3
03.3
159. 0 218. 7
60. 0 i 19. 7
61.0 20.6
62. Oi 21.6
63.0 i 22.6
278. 4
79.4
80.4
81.4
82.4
338.2
39.2
40.2
41.2
42. 2
398.2
99.2
400.2
01.2
02.2
458.3
59.3
60.3
61.3
62.3
518.5
19.5
20.5
21.5
22.5
578.8
79.9
80.9
81.9
82.9
40
41
42
43
44
45
46
47.
48
49
44.7
45.7
46.7
47.7
48.7
104.3
05.3
06.3
07.3
08.3
164.0 i 223.6
65. 0 ! 24. 6
66. 0 i 25. 6
67. 0 26. 6
68.0 : 27.6
283.4
84.4
85.4
86.4
87.4
343.2
44.2
45.2
46.2
47.2
403.2
04.2
05.2
06.2
07.2
463.3
64.3
65.3
66.3
67.3
523.5
24.5
25.5
26.5
27.5
583.9
84.9
85.9
86.9
87.9
45
46
47
48
49
50
51
52
53
54
49.7
50.7
51.6
52.6
53.6
109.3
10.3
11.3
12.3
13.2
168.9
69.9
70.9
71.9
72.9
228.6
29.6
30.6
31.6
32.6
288. 4
89.4
90.4
91.4
92.4
348.2
49.2
50.2
51.2
52.2
408.2
09.2
10.2
11.2
12.2
468.3
69.3
70.3
71.3
72.3
528. 5
29.5
30.5
31.5
32.5
588.9
89.9
90.9
91.9
93.0
50
51
52
53
54
55
56
57
58
59
54.6
55.6
56.6
57.6
58.6
114.2
15.2
16.2
17.2
18.2
173.9 i
74.9
75.9
76.9
77.9
233.6
34.6
35.6
36.6
37.6
293.4
94.4
95.4
96.3
97.3
353.2
54.2
55.2
56.2
57.2
413. 2
14.2
15.2
16.2
17.2
473.3
74.3
75.3
76.3
1 i . O
533. 5
34.6
35.6
36.6
37.6
594.0
95.0
96.0
97.0
98.0
oo
56
57
58
59
M. 0° 1° 2° 3° 4°
IF
6= 7° 8° 9°
M.
61828°— 16 33
Page 622] TAB
Meridional Parts, or
Comp.
^ • ~~
LE 3.
Increased Latitudes,
i
2^3.465
M.
10°
~Tl°
12°
13°
14°
15°
16°
17°
18°
19°
M.
0
1
2
3
4
599.0
, 600.0
01.0
02.0
03.0
659.6
60.6
61.7
62.7
63.7
720.5
21.5
22.5
23.5
24.5
781.5
82.5
83.6
84.6
85.6
842.8
43.9
44.9
45.9
46.9
904.4
05.4
06.5
07.5
08.5
966.3
67.3
68.3
69.4
70.4
1028. 5
29.5
30.5
31.6
32.6
1091.0
92.0
93.1
94.1
95.2
1153. 9
54.9
56.0
57.0
58.1
0
' 1
2
3
4
5
6
7
8
9
604.1
05.1
06.1
07.1
08.1
664.7
65.7
66.7
67.7
68.7
725.5
26.6
27.6
28.6
29.6
786.6
87.6
88.7
89.7
90.7
847.9
49.0
50.0
51.0
52.0
909.6
10.6
11.6
12.6
13.7
971.4
72.5
73.5
74.6
75.6
1033. 7
34.7
35.7
36.8
37.8
1096. 2
97.3
98.3
99.4
1100. 4
1159. 1
60.2
61.2
62.3
63.3
5
6
7
8
9
10
11
12
13
14
609.1
10.1
11.1
12.1
13.1
669.8
70.8
71.8
72.8
73.8
730.6
31.6
32.7
33.7
34.7
791.7
92.7
93.8
94.8
95.8
853.1
54.1
55.1
56.1
57.2
914.7
15.7
16.8
17.8
18.8
976.6
77.7
78.7
79.7
80.8
1038. 9
39.9
40.9
42.0
43.0
1101.4
02.5
03.5
04.6
05.6
1164. 4
65.4
66.5
67.5
68.6
10
11
12
13
14
15
16
17
18
19
614.1
15.2
16.2
17.2
18.2
674.8
75.8
76.8
77.9
78.9
735.7
36.7
37.7
38.8
39.8
796.8
97.8
98.9
99.9
800.9
858.2
59.2
60.2
61.3
62.3
919.8
20.9
21.9
22.9
24.0
981.8
82.8
83.9
84.9
85.9
1044.1
45.1
46.1
47.2
48.2
1106. 7
07.7
08.8
09.8
10.9
1169. 7
70.7
71.8
72.8
73.9
15
16
17
18
19
20
21
22
23
24
619.2
20.2
21.2
22.2
23.2
679.9
80.9
81.9
82.9
83.9
740.8
41.8
42.8
43.8
44.9
801.9
02.9
04.0
05.0
06.0
863.3
64.3
65.4
66.4
67.4
925.0
26.0
27.1
28.1
29.1
987.0
88.0
89.0
90.1
91.1
1049. 3
-50.3
51.3
52.4
53.4
1111.9
13.0
14.0
15.0
16.1
1174. 9
76.0
77.0
78.1
79.1
20
21
22
23
24
25
26
27
28
29
624.2
25.3
26.3
27.3
28.3
684.9
86.0
87.0
88.0
89.0
745.9
46.9
47.9
48.9
49.9
807.0
08.1
09.1
10.1
11.1
868.5
69.5
70.5
71.5
72.6
930.1
31.2
32.2
33.2
34.3
992.1
93.2
94.2
95.3
96.3
1054. 5
55.5
56.6
57.6
58.6
1117. 1
~I8. 2
19.2
20.3
21.3
1180. 2
81.2
82.3
83.3
84.4
25
26
27
28
29
30
31
32
33
34
629.3
30.3
31.3
32.3
33.3
690.0
91.0
92.0
93.1
94.1
751.0
52.0
53.0
54.0
55.0
812.1
13.2
14.2
15.2
16.2
873.6
74.6
75.6
76.7
77.7
935.3
36.3
37.4
38.4
39.4
997.3
98.4
99.4
1000. 4
01.5
1059. 7
60.7
61.8
62.8
63.9
1122. 4
23.4
24.5
25.5
26.6
1185. 5
86.5
87.6
88.6
89.7
30
31
32
33
34
35
36
37
38
39
634.3
35.4
36.4
37.4
38.4
695.1
96.1
97.1
98.1
99.1
756.0
57.1
58.1
59.1
60.1
817.3
18.3
19.3
20.3
21.3
878.7
79.7
80.8
81.8
82.8
940.5
41.5
42.5
43.6
44.6
1002. 5
03.6
04.6
05.6
06.7
1064. 9
65.9
67.0
68.0
69.1
1127. 6
28.7
29.7
30.8
31.8
1190. 7
91.8
92.8
93.9
95.0
35
36
37
38
39
40
41
42
43
44
639.4
40.4
41.4
42.4
43.4
700.2
01.2
02.2
03.2
04.2
761.1
62.2
63.2
64.2
65.2
822.4
23.4
24.4
25.4
26.5
883.8
84.9
85.9
86.9
88.0
945.6
46.7
47.7
48.7
49.7
1007. 7
08.7
09.8
10.8
11.8
1070. 1
71.2
72.2
73.2
74.3
1132. 9
33.9
35.0
36.0
37.1
1196. 0
97.1
98.1
99.2
1200. 2
40
41
42
43
44
45
46
47
48
49
644.5
45.5
46.5
47.5
48.5
705.2
06.2
07.3
08.3
09.3
766.2
67.3
68.3
69.3
70.3
827.5
28.5
29.5
30.5
31.6
889.0
90.0
91.0
92.1
93.1
950.8
51.8
52.8
53.9
54.9
1012. 9
13.9
15.0
16.0
17.0
1075. 3
76.4
77.4
78.5
79.5
1138. 1
39.2
40.2
41.3
42.3
1201.3
02.3
03.4
04.5
05.5
45
46
47
48
49
50
51
52
53
54
649.5
50.5
51.5
52.5
53.6
710.3
11.3
12.3
13.4
14.4
771.3
72.3
73.4
74.4
75.4
832.6
33.6
34.6
35.7
36.7
894.1
95.2
96.2
97.2
98.2
955.9
57.0
58.0
59.0
60.1
1018. 1
19.1
20.2
21.2
22.2
1080. 5
81.6
82.6
83.7
84.7
1143. 4
44.4
45.5
46.5
47.6
1206. 6
07.6
08.7
09.7
10.8
50
51
52
53
54
55
56
57
58
59
654.6
55.6
56.6
57.6
58.6
715.4
16.4
17.4
18.4
19.4
776.4
77.4
78.5
79.5
80.5
837.7
38.7
39.8
40.8
41.8
899.3
900.3
01.3
02.3
03.4
961.1
62.1
63.2
64.2
65.2
1023. 3
24.3
25.3
26.4
27.4
1085. 8
86.8
87.9
88.9
89.9
1148. 6
49.7
50.7
51.8
52.8
1211.8
12.9
14.0
15.0
16.1
55
56
57
58
59
M.
10°
11°
12°
13°
14°
15°
10°
17° 1 18°
19°
M.
TABI
Meridional Parts, or
Comp
^E 3. [Page 623
Increased Latitadee.
i
293.465
M.
20°
21°
22°
28°
24°
25°
26°
27°
28°
29°
M.
0
1
2
3
4
1217. 1
18.2
19.3
20.3
21.4
1280.8
81.9
82.9
84.0
85.1
1344.9
46.0
47.1
48.1
49.2
1409.5
10.6
11.6
12.7
13.8
1474. 5
75.6
76.7
77.8
78.9
1540.1
41.2
42.3
43.4
44.5
1606.2
07.3
08.4
09.5
10.6
1672. 9
74.0
75.1
76.2
77.4
1740. 2
41.3
42.4
43.6
44.7
1808.1
09.2
10.4
11.5
12.6
0
1
2
3
4
5
6
7
8
9
1222. 4
23.5
24.5
25.6
26.7
1286. 1
87.2
88.3
89.3
90.4
1350.3
51.4
52.4
53.5
54.6
1414. 9
16.0
17.1
18.1
19.2
1480. 0
81.1
82.2
83.3
84.3
1545.6
46.7
47.8
48.9
50.0
1611. 7
12.9
14.0
15.1
16.2
1678. 5
79.6
80.7
81.8
82.9
1745.8
46.9
48.1
49.2
50.3
1813. 8
14.9
16.1
17.2
18.3
5
6
7
8
9
10
11
12
13
14
1227. 7
28.8
29.8
30.9
32.0
1291.5
92.5
93.6
94.7
95.7
1355. 7
56.7
57.8
58.9
59.9
1420. 3
21.4
22.5
23.5
24.6
1485.4
86.5
87.6
88.7
89.8
1551. 1
52.2
53.3
54.4
55.5
1617. 3
18.4
19.5
20.6
21.7
1684.1
85.2
86.3
87.4
88.5
1751. 5
52.6
53.7
54.8
56.0
1819. 5
20.6
21.8
22.9
24.0
10
11
12
13
14
15 1233. 0
16 34. 1
17 35.1
18 1 36.2
19 i 37. 3
1296. 8
97.9
98.9
1300.0
01.1
1361. 0
62.1
63.2
64.2
65.3
1425. 7
26.8
27.9
29.0
30.0
1490.9
92.0
93.1
94.2
95.2
1556. 6
57. 7
58.8
59.9
61.0
1622. 8
23.9
25.0
26.2
27.3
1689. 7
90.8
91.9
93.0
94.1
1757. 1
58.2
59.4
60.5
61.6
1825.2
26.3
27.5
28.6
29.7
15
16
17
18
19
20
21
22
23
24
1238. 3
39.4
40.4
41.5
42.6
1302. 1
03.2
04.3
05.3
06.4
1366. 4
67.5
68.5
69.6
70.7
1431. 1
32.2
33.3
34.4
35.4
1496. 3
97.4
98.5
99.6
1500.7
1562. 1
63.2
64.3
65.4
66.5
1628. 4
29.5
30.6
31.7
32.8
1695. 3
96.4
97.5
98.6
99.7
1762. 7
63.9
65.0
66.1
67.3
1830. 9
32.0
33.2
34.3
35.4
20
21
22
23
24
25 : 1243.6
26 i 44.7
27 ' 45. 7
28 46. 8
29 47.9
1307. 5
08.5
09.6
10.7
11.7
1371.8
72.8
73.9
75.0
76.1
1436. 5
37.6
38.7
39.8
40.9
1501. 8
02.9
04.0
05.1
06.2
1567. 6
68.7
69.8
70.9
72.0
1633. 9
35.0
36.1
37.3
38.4
1700.9
02.0
03.1
04.2
05.3
1768.4
69.5
70.7
71.8
72.9
1836. 6
37.7
38.9
40.0
41.2
25
26
27
28
29
30 ; 1248.9
31 50. 0
32 i 51. 0
33 1 52. 1
34 53.2
1312. 8 1377. 1
13. 9 78. 2
14. 9 79. 3
16. 0 80. 4
17. 1 81. 5
1442.0
43.0
44.1
45.2
46.3
1507. 3
08.4
09.4
10.5
11.6
1573. 1
74.2
75.3
76.4
77.5
1639. 5
40.6
41.7
42.8
43.9
1706.5
07.6
08.7
09.8
10.9
1774.1
75.2
76.3
77.4
78.6
1842.3
43.4
44.6
45.7
46.9
30
31
32
33
34
35
36
37
38
39
1254. 2
55.3
56.4
57.4
58.5
1318. 2
19.2
20.3
21.4
22.4
1382.5 i 1447.4
83.6 48.5
84.7 i 49.5
85. 8 50. 6
86.8 I 51.7
1512. 7
13.8
14.9
16.0
17.1
1578. 6
79.7
80.8
81.9
83.0
1645.0
46.2
47.3
48.4
49.5
1712. 1
13.2
14.3
15.4
16.6
1779. 7
80.8
82.0
83.1
84.2
1848. 0
49.2
50.3
51.4
52.6
35
36
37
38
39
40
41
42
43
44
1259.5 1323.5 i 1387.9
60. 6 24. 6 89. 0
61. 7 25. 6 i 90. 1
62.7 26.7 91.1
63. 8 27. 8 I 92. 2
1452. 8
53.9
55.0
56.1
57.1
1518. 2
19.3
20.4
21.5
22.6
1584.1
85.2
86.3
87.4
88.5
1650. 6 1717. 7
51. 7 18. 8
52. 8 19. 9
53. 9 21. 1
55.1 i 22.2
1785.4
86.5
87.6
88.8
89.9
1853.7
54.9
56.0
57.2
58.3
40
41
42
43
44
45
46
47
48
49
1264.9
65.9
67.0
68.0
69.1
1328.9
29.9
31.0
32.1
33.1
1393. 3
- 94.4
95.5
96.5
97.6
1458.2
59.3
60.4
61.5
62.6
1523. 7
24.8
25.9
27.0
28.0
1589. 6
90.7
91.8
92.9
94.1
1656.2
57.3
58.4
59.5
60.6
1723. 3
24.4
25.5
26.7
27.8
1791.1
92.2
93.3
94.5
95.6
1859.5
60.6
61.8
62.9
64.0
45
46
47
48
49
50
51
52
53
54
1270. 2
71.2
72.3
73.4
74.4
1334. 2
35.3
36.3
37.4
38.5
1398. 7
99.8
1400.9
01.9
03.0
1463. 7
64.8
65.8
66.9
68.0
1529.1
30.2
31.3
32.4
33.5
1595. 2
96.3
97.4
98.5
99.6
1661.7
62.9
64.0
65.1
66.2
1728. 9
30.0
31.2
32.3
33.4
1796. 7
97.9
99.0
1800.1
01.3
1865.2
66.3
67.5
68.6
69.8
50
51
52
53
54
55
56
57
58
59
1275. 5
76.6
77.6
78.7
79.7
1339. 6
40.6
41.7
42.8
43.8
1404. 1
05.2
06.2
07.3
08.4
1469.1
70.2
71.3
72.4
73.5
1534.6
35.7
36.8
37.9
39.0
1600.7
01.8
02.9
04.0
05.1
1667.3
68.4
69.5
70.7
71.8
1734. 5
35.7
36.8
37.9
39.1
1802. 4
03.5
04.7
05.8
07.0
1870. 9
72.1
73.2
74.4
75.5
55
56
57
58
59
M.
20°
21°
22°
23°
24° 25° 26° -21°
28°
29°
If.
Page 624] TABI
Meridional Parts, or
Comp.
,E 3.
Increased Latitudes.
1
293.465
M.
30°
31°
32°
33°
34°
35° 36°
37°
38°
39°
M.
0
1
2
3
4
1876. 7
77.8
79.0
80.1
81.3
1946. 0
47.1
48.3
49.4
50.6
2016. 0
17.2
18.3
19.5
20.7
2086. 8
88.0
89.2
90.3
91.5
2158. 4
59.6
60.8
62.0
63.2
2230. 9
32.1
33.3
34.5
35.7
2304. 2
05.5
06.7
07.9
09.2
2378. 5
79.8
81.0
82.3
83.5
2453. 8
55.1
56.4
57.6
58.9
2530. 2
31.5
32.8
34.0
35.3
0
1
2
3
4
5
6
7
8
9
1882. 4
83.6
84.7
85.9
87.0
1951. 8
52.9
54.1
55.3
56.4
2021. 9
23.0
24.2
25.4
26.6
2092. 7
93.9
95.1
96.3
97.5
2164. 4
65.6
66.8
68.0
69.2
2236. 9
38.2
39.4
40.6
41.8
2310. 4
11.6
12.9
14.1
15.3
2384. 8
86.0
87.3
88.5
89.8
2460. 2
61.4
62.7
64.0
65.2
2536. 6
37.9
39.2
40.5
41.7
5
6
7
8
9
10
11
12
13
14
1888. 2
89.3
90.5
91.6
92.8
1957. 6
58.7
59.9
61.1
62.2
2027. 7
28.9
30.1
31.3
32.4
2098. 7
99.8
2101. 0
02.2
03.4
2170. 4
71.6
72.8
74.0
75.2
2243. 0
44.2
45.5
46.7
47.9
2316. 5
17.8
19.0
20.3
21.5
2391. 0
92.3
93.5
94.8
96.0
2466. 5
67.8
69.0
70.3
71.6
2543. 0
44.3
45.6
46.9
48.2
10
11
12
13
14
15
16
17
18
19
1893. 9
95.1
96.2
97.4
98.5
1963. 4
64.6
65.7
66.9
68.1
2033. 6
34.8
36.0
37.1
38.3
2104. 6
05.8
07.0
08.2
09.4
2176. 4
77.6
78.8
80.0
81.2
2249. 1
50.3
51.6
52.8
54.0
2322. 7
24.0
25.2
26.4
27.7
2397. 3
98.5
99.8
2401. 0
02.3
2472. 8
74.1
75.4
76.6
77.9
2549. 5
50.7
52.0
53.3
54.6
15
16
17
18
19
20
21
22
23
24
1899. 7
1900. 8
02.0
03.1
04.3
1969. 2
70.4
71.5
72.7
73.9
2039. 5
40.7
41.8
43.0
44.2
2110. 6
11.8
12.9
14.1
15.3
2182. 5
83.7
84.9
86.1
87.3
2255. 2
56.4
57.7
58.9
60.1
2328. 9
30.1
31.4
32.6
33.8
2403. 5
04.8
06.0
07.3
08.5
2479. 2
80.4
81.7
83.0
84.3
2555. 9
57.2
58.5
59.8
61.0
20
21
22
23
24
25
26
27
28
29
1905. 5
06.6
07.8
08.9
10.1
1975. 0
76.2
77.4
78.5
79.7
2045. 4
46.6
47.7
48.9
50.1
2116. 5
17.7
18.9
20.1
21.3
2188. 5
89.7
90.9
92.1
93.3
2261. 3
62.5
63.8
65.0
66.2
2335. 1
36.3
37.6
38.8
40.0
2409. 8
11.1
12.3
13.6
14.8
2485. 5
86.8
88.1
89.3
90.6
2562. 3
63.6
64.9
66.2
67.5
25
26
27
28'
29
30
31
32
33
34
1911.2
12.4
13.5
14.7
15.8
1980. 9
82.0
83.2
84.4
85.5
2051. 3
52.5
53.6
54.8
56.0
2122. 5
23.7
24.9
26.1
27.3
2194. 5
95.7
96.9
98.1
99.4
2267. 4
68.7
69.9
71.1
72.3
2341. 3
42.5
43.7
45.0
46.2
2416. 1
17.3
18.6
19.8
21.1
2491. 9
93.2
94.4
95.7
97.0
2568. 8
70.1
71.4
72.7
73.9
30
31
32
33
34
35
36
37
38
39
1917. 0
18.2
19.3
20.5
21.6
1986. 7
87.9
89.1
90.2
91.4
2057. 2
58.4
59.5
60.7
61.9
2128. 5
29.6
30.8
32.0
33.2
2200. 6
01.8
03.0
04.2
05.4
2273. 5
74.8
76.0
77.2
78.4
2347. 5
48.7
49.9
51.2
52.4
2422. 3
23.6
24.9
26.1
27.4
2498. 3
99.5
2500. 8
02.1
03.4
2575. 2
76.5
77.8
79.1
80.4
35
36
37
38
39
40
41
42
43
44
1922. 8
23.9
25.1
26.3
27.4
1992. 6
93.7
94.9
96.1
97.2
2063. 1
64.3
65.5
66.6
67.8
2134. 4
35.6
36.8
38.0
39.2
2206. 6
07.8
09.0
10.2
11.5
2279. 7
80.9
82.1
83.3
84.6
2353. 7
54.9
56.1
57.4
58.6
2428. 6
29.9
31.2
32.4
33.7
2504. 6
05.9
07.2
08.5
09.7
2581. 7
83.0
84.3
85.6
86.9
40
41
42
43
44
45
46
47
48
49
1928. 6
29.7
30.9
32.0
33.2
1998. 4
99.6
2000. 7
01.9
03.1
2069. 0
70.2
71.4
72.6
73.7
2140. 4
41.6
42.8
44.0
45.2
2212. 7
13.9
15.1
16.3
17.5
2285. 8
87.0
88.3
89.5
90.7
2359. 9
61.1
62.4
63.6
64.8
2434. 9
36.2
37.4
38.7
40.0
2511. 0
12.3
13.6
14.8
16.1
2588. 2
89.5
90.8
92.1
93.4
45
46
47
48
49
50
51
52
53
54
1934. 4
35.5
36.7
37.8
39.0
2004. 3
05.4
06.6
07.8
08.9
2074. 9
76.1
77.3
78.5
79.7
2146. 4
47.6
48.8
50.0
51.2
2218. 7
19.9
21.1
22.4
23.6
2291. 9
93.2
94.4
95.6
96.9
2366. 1
67.3
68.6
69.8
71.1
2441. 2
42.5
43.7
45.0
46.3
2517. 4
18.7
20.0
21.2
22.5
2594. 7
96.0
97.3
98.5
99.8
50
51
52
53
54
55
56
57
58
59
1940. 2
41.3
42.5
43.6
44.8
2010. 1
11.3
12.5
13.6
14.8
2080. 8
82.0
83.2
84.4
85.6
2152. 4
53.6
54.8
56.0
57.2
2224. 8
26.0
27.2
28.4
29.6
2298. 1
99.3
2300. 5
01.8
03.0
2372. 3
73.6
74.8
76.1
77.3
2447.5
48.8
50.1
51.3
er» a
2523. 8
25.1
26.4
27.6
28.9
2601. 1
02.4
03.7
05.0
06.3
55
56
57
58
59
M.
80°
31° 32°
33°
34°
85°
36°
37°
38°
30°
M.
TAB
Meridional Parts, or
Comp
LE 3. [Page 625
Increased Latitudes.
•
l
293.465
M.
40°
41°
42°
43°
44°
45°
46°
47°
48°
49°
M.
0
1
2
3
4
2607. 6
08.9
10.2
11.5
12.8
2686. 2
87.6
88.9
90.2
91.5
2766.0
67.4
68.7
70.1
71.4
2847.1
48.5
49.9
51.2
52.6
2929.5
30.9
32.3
33.7
35.1
3013. 4
14.8
16.2
17.6
19.0
3098.7
3100.1
01.6
03.0
04.4
3185. 6
87.1
88.5
90.0
91.4
3274. 1
75.6
77.1
78.6
80.1
3364.4
65.9
67.4
69.0
70.5
0
1
2
3
4
5
6
7
8
9
2614. 1
15.4
16.8
18.1
19.4
2692. 8
94.2
95.5
96.8
98.1
2772. 8
74.1
75.4
76.8
78.1
2853.9
55.3
56.7
58.0
59.4
2936.5
37.9
39.3
40.6
42.0
3020. 4
21.8
23.3
24.7
26.1
3105. 9
07.3
08.8
10.2
11.6
3192. 9
94.4
95.8
97.3
98.8
3281. 6
83.1
84.6
86.1
87.6
3372. 0
73.5
75.1
76.6
78.1
5
6
7
8
9
10
11
12
13
14
2620. 7
22.0
23.3
24.6
25.9
2699. 5
2700.8
02.1
03.4
04.8
2779. 5
80.8
82.2
83.5
84.8
2860.8
62.1
63.5
64.9
66.2
2943.4
44.8
46.2
47.6
49.0
3027. 5
28.9
30.3
31.7
33.2
3113. 1
14.5
16.0
17.4
18.8
3200.2
01.7
03.2
04.6
06.1
3289. 0
90.5
92.0
93.5
95.0
3379. 6
81.2
82.7
84.2
85.7
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
2627. 2
28.5
29.8
31.1
32.4
2706.1
07.4
08.7
10.1
11.4
2786. 2
87.5
88.9
90.2
91.6
2867. 6
69.0
70.3
71.7
73.1
2950.4
51.8
53.2
54.5
55.9
3034. 6
36.0
37.4
38.8
40.2
3120. 3
21.7
23.2
24.6
26.0
3207. 6
09.0
10.5
12.0
13.4
3296. 5
98.0
99.5
3301. 0
02.5
3387. 3
88.8
90.3
91.8
93.4
15
16
17
18
19
2633. 7
35.0
36.3
37.6
38.9
2712. 7
14.0
15.4
16.7
18.0
2792. 9
94.3
95.6
97.0
98.3
2874. 4
75.8
77.2
78.6
79.9
2957.3
58.7
60.1
61.5
62.9
3041.7
43.1
44.5
45.9
47.3
3127. 5
28.9
30.4
31.8
33.3
3214. 9
16.4
17.9
19.3
20.8
3304.0
05.5
07.0
08.5
10.0
3394. 9
96.4
98.0
99.5
3401.0
20
21
22
23
24
25
26
27
28
29
2640.2
41.6
42.9
44.2
45.5
2719. 3
20.7
22.0
23.3
24.7
2799. 7
2801. 0
02.4
03.7
05.1
2881. 3
82.7
84.0
85.4
86.8
2964.3
65.7
67.1
68.5
69.9
3048. 7
50.2
51.6
53.0
54.4
3134. 7
36.2
37.6
39.0
40.5
3222. 3
23.7
25.2
26.7
28.2
3311.5
13.0
14.5
16.0
17.5
3402. 6
04.1
05.6
07.2
08.7
25
26
27
28
29
30
31
32
33
34
2646.8
48.1
49.4
50.7
52.0
2726. 0
27.3
28.6
30.0
31.3
2806. 4
07.8
09.1
10.5
11.8
2888. 2 2971. 3
89. 5 72. 7
90. 9 74. 1
92.3 75.5
93. 7 76. 9
3055.9
57.3
58.7
60.1
61.5
3141.9
43.4
44.8
46.3
47.7
3229.6
31.1
32.6
34.1
35.6
3319. 0
20.5
22.1
23.6
25.1
3410. 2
11.8
13.3
14.8
16.4
30
31
32
33
34
35
36
37
38
39
2653. 3
54.7
56.0
57.3
58.6
2732.6 ; 2813.2
34.0 14.5
35.3 ; 15.9
36.6 i 17.2
38.0 i 18.6
2895. 0 2978. 3
96. 4 79. 7
97. 8 81. 1
99. 2 82. 5
2900.5 83.9
3063.0
64.4
65.8
67.2
68.7
3149. 2
50.6
52.1
53.5
55.0
3237. 0
38.5
40.0
41.5
42.9
3326. 6
28.1
29.6
31.1
32.6
3417.9
19.5
21.0
22.5
24.1
35
36
37
38
39
40
41
42
43
44
2659.9
61.2
62.5
63.9
65.2
2739. 3
40.6
42.0
43.3
44.6
2820. 0
21.3
22.7
24.0
25.4
2901.9 2985.3
03.3 86.7
04.7 ! 88.1
06.1 89.5
07. 4 i 90. 9
3070. 1
71.5
72.9
74.4
75.8
3156. 4
57.9
59.4
60.8
62.3
3244.4
45.9
47.4
48.9
50.3
3334. 1
35.6
37.1
38.6
40.2
3425. 6
27.2
28.7
30.2
31.8
40
41
42
43
44
45 2666. 5
46 i 67.8
47 '' 69.1
48 70. 4
49 71. 7
2746. 0
47.3
48.6
50.0
51.3
2826. 7
28.1
29.4
30.8
32.2
2908.8 2992.3
10. 2 ! 93. 7
11.6 ! 95.1
13. 0 ! 96. 5
14.3 i 97.9
3077. 2
78.7
80.1
81.5
82.9
3163. 7
65.2
66.6
68.1
69.5
3251.8
53.3
54.8
56.3
57.8
3341.7
43.2
44.7
46.2
47.7
3433. 3
34.9
36.4
38.0
39.5
45
46
47
48
49
50 2673. 1
51 74. 4
52 j 75. 7
53 I 77. 0
54 78. 3
2752. 7
54.0
55.3
56.7
58.0
2833. 5
34.9
36.2
37.6
39.0
2915.7 2999.3
17. 1 3000. 7
18. 5 02. 1
19.9 03.5
21.2 i 04.9
3084.4
85.8
87.2
88.7
90.1
3171.0
72.5
73.9
75.4
76.8
3259. 3
60.7
62.2
63.7
65.2
3349.2
50.8
52.3
53.8
55.3
3441.0
42.6
44.1
45.7
47.2
50
51
52
53
54
55
56
57
58
59
2679. 6
81.0
82.3
83.6
84.9
2759. 3
60.7
62.0
63.4
64.7
2840.3
41.7
43.0
44.4
45.8
2922.6 3006.3
24. 0 07. 7
25.4 09.2
26. 8 10. 6
28. 2 12. 0
3091. 5
93.0
94.4
95.8
97.3
3178. 3
79.7
81.2
82.7
84.1
3266. 7
68.2
69.7
71.1
72.6
3356.8
58.3
59.9
61.4
62.9
3448.8
50.3
51.9
53.4
55.0
55
56
57
58
59
M.
••MM
40°
41°
42°
43° 44°
45°
46°
47°
48° 49°
M.
Page 626] TAB!
Meridional Parts, or
Comp.
^E 3. 1
Increased Latitudes. ]
1
293.466
M.
60°
51°
62°
68°
&4°
55°
66°
57°
58°
59°
M.
0
1
2
3
4
3456. 5
58.1
59.6
61.2
62.7
3550. 6
52.2
53.8
55.4
56.9
3646. 7
48.4
50.0
51.6
53.2
3745.1
46.7
48.4
50.0
51.7
3845. 7
47.4
49.1
50.8
52.5
3948. 8
50.5
52.3
54.0
55.7
4054. 5
56.3
58.1
59.8
61.6
4163. 0
64.8
66.6
68.5
70.3
4274. 4
76.3
78.2
80.1
82.0
4389. 1
91.0
92.9
94.9
96.8
0
1
2
3
4
5
6
7
8
9
3464.3
65.9
67.4
69.0
70.5
3558. 5
60.1
61.7
63.3
64.9
3654. 8
56.5
58.1
59.7
61.3
3753. 4
55.0
56.7
58.3
60.0
3854. 2
55.9
57.6
59.3
61.0
3957. 5
59.2
61.0
62.7
64.5
4063. 4
65.2
67.0
68.8
70.6
4172. 1
74.0
75.8
77.7
79.5
4283. 9
85.7
87.6
89.5
91.4
4398. 8
4400. 7
02.6
04.6
06.5
5
6
7
8
9
10
11
12
13
14
3472. 1
73.6
75.2
76.7
78.3
3566. 5
68.1
69.7
71.3
72.8
3663. 0
64.6
66.2
67.9
69.5
3761. 7
63.3
65.0
66.7
68.3
3862. 7
64.4
66.1
67.8
69.5
3966. 2
68.0
69.7
71.5
73.2
4072.4
74.2
76.0
77.7
79.5
4181. 3
83.2
85.0
86.9
88.7
4293. 3
95.2
97.1
99.0
4300. 9
4408. 5
10.4
12.4
14.3
16.3
10
11
12
13
14
15
16
17
18
19
3479. 9
81.4
83.0
84.5
86.1
3574. 4
76.0
77.6
79.2
80.8
3671. 1
72.7
74.4
76.0
77.6
3770. 0
71.7
73.3
75.0
76.7
3871. 2
72.9
74.6
76.3
78.1
3975. 0
76.7
78.5
80.2
82.0
4081. 3
83.1
84.9
86.7
88.5
4190.6
92.4
94.2
96.1
97.9
4302. 8
04.7
06.6
08.5
10.4
4418. 2
20.2
22.1
24.1
26.1
15
16
17
18
19
20
21
22
23
24
3487. 7
89.2
90.8
92.4
93.9
3582. 4
84.0
85.6
87.2
88.8
3679. 3
80.9
82.5
84.2
85.8
3778. 3
80.0
81.7
83.3
85.0
3879. 8
81.5
83.2
84.9
86.6
3983. 7
85.5
87.2
89.0
90.7
4090. 3
92.1
93.9
95.7
97.5
4199. 8
4201. 6
03.5
05.3
07.2
4312. 3
14.2
16.1
18.0
19.9
4428. 0
30.0
31.9
33.9
35.8
20
21
22
23
24
25
26
27
28
29
3495. 5
97.1
98.6
3500. 2
01.8
3590. 4
92.0
93.6
95.2
96.8
3687. 4
89.1
90.7
92.3
94.0
3786. 7
88.4
90.0
91.7
93.4
3888. 3
90.0
91.8
93.5
95.2
3992. 5
94.3
96.0
97.8
99.5
4099. 3
4101. 1
02.9
04.8
06.6
4209. 0
10.9
12.8
14.6
16.5
4321. 8
23.7
25.6
27.5
29.4
4437.8
39.8
41.7
43.7
45.7
25
26
27
28
29
30
31
32
33
34
3503. 3
04.9
06.5
08.0
09.6
3598. 4
3600. 0
01.6
03.2
04.8
3695. 6
97.3
98.9
3700. 5
02.2
3795. 1
96.8
98.4
3800.1
01.8
3896. 9
98.6
3900.4
02.1
03.8
4001. 3
03.1
04.8
06.6
08.3
4108. 4
10.2
12.0
13.8
15.6
4218. 3
20.2
22.0
23.9
25.8
4331. 3
33.2
35.2
37.1
39.0
4447. 6
49.6
51.6
53.5
55.5
30
31
32
33
34
35
36
37
38
39
3511. 2
12.7
14.3
15.9
17.5
3606.4
08.0
09.6
11.2
12.8
3703. 8
05.5
07.1
08.7
10.4
3803. 5
05.1
06.8
08.5
10.2
3905. 5
07.2
09.0
10.7
12.4
4010. 1
11.9
13.6
15.4
17.2
4117. 4
19.2
21.0
22.9
24.7
4227. 6
29.5
31.3
33.2
35.1
4340. 9
42.8
44.7
46.6
48.6
4457. 5
59.4
61.4
63.4
65.4
35
36
37
38
39
40
41
42
43
44
3519. 0
20.6
22.2
23.7
25.3
3614. 5
16.1
17.7
19.3
20.9
3712. 0
13.7
15.3
17.0
18.6
3811. 9
13.6
15.2
17.0
18.6
3914. 1
15.9
17.6
19.3
21.0
4018.9
20.7
22.5
24.3
26.0
412o. 5
28.3
30.1
31.9
33.8
4236. 9
38.8
40.7
42.5
44.4
4350. 5
52.4
54.3
56.2
58.2
4467. 3
69.3
71.3
73.3
75.3
40
41
42
48
44
45
46
47
48
49
3526. 9
28.5
30.1
31.6
33.2
3622. 5
24.1
25.7
27.3
29.0
3720. 3
21.9
23.6
25.2
26.9
3820. 3
22.0
23.7
25.4
27.1
3922. 8
24.5
26.2
28.0
29.7
4027. 8
29.6
31.4
33.1
34.9
4135.6
37.4
39.2
41.0
42.9
4246. 3
48.1
50.0
51.9
53.8
4366. 1
62.0
63.9
65.9
67.8
4477.2
79.2
81.2
83.2
85.2
45
46
47
48
49
50
51
52
53
54
50
51
52
53
54
3534. 8
36.4
37.9
39.5
41.1
3630. 6
32.2
33.8
35.4
37.0
3728. 5
30.2
31.8
33.5
35.1
3828. 7
30.4
32.1
33.8
35.5
3931. 4
33.2
34.9
36.6
38.4
4036. 7
38.5
40.2
42.0
43.8
4144. 7
46.5
48.3
50.2
52.0
4255. 6
57.5
59.4
61.3
63.1
4369. 7
71.7
73.6
75.5
77.4
4487.2
89.1
91.1
93.1
95.
55
56
57
58
59
3542. 7
44.3
45.9
47.4
49.0
3638. 6
40.3
41.9
43.5
45.1
3736. 8
38.4
40.1
41.7
43.4
3837. 2
38.9
40.6
42.3
45/0
3940. 1
41.8
43.6
45.3
47.0
4045. 6
47.4
49.1
50.9
52.7
4153. 8
55.7
57.5
59.3
61.1
4265.0
66.9
68.8
70.7
72.5
4379. 4
81.3
83.2
85.2
87.1
4497.
99.
4501.
03.
05.
55 1
56
57
58
59
"*•]
M.
50°
51°
52°
53°
64°
55°
66°
57°
58°
69°
TABLE 3. [Page 627
Meridional Parts, or Increased Latitudes.
C°mP- 2ST466
M.
60°
61°
62°
63°
64°
65° 66°
67°
68°
69°
M.
0
1
2
3
4
4507.1
09.1
11.1
13.1
15.1
4628.7
30.8
32.9
34.9
37.0
4754.3
56.4
58.6
60.7
62.8
4884.1
86.3
88.5
90.7
92.9
5018.4
20.6
22.9
25.2
27.5
5157. 6
59.9
62.3
64.7
67.0
5302. 1
04.6
07.0
09.5
11.9
5452.4
55.0
57.6
60.1
62.7
5609.1
11.8
14.4
17.1
19.8
5772. 7
75.5
78.3
81.1
83.8
0
1
2
3
4
5
6
7
8
9
4517.1
19.1
21.1
23.1
25.1
4639.0
41.1
43.2
45.2
47.3
4764.9
67.1
69.2
71.3
73.5
4895. 1
97.3
99.5
4901.7
03.9
5029.8
32.1
34.3
36.6
38.9
5169. 4
71.8
74.2
76.5
78.9
5314. 4
16.9
19.3
21.8
24.3
5465.2
67.8
70.4
72.9
75. 5
5622. 4
25.1
27.8
30.5
33.2
5786. 6
89.4
92.2
95.1
97.9
5
6
7
8
9
10
11
12
13
14
4527. 1
29.1
31.1
33.1
35.1
4649.4
51.5
53.5
55.6
57.7
4775. 6
77.8
79.9
82.0
84.2
4906.1
08.3
10.5
12.8
15.0
5041.2
43.5
45.8
48.1
50.4
5181.3
83.7
86.0
88.4
90.8
5326. 7
29.2
31.7
34.2
36.6
5477. 1
80.7
83.2
85.8
88.4
5635.9
38.5
41.2
43.9
46.6
5800.7
03.5
06.3
09.1
11.9
10
11
12
13
14
15
16
17
18
19
4537.1
39.2
41.2
43.2
45.2
4659. 7
61.8
63.9
66.0
68.1
4786. 3
88.5
90.6
92.8
94.9
4917. 2
19.4
21.6
23.9
26.1
5052. 7
55.0
57.3
59.6
61.9
5193. 2
95.6
98.0
5200.4
02.7
5339. 1
41.6
44.1
46.6
49.1
5491. 0
93.6
96.2
98.7
5501. 3
5649. 3
52.0
54.7
57.4
60.1
5814. 7
17.6
20.4
23.2
26.0
15
16
17
18
19
20 4547.2
21 49.2
22 51. 3
23 53. 3
24 55. 3
• 4670. 1
72.2
74.3
76.4
78.5
4797. 1
99.2
4801. 4
03.5
05.7
4928. 3
30.5
32.8
35.0
37.2
5064.2
66.5
68.8
71.1
73.4
5205. 1
07.5
09.9
12.3
14.7
5351. 5
54.0
56.5
59.0
61.5
5503. 9
06.5
09.1
11.7
14.3
5662. 8
65.5
68.2
70.9
73.7
5828. 9
31.7
34.5
37.4
40.2
20
21
22
23
24
25 4557. 3
26 59. 3
27 61. 4
28 63. 4
29 65.4
4680.6
82.6
84.7
86.8
88.9
4807. 8
10.0
12.1
14.3
16.5
4939. 4
41.7
43.9
46.1
48.4
5075.7
78.1
80.4
82.7
85.0
5217. 1
19.5
21.9
24.3
26.7
5364.0
66.5
69.0
71.5
74.0
5516. 9
19.5
22.1
24.7
27.3
5676. 4
79.1
81.8
84.5
87.3
5843.0
45.9
48.7
51.6
54.4
25
26
27
28
29
30
31
32
33
34
4567. 4
69.5
71.5
73.5
75.6
4691. 0
93.1
95.2
97.3
99.4
4818. 6
20.8
23.0
25.1
27.3
4950.6
52.9
55.1
57.3
59.6
5087. 3
89.6
92.0
94.3
96.6
5229. 1
•31.6
34.0
36.4
38.8
5376. 5
79.0
81.5
84.0
86.5
5529. 9
32.5
35.2
37.8
40.4
5690.0
92.7
95.4
98.2
5700.9
5857.3
60.1
63.0
65.9
68.7
30
31
32
33
34
35
36
37
38
39
4577.6
79.6
81.7
83.7
85.7
4701. 5
03.6
05.7
07.8
09.9
4829.5
31.6
33.8
36.0
38.1
4961. 8
64.1
66.3
68.6
70.8
5098.9
5101. 3
03.6
05.9
08.3
5241. 2
43.6
46.0
48.5
50.9
5389. I
91.6
94.1
96.6
99.1
5543. 0
45.6
48.3
50.9
53.5
5703. 6
06.4
09.1
11.9
14.6
5871. 6
74.4
77.3
80.2
83.1
35
36
37
38
39
40
41
42
43 1
44 !
4587. 8
89.8
91.8
93.9
95.9
4712. 0
14.1
16.2
18.3
20.4
4840. 3
42.5
44.7
46.8
49.0
4973. 1
75.3
77.6
79.8
82.1
5110. 6
12.9
15.3
17.6
19.9
5253. 3
55.7
58.2
60.6
63.0
5401. 6
04.2
06.7
09.2
11.8
5556. 1
58.8
61.4
64.0
66.7
5717. 3
20.1
22.8
25.6
28.3
5885.9
88.8
91.7
94.6
97.4
40
41
42
43
44
45
46
47
48
49
4598.0
4600.0
02.1
04.1
06.1
4722. 5
24.6
26.7
28.9
31.0
4851.2
53.4
55.6
57.8
59.9
4984.3
86.6
88.9
91.1
93.4
5122. 3
24.6
27.0
29.3
31.7
5265. 4
67.9
70.3
72.8
75.2
5414.3
16.8
19.3
21.9
24.4
5569. 3
71.9
74.6
77.2
79.9
5731. 1
33.9
36.6
39.4
42.1
5900.3
03.2
06.1
09.0
11.9
45
46
47
48
49
50
51
52
53
54
4608. 2
10.2
12.3
14.3
16.4
4733. 1
35.2
37.3
39.4
41.6
4862. 1
64.3
66.5
68.7
70.9
4995. 6
97.9
5000.2
02.4
04.7
5134. 0
36.4
38.7
41.1
43.4
5277. 6
80.1
82.5
85.0
87.4
5427.0
29.5
32.0
34.6
37.1
5582.5
85.2
87.8
90.5
93.1
5744.9
47.7
50.4
53.2
56.0
5914. 8
17.7
20.6
23.5
26.4
50
51
52
53
54
55
56
57
58
59
4618. 5
20.5
22.6
24.6
26.7
4743. 7
45.8
47.9
50.0
52.2
4873. 1
75.3
77.5
79.7
81.9
5007.0
09.3
11.5
13.8
16.1
5145. 8
48.1
50.5
52.8
55.2
5289. 8
92.3
94.7
97.2
99.7
5439. 7
42.2
44.8
47.3
49.9
5595. 8
98.4
5601. 1
03.8
06.4
5758. 8
61.5
64.3
67,1
69.9
5929.3
32.2
35.1
38.1
41.0
55
56
57
58
59
iL
60°
61°
62°
68°
64°
65°
6«°
61°
68°
69°
M.
Page 628] TABI
Meridional Parts, or
Comp.
JE 3.
Increased Latitudes,
i
293.465
M.
70°
71°
72°
73°
74°
76°
76°
77°
78°
79°
M.
o-
1
2
3
4
5943. 9
46.8
49.7
52.7
55.6
6123. 5
26.6
29.7
32.8
35.8
6312. 5
15.8
19.0
22.3
25.5
6512. 0
15.4
18.9
22.3
25.7
6723. 2
26.8
30.5
34.1
37.7
6947. 7
51.6
55.4
59.3
63.2
7187. 3
91.5
95.6
99.7
7203. 9
7444.4
48.8
53.3
57.7
62.2
7721. 6
26.4
31.3
36.1
40.9
8022. 7
27.9
33.2
38.5
43.7
0
1
2
3
4
5
6
7
8
9
5958. 5
61.5
64.4
67.3
70.3
6138. 9
42.0
45.1
48.2
51.3
6328. 8
32.0
35.3
38.5
41.8
6529. 1
32.6
36.0
39.5
42.9
6741.4
45.0
48.7
52.3
56.0
6967. 1
70.9
74.8
78.7
82.6
7208. 0
12.2
16.4
20.5
24.7
7466. 7
71.1
75.6
80.1
84.6
7745. 8
50.6
55.5
60.3
65.2
8049. 0
54.3
59.6
64.9
70,2
5
6
7
8
9
10
11
12
13
14
5973. 2
76.2
79.1
82.1
85.0
6154. 4
57.5
60.6
63.7
66.8
6345. 0
48.3
51.6
54.8
58.1
6546. 4
49.8
53.3
56.7
60.2
6759. 7
63.3
67.0
70.7
74.3
6986. 5
90.4
94.3
98.3
7002. 2
7228. 9
33.1
37.3
41.5
45.7
7489. 1
93.6
98.1
7502. 6
07.1
7770. 1
74.9
79.8
84.7
89.6
8075. 5
80.8
86.1
91.5
96.8
10
11
12
13
14
15
16
17
18
19
5988. 0
90.9
93.9
96.9
99.8
6169. 9
73.0
76.1
79.2
82.3
6361. 4
64.7
67.9
71.2
74.5
6563. 7
67.1
70.6
74.1
77.6
6778. 0
81.7
85.4
89.1
92.8
7006. 1
10.0
14.0
17.9 .
21.8
7249. 9
54.1
58.3
62.5
66.7
7511. 7
16.2
20.7
25.3
29.8
7794. 5
99.4
7804. 3
09.3
14,2
8102. 2
07.5
12.9
18.3
23.7
15
16
17
18
19
20
21
22
23
24
6002. 8
05.8
08.7
11.7
14.7
6185. 5
88.6
91.7
94.8
98.0
6377. 8
81.1
84.4
87.7
91.0
6581. 0
84.5
88.0
91.5
95.0
6796. 5
6800. 2
03.9
07.6
11.3
7025. 8
29.7
33.7
37.7
41.6
7270. 9
75.2
79.4
83.7
87.9
7534. 4
38.9
43.5
48.1
52.7
7819. 1
24.1
29.0
34.0
39.0
8129. 1
34.5
39.9
45.3
50.8
20
21
22
23
24
25
26
27
28
29
6017. 7
20.7
23.6
26.6
29.6
6201.1
04.2
07.4
10.5
13.7
6394. 3
97.6
6400.9
04.3
07.6
6598. 5
6602. 0
05.5
09.0
12.5
6815. 0
18.8
22.5
26.2
30.0
7045. 6
49.6
53.5
57.5
61.5
7292. 2
96.4
7300. 7
05.0
09.2
7557. 3
61.8
66.4
71.0
75.7
7844. 0
48.9
53.9
58.9
63.9
8156. 2
61.6
67.1
72.6
78.0
25
26
27
28
29
80
31
32
33
34
6032. 6
35.6
38.6
41.6
44.6
6216. 8
20.0
23.1
26.3
29.4
6410.9
14.2
17.6
20.9
24.2
6616. 1
19.6
23.1
26.6
30.2
6833. 7
37.4
41.2
44.9
48.7
7065. 5
69.5
73.5
77.5
81.5
7313. 5
17.8
22.1
26.4
30.7
7580. 3
84.9
89.5
94.2
98.8
7868. 9
74.0
79.0
84.0
89.1
8183. 5
89.0
94.5
8200. 0
05.5
30
31
32
33
34
35
36
37
38
39
6047. 6
50.6
53.6
56.6
59.7
6232. 6
35.8
38.9
42.1
45.3
6427. 6
30.9
34.2
37.6
40.9
6633. 7
37.2
40.8
44.3
47.9
6852. 4
56.2
60.0
63.7
67.5
7085. 5
89.5
93.5
97.6
7101. 6
7335. 0
39.3
43.6
47.9
52.3
7603. 4
08.1
12.8
17.4
22.1
7894. 1
99.2
7904. 2
09.3
14.4
8211. 1
16.6
22.1
27.7
33.3
35
36
37
38
39
40
41
42
43
44
6062. 7
65.7
68.7
71.7
74.8
6248. 4
51.6
54.8
58.0
61.2
6444.3
47.6
51.0
54.4
57.7
6651.4
55.0
58.5
62.1
65.7
6871. 3
75.1
78.9
82.6
86.4
7105. 6
09.7
13.7
17.8
21.8
7356. 6
60.9
65.3
69.6
74.0
7626. 8
31.4
36.1
40.8
45.5
7919. 4
24.5
29.6
34.7
39.9
8238. 8
44.4
50.0
55.6
61.2
40
41
42
43
44
45
46
47
48
49
6077. 8
80.8
83.9
86.9
89.9
6264. 4
67.6
70.8
74.0
77.2
6461. 1
64.5
67.8
71.2
74.6
6669. 2
72.8
76.4
80.0
83.5
6890. 2
94.0
97.8
6901. 7
05.5
7125. 9
29.9
34.0
38.1
42.2
7378. 3
82.7
87.1
91.4
95.8
7650. 2
55.0
59.7
64.4
69.1
7945. 0
50.1
55.2
60.4
65.5
8266. 8
72.4
78.1
83.7
89.3
45
46
47
48
49
50
51
52
53
54
6093. 0
96.0
99.1
6102. 1
05.2
6280. 4
83.6
86.8
90.0
93.2
6478. 0
81.4
84.8
88.2
91.6
6687. 1
90.7
94.3
97.9
6701. 5
6909. 3
13.1
16.9
20.8
24.6
7146. 2
50.3
54.4
58.5
62.6
7400. 2
04.6
09.0
13.4
17.8
7673. 9
78.6
83.4
88.1
92.9
7970. 7
75.9
81.0
86.2
91.4
8295. 0
8300. 7
06.4
12.0
17.7
50
51
52
53
54
55
56
57
58
59
6108.2
11.3
14.3
17.4
20.5
6296. 4
99.6
6302. 9
06.1
09.3
6495. 0
98.4
6501. 8
05.2
08.6
6705. 1
08.7
12.4
16.0
19.6
6928. 4
32.3
36.1
40.0
43.8
7166. 7
70.8
75.0
79.1
83.2
7422. 2
26.6
31.1
35.5
39.9
7697. 7
7702. 5
07.2
12.0
16.8
7996. 6
8001. 8
07.0
12.2
17.5
8323. 4
29.2
34.9
40.6
46.4
55
56
57
58
59
M.
70°
71°
72°
73°
74°
75°
76°
77°
78°
79°
M.
TABLE 4. [Page 629
Length of a Degree in Latitude and Longitude.
Lat.
Degree of Long.
Degree of Lat.
Lat.
Naut. miles.
Statute miles.
Meters.
Naut. miles.
Statute miles.
Meters.
o
0
1
2
3
4
60.068
0.059
0.031
59. 986
9.922
69. 172
9.162
9.130
9.078
9. 005
Ill 321
1 304
1 253
1 169
1 051
59.661
.661
.662
.663
.664
68.704
.704
.705.
.706
.708
110 567
568
569
570
573
0
0
1
2
3
4
5
6
7
8
9
59.840
9.741
9.622
9.487
9.333
68. 911
8.795
8.660
8.504
8.326
110 900
0 715
0 497
0 245
109 959
59. 666
.668
.670
.673
.676
68. 710
.712
.715
.718
.721
110 576
580
584
589
595
5
6
7
8
9
10
11
12
13
14
59. 161
8.971
8.764
8.538
8.295
68.129
7.910
7.670
7.410
7.131
109 641
9 289
8 904
8 486
8 036
59. 680
.684
.687
.692
.697
68. 725
.730
.734
.739
.744
110 601
608
616
624
633
10
11
12
13
14
15
16
17
18
19
58. 034
7.756
7.459
7.146
6.816
66. 830
6.510
6.169
5.808
5.427
107 553
7 036
6 487
5 906
5 294
59. 702
.707
.713
.719
.725
68.751
.757
.764
.771
.778
110 643
653
663
675
686
15
16
17
18
19
20
21
22
23
24
56.468
6.102
5.720
5.321
4.905
65.026
4.606
4.166
3.706
3.228
104 649
3 972
3 264
2 524
1 754
59. 732
.739
.746
.754
.761
68. 786
.794
.802
.811
.820
110 699
712
725
739
753
20
21
22
23
24
25
26
27
28
29
54. 473
4.024
3.558
3.076
2.578
62.729
2.212
1.676
1.122
0.548
100 952
0 119
99 257
8 364
7 441
59. 769
.777
.786
.795
.804
68.829
.839
.848
.858
.869
110 768
783
799
815
832
25
26
27
28
29
30
31
32
33
34
52.064
1.534
0.989
0.428
49.851
59. 956
9.345
8.716
8.071
7.407
96 488
5 506
4 495
3 455
2 387
59. 813
.822
.831
.841
.851
68. 879
.890
.901
.912
.923
110 849
866
883
901
919
30
31
32
33
34
35
36
37
38
39
49. 259
8.653
8.031
7.395
6.744
56.725
6.027
5.311
4.579
3.829
91 290
0 166
89 014
7 835
6 629
59. 861
.871
.881
.891
.902
68. 935
.946
.958
.969
.981
110 938
956
975
994
111 013
35
36
37
38
39
40
41
42
43
44
45
46. 079
5.399
4.706
4.000
3.280
2.546
53.063
2.281
1.483
0.669
49.840
8.995
85 396
4 137
2 853
1 543
0 208
78 849
59. 912
.923
.933
.944
.954
.965
68.993
69.006
.018
.030
.042
.054
111 033
052
072
091
111
131
40
41
42
43
44
45
p
age 630] TABLE 4.
Length of a Degree in Latitude and Longitude.
T^it
Degree of Long.
Degree of Lat.
Lftt.
Naut. miles.
Statute miles.
Meters.
Naut. miles.
Statute miles.
Meters.
o
45
46
47
48
49
42. 546
1.801
1.041
0.268
39. 484
48. 995
8.136
7.261
6.372
5.469
78 849
7 466
6 058
4 628
3 174
59.965
.976
.987
.997
60. 008
69. 054
.066
.079
.091
.103
Ill 131
151
170
190
210
0
45
46
47
48
49
50
51
52
53
54
38. 688
7.880
7.060
6.229
5.386
44.552
3.621
2.676
1.719
0.749
71 698
0 200
68 680
7 140
5 578
60. 019
.029
.039
.050
.060
69. 115
.127
.139
.151
.163
111 229
249
268
287
306
50
51
52
53
54
55
56
57
58
59
34. 532
3.668
2.794
1.909
1.015
39. 766
8.771
7.764
6.745
5.716
63 996
2 395
0 774
59 135
7 478
60. 070
.080
.090
.100
.109
69. 175
.086
.197
.209
.220
111 325
343
362
380
397
55
56
57
58
59
60
61
62
63
64
30. 110
29. 197
8. 275
7.344
6.404
34. 674
3.623
2.560
1.488
0.406
55 802
4 110
2 400
0 675
48 934
60. 118
.128
.137
.145
.154
69. 230
.241
.251
.261
.271
111 415
432
448
464
480
60
61
62
63
64
65
66
67
68
69
25.456
4.501
3.538
2.567
1.590
29. 315
8.215
7.106
5.988
4.862
47 177
5 407
3 622
1 823
0 012
60. 162
.170
.178
.186
.193
69. 281
.290
.299
.308
.316
111 496
511
525
539
553
65
66
67
68
69
70
71
72
73
74
20.606
19. 616
8.619
7.617
6.609
23. 729
2.589
1.441
0.287
19. 127
38 188
6 353
4 506
2 648
0 781
60.200
.207
.213
.220
.225
69. 324
.332
.340
.347
.354
111 566
578
590
602
613
70
71
72
73
74
75
76
77
78
79
15. 596
4.578
3.556
2.529
1.499
17. 960
6.788
5.611
4.428
3.242
28 903
7 017
5 123
3 220
1 311
60. 231
.236
.241
.246
.250
69. 360
.366
.372
.377
.382
111 623
633
642
650
658
75
76
77
78
79
80
81
82
83
84
10. 465
9.428
8.388
7.345
6.300
12. 051
10.857
9.659
8.458
7.255
19 394
7 472
5 545
3 612
1 675
60. 254
.257
.260
.263
.265
69. 386
.390
.394
.397
.400
111 665
671
677
682
687
80
81
82
83
84
85
86
87
88
89
90
5.253
4.205
3.154
2.103
1.052
0
6.049
4.842
3.632
2.422
1.211
0
9 735
7 792
5 846
3 898
1 949
0
60. 268
.269
.270
.271
.272
.272
69. 402
.404
.405
.407
.407
.407
111 691
694
696
698
699
699
85
86
87
88
89
90
TABLE 5A. [Page 631 1
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing, in points.
and second
beuring1, in
points.
2
2*
*%
2K
8
i*
8M
3
1.96
1.09
3*
1.57
0.94
2.19
1.31
3l
1.32
0.84
1.76
1.12
2. 42
1.53
-
3|
1.14
0.76
1.47
0.99
L94
1.30
2.64
1.77
4
1.00
0.71
1.27
0.90
1.62
1.15
2.12
1.50
2.85
2.01
4}
0.90
0.66
1.12
0.83
1.40
1.04
1.77
1.31
2.29
1.69
3.05
2.26
4
0.81
0.63
1.00
0.77
1.23
0.95
1.53
1.18
1.91
1.48
2.45
1.90
3.25
2.51
4f
0.74
0.60
0.91
0.73
1.10
0.89
1.34
1.08
1.65
1.32
2.05
1.65
2.61
2.10
5
0.69
0.57
0.83
0.69
1.00
0.83
1.20
1.00
1.45
1.21
1.77
1.47
2.19
1.82
H
0.64
0.55
0.77
0.66
0.92
0.79
1.09
0.94
1.30
1.11
1.56
1.34
1.88
1.62
5*
0.60
0.53
0.72
0.63
0.85
0.75
1.00
0.88
1.18
1.04
1.39
1.23
1.66
1.46
5|
0.57
0.52
0.68
0.61
0.79
0.72
0.93
0.84
1.08
0.98
1.26
1.14
1.48
1.34
6
0.54
0.50
0.64
0.59
0.74
0.69
0.86
0.80
1.00
0.92
1.16
1.07
1.35
1.24
H
0.52
0.49
0.60
0.57
0.70
0.66
0.81
0.76
0.93
0.88
1.07
1.01
1.23
1.16
6*
0.50
0.47
0.58
0.55
0.67
0.64
0.77
0.73
0.88
0.84
1.00
0.96
1.14
1.09
6|
0.48
0.46
0.55
0.54
0.64
0.62
0.73
0.71
0.83
0.80
0.94
0.91
1.06
1.03
7
0.46
0.45
0.53
0.52
0.61
0.60
0.69
0.68
0.79
0.77
0. 89 0. 87
1.00
0.98
7i
0.45
0.44
0.51
0.51
0.59
0.58
0.67
0.66
0.75
0.74
0. 84 | 0. 83
0.94
0.93
7£
0.43
0.43
0.50
0.50
0.57
0.56
0.64
0.64
0.72
0.72
0.80
0.80
0.90
0.89
7|
0.42
0.42
0.48
0.48
0.55
0.55
0.62
0.62
0.69
0.69
0.77
0.77
0.86
0.86
8
0.41
0.41
0.47
0.47
0.53
0.53
0.60
0.60
0.67
0.67
0.74
0.74
0.82
0.82
8*
0.41
0.41
0.46
0.46
0.52
0.52
0.58
0.58
0.65
0.65
0.72
0.72
0.79
0.79
s
0.40
0.40
0.45
0.45
0.51
0.51
0.57
0.57
0.63
0.63
0.69
0.69
0.76
0.76
8|
0.39
0.39
0.45
0.44
0.50
0.50
0.56
0.55
0.61
0.61
0.68
0.67
0.74
0.73
9
0.39
0.38
0.44
0.43
0.49
0.48
0.55
0.54
0.60
0.59
0.66
0.65
0.72
0.71
91
0.39
0.38
0.44
0.42
0.49
0.47
0.54
0.52
0.59
0.57
0.64
0.63
0.70
0.68
9|
0.38
0.37
0.43
0.41
0.48
0.46
0.53
0.51
0.58
0.56
0.63
0.61
0.69
0.66
9|
0.38
0.36
0.43
0.40
0.48
0.45
0.52
0.49
0.57
0.54
0.62
0.59
0.67
0.63
10
0.38
0.35
0.43
0.40
0.47
0.44
0.52
0.48
0.57
0.52
0.61
0.57
0.66
0.61
10J
0.38
0.35
0.43
0.39
0.47
0.43
0.52
0.47
0.56
0.51
0.61
0.55
0.65
0.59
10*
0.38
0.34
0.43
0.38
0.47
0.42
0.51
0.45
0.56
0.49
0.60
0.53
0.65
0.57
10|
0.39
0.33
0.43
0.37
0.47
0.40
0.51
0.44
0.56
0.48
0.60
0.51
0.64
0.55
11
0.39
0.32
0.43
0.36
0.47
0.39
0.51
0.43
0.56
0.46
0.60
0.50
0.64
0.53
11}
0.39
0.31
0.44
0.35
0.48
0.38
0.52
0.41
0.56
0.45
0.60
0.48
0.64
0.51
111
0.40
0.31
0.44
0.34
0.48
0.37
0.52
0.40
0.56
0.43
0.60
0.46
0.63
0.49
llf
0.41
0.30
0.45
0.33
0.49
0.36
0.52
0.39
0.56
0.42
0.60
0.44
0.64
0.47
12
0.41
0.29
0.45
0.32
0.49
0.35
0.53
0.37
0.57
0.40
0.60
0.43
0.64
0.45
12*
0.42
0.28
0.46
0.31
0.50
0.34
0.54
0.36
0.57
0.38
0.61
0.41
0.64
0.42
12|
0.43
0.28
0.47
0.30
0.51
0.32
0.55
0.35
0.58
0.37
0.61
0.39
0.65
0.41
12|
0.45
0.27
0.48
0.29
0.52
0.31
0.56
0.33
0.59
0.35
0.62
0.37
0.65
0.39
13
0.46
0.26
0.50
0.28
0.53
0.30
0.57
0.32
0.60
0.33
0.63
0.35
0.66
0.37
m
0.48
0.24
0.51
0.26
0.55
0.28
0.58
0.30
0.61
0.32
0.64
0.33
0.67
0.35
id
0.50
0.23
0.53
0.25
0.57
0.27
0.60
0.28
0.63
0.30
0.66
0.31
0.69
0.32
13|
0.52
0.22
0.55
0.24
0.59
0.25
0.62
0.26
0.65
0.28
0.68
0.29
0.70
0.30
14
0.54
0.21
0.58
0.22
0.61
0.23
0.64
0.24
0.67
0.26
0.69
0.27
0.72
0.28
Page 632] TABLE 5A.
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing, in points.
and second
ueRrin^f, in
points.
3K
4
*K
*1A
4^
5
6#
4f
3.44
2.76
5
2.76
2.30
3.62
3.01
61
2.31
1.98
2.91
2.50
3.80
3.26
8
1.99
1.76
2.44
2.15
3.05
2.69
3.96
3.49
5|
1.75
1.59
2.10
1.90
2.55
2.31
3.18
2.88
4.12
3.72
6
1.57
1.45
1.85
1.71
2.20
2.03
2.66
2.46
3.31
3.05
4.26
3.94
6J
1.42
1.34
1.65
1.56
1.94
1.82
2.29
2.16
2.77
2.61
3.42
3.22
4.40
4.14
6£
1.31
1.25
1.50
1.44
1.73
1.66
2.02
1.93
2.38
2.28
2.86
2.74
3.53
3.38
63
T
1.21
1.17
1.38
1.33
1.57
1.52
1.81
1.75
2.10
2.04
2.47
2.39
2.95
2.87
7
1.13
1.11
1.27
1.25
1.44
1.41
1.64
1.61
1.88
1.84
2.17
2.13
2.55
2.50
7i
1.06
1.05
1.19
1.17
1.33
1.32
1.50
1.49
1.70
1.69
1.94
1.92
2.24
2.22
n
1.00
1.00
1.11
1.11
1.24
1.24
1.39
1.38
1.56
1.55
1.76
1.76
2.01
2.00
n
0.95
0.95
1.05
1.05
1.17
1.17
1.30
1.30
1.45
1.44
1.62
1.62
1.82
1.82
8
0.91
0.91
1.00
1.00
1.10
1.10
1.22
1.22
1.35
1.35
1.50
1.50
1.67
1.67
8J
0.87
0.87
0.95
0.95
1.05
1.05
1.15
1.15
1.27
1.26
1.40
1.39
1.54
1.54
8*
0.84
0.83
0.91
0.91
1.00
1.00
1.09
1.09
1.20
1.19
1.31
1.30
1.44
1.43
8f
0.81
0.80
0.88
0.87
0.96
0.95
1.04
1.03
1.14
1.12
1.24
1.22
1.35
1.34
9
0.78
0.77
0.85
0.83
0.92
0.90
1.00
0.98
1.08
1.06
1.18
1.15
1.28
1.25
9|
0.76
0.74
0.82
0.80
0.89
0.86
0.96
0.93
1.04
1.01
1.12
1.09
1.21
1.18
9*
0.74
0.71
0.80
0.77
0.86
0.83
0.93
0.89
1.00
0.96
1.08
1.03
1.16
1.11
9|
0.73
0.68
0.78
0.74
0.84
0.79
0.90
0.85
0.97
0.91
1.04
0.97
1.11
1.04
10
0.71
0.66
0.77
0.71
0.82
0.76
0.88
0.81
0.94
0.87
1.00
0.92
1.07
0.99
m
0.70
0.63
0.75
0.68
0.80
0.72
0.86
0.77
0.91
0.82
0.97
0.88
1.03
0.93
m
0.69
0.61
0.74
0.65
0.79
0.69
0.84
0.74
0.89
0.78
0.94
0.83
1.00
0.88
10|
0.68
0.59
0.73
0.63
0.77
0.66
0.82
0.70
0.87
0.75
0.92
0.79
0.97
0.83
11
0.68
0.56
0.72
0.60
0.76
0.64
0.81
0.67
0.85
0.71
0.90
0.75
0.95
0.79
iu
0.67
0.54
0.71
0.57
0.76
0.61
0.80
0.64
0.84
0.67
0.88
0.71
0.93
0.75
ni
0.67
0.52
0.71
0.55
0.75
0.58
0.79
0.61
0.83
0.64
0.87
0.67
0.91
0.70
iif
0.67
0.50
0.71
0.52
0.74
0.55
0.78
0.58
0.82
0.61
0.86
0.64
0.90
0.66
12
0.67
0.48
0.71
0.50
0.74
0.52
0.78
0.55
0.81
0.57
0.85
0.60
0.88
0.63
m
0.67
0.45
0.71
0.48
0.74
0.50
0.77
0.52
0.81
0.54
0.84
0.56
0.-87
0.59
12}
0.68
0.43
0.71
0.45
0.74
0.47
0.77
0.49
0.80
0.51
0.84
0.53
0.87
0.55
12|
0.68
0.41
0.71
0.43
0.74
0.44
0.77
0.46
0.80
0.48
0.83
0.50
0.86
0.51
13
0.69
0.38
0.72
0.40
0.75
0.42
0.78
0.43
0.80
0.45
0.83
0.46
0.86
0.48
13*
0.70
0.36
0.73
0.37
0.76
0.39
0.78
0.40
0.81
0.41
0.83
0.43
0.86
0.44
13}
0.71
0.34
0.74
0.35
0.76
0.36
0.79
0.37
0.81
0.38
0.84
0.39
0.86
0.41
13}
0.73
0.31
0.75
0.32
0.77
0.33
0.80
0.34
0.82
0.35
0.84
0.36
0.86
0.37
14
0.74
0.28
0.77
0.29
0.79
0.30
0.81
0.31
0.83
0.32
0.85
0.32
0.87
0.33
VA
5#
6
5
W
5
7
W
4.52
4.33
6|
3.63
3.52
4.63
4.49
7
3.04
2.98
3.72
3.65
4.74
4.64
7*
2.62
2.59
3.11
3.08
3.80
3.76
4.83
4.77
7$
2.30
2.29
2.68
2.67
3.18
3.17
3.87
3.86
4.91
4.88
7f
2.06
2.06
2.36
2.36
2.74
2.74
3.24
3.24
3.94
3.93
4.97
4.97
8
1.87
1.87
2.11
2.11
2.41
2.41
2.79
2.79
3.30
3.30
3.99
3.99
5.03
5.03
8}
1.72
1.71
1.92
1.92
2.16
2.16
2.46
2.46
2.84
2.84
3.34
3.34
4.04
4.03
85
1.59
1.58
1.76
1.75
1.96
1.95
2.20
2.19
2.50
2.49
2.88
2.87
3.38
3.36
8f
1.48
1.46
1.63
1.61
1.80
1.78
2.00
1.98
2.24
2.21
2.53
2.51
2.91
2.88
9
1.39
1.36
1.52
1.49
1.66
1.63
1.83
1.80
2.03
1.99
2.27
2.23
2.56
2.51
9*
1.31
1.27
1.42
1.38
1.55
1.50
1.69
1.64
1.86
1.81
2.06
2.00
2.29
2.23
9i
1.25
1.19
1.35
1.29
1.46
1.39
1.58
1.51
1.72
1.65
1.89
1.81
2.08
1.99
9f
1.19
1.12
1.28
1.20'
1.38
1.30
1.48
1.40
1.61
1.51
1.75
1.64
1.91
.80
10
1.14
1.05
1.22
1.13
1.31
1.21
1.40
1.30
1.51
1.39
1.62
1.50
1.77
.63
10*
1.10
0.99
1.17
1.06
1.25
1.13
1.33
1.20
1.42
1.29
1.53
1.38
1.65
.49
101
1.06
0.94
1.13
0.99
1.20
1.05
1.27
1.12
1.35
1.19
1.44
1.27
1.55
.36
lOf
1.03
0.88
1.09
0.93
1.15
0.99
1.22
1.04
1.29
1.11
1.37
1.18
1.46
.25
11
1.00
0.83
1.05
0.88
1. 11 I 0. 92
1.17
0.97
1.24
1.03
1.31
1.09
1.39
.15
itt
0.98
0.78
1.03
0.82
1.08
0.87
1.13
0.91
1.19
0.96
1.25
1.01
1.32
.06
11*
0.95
0.73
1.00
0.77
1.05
0.81
1.10
0.85
1.15
0.89
1.21
0.93
1.27
0.98
111
0.94
0.69
0.98
0.72
1.02
0.76
1.07
0.79
1.12
0.83
1.17
0.86
1.22
0.90
12
0.92
0.65
0.96
0.68
1.00
0.71
1.04
0.73
1.09
0.77
1.13
0.80
.18
0.83
12}
0.91
0.61
0.94
0.63
0.98
0.66
1.02
0.68
1.06
0.71
1.10
0.74
.14
0.77
12|
0.90
0.57
0.93
0.59
0.97
0.61
1.00
0.63
1.04
0.66
1.07
0.68
.11
0.71
12|
0.89
0.53
0.92
0.55
0.95
0.57
0.98
0.59
1.02
0.61
1.05
0.63
.08
0.65
13
0.89
0.49
0.91
0.51
0.94
0.52
0.97
0.54
1.00
0.56
1.03
0.57
.06
0.59
131
0.88
0.45
0.91
0.47
0.93
0.48
0.96
0.49
0.99
0.51
1.01
0.52
.04
0.54
13}
0.88
0.42
0.91
0.43
0. 93 0. 44
0.95
0.45
0.98
0.46
1.00
0.47
.02
0.48
* 13|
0.88
0.38
0.90
0.39
0.92 0.40
0.95
0.41
0.97
0.41
0.99
0.42
1.01
0.43
14
0.89
0.34
0.91
0.35
0. 92 0. 35
0.94
0.36
0.90
0.37
0.98
0.38
1.00
0.38
TABLE 5A.
[Page 633
Distance of an Object by Two Bearings.
Difference
; between
Difference between the course and first bearing, in points.
the course
jandseconc
{bearing, in
iy
8
8#
8*
9
points.
4
*
8}
5.07
5.06
i
8J
4.07
4.05
5.10 5.08
8|
3.41
3.37
4.10
4.06
5.12
5.06
9
2.94
2.88
3.43
3.36
4.11
4.03
5.13
5.03
9}
2.58
2.51
2.95 2.87
3.44
3.34
4.12
3.39
5.12
4.97
2.31
2.21
2.60
2.49
2.96
2.84
3.44
3.30
4.11
3.93
5.10
4.88
9f
2.10
1.98
2.33
2.19
2.61
2.46
2.97
2.79
3.44
3.24
4.10
3.86
5.07
4.77
10
1.92
1.78
2.11
1.95
2.34
2.16
2.61
2.41
2.96
2.74
3.43
3.17
4.07
3.76
5.03
4.64
10}
1.78
1.61
1.93
1.75
2.12
1.92
2.34
2.11
2.61
2.36
2.95
2.67
3.41
3.08
4.04
3.65
10*
1.66
1.46
1.79
1.58
1.94
1.71
2.12-
1.87
2.34
2.06
2.60
2.29
2.94
2.59
3.38
2.98
10|
1.56
1.34
1.67
1.43
1.80
1.54
1.95
1.67
2.12
1.82
2.33
2.00
2.58
2.22
2.91
2.50
11
1.47
1.22
1.57
1.30
1.68
1.39
1.80
1.50
.94
1.62
2.11
1.76
2.31
1.92
2.56
2.13
11}
1.40
1.12
1.48 ! 1.19
1.57
1.26
1.68
1.35
.80
1.44
1.93
1.55
2.10
1.69
2.29
1.84
111
1.34
1.03
1.41
1.09
1.49 1.15
1.58
1.22
.68
1.30
1.79
1.38
1.92
1.49
2.08
1.61
111
1.28
0.95
1.34
1.00
1.41 1.05
1.49
1.10
.57
1.17
1.67
1.24
1.78
1.32
1.91
1.41
12
1.23
0.87
1.29
0.91
1.35
0.95
1.41
1.00
.49 1.05
1.57
1.11
1.66 1.17
1.77
1.25
121
1.19
0.80
1.24
0.83
1.29
0.87
1.35
0.91
1.41 0.95
1.48
1.00
1.56
1.05
1.65
1.11
12*
1.15
0.73
1.20
0.76
1.24
0.79
1.29
0.82
1.35 0.86
1.41
0.89
1.47
0.93
1.55
0.98
la
1.12
0.67
1.16
0.69
1.20
0.72
1.25
0.74
1.29 0.77
1.34
0.80
1.40
0.83
1.46
0.87
13
1.09
0.61
1.13
0.63
1.16
0.65
1.20
0.67
1.24
0.69
1.29
0.72
1.34
0.74
1.39
0.77
13}
1.07
0.55
1.10
0.57
1.13
0.58
1.17
0.60
1.20
0.62
1.24
0.64
1.28
0.66
1.32
0.68
13*
1.05
0.50
1.08
0.51
1.10
0.52
1.13 0.53
1.16
0.55
1.20
0.56
1.23
0.58
1.27
0.60
13§
1.03
0.44
1.06
0.45
1.08
0.46
1.11 0.47
1.13
0.48
1.16
0.50
1.19
0.51
1.22
0.52
14
1.02
0.39
1.04
0.40
1.06
0.41
1.08 0.41
1.10 0.42
1.13
0.43
1.15 0.44
L18 0.45
i*
»K
9K
10
it*
10,4
10?,'
11
i
10}
4.97
4.50
10|
3.99
3.52
4.91
4.33
3.34
2.87
3.94
3.38
4.83
4.14
II4
2.88
2.39
3.30
2.74
3.87
3.22
4.74
3.94
11}
2.53
2.04
2.84
2.2S
3.24
2.61
3.80
3.05
4.63 3.72
llf
o o-
1.75
2.50
1.93
2.79
2.16
3.18 2.46
3.72 i 2.88
4.52
3.49
llf
2! 06
1.52
2.24 1.66
2.46
1.82
2. 74 ' 2. 03
3.11 2.31
3.63
2.69
4.40 3.20
12
1.89
1.33
2.03 1.44
2.20
1.56
2.41 i 1.71
2.68 1.90
3.04
2.15
3.53 2.50
4.26
3.01
12}
1.75
1.18
1.86 • 1.25
2.00
1.34
2.16 1.45
2.36 1.59
2.62 [
1.76
2.95 1.98
3.42
2.30
12*
1.62
1.03
1.72 ; 1.09
1.83
1.16
1.96 1.24
2.11 1.34
2.30
1.46
2.55 1.62
2.86
1.82
12|
1.53
0.91
1.61 ; 0.96
1.69
1.01
1.80 1.07
1.92 1.14
2.06!
1.23
2.24 1.34
2.47
1.47
13
1.44
0.80
1.51 0.84
1.58
0.88
1.66
0.92
1.76 0.98
1.87
1.04
2.01 1.11
2.17
1.21
13}
1.37
0.71
1.42 0.73
1.48
0.76
1.55
0.80
1.63 0.84
1.72
0.88
1.82 0.94
1.94
1.00
13£
1.31
0.62
1.35 0.64
1.40
0.66
1.46 0.69
1.52 0.72
1.59 '
0.75
1.67 0.79
1.76
0.83
13J
1.25
054
1.29 0.55
1.33
0.57
1.38
0.59
1.42 0.61
1.48 1
0.63
1 54 0.66
1 62
06Q
14
1.21
0.46
1.24 0.47
1.27
0.49
1.31
0.50
1.35 0.52
1.39
0.53
1.44 0.55
1.50 0.57
u*
11^
11*
12
12*
W*
12*
13
12}
4.12
2.77
12*
3.31 2.10
3.96 2.51
12|
2.77 1.65
3.18 1.90
3.80
2.26
13
2.38
1.32
2.66
1.4S
3.05
1.69
3.62
2.01
13}
2.10
1.08
2.29
1.18
2.55
1.31
2.91
1.50
3.44 1.77
13*
1.88 0.89
2.02 0.95
2.20
1.04
2.44
1.15
2.76 1.30
3.25
1.53
13f
1.70 0.73
1.81 0.77
1.94
0.83
2.10
0.90
2.31 0.99
2.61
1.12
3.05
1.31
14
1.56 0.60
1.64 0.63
1.73
0.66
1.85
0.71
1.99 0.76
2.19
0.84
2.45 0.94
2.85
1.09
Page 634] TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
Difference between the course and first bearing.
the course
and second
bearing.
20°
22°
.. 24°
36°
28°
30°
32°
30°
1.97
0.98
32
1.64
0.87
2.16
1.14
34
1.41
0.79
1.80
1.01
2.34
1.31
36
1.24
0.73
1.55
0.91
1.96
1.15
2.52
1.48
38
1.11
0.68
1.36
0.84
1.68
1.04
2.11
1.30
2.70
1.66
40
1.00
0.64
1.21
0.78
1.48
0.95
1.81
1.16
2.26
1.45
2.88
1.85
42
0.91
0.61
1.10
0.73
1.32
0.88
1.59
1.06
1.94
1.30
2.40
.61
3.05
2.04
44
0.84
0.58
1. 00
0.69
1.19
0.83
1.42
0.98
1.70
1.18
2.07
.44
2.55
1.77
46
0.78
0.56
0.92
0.66
1.09
0.78
1.28
0.92
1.52
1.09
1.81
.30
2.19
1.58
48
0.73
0.54
0.85
0.64
1.00
0.74
1.17
0.87
1.37
1.02
1.62
.20
1.92
1.43
50
0.68
0.52
0.80
0.61
0.93
0.71
1.08
0.83
1.25
0.96
1.46
.12
1.71
1.31
52
0.65
0.51
0.75
0.59
0.87
0.68
1.00
0.79
1.15
0.91
1.33
.05
1.55
1.22
54
0.61
0.49
0.71
0.57
0.81
0.66
0.93
0.76
1.07
0.87
1.23
0.99
1.41
1.14
56
0.58
0.48
0.67
0.56
0.77
0.64
0.88 '
0.73
1.00
0.83
1.14
0.95
1.30
1.08
58
0.56
0.47
0.64
0.54
0.73
0.62
0.83
0.70
0.94
0.80
1.07
0.90
1.21
1.03
60
0.53
0.46
0.61
0.53
0.69
0.60
0.78
0.68
0.89
0.77
1.00
0.87
1.13
0.98
62
0.51
0.45
0.58
0.51
0.66
0.58
0.75
0.66
0.84
0.74
0.94
0.83
1.06
0.94
64
0.49
0.44
0.56
0.50
0.63
0.57
0.71
0.64
0.80
0.72
0.89
0.80
1.00
0.90
66
0.48
0.43
0.54
0.49
0.61
0.56
0.68
0.62
0.76
0.70
0.85
0.78
0.95
0.87
68
0.46
0.43
0.52
0.48
0.59
0.54
0.66
0.61
0.73
0.68
0.81
0.75
0.90
0.84
70
0.45
0.42
0.50
0.47
0.57
0.53
0.63
0.59
0.70
0.66
0.78
0.73
0.86
0.81
72
0.43
0.41
0.49
0.47
0.55
0.52
0.61
0.58
0.68
0.64
0.75
0.71
0.82
0.78
74
0.42
0.41
0.48
0.46
0.53
0.51
0.59
0.57
0.65
0.63
0.72
0.69
0.79
0.76
76
0.41
0.40
0.46
0.45
0.52
0.50
0.57
0.56
0.63
0.61
0.70
0.67
0.76
0.74
78
0.40
0.39
0.45
0.44
0.50
0.49
0.56
0.54
0.61
0.60
0.67
0.66
0.74
0.72
80
0.39
0.39
0.44
0.44
0.49
0.48
0.54
0.53
0.60
0.59
0.65
0.64
0.71
0.70
82
0.39
0.38
0.43
0.43
0.48
0.47
0.53
0.52
0.58
0.57
0.63
0.63
0.69
0.69
84
0.38
0.38
0.42
0.42
0.47
0.47
0.52
0.51
0.57
0.56
0.62
0.61
0.67
0.67
86
0.37
0.37
0.42
0.42
0.46
0.46
0.51
0.51
0.55
0.55
0.60
0.60
0.66
0.65
88
0.37
0.37
0.41
0.41
0.45
0.45
0.50
0.50
0.54
0.54
0.59
0.59
0.64
0.64
90
0.36
0.36
0.40
0.40
0.45
0.45
0.49
0.49
0.53
0.53
0.58
0.58
0.62
0.62
92
0.36
0.36
0.40
0.40
0.44
0.44
0.48
0.48
0.52
0.52
0.57
0.57
0.61
0.61
94
0.36
0.35
0.39
0.39
0.43
0.43
0.47
0.47
0.51
0.51
0.56
0.55
0.60
0.60
96
0.35
0.35
0.39
0.39
0.43
0.43
0.47
0.46
0.51
0.50
0.55
0.54
0.59
0.59
98
0.35
0.35
0.39
0.38
0.42
0.42
0.46
0.46
0.50
0.50
0.54
0.53
0.58
0.57
100
0.35
0.34
0.38
0.38
0.42
0.41
0.46
0.45
0.49
0.49
0.53
0.52
0.57
0.56
102
0.35
0.34
0.38
0.37
0.42
0.41
0.45
0.44
0.49
0.48
0.53
0.51
0.56
0.55
104
0.34
0.33
0.38
0.37
0.41
0.40
0.45
0.43
0.48
0.47
0.52
0.50
0.56
0.54
106
0.34
0.33
0.38
0.36
0.41
0.39
0.45
0.43
0.48
0.46
0.52
0.50
0.55
0.53
108
0.34
0.32
0.38
0.36
0.41
0.39
0.44
0.42
0.48
0.45
0.51
0.49
0.55
0.52
110
0.34
0.32
0.37
0.35
0.41
0.38
0.44
0.41
0.47
0.44
0.51
0.48
0.54
0.51
112
0.34
0.32
0.37
0.35
0.41
0.38
0.44
0.41
0.47
0.44
0.50
0.47
0.54
0.50
114
0.34
0.31
0.37
0.34
0.41
0.37
0.44
0.40
0.47
0.43
0.50
0.46
0.54
0.49
116
0.34
0.31
0.38
0.34
0.41
0.37
0.44
0.39
0.47
0.42
0.50
0.45
0.53
0.48
118
0.35
0.31
0.38
0.33
0.41
0.36
0.44
0.39
0.47
0.41
0.50
0.44
0.53
0.47
120
0.35
0.30
0.38
0.33
0.41
0.36
0.44
0.38
0.47
0.41
0.50
0.43
0.53
0.46
122
0.35
0.30
0.38
0.32
0.41
0.35
0.44
0.37
0.47
0.40
0.50
0.42
0.53
0.45
124
0.35
0.29
0.38
0.32
0.41
0.34
0.44
0.37
0.47
0.39
0.50
0.42
0.53
0.44
126
0.36
0.29
0.39
0.31
0.42
0.34
0.45
0.36
0.47
0.38
0.50
0.41
0.53
0.43
128
0.36
0.28
0.39
0.31
0.42
0.33
0.45
0.35
0.48
0.38
0.50
0.40
0.53
0.42
130
0.36
0.28
0.39
0.30
0.42
0.32
0.45
0.35
0.48
0.37
0.51
0.39
0.54
0.41
132
0.37
0.27
0.40
0.30
0.43
0.32
0.46
0.34
0.48
0.36
0.51
0.38
0.54
0.40
134
0.37
0.27
0.40
0.29
0.43
0.31
0.46
0.33
0.49
0.35
0.52
0.37
0.54
0.39
136
0.38
0.26
0.41
0.28
0.44
0.30
0.47
0.32
0.49
0.34
0.52
0.36
0.55
0.38
138
0.39
0.26
0.42
0.28
0.45
0.30
0.47
0.32
0.50
0.33
0.53
0.35
0.55
0.37
140
0.39
0.25
0.42
0.27
0.45
0.29
0.48
0.31
0.51
0.33
0.53
0.34
0.56
0.36
142
0.40
0.25
0.43
0.27
0.46
0.28
0.49
0.30
0.51
0.32
0.54
0.33
0.56
0.35
144
0.41
0.24
0.44
0.26
0.47
0.28
0.50
0.29
0.52
0.31
0.55
0.32
0.57
0.34
146
0.42
0.24
0.45
0.25
0.48
0.27
0.51
0.28
0.53
0.30
0.56
0.31
0.58
0.32
148
0.43
0 23
0.46
0.25
0.49
0.26
0.52
0.27
0.54
0.29
0.57
0.30
0.59
0.31
150
0.45
0.22
0.48
0.24
0.50
0.25
0.53
0.26
0.55
0.28
0.58
0.29
0.60
0.30
152
0.46
0.22
0.49
0.23
0.52
0.24
0.54
0.25
0.57
0.27
0.59
0.28
0.61
0.29
154
0.48
0.21
0.50
0.22
0.53
0.23
0.56
0.24
0.58
0.25
0.60
0 26
0.62
0.27
156
0.49
0.20
0.52
0.21
0.55
0.22
0.57
0.23
0.60
0.24
0.62
0 25
0.64
0.26
158
0.51
0.19
0.54
0.20
0.57
0.21
0.59
0.22
0.61
0.23
0.63
0.24
0.66
0.25
160
0.53
0.18
0.56
0.19
0.59
0.20
0.61
0.21
0.63
0.22
0.65
0.22
0.67
0.23
TABLE 5B. [Page 635
Distance of an Object by Two Bearings.
Difference
between
Difference between the course and first bearing.
the course
md second
bearing.
34°
86°
38°
40°
42o
44°
46°
j
•
44°
3.22
2.24
46
2.69
1.93
3.39
2.43
48
2.31
1.72
2.83
2.10
3.55
2.63
50
2.03
1.55
2.43
1.86
2.96
2.27
3.70
2.84
52
1.81
1.43
2.13
1.68
2.54
2.01
3.09
2.44
3.85
3.04
54
1.63
1.32
1.90 1.54
2.23 1.81
2.66
2.15
3.22
2.60
4.00
3.24
56
1.49
1.24
1.72
1.42
1. 99 i 1. 65
2.33
1.93
2.77
2.29
3.34
2.77
4.14
3.43
58
1.37
1.17
1.57
1.33
1.80 1.53
2.08
1.76
2.43
2.06
2.87
2.44
3.46
2.93
60
1.28
1.10
1.45
1.25
1.64 1.42
1.88
1.63
2.17 i 1.88
2.52
2.18
2.97
2.57
62
1.19
1.05
1.34
1.18
1.51 1.34
1.72
1.52
1. 96 1. 73
2:25
1.98
2.61
2.30
64
1.12
1.01
1.25
1.13
1. 40 1 1. 26
1.58
1.42
1. 79 1. 61
2.03
1.83
2.33
2.09
66
1.06
0.96
1.18
1.07
1. 31 ! 1. 20
1.47
1.34
1.65
1.51
1.85
1.69
2.10
1.92
68
1.00
0.93
1.11
1.03
1. 23 1. 14
1.37
1.27
1.53
1.42
1.71
1.58
1.92
1.78
70
0.95
0.89
1.05 0.99
1.16 1.09
1.29
1.21
1.43
1.34
1.58
1.49
1.77
1.66
72
0.91
0.86
1.00 0.95
l.lOi 1.05
1.21
1.15
1.34
1.27
1.48
1.41
1.64
1.56
74
0.37
0.84
0.95 0.92
1.05 1.01
1.15
1.10
1.26
1.21
1.39
1.34
1.53
1.47
76
0.84
0.81
0.91 0.89
1.00 0.97
1.09
1.06
1.20
1.16
1.31
1.27
1.44
1.40
78
0.80
0.79
0.88 0.86
0. 96 0. 94
1.04
1.02
1.14
1.11
1.24
1.22
1.36
1.33
80
0.78
0.77
0.85 0.83
0. 92 i 0. 91
1.00
0.98
1.09
1.07
1.18
1.16
1.28
1.27
82
0. 75
0.75
0.82 0.81
0. §9 i 0. 88
0.96
0.95
1.04
1.03
1.13
1.12
1.22
1.21
84
0.73
0.73
0.79 0.79
0. 86 | 0. 85
0.93
0.92
1.00
0.99
1.08
1.07
1.17
1.16
86
0.71
0.71
0.77 0.77
0. 83 0. 83
0.89
0.89
0.96
0.96
1.04
1.04
1.12
1.12
88
0.69
0.69
0.75 0.75
0.80 0.80
0.86
0.86
0.93
0.93
1.00
1.00
1.08
1.07
90
0.67
0.67
0.73 0.73
0. 78 0. 78
0.84
0.84
0.90
0.90
0.97
0.97
1.04
1.04
92
0.66
0.66
0.71 0.71
0. 76 i 0. 76
0.82
0.82
0.87
0.87
0.93
0.93
1.00
1.00
94
0.65
0.64
0.69 0.69
0. 74 i 0. 74
0.79
0.79
0.85
0.85
0.91
0.90
0.97
0.97
96
0.63
0.63
0.68 0.67
0. 73 0. 72
0.78
0.77
0.83
0.82
0.88
0.88
0.94
0.93
98
0.62
0.62
0.67 0.66
0. 71 0. 70
0.76
0.75
0.81
0.80
0.86
0.85
0.91
0.90
100
0.61
0.60
0.65 0.64
0. 70 i 0. 69
0.74
0.73
0.79
0.78
0. 84 0. 83
0.89
0.88
102
0.60
0.59
0.64 0.63
0.68 0.67
0.73
0.71
0.77
0.76
0. 82 ! 0. 80
0. 87 0. 85
104
0.60
0.58
0.63 0.61
0.67 0.65
0.72
0.69
0.76
0.74
0.80
0.78
0. 85 0. 82
106
0.59
0.57
0.63 0.60
0.66 0.64
0.70
0.68
0.74
0.72
0.79
0.76
0.83
0.80
108
0.58
0.55
0.62 0.59
0.66
0.62
0.69
0.66
0.73
0.70
0.77
0.74
0.81
0.77
110
0. 58 j 0. 54
0.61 0.57
0.65
0.61
0.68
0.64
0.72
0.68
0.76
0.71
0.80
0.75
112
0.57
0.53
0.61
0.56
0. 64 0. 59
0.68
0.63
0.71
0.66
0.75
0.69
0.79
0.73
114
0.57
0.52
0.60
0.55
0.63 0.58
0.67
0.61
0.70
0.64
0.74
0.68
0.78
0.71
116
0.56
0.51
0.60 0.54
0.63
0.57
0.66
0.60
0.70
0.63
0.73
0.66
0.77
0.69
118
0.56
0.50
0. 59 0. 52
0.63
0.55
0.66
0.58
0.69
0.61
0.72
0.64
0.76
0.67
120
0.56
0.49
0.59 0.51
0. 62 0. 54
0.65
0.57
0.68
0.59
0.72
0.62
0.75
0.65
122
0.56
0.47
0.59 0.50
0. 62 0. 53
0.65
0.55
0.68
0.58
0.71
0.60
0.74
0.63
124
0.56
0.46
0.59 0.49
0.62
0.51
0.65
0.54
0.68
0.56
0.71
0.58
0.74
0.61
126
0.56
0.45
0.59 0.48
0.62
0.50
0.64
0.52
0.67
0.54
0.70
0.57
0.73
0.59
128
0.56
0.44
0.59 0.46
0.62
0.49
0.64
0.51
0.67
0.53
0.70
0.55
0.73
0.57
130
0.56
0.43
0.59
0.45
0.62
0.47
0.64
0.49
0.67
0.51
0.70
0.53
0.72
0.55
132
0.56
0.42
0.59
0.44
0.62
0.46
0.64
0.48
0.67
0.50
0.70
0.52
0.72
0.54
134
0.57
0.41
0.59
0.43
0.62
0.45
0.64
0.46
0.67
0.48
0.69
0.50
0.72
0.52
136
0.57
0.40
0.60
0.41
0.62
0.43
0.65
0.45
0.67
0.47
0.70
0.48
0.72
0.50
138
0.58
0.39
0.60
0.40
0.63
0.42
0.65
0.43
0.67
0.45
0.70
0.47
0.72-
0.48-
140
0.58
0.37
0.61
0.39
0.63
0.40
0.65
0.42
0.68
0.43
0.70
0.45
0.72
0.46
142
0.59
0.36
0.61
0.38
0.63
0.39
0.66
0.41
0.68
0.42
0.70
0.43
0.72
0.45
144
0.60
0.35
0.62
0.36
0.64
0.38
0.66
0.39
0.68
0.40
0.71
0.41
0.73
0.43
146
0.60
0.34
0.63
0.35
0.65
0.36
0.67
0.37
0.69
0.39
0.71
0.40
0.73
0.41
148
0.61
0.32
0.63
0.34
0.66
0.35
0.68
0.36
0.70
0.37
0.72
0.38
0.74
0.39
150
0.62
0.31
0.64
0.32
0.66
0.33
0.68
0.34
0.70
0.35
0.72
0.36
0.74
0.37
152
0.63
0.30
0.65
0.31
0.67
0.32
0.69
0.33
0.71
0.33
0.73
0.34
0.75
0.35
154
0.65
0.28
0.67
0.29
0.68
0.30
0.70
0.31
0.72
0.32
0.74
0.32
0.76
0.33
156
0.66
0.27
0.68
0.28
0.70
0.28
0.72
0.29
0.73
0.30
0. 75
0.30
0.77
0.31
158
0.67
0.25
0.69
0.26
0.71
0.27
0.73
0.27
0.74
0.28
0.76
0.28
0.78
0.29
160
0.69
0.24
0.71
0.24
0.73
0.25
0.74
0.25
0.76
0.26
0.77
0.26
0.79
0.27
Page 636] TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
trie course
Difference between the course and first bearing.
and second
bearing.
48°
50°
52°
54°
56°
58°
60°
58°
4.28
3.63
'
60
3.57
3.10
4.41
3.82
62
3.07
2.71
3.68
3.25
4.54
4.01
64
2.70
2.42
3.17
2.85
3.79
3.41
4.66
4.19
66
2.40
2.20
2.78
2.54
3.26
2.98
3.89
3.55
4.77
4.36
68
2.17
2.01
2.48
2.30
2.86
2.65
3.34
3.10
3.99
3.71
'4.88
4.53
70
1.98
1.86
2.24
2.10
2.55
2.39
2.94
2.76
3.43
3.22
4.08
3.83
4.99
4.69
72
1.83
1.74
2.04
1.94
2.30
2.19
2.62
2.49
3.01
2.86
3.51
3.33
4.17
3.96
74
1.70
1.63
1.88
1.81
2.10
2.02
2.37
2.27
2.68
2.58
3.08
2.96
3.58
3.44
76
1.58
1.54
1.75
1.70
1.94
1.88
2.16
2.10
2.42
2.35
2.74
2.66
3.14
3.05
78
1.49
1.45
1.63
1.60
1.80
1.76
1.99
1.95
2.21
2.16
2.48
2.43
2.80
2.74
80
1.40
1.38
1.53
1.51
1.68
1.65
1.85
1.82
2.04
2.01
2.26
2.23
2.53
2.49
82
1.33
1.32
1.45
1.43
1.58
1.56
1.72
1.71
1.89
.87
2.08
2.06
2.31
2.29
84
1.26
1.26
1.37
1.36
1.49
1.48
1.62
1.61
1.77
.76
1.93
1.92
2.13
2.12
86
1.21
1.20
1.30
1.30
1.41
1.41
1.53
1.52
1.66
.65
1.81
1.80
1.98
1.97
88
1.16
1.16
1.24
1.24
1.34
1.34
1.45
1.45
1.56
.56
1.70
1.70
1.84
1.84
90
1.11
1.11
1.19
1.19
1.28
1.28
1.38
1.38
1.48
.48
1.60
1.60
1.73
1.73
92
1.07
1.07
1.14
1.14
1.23
1.23
1.31
1.31
1.41
.41
1.52
1.52
1.63
1.63
94
1.03
1.03
1.10
1.10
1.18
1.17
1.26
1.26
1.35
.34
1.44
1.44
1.55
1.54
96
1.00
0.99
1.06
1.06
1.13
1.13
1.21
1.20
1.29
.28
1.38
1.37
1.47
1.47
98
0.97
0.96
1.03
1.02
1.10
1.08
1.16
1.15
1.24
.23
1.32
1.31
1.41
1.39
100
0.94
0.93
1.00
0.98
1.06
1.04
1.12
1.11
1.19
.18
1.27
1.25
1.35
1.33
102
0.92
0.90
0.97
0.95
1.03
1.01
1.09
1.06
1.15
1.13
1.22
1.19
1.29
1.27
104
0.90
0.87
0.95
0.92
1.00
0.97
1.06
1.02
1.12
1.08
1.18
1.14
1.25
1.21
106
0.88
0.84
0.92
0.89
0.97
0.94
1.03
0.99
1.09
1.04
1.14
1.10
1.20
1.16
108
0.86
0.82
0.90
0.86
0.95
0.90
1.00
0.95
1.05
1.90
1.11
1.05
1.17
1.11
110
0.84
0.79
0.88
0.83
0.93
0.87
0.98
0.92
1.02
0.96
1.08
1,01
1.13
1.06
112
0.83
0.77
0.87
0.80
0.91
0.84
0.95
0.88
1.00
0.93
1.05
0.97
1.10
1.02
114
0.81
0.74
0.85
0.78
0.89
0.82
0.93
0.85
0.98
0.89
1.02
0.93
1.07
0.98
116
0.80
0.72
0.84
0.75
0.88
0.79
0.92
0.82
0.96
0.85
1.00
0.90
1.04
0.94
118
0.79
0.70
0.83
0.73
0.86
0.76
0.90
0.79
0.94
0.83
0.98
0.86
1.02
0.90
120
0.78
0.68
0.82
0.71
0.85
0.74
0.89
0.77
0.91
0.80
0.96
0.83
1.00
0.87
122
0.77
0.66
0.81
0.68
0.84
0.71
0.87
0.74
0.90
0.77
0.95
0.80
0.98
0.83
124
0.77
0.63
0.80
0.66
0.83
0.69
0.86
0.71
0.90
0.74
0.93
0.77
0.96
0.80
126
0.76
0.61
0.79
0.64
0.82
0.66
0.85
0.69
0.88
0.71
0.91
0.74
0.95
0.77
128
0.75
0.59
0.78
0.62
0.81
0.64
0.84
0.66
0.87
0.69
0.90
0.71
0.93
0.74
130
0.75
0.57
0.78
0.60
0.81
0.62
0.83
0.64
0.86
0.66
0.89
0.68
0.92
0.71
132
0.75
0.56
0.77
0.57
0.80
0.59
0.83
0.61
0.85
0.64
0.88
0.66
0.'91
0.68
134
0.74
0.54
0.77
0.55
0.80
0.57
0.82
0.59
0.85
0.61
0.87
0.63
0.90
0.65
136
0.74
0.52
0.77
0.53
0.80
0.55
0.82
0.57
0.84
0.58
0.87
0.60
0.89
0.62
138
0.74
0.50
0.77
0.51
0.79
0.53
0.81
0.54
0.84
0.56
0.86
0.58
0.89
0.59
140
0.74
0.48
0.77
0.49
0.79
0.51
0.81
0.52
0.83
0.54
0.86
0.55
0.88
0.57
142
0.74
0.46
0.77
0.47
0.79
0.49
0.81
0.50
0.83
0.51
0.85
0.52
0.87
0.54
144
0.75
0.44
0.77
0.45
0.79
0.46
0.81
0.48
0.83
0.49
0.85
0.50
0.87
0.51
146
0.75
0.42
0.77
0.43
0.79
0.44
0.81
0.45
0.83
0.46
0.85
0.47
0.87
0.49
148
0.76
0.40
0.77
0.41
0.79
0.42
0.81
0.43
0.83
0.44
0.85
0.45
0.87
0.46
150
0.76
0.38
0.78
0.39
0.80
0.40
0.81
0.41
0.83
0.42
0.85
0.42
0.87
0.43
152
0.77
0.36
0.78
0.37
0.80
0.38
0.82
0.38
0.83
0.39
0.85
0.40
0.87
0.41
154
0.77
0.34
0.79
0.35
0.81
0.35
0.82
0.36
0.84
0.37
0.85
0.37
0.87
0.38
156
0.78
0.32
0.80
0.32
0.81
0.33
0.83
0.34
0.84
0.34
0.86
0.35
0.87
0.35
158
0.79
0.30
0.81
0.30
0.82
0.31
0.83
0.31
0.85
0.32
0.86
0.32
0.87
0.33
160
0.80
0.27
0.82
0.28
0.83
0.28
0.84
0.29
0.85
0.29
0.86
0.30
0.88
0.30
TABLE 5B. [Page 637
Distance of an Object by Two Bearings.
Difference
between
Difference between the course and first bearing.
ttiG course
md second
62°
64°
66°
6S°
70°
72°
74°
76°
bearing'.
•
72°
5.08
4.84
74
4.25
4.08
5.18
4.98
76
3.65
3.54
4.32
4.19
5.26
5.10
•
78
3.20
3.13
3.72
3.63
4.39
4.30
5.34
5.22
80
2.86
2.81
3.26
3.21
3.78
3.72
4.46
4.39
5.41
5.33
82
2.58
2.56
2.91
2.88
3.31
3.28
3.83
3.80
4.52
4.48
5.48
5.42
84
2.36
2.34
2.63
2.61
2.96
2.94
3.36
3.35
3.88
3.86
4.57
4. 55
5. 54
5.51
86
2.17
2.17
2.40
2.39
2.67
2.66
3.00
2.99
3.41
3.40
3.93
3.92
4.62
4.61
5.59
5.57
88
2.01
2.01
2.21
2.21
2.44
2.44
2.71
2.71
3.04
3.04
3.45
3.45
3.97
3.97
4.67
4.66
90
1.88
1.88
2.05
2.05
2.25
2.25
2.48
2.48
2.75
2.75
3.08
3.08
3.49
3.49
4.01
4.01
92
1.77
1.76
1.91
1.91
2.08
2.08
2.28
2.28
2.51
2.51
2.78
2.78
3.11
3.11
3.52
3.52
94
1.67
1.66
1.80
1.79
1.95
1.94
2.12
2.11
2.31
2.30
2.54
2.53
2.81
2.80
3.14
3.13
96
1.58
1.57
1.70
1.69
1.83
1.82
1.97
1.96
2.14
2.13
2.34
2.33
2.57
2.55
2.84
2.82
98
1.50
1.49
1.61
1.59
1.72
1.71
1.85
1.84
2.00
1.98
2.17
2.15
2.36
2.34
2.59
2.56
100
1.43
1.41
1.53
1.51
1.63
1.61
1.75
1.72
1.88
1.85
2.03
2.00
2.19
2.16
2.39
2.35
102
1.37
1.34
1.46
1.43
1.55
1.52
1.66
1.62
1.77
1.73
1.90
1.86
2.05
2.00
o 21
2.16
104
1.32
1.28
1.40
1.36
1.48
1.44
1.58
1.53
1.68
1.63
1.79
1.74
1.92
1.87
2.07
2.01
106
1.27
1.22
1.34
1.29
1.42
1.37
1.51
1.45
1.60
1.54
1.70
1.63
1.81
1.74
1.94
1.87
108
1.23
1.17
1.29
1.23
1.37
1.30
1.44
1.37
1.53
1.45
1.62
1.54
1.72
1.63
1.83
1.74
110
1.19
1.12
1.25
1.17
1.32
1.24
1.39
1.30
1.46
1.37
1.54
1.45
1.64
1.54
1.74
1.63
112
1.15
1.07
1.21
1.12
1.27
1.18
1.33
1.24
1.40
1.30
1.48
1.37
1.56
1.45
1.65
1.53
114
1.12
1.02
1.17
1.07
1.23
1.12
1.29
1.18
1.35
1.24
1.42
1.30
1.50
1.37
1.58
1.44
116
1.09
0.98
1.14
1.03
1.19
1.07
1.25
1.12
1.31
1.17
1.37
1.23
1.44
1.29
1.51
1.36
118
1.07
0.94
1.11
0.98
1.16
1.02
1.21
1.07
1.26
1.12
1.32
1.17
1.38
1. 22
1.45
1.28
120
1.04
0.90
1.08
0.94
1.13
0.98
1.18
1.02
1.23
1.06
1.28
1.11
1.34
1.16
1.40
1.21
122
1.02
0.86
1.06
0.90
1.10
0.93
1.15
0.97
1.19
1.01
1.24
1.05
1.29
1.10
1.35
1.14
124
1.00
0.83
1.04
0.86
1.08
0.89
1.12
0.93
1.16
0.96
1.21
1.00
1.25
1.04
1.31
1.08
126
0.98
0.79
1.02
0.82
1.05
0.85
1.09
0.88
1.13
0.92
1.18
0.95
1.22
0.99
1.27
1.02
128
0.97
0.76
1.00
0.79
1.03
0.82
1.07
0.84
1.11
0.87
1.15
0.90
1.19
0.94
1.23
0.97
130
0.95
0.73
0.98
0.75
1.02
0.78
1.05
0.80
1.09
0.83
1.12
0.86
1.16 0.89
1.20
0.92
132
0.94
0.70
0.97
0.72
1.00
0.74
1.03
0.77
1.06
0.79
1.10
0.82
1.13
0.84
1.17
0.87
134
0.93
0.67
0.96
0.69
0.99
0.71
1.01
0.73
1.04
0. 75
1.08
0.77
1.11
0.80
1.14
0.82
136
0.92
0.64
0.95
0.66
0.97
0.68
1.00
0.69
1.03
0.71
1.06
0.74
1.09
0.76
1.12
0.78
138
0.91
0.61
0.94
0.63
0.96
0.64
0.99
0.66
1.01
0.68
1.04
0.70
1.07
0.72
1.10
0.74
140
0.90
0.58
0.93
0.60
0.95
0.61
0.97
0.63
1.00
0.64
1.03
0.66
1.05
0.68
1.08
0.70
142
0.90
0.55
0.92
0.57
0.94
0.58
0.96
0.59
0.99
0.61
1.01
0.62
1.04
0.64
1.06
0.65
144
0.89
0.52
0.91
0.54
0.93
0.55
0.96
0.56
0.98
0.57
1.00
0.59
1.02
0.60
1.05
0.62
146
0.89
0.50
0.91
0.51
0.93
0.52
0.95
0.53
0.97
0.54
0.99
0.55
1.01
0.57
1.03
0.58
148
0.89
0.47
0.90
0.48
0.92
0.49
0.94
0.50
0.96
0.51
0.98
0.52
1.00
0.53
1.02
0.54
150
0.88
0.44
0.90
0.45
0.92
0.46
0.94
0.47 0.95 JO. 48
0.97
0.49
0.99
0.50
1.01
0.50
152
0.88
0.41
0.90
0.42
0.92
0.43
0.93
0.44|jfl|Lo.45
0.97
0.45
0.98
0.46
1.00
0.47
154
0. 88 j 0. 39
0.90
0.39
0.91
0.40
0.93
:
0.96
0.42
0.98
0.43
0.99
0.43
156
0. 89 ! 0. 36
0.90
0.37
0.91
0.37
0.93
0.96
0.39
0.97
0.39
0.99
0.40
158
0. 89 ! 0. 33
0.90
0.34
0.91
0.34
0.93
°- 3»HRO. 35
0.95
0.36
0.97
0.36
0.98
0.37
160
0. 89 ! 0. 30
0.90
0.31
0.91
0.31
0.93
0. 3BK V 32
0.95
0.33
0.96
0.33
0.98
0.33
61828°— 16 34
Page 638] TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
tliG course
Difference between the course and first bearing.
and second
bearing.
78°
80°
82°
84°
se°
88°
90°
91°
88°
5.63
5.63
90
4.70
4.70
5.67
5.67
92
4.04
4.04
4.74
4.73
5.70
5.70
94
3.55
3.54
4.07
4.06
4.76
4.75
5.73
5.71
96
3.17
3.15
3.57
3.55
4.09
4.07
4.78
4.76
5.74
5.71
98
2.86
2.83
3.19
3.16
3. od
3.56
4.11
4.07
4.80
4.75
5.76
5.70
100
2.61
2.57
2.88
2.84
3.20
3.16
3.61
3.55
4.12
4.06
4.81
4.73
5.76
5.67
102
2.40
2.35
2.63
2.57
2.90
2.83
3.22
3.15
3.62
3.54
4.13
4.04
4.81
4.70
5.76
5.63
104
2.23
2.16
2.42
2.35
2.64
2.56
2.91
2.82
3.23
3.13
3.63
3.52
4.13
4.01
4.81
4.66
106
2.08
2.00
2.25
2.16
2.43
2.34
2.65
2.55
2.92
2.80
3.23
3.11
3.63
3.49
4.13
3.97
108
1.96
1.86
2.10
2.00
2.26
2.15
2.45
2.33
2.66
2.53
2.92
2.78
3.24
3.08
3.63
3.45
110
1.85
1.73
1.97
1.85
2.11
1.98
2.27
2.13
2.45
2.31
2.67
2.51
2.92
2.75
3.23
3.04
112
1.75
1.62
1.86
1.72
1.98
1.83
2.12
1.96
2.28
2.11
2.46
2.28
2.67
2.48
2.92
2.71
114
1.66
1.52
1.76
1.61
1.87
1.71
1.99
1.82
2.12
1.94
2.28
2.08
2.46
2.25
2.67
2.44
116
1.59
1.43
1.68
1.51
1.77
1.59
1.88
1.69
2.00
1.79
2.13
1.91
2.28
2.05
2.46
2.21
118
1.52
1.34
1.60
1.41
.68
1.49
1.78
1.57
1.88
1.66
2.00
1.76
2.13
1.88
2.28
2.01
120
1.46
1.27
1.53
1.33
.61
1.39
1.69
1.47
1.78
1.54
1.89
1.63
2.00
1.73
2.13
1.84
122
1.41
1.19
1.47
1.25
.54
1.31
1.62
1.37
1.70
1.44
1.79
1.52
1.89
1.60
2.00
1.70
124
1.36
1.13
1.42
1.18
.48
1.23
1.55
1.28
1.62
1.34
1.70
1.41
1.79
1.48
1/89
1.56
126
1.32
1.06
1.37
1.11
.43
1.15
1.48
1.20
1.55
1.26
1.62
1.31
1.70
1.38
1.79
1.45
128
1.28
1.01
1.33
1.04
.38
1.08
1.43
1.13
1.49
1.17
1.55
1.23
1.62
1.28
1.70
1.34
130
1.24
0.95
1.29
0.98
1.33
1.02
.38
1.06
1.44
1.10
1.49
1.14
1.56
1.19
1.62
1.24
132
1.21
0.90
1.25
0.93
1.29
0.96
.34
0.99
1.39
1.08
1.44
1.07
1.49
1.11
1.55
1.16
134
1.18
0.85
1.22
0.88
1.26
0.90
.30
0.93
1.34
0.97
1.39
1.00
1.44
1.04
1.49
1.07
136
1.15
0.80
1.19
0.83
1.22
0.85
.26
0.88
1.30
0.90
1.34
0.93
1.39
0.97
1.44
1.00
138
1.13
0.76
1.16
0.78
1.19
0.80
.23
0.82
1.27
0.85
1.30
0.87
1.35
0.90
1.39
0.93
140
.11
0.71
1.14
0.73
1.17
0.75
.20
0.77
1.23
0.79
1.27
0.82
1.31
0.84
1.34
0.86
142
.09
0.67
.12
0.69
1.14
0.70
1.17
0.72
1.20
0.74
1.24
0.76
1.27
0.78
1.30
0.80
144
.07
0.63
.10
0.64
1.12
0.66
1.15
0.67
1.18
0.69
1.21
0.71
1.24
0.73
1.27
0.75
146
.05
0.59
.08
0.60
1.10
0.62
1.13
0.63
1.15
0.64
1.18
0.66
1.21
0.67
1.24
0.69
148
1.04
0.55
.06
0.56
1.08
0.57
1.11
0.59
1.13
0.60
1.15
0.61
1.18
0.62
1.21
0.64
150
1.03
0.51
.05
0.52
1.07 0.53
1.09
0.54
1.11
0.55
1.13
0.57
1.15
0.58
1.18
0.59
152
1.02
0.48
.04
0.49
1.05 0.49
1.07
0.50
1.09
0.51
1.11
0.52
1.13
0.53
1.15
0.54
154
1.01
0.44
.02
0.45
1.04 0.46
1.06
0.46
1.08
0.47
1.09
0.48
1.11
0.49
1.13
0.50
156
1.00
0.41
.01
0.41
1.03 0.42
1.05
0.43
1.06
0.43
1.08
0.44
1.09
0.45
1.11
0.45
158
0.99
0.37
.01
0.38
1.02 0.38
1.03
0.39
1.05
0.39
1.06
0.40
1.08
0.40
1.09
0.41
160
0.99
0.34
.00
0.34
1. 01 i 0. 35
1.02
0.35
1.04
0.35
1.05
0.36
1.06
0.36
1.08
0.37
94°
96°
98°
100°
102°
104°
106°
108°
104°
5.74
5.57
106
4.80
4.61
5.78
5.51
108
4.12
3.92
4.78
4.55
5.70
5.42
110
3.62
3.40
4.11
3.86
4.76
4.48
5.67
5.33
112
3.23
2.99
3.61
3.35
4.09
3.80
4.74
4.40
5.63
5.22
114
2.92
2.66
3.22
2.94
3.59
3.28
4.07
3.72
4.70
4.30
5.59
5.10
116
2.66
2.39
2.91
2.61
3.20
2.88
3.57
3.21
4.04
3.63
4.67
4.19
5.54
4.98
118
2.45
2.17
2.65
2.34
2.90
2.56
3.19
2.81
3.55
3.13
4.01
3.54
4.62
4.08
5.48
4.84
120
2.28
1.97
2.45
2.12
2.64
2.29
2.88
2.49
3.17
2.74
3.52
3.05
3.97
3.44
4.57
3.96
122
2.12
1.80
2.27
1.92
2.43
2.06
2.63
2.23
2.86
2.43
3.14
2.66
3.49
2.96
3.93
3.33
124
2.00
1.65
2.12
1.76
2.26
1.87
2.42
2.01
2.61
2.16
2.84
2.35
3.11
2.58
3.45
2.86
126
.88
1.52
1.99
1.61
2.11
1.71
2.25
1.82
2.40
1.95
2.59
2.10
2.81
2.27
3.08
2.49
128
.78
1.41
1.88
1.48
1.98
1.56
2.10
1.65
2.23
1.76
2.39
1.88
2.57
2.02
2.78
2.19
130
.70
1.30
1.78
1.36
1.87
1.43
1.97
1.51
2.08
1.60
2.21
1.70
2.36
1.81
2.54
1.94
132
.62
1.20
1.69
1.26
1.77
1.32
1.86
1.38
1.96
1.45
2.07
1.54
2.19
1.63
2.34
1.74
134
.55
1.12
1.62
1.16
1.68
1.21
1.76
1.27
1.85
1.33
1.94
1.40
2.05
1.47
2.17
1.56
136
1.49
1.04
1.55
1.07
1.61
1.12
1.68
1.16
1.75
1.22
1.83
1.27
1.92
1.34
2.03
1.41
138
.44
0.96
1.49
0.99
1.54
1.03
1.60
1.07
1.66
1.11
1.74
1.16
1.81
1.21
1.90
1.27
140
.39
0.89
1.43
0.92
1.48
0.95
1.53
0.98
1.59
1.02
1.65
1.06
1.72
1.10
1.79
1.15
142
.34
0.83
1.38
0.85
1.43
0.88
1.47
0.91
1.52
0.94
1.58
0.97
1.64
1.01
1.70
1.05
144
.30
0.77
1.34
0.79
1.38
0.81
1.42
0.83
1.46
0.86
1.51
0.89
1.56
0.92
1.62
0.95
146
.27
0.71
1.30
0.73
1.33
0.75
1.37
0.77
1.41
0.79
1.45
0.81
1.50
0.84
1.54
0.86
148
.23
0.65
1.26
0.67
1.29
0.69
1.33
0.70
1.36
0.72
1.40
0.74
1.44
0.76
1.48
0.78
150
.20
0.60
1.23
0.61
1.26
0.63
1.29
0.64
1.32
0.66
1.35
0.67
1.38
0.69
1.42
0.71
152
.18
0.55
1.20
0.56
1.22
0.57
1.25
0.59
1.28
0.60
1.31
0.61
1.34
0.63
1.37
0.64
154
.15
0.50
1.17
0.51
1.19
0.52
1.22
0.53
1.24
0.54
1.27
0.56
1.29
0.57
1.32
0.58
156
.13
0.46
1.15
0.47
1.17
0.47
1.19
0.48
1.21
0.49
1.23
0.50
1.25
0.51
1.28
0.52
158
1.11
0.42
1.13
0.42
1.14
0.43
1.16
0.44
1.18
0.44
1.20
0.45
1.22
0.46
1.24
0.47
160
1.09
0.37
1.11
0.38
1.12
0.38
1.14
0.39
1.15
0.39
1.17
0.40
1.19
0.41
1.21
0.41
TABLE 5B. [Page 639
Distance of an Object by Two Bearings.
Difference
Difference between the course and first bearing.
between
the course
and second
bearing.
110°
112°
114°
116°
118°
120°
128°
120°
5.41
4.69
122
4.52
3.83
5.34
4.53
124
3.88
3.22
4.46
3.70
5.26
4.36
126
3.41
2.76
3.83
3.10
4.39
3.55
5.18
4.19
128
3.04
2.40
3.36
2.65
3.78
2.98
4.32
3.41
5.08
4.01
130
2.75
2.10
3.00
2.30
3. 31 i 2. 54
3.72
2.85
4.25
3.25
4. 99 3. 82
132
2.51
1.86
2.71
2.01
2. 96 ! 2. 20
3.26
2.42
3.65
2.71
4. 17 3. 10
4.88
3.63
134
2.31
1.66
2.48
1.78
2.67 1.92
2.91
2.09
3.20
2.30
3. 58 2. 57
4.08
2.93
136
2.14
1.49
2.28
1.58
2.44 1.69
2.63
1.83
2.86
1.98
3. 14 2. 18
3.51
2.44
138
2.00
1.34
2.12
1.42
2. 25 ! 1. 50
2.40
1.61
2.58
1.73
2.80 i 1.88
3.08
2.06
140
1.88
1.21
1.97
1.27
2. 08 1. 34
2.21
1.42
2.36
1.52
2. 53 i 1. 63
2.74
1.76
142
1.77
1.09
1.85 1.14
1. 95 1. 20
2.05
1.26
2.17
1.34
2. 31 1. 42
2.48
1.53
144
1.68
0.99
1.75
1.03
1.83 1.07
1.91
1.13
2.01
1.18
2.13 i 1.25
2.26
1.33
146
1.60
0.89
1.66
0.93
1. 72 0. 96
1.80
1.01
1.88
1.05
1.98 | 1.10
2.08
1.17
148
1.53
0.81
1.58
0.84
1. 63 ! 0. 87
1.70
0.90
1.77
0.94
1.84 ; 0.98
1.93
1.03
150
1.46
0.73
1.51
0.75
1. 55 I 0. 78
1.61
0.80
1.67
0.83
1. 73 1 0. 87
1.81
0.90
152
1.40
0.66
1.44
0.68
1. 48 ! 0. 70
1.53
0.72
1.58
0.74
1. 63 0. 77
1.70
0.80
154
1.35
0.59
1.39
0.61
1. 42 0. 62
1.46
0.64
1.50
0.66
1. 55 0. 68
1.60
0.70
156
1.31
0.53
1.33
0.54
1. 37 0. 56
1.40
0.57
1.43
0.58
1. 47 0. 60
1.52
0.62
158
1.26 0.47
1.29
0.48
1. 32 0. 49
1.34
0.50
1.37
0.51
1.41 • 0.53
1.44
0.54
160
1. 23 | 0. 42
1.25
0.43
1. 27 I 0. 43
1.29
0.44
1.32
0.45
1. 35 0. 46
1.38
0.47
124°
126°
128°
130°
132°
134°
136°
134°
4.77
3.43
136
3.99
2.77
4.66
3.23
138
3.43
2.29
3.89
2.60
4.54
3.04
9
140
3.01
1.93
3.34
2.15
3.79
2.44
4.41
2.84
142
2.68
1.65
2.94
1.81
3.26
2.01
3.68
2.27
4.28
2.63
144
2.42
1.42
2.62
1.54
2.86
1.68
3.17
1.86
3.57
2.10
4.14
2.43
146
2.21
1.24
2.37
1.32
2.55
1.43
2.78
1.55
3. 07 ! 1. 72
3.46
1.93
4.00
2.24
148
2.04
1.08
2.16
1.14
2.30
1.22
2.48
1.31
2.70
1.43
2.97
1.58
3.34
1.77
150
1.89
0.95
1.99
0.99
2.10
1.05
2.24
1.12
2.40
1.20
2.61
1.30
2.87
1.44
152
1.77
0.83
1.85
0.87
1.94
0.91
2.04
0.96
2.17
1.02
2.33
1.09
2.52
1.18
154
1.66
0.73
1.72
0.76
1.80
0.79
1.88
0.83
1.98
0.87
2.10
0.92
2.25
0.99
156
1.56
0.64
1.62
0.66
1. 68 0. 68
1.75
0.71
1.83
0.74
1.92
0.78
2.03
0.83
158
1.48
0.56
1.53
0.57
1.58
0.59
1.63
0.61
1.70
0.64
1.77
0.66
1.85
0.69
160
1.41
0.48
1.45
0.49
1.49
0.51
1.53
0.52
1.58 j 0.54
1.64
0.56
1.71
0.58
138°
140°
142C
144°
146°
148°
160°
148°
3.85
2.04
-
150
3. 22 1. 61
3.70
1.85
152
2. 77 1. 30
3.09
1.45
3.55
1.66
154
2.43 1.06
2.66
1.16
2.96
1.30
3.38
1.48
156
2. 17 0. 88
2.33
0.95
2. 54 I 1. 04
2.83
1.15
3.22
1.31
158
1. 96 1 0. 73
2.08
0.78
2. 23 0. 84
2.43 ; 0.91
2.69
1.01
3.05
1.14
160
1. 79 0. 61
1.88
0.64
1. 99 0. 68
2.13 0.73
2.31
0.79
2.55
0.87
2.88
0.98
Ps
ige 640] TABLE 6.
Distance of Visibility of Objects at Sea.
Height,
feet.
Nautical
miles.
Statute
miles.
Height,
feet.
Nautical
miles.
Statute
miles.
Height,
feet.
Nautical
miles.
Statute
miles.
1
1.1
1.3
100
11.5
13.2
760
31.6
36.4
2
1:7
1.9
105
11.7
13.5
780
32.0
36.9
3
2.0
2.3
110
12.0
13.8
800
32.4
37.3
4
2.3
2.6
115
12.3
14.1
820
32.8
37.8
5
2.5
2.9
120
12.6
14.5
840
33.2
38.3
6
2.8
3.2
125
12.9
14.8
860
33.6
38.7
7
2.9
3.5
130
13.1
15.1
880
34.0
39.2
8
3.1
3.7
135
13.3
15.3
900
34.4
39.6
9
3.5
4.0
140
13.6
15.6
920
34.7
40.0
10
3.6
4.2
145
13.8
15.9
940
35.2
40.5
11
3.8
4.4
150
14.1
16.2
960
35.5
40.9
12
4.0
4.6
160
14.5
16.7
980
35.9
41.3
13
4.2
4.8
170
14.9
17.2
1,000
36.2
41.7
14
4.3
4.9
180
15.4
17.7
1,100
38.0
43.8
15
4.4
5.1
190
15.8
18.2
1,200
39.6
45.6
16
4.6
5.3
200
16.2
18.7
1,300
41,3
47.6
17
4.7
5.4
210
16.6
19.1
1,400
42.9
49.4
18
4.9
5.6
220
17.0
19.6
1,500
44.4
51.1
19
5.0
5.8
230
17.4
20.0
1,600
45.8
52.8
20
5.1
5.9
240
17.7
20.4
1,700
47.2
54.4
21
5.3
6.1
250
18.2
20.9
1,800
48.6
56.0
22
5.4
6.2
260
18.5
21.3
1,900
49.9
57.5
23
5.5
6.3
270
18.9
21.7
2,000
51.2
59.0
24
5.6
6.5
280
19.2
22.1
2,100
52.5
60.5
25
5.7
6.6
290
19.6
22.5
2,200
53.8
61.9
26
5.8
6.7
300
19.9
22.9
2,300
55.0
63.3
27
6.0
6.9
310
20.1
23.2
2, 400 1 56. 2
64.7
28
6.1
7.0
320
20.5
23.6
2,500
57. 3 66. 0
29
6.2
7.1
330
20.8
24.0
2,600
58.5
67.3
30
6.3
7.2
340
21.1
24.3
2,700
59.6
68.6
31
6.4
7.3
350
21.5
24.7
2,800
60.6
69.8
32
6.5
7.5
360
21.7
25.0
2,900
61.8
71.1
33
6.6
7.6
370
22.1
25.4
3,000
62.8
72.3
34
6.7
7.7
380
22.3
25.7
3,100
63.8
73.5
35
6.8
7.8
390
22.7
26.1
3,200
64.9
74.7
36
6.9
7.9
400
22.9
26.4
3,300
65.9
75.9 .
37
6.9
8.0
410
23.2
26.7
3,400
66.9
77.0
38
7.0
8.1
420
23.5
27.1
3,500
67.8
78.1
39
7.1
8.2
430
23.8
27.4
3, 600
68.8
79.2
40
7.2
' 8.3
440
24.1
27.7
3,700
69.7
80.3
41
7.3
8.4
450
24.3
28.0
3,800
70.7
81.4
42
7.4
8.5
460
24.6
28.3
3,900
71.6
82.4
43
7.5
8.7
470
24.8
28.6
4,000
72.5
83.5
44
7.6
8.8
480
25.1
28.9
4,100
73.4
84.5
45
7.7
8.9
490
25.4
29.2
4,200
74.3
85.6
46
7.8
9.0
500
25.6
29.5
4,300
75.2
86.6
47
7.9
9.0
520
26.1
30.1
4,400
76.1
87.6
48
7.9
9.1
540
26.7
30.7
4,500
76.9
88.5
49
8.0
9.2
560
27.1
31.2
4,600
77.7
89.5
50
8.1
9.3
580
27.6
31.8
4,700
78.6
90.5
55
8.5
9.8
600
28.0
32.3
4,800
79.4
91.4
60
8.9
10.2
620
28.6
32.9
4,900
80.2
92.4
65
9.2
10.6
640
29.0
33.4
5,000
81.0
93.3
70
9.6
11.0
660
29.4
33.9
6,000
88.8
102.2
75
9.9
11.4
680
29.9
34.4
7,000
96.0
110.5
80
10.3
11.8
700
30.3
34.9
8,000
102.6
118.1
85
10.6
12.2
720
30.7
35.4
9,000
108.7
125.2
90
10. 9
12.5
740
31.1
35.9
10, 000
114.6
132.0
95
11.2
12.9
: TABLE 7. [Page 641
; For converting Arc into Time, and the reverse.
0
H. M.
o
H. M.
0
H. M.
o
H. M.
H. M.
0
H. M.
'
M. S.
M. S.
'
M. S.
•
M. S.
'
M. 8.
e
M. S.
. „
s. *v
//
& &
II
s. &
It
S. A
rr
s. &
//
s. *
1 i~
• 1
0 4
61
4 4
121
8 4
181
12 4
241 16 4
301
20 4
2
0 8
62
4 8
122
8 8
182
12 8
242
16 8
302
20 8
7 3
0 12"
63
4 12
123
8 12
183
12 12
243
16 12
303
20 12
4
0 16
64
4 16
124
8 16
184
»12 16
244
16 16
304
20 16
5
0 20
65
4 20
126
8 20
185
12 20
245
16 20
305
20 20 -
1 6 0 24
66
4 24
126
8 24
186
12 24
246
16 24
306
20 24
7(0 28^
67
4 28
127
8 28
187
12 28
247
16 28
307
20 28
8 0 32
68
4 32
128
8 32
188 12 32
248
16 32
308
20 32
9 0 36
69
4 36
129
8 36
189 12 36
249
16 36
309
20 36
10 , 0 40
70
4 40
130
8 40
190 12 40
250
16 40
310
20 40
11 0 44
71
4 44
131
8 44
191 ; 12 44
251
16 44
311
20 44
12 0 48*
72
4 48
132
8 48
192 12 48
252
16 48
312
20 48
13 0 52
73
4 52
133
8 52
193 12 52
253
16 52
313
20 52
14 0 56
74
4 56
134
8 56
194
12 56
254
1656
314
20 56
15 10
75
5 0
135
9 0
195
13 0
255
17 0
315
21 0
16 14
76
5 4
.-136
9 4
196
13 4
256
17 4
316
21 4
17 18
77
5 8
137
9 8
197
13 8
257 17 8
317
21 8
18 1 1 12
78
5 12
138
9 12
198
13 12
258 17 12
318
21 12
i 19 • 1 16
79
5 16
139
9 16
199
13 16
259 i 17 16
319
21 16
II 20 1 20
80
5 20
140
9 20
200
13 20 260 ! 17 20
320
21 20
21
1 24
81
5 24
141
9 24
201
13 24 261 ! 17 24
321
21 24
; 22
1 28
82
5 28
142
9 28
202
13 28
. 262 i 17 28
322
21 28
i 23
1 32
83
5 32
143
9 32
203
13 32
263 17 32
323
21 32
•• 24
1 36
84
5 36
144
9 36
201
13 36
264 17 36
324
21 36
I 25
1 40
85
5 40
145
9 40
205
13 40
265 17 40
325
21 40
' 26
1 44
86
5 44
146
9 44
206
13 44
266 17 44
326
21 44
i 27
1 48
87
5 48
147
9 48
207
13 48
267 17 48
327
21 48
; 28
1 52
88
5 52
148
9 52
208
13 52
268
17 52
328
21 52
; 29
1 56
89
5 56
149
9 56
209
13 56
269
17 56
329
21 56
i 30
2 0
90
6 0
150
10 0
210
14 0
270
18 0
330
22 0
; 31
2 4
91
6 4
151
10 4
211
14 4
271 18 4
331
22 4
I 32
2 8
92
6 8
152
10 8
212
14 8
272 18 8
332
22 8
j 33
2 12
93
6 12
153
10 12
213
14 12
273 18 12
333
°2 12
I 34
2 16
94
6 16
154
10 16
214
14 16
274
18 16
334
22 16
1 35
2 20
95
6 20
155
10 20
215
14 20
275 18 20
335 ,
22 20
! 36
2 24
96
6 24
156
10 24
216
14 24
276 18 24
336
22 24
1 37
2 28
97
6 28
157
10 28
217
14 28
277
18 28
337 i
22 28
i 38
2 32
98
6 32
158 !
10 32
218
14 32
278
18 32
338
22 32
* 39
2 36
99
6 36
159 '
10 36
219
14 36
279
18 36
339
22 36
| 40
2 40
100
6 40
160
10 40
220
14 40
280 18 40
340
22 40
41
2 44
101
6 44
161
10 44
221
14 44
281 i 18 44
341
22 44
1 42
2 48
102
6 48
162
10 48
222
14 48
282 18 48
342
22 48
i 43
2 52
103
6 52
163
10 52
223
14 52
283
18 52
343
22 52
| 44
2 56
104
6 56
164 i
10 56
224
14 56
284
18 56
344
22 56
! 45
3 0
105
7 0
165
11 0
225
15 0
285
19 0
345
23 0
3 4
106
7 4
166
11 4
226
15 4
286
19 4
346
23 4
! 47
3 8
107
7 8
167
11 8
227
15 8
287
19 8
347 |
23 8
: 48
3 12
108
7 12
163
11 12
228
15 12
288
19 12
348
23 12
49
3 16
109
7 16
169
11 16
229
15 16
289
19 16
349
23 16
I 50
3 20
110
7 20
170
11 20
230
15 20
290
19 20
350
23 20
i 51
3 24
111
7 24
171 !
11 24
231
15 24
291 i 19 24
351 !
23 24
[ 52
3 28
112
7 28
172 :
11 28
232
15 28
292 19 28
352
23 28
] 53
3 32
113
7 32
173 1
11 32
233
15 32
293
19 32
353
23 32
' 54
3 36
114
7 36-
174 !
11 36
234
15 36
294
19 36
354 i
23 36
i 55
3 40
115
7 40
175 !
11 40
235
15 40
295
19 40
355
23 40
: 56
3 44
116
7 44
176 !
11 44
236
15 44
296 19 44
356
23 44
57
3 48
117
7 48
177
11 48
237
15 48
297 19 48
357
23 48
58
3 52
118
7 52
178
11 52
238
15 52
298 19 52
358
23 52
• 59
3 56
119
7 56
179 !
11 56
239
15 56
299
19 56
359
23 56
60
4 0
120
8 0
180 ;
12 0
240
16 0
300 20 0
360
24 0
NOTE. — When turning seconds of arc into time, and vice versa, it should be remembered that the fractions are sixtieths:
thus, the value in time 01 42" is not 23.4e, but 2!!3$a-23.S.
Page 642] TABLE 8.
Sidereal into Mean Solar Time.
1
B
a
OQ
To be subtracted from a sidereal time interval.
<*
Ik
2h
3*
4h
6»
6*
7h
For seconds.
tn.
0
1
2
3
4
m. s.
0 0.000
0 0.164
0 0. 328
0 0. 491
0 0.655
m. s.
0 9.830
0 9.993
0 10. 157
0 10. 321
0 10. 485
m. s.
0 19. 659
0 19. 823
0 19.987
0 20. 151
0 20. 314
m. «.
0 29. 489
0 29. 653
0 29. 816
0 29. 980
0 30. 144
m. s.
0 39. 318
0 39. 482
0 39. 646
0 39. 810
0 39. 974
TO. S.
0 49. 148
0 49. 312
0 49. 475
0 49. 639
0 49. 803
m. s.
0 58. 977
0 59. 141
0 59. 305
0 59. 469
0 59. 633
TO. S.
1 8. 807
1 8.971
1 9.135
1 9. 298
1 9. 462
s.
1
2
3
4
8.
0.003
.005
.008
.011
5
6
7
8
9
0 0. 819
0 0. 983
0 1. 147
0 1. 311
0 1. 474
0 10.649
0 10. 813
0 10. 976
0 11. 140
0 11. 304
0 20. 478
0 20. 642
0 20. 806
0 20. 970
0 21. 134
0 30. 308
0 30. 472
0 30. 635
0 30. 799
0 30. 963
0 40. 137
0 40. 301
0 40. 465
0 40. 629
0 40. 793
0 49. 967
0 50. 131
0 50. 295
0 50. 458
0 50. 622
0 59. 796
0 59. 960
1 0. 124
1 0. 288
1 0. 452
1 9.626
1 9.790
1 9.954
1 10.118
1 10.281
5
6
7
8
9
.014
.016
.019
.022
.025
10
11
12
13
14
0 1.638
0 1.802
0 1.966
0 2. 130
0 2. 294
0 11.468
0 11. 632
0 11. 795
0 11. 959
0 12. 123
0 21. 297
0 21. 461
0 21. 625
0 21. 789
0 21. 953
0 31. 127
0 31. 291
0 31. 455
0 31. 618
0 31. 782
0 40. 956
0 41. 120
0 41. 284
0 41. 448
0 41.612
0 50. 786
0 50. 950
0 51. 114
0 51. 278
0 51. 441
1 0. 616
1 0.779
1 0.943
1 1.107
1 1.271
1 10.445
1 10.609
1 10.773
1 10. 937
1 11.100
10
11
12
13
14
.027
.030
.033
.035
.038
15
16
17
18
19
0 2. 457
0 2. 621
0 2. 785
0 2. 949
0 3. 113
0 12.287
0 12. 451
0 12. 615
0 12. 778
0 12.942
0 22. 117
0 22. 280
0 22. 444
0 22. 608
0 22. 772
0 31. 946
0 32. 110
0 32. 274
0 32. 438
0 32. 601
0 41. 776
0 41. 939
0 42. 103
0 42. 267
0 42. 431
0 51. 605
0 51. 769
0 51. 933
0 52.097
0 52. 260
1 1. 435
1 1.599
1 1.762
1 1.926
1 2.090
1 11.264
1 11.428
1 11.592
1 11. 756
1 11.920
15
16
17
18
19
20
21
22
23
24
.041
.044
.046
.049
.052
20
21
22
23
24
0 3. 277
0 3. 440
0 3. 604
0 3. 768
0 3. 932
0 13. 106
0 13. 270
0 13.434
0 13. 598
0 13. 761
0 22. 936
0 23. 099
0 23. 263
0 23. 427
0 23. 591
0 32. 765
0 32. 929
0 33. 093
0 33. 257
0 33. 420
0 42. 595
0 42. 759
0 42. 922
0 43. 086
0 43. 250
0 52. 424
0 52. 588
0 52. 752
0 52. 916
0 53. 080
1 2. 254
1 2. 418
1 2.582
1 2.745
1 2.909
1 12.083
12. 247
12. 411
12. 575
12. 739
.055
.057
.060
.063
.066
25
26
27
28
29
0 4. 096
0 4. 259
0 4. 423
0 4. 587
0 4. 751
0 13. 925
0 14. 089
0 14. 253
0 14.417
0 14. 581
0 23. 755
0 23. 919
0 24. 082
0 24. 246
0 24. 410
0 33. 584
0 33. 748
0 33.912
0 34. 076
0 34. 240
0 43. 414
0 43. 578
0 43. 742
0 43. 905
0 44. 069
0 53. 243
0 53. 407
0 53. 571
0 53. 735
0 53. 899
1 3. 073
1 3. 237
1 3. 401
1 3. 564
1 3. 728
12. 903
13. 066
1 13.230
1 13.394
1 13.558
25
26
27
28
29
.068
.071
.074
.076
.079
30
31
32
33
34
0 4. 915
0 5.079
0 5. 242
0 5. 406
0 5. 570
0 14. 744
0 14. 908
0 15. 072
0 15. 236
0 15. 400
0 24. 574
0 24. 738
0 24. 902
0 25. 065
0 25. 229
0 34. 403
0 34. 567
0 34. 731
0 34. 895
0 35. 059
0 44. 233
0 44. 397
0 44. 561
0 44. 724
0 44. 888
0 54. 063
0 54. 226
0 54. 390
0 54. 554
0 54. 718
1 3.892
1 4.056
1 4.220
1 4.384
1 4.547
1 13. 722
1 13. 886
1 14.049
1 14.213
1 14.377
30
31
32
33
34
.082
.085
.087
.090
.093
35
36
37
38
39
0 5. 734
0 5. 898
0 6. 062
0 6. 225
0 6. 389
0 15.563
0 15. 727
0 15. 891
0 16.055
0 16.219
0 25. 393
0 25. 557
0 25. 721
0 25. 885
0 26.048
0 35. 223
0 35. 386
0 35.550
0 35. 714
0 35. 878
0 45. 052
0 45. 216
0 45. 380
0 45. 544
0 45. 707
0 54. 882
0 55. 046
0 55. 209
0 55. 373
0 55. 537
1 4. 711
1 4. 875
1 5.039
1 5.203
1 5.367
1 14.541
1 14.705
1 14.868
1 15.032
1 15. 196
35
36
37
38
39
.096
.098
.101
.104
.106
40
41
42
43
44
0 6. 553
0 6. 717
0 6. 881
0 7.045
0 7.208
0 16.383
0 16. 546
0 16. 710
0 16. 874
0 17.038
0 26. 212
0 26. 376
0 26. 540
0 26. 704
0 26. 867
0 36. 042
0 36. 206
0 36. 369
0 36. 533
0 36. 697
0 45. 871
0 46. 035
0 46. 199
0 46. 363
0 46. 527
0 55. 701
0 55. 865
0 56. 028
0 56. 192
0 56. 356
1 5. 530
1 5. 694
1 5. 858
1 6. 022
1 6. 186
1 15.360
1 15.524
1 15.688
1 15.851
1 16.015
40
41
42
43
44
.109
.112
.115
.117
.120
45
46
47
48
49
0 7. 372
0 7.536
0 7. 700
0 7.864
0 8. 027
0 17. 202
0 17. 366
0 17. 529
0 17.693
0 17. 857
0 27. 031
0 27. 195
0 27. 359
0 27.523
0 27. 687
0 36. 861
0 37. 025
0 37. 188
0 37. 352
0 37. 516
0 46. 690
0 46. 854
0 47. 018
0 47. 182
0 47. 346
0 56.520
0 56. 684
0 56. 848
0 57. Oil
0 57. 175
1 6.350
1 6.513
1 6.677
1 6. 841
1 7. 005
1 16.179
1 16.343
1 16.507
1 16.671
1 16.834
45
46
47
48
49
.123
.126
.128
.131
.134
50
51
52
53
54
0 8. 191
0 8. 355
0 8.519
0 8. 683
0 8. 847
0 18. 021
0 18. 185
0 18. 349
0 18. 512
0 18.676
0 27. 850
0 28.014
0 28. 178
0 28. 342
0 28. 506
0 37. 680
0 37. 844
0 38. 008
0 38. 171
0 38. 335
0 47.510
0 47. 673
0 47. 837
0 48. 001
0 48. 165
0 57. 339
0 57. 503
0 57. 667
0 57. 831
0 57. 994
1 7.169
1 7.332
1 7.496
1 7.660
1 7. 824
1 .16. 998
1 17. 162
1 17. 326
1 17.490
1 17.654
50
51
52
53
54
.137
.139
.142
.145
.147
55
56
57
58
59
0 9. 010
0 9. 174
0 9. 338
0 9. 502
0 9. 666
0 18.840
0 19. 004
0 19. 168
0 19. 331
0 19. 495
0 28. 670
0 28. 833
0 28. 997
0 29. 161
0 29. 325
0 38.499
0 38. 663
0 38. 827
0 38. 991
0 39. 154
0 48. 329
0 48. 492
0 48. 656
0 48. 820
0 48. 984
0 58. 158
0 58. 322
0 58. 486
0 58. 650
0 58. 814
1 7.988
1 8.152
1 8.315
1 8. 479
1 8.643
1 17.817
1 17.981
1 18. 145
1 18.309
1 18.473
55
56
57
58
59
.150
.153
.156
.158
0.161
TABLE 8.
Sidereal into Mean Solar Time.
[Page 643
1
To be subtracted from a sidereal time interval.
3
8*
9*
10*
1H>
12*
13*
U*
15*
For seconds.
771.
0
1
2
3
4
5
6
7
8
9
LO"
11
[O
i3
14
m. t.
1 18.636
1 18.800
1 1 18.964
1 19.128
1 19.292
m. s.
1 28.466
1 28.630
1 28. 794
1 28. 958
1 29. 121
TO. 8.
1 38. 296
1 38.459
1 38. 623
1 38. 787
1 38. 951
m. s.
1 48. 125
1 48.289
1 48.453
1 48. 617
1 48. 780
m. s.
1 57. 955
1 58. 119
1 58.282
1 58.446
1 58.610
m. s.
2 7.784
2 7.948
2 8. 112
2 8.276
2 8.440
m. s.
2 17.614
2 17. 778
2 17.941
2 18.105
2 18. 269
m. s.
2 27.443
2 27. 607
2 27. 771
2 27. 935
2 28.099
s.
1
2
3
4
8.
0.003
.005
.008
.011
1 19.456 1 29.285
1 19. 619 ! 1 29. 449
1 19. 783 1 29. 613
1 19. 947 i 1 29. 777
1 20.111 1 29.940
1 39.115
1 39.279
1 39.442
1 39. 606
1 39. 770
1 48.944
1 49. 108
1 49. 272
1 49. 436
1 49.600
1 58.774
1 58. 938
1 59. 101
1 59.265
1 59.429
2 8. 603
2 8.767
2 8.931
2 9.095
2 9.259
2 18.433
2 18.597
2 18. 761
2 18. 924
2 19.088
2 28. 263
2 28. 426
2 28.590
2 28. 754
2 28. 918
5
6
7
8
9
10
11
12
13
14
.014
.016
.019
.022
.025
1 20. 275 ; 1 30. 104 { 1 39. 934
1 20. 439 ! 1 30. 268 1 40. 098
1 20. 602 ' 1 30. 432 ' 1 40. 261
1 20. 766 ; 1 30. 596 i 1 40. 425
1 20.930 | 1 30.760 1 40.589
1 49. 763 ; 1 59. 593 2 9. 423
1 49. 927 ! 1 59. 757 2 9. 586
1 50. 091 1 59. 921 2 9. 750
1 50.255 2 0.084 2 9.914
1 50.419 2 0.248 2 10.078
! 2 19.252
2 19.416
2 19. 580
' 2 19. 744
; 2 19.907
2 29. 082
2 29. 245
2 29. 409
2 29. 573
2 29. 737
.027
.030
.033
.035
.038
>O CO 1- 00 Oi
r— I f— 1 rH i— 1 i— 1
1 21. 094 1 30. 923 ; 1 40. 753
l 21.258 1 1 31.087 ; 1 40.917
1 21. 422 : 1 31. 251 1 41. 081
1 21. 585 1 31. 415 i 1 41. 244
1 21.749 • 1 31.579 ! 1 41.408
1 50. 583 I 2 0. 412
1 50. 746 2 0. 576
1 50. 910 2 0. 740
1 51.074 2 0.904
1 51.238 2 1.067
2 10. 242
2 10.405
2 10.569
2 10. 733
2 10.897
2 20. 071
2 20. 235
2 20. 399
! 2 20. 563
! 2 20. 727
2 29.901
2 30.065
2 30. 228
2 30. 392
2 30. 556
15
16
17
18
19
.041
.044
.046
.049
.052
20
21
22
23
24
1 21. 913 1 31. 743 1 41. 572
1 22. 077 1 31. 906 1 41. 736
1 22.241 1 32.070 1 41.900
1 22.404 1 32.234 1 42.064
1 22. 568 1 32. 398 1 42. 227
1 51.402 2 1.231
1 51.565 : 2 1.395
1 51.729 2 1.559
1 51. 893 2 1. 723
1 52.057 2 1.887
2 11.061
2 11. 225
2 11.388
2 11.552
2 11. 716
! 2 20. 890
I 2 21. 054
I 2 21. 218
! 2 21. 382
2 21.546
2 30. 720
2 30. 884
2 31. 048
2 31. 211
2 31. 375
20
21
22
23
24
25~
26
27
28
29
.055
.057
.060
.063
.066
25
26
27
28
29
30
31
12
33
34
1 22. 732 1 32. 562
1 22. 896 1 32. 726
1 23.060 1 32.889
1 23.224 1 33.053
1 23. 387 ! 1 33. 217
1 42.391
1 42.555
1 42. 719
1 42.883
1 43. 047
1 52.221 2 2.050 2 11.880
1 52.385 2 2.214 2 12.044
1 52.548 2 2.378 i 2 12.208
1 52. 712 2 2. 542 I 2 12. 371
1 52. 876 2 2. 706 i 2 12. 535
2 21. 709
2 21. 873
2 22. 037
2 22. 201
2 22. 365
2 31. 539
2 31. 703
2 31. 867
2 32. 031
2 32. 194
.068
.071
.074
.076
.079
1 23.551 i 1 33.381
1 23. 715 1 33. 545
1 23.879 i 1 33.708
1 24. 043 \ 1 33. 872
1 24. 207 1 34. 036
1 43.210
1 43.374
1 43. 538
1 43. 702
1 43. 866
1 53.040 2 2.869
1 53.204 2 3.033
1 53. 368 2 3. 197
1 53. 531 i 2 3. 361
1 53. 695 2 3. 525
2 12.699
2 12.863
2 13. 027
2 13.191
2 13. 354
2 22. 529
2 22.692
2 22. 856
2 23. 020
2 23. 184
2 32. 358
2 32. 522
2 32. 686
2 32. 850
2 33. 013
30
31
32
33
34
.082
.085
.087
.090
.093
15
16
18
19
1 24.370 j 1 34.200
1 24. 534 1 34. 364
1 24. 698 1 34. 528
1 24.862 ! 1 34.691
1 25.026 i 1 34.855
1 44.029
1 44.193
1 44.357
1 44.521
1 44.685
1 53. 859
1 54. 023
1 54. 187
1 54.351
1 54.514
2 3.689
2 3.852
2 4.016
2 4.180
2 4.344
2 13.518
2 13.682
2 13.846
2 14. 010
2 14. 173
2 23. 348
2 23.512
2 23. 675
2 23. 839
2 24.003
2 33. 177
2 33.341
2 33. 505
2 33. 669
2 33. 833
35
36
37
38
39
.096
.098
.101
.104
.106
40
41
.0
3
44
rO
:6
ti
48
49
50
51
52
53
54
1 25. 190
1 25. 353
1 25. 517
1 25. 681
1 25.845
1 35. 019
1 35. 183
1 35.347
1 35.511
1 35.674
1 44.849
1 45.012
1 45.176
1 45.340
1 45.504
1 54.678
1 54.842
1 55.006
1 55. 170
1 55. 333
2 4.508
2 4.672
2 4.835
2 4.999
2 5.163
2 14. 337
2 14.501
2 14.665
2 14.829
2 14.993
2 24. 167
2 24. 331
2 24. 495
2 24.658
2 24.822
2 33. 996
2 34. 160
2 34.324
2 34. 488
2 34. 652
40
41
42
43
44
.109
.112
.115
.117
.120
1 26.009
1 26.172
1 26.336
1 26.500
1 26.664
1 35.838
1 36.002
1 36.166
1 36. 330
1 36. 493
1 45.668
1 45.832
1 45. 995
1 46. 159
1 46. 323
1 55.497
1 55.661
1 55. 825
1 55. 989
1 56. 153
2 5.327
2 5.491
2 5.655
2 5.818
2 5.982
2 15. 156
2 15. 320
2 15.484
2 15. 648
2 15. 812
2 24.986
2 25. 150
2 25.314
2 25.477
2 25.641
2 34. 816
2 34. 979
2 35. 143
2 35. 307
2 35. 471
45
46
47
48
49
.123
.126
.128
.131
.134
1 26.828
1 26. 992
1 27. 155
1 27. 319
1 27.483
1 36.657
1 36.821
1 36. 985
1 37. 149
1 37.313
1 46.487
1 46. 651
1 46. 815
1 46.978
1 47.142
1 56. 316
1 56. 480
1 56.644
1 56.808
1 56.972
2 6.146
2 6.310
2 6.474
2 6. 637
2 6.801
2 15.976
2 16. 139
2 16. 303
2 16. 467
2 16.631
2 25. 805
2 25. 969
2 26. 133
2 26.297
2 26. 460
2 35.635
2 35. 798
2 35. 962
2 36. 126
2 36.290
50
51
52
53
54
.137
.139
.142
.145
.147
55
56
57
58
59
1 27.647
1 27.811
1 27.975
1 28.138
1 28.302
1 37. 476
1 37. 640
1 37.804
1 37.968
1 38. 132
1 47.306
1 47.470
1 47.634
1 47. 797
1 47.961
1 57.136
1 57.299
1 57.463
1 57. 627
1 57. 791
2 6.965
2 7.129
2 7.293
2 7.457
2 7. 620
2 16. 795
2 16. 959
2 17. 122
2 17.286
2 17. 450
2 26.624
2 26. 788
2 26. 952
2 27. 116
2 27. 280
2 36. 454
2 36. 618
2 36. 781
2 36. 945
2 37. 109
oo
56
57
58
59
.150
.153
.156
.158
0.161
Page 644] TABLE 8.
Sidereal into Mean Solar Time.
1
o>
To be subtracted from a sidereal time interval.
IB*
17h
18*
19^
20*>
21h
22*
23*
For seconds.
m.
0
1
2
3
4
m. s.
2 37. 273
2 37.437
2 37.601
2 37. 764
2 37. 928
m. s.
2 47. 102
2 47. 266
2 47. 430
2 47. 594
2 47. 758
m. s.
2 56. 932
2 57. 096
2 57.260
2 57.424
2 57. 587
m. s.
3 6.762
3 6.925
3 7.089
3 7. 253
3 7. 417
m. s.
3 16.591
3 16. 755
3 16. 919
3 17.083
3 17.246
m. s.
3 26.421
3 26.585
3 26. 748
3 26. 912
3 27. 076
m. s.
3 36. 250
3 36.414
3 36.578
3*36. 742
3 36.906
TO. S.
3 46. 080
3 46. 244
3 46. 407
3 46. 571
3 46. 735
s.
1
2
3
4
s.
0.003
.005
.008
.011
5
6
7
8
9
2 38.092
2 38.256
2 38. 420
2 38. 584
2 38. 747
2 47. 922
2 48.085
2 48. 249
2 48. 413
2 48. 577
2 57. 751
2 57.915
2 58. 079
2 58. 243
2 58. 406
3 7.581
3 7.745
3 7.908
3 8. 072
3 8. 236
3 17.410
3 17.574
3 17. 738
3 17. 902
3 18. 066
3 27.240
3 27. 404
3 27. 568
3 27. 731
3 27.895
3 37.069
3 37. 233
3 37. 397
3 37.561
3 37. 725
3 46. 899
3 47. 063
3 47. 227
3 47. 390
3 47. 554
5
6
7
8
9
• .014
.016
.019
.022
.025
10
11
12
13
14
2 38.911
2 39. 075
2 39. 239
2 39. 403
2 39. 566
2 48. 741
2 48. 905
2 49. 068
2 49.232
2 49. 396
2 58. 570
2 58. 734
2 58. 898
2 59.062
2 59.226
3 8.400
3 8.564
3 8.728
3 8.891
3 9. 055
3 18.229
3 18.393
3 18. 557
3 18. 721
3 18.885
3 28. 059
3 28. 223
3 28.387
3 28. 550
3 28. 714
3 37. 889
3 38.052
3 38.216
3 38.380
3 38.544
3 47. 718
3 47. 882
3 48. 046
3 48.210
3 48. 373
10
11
12
13
14
.027
.030
.033
.035
.038
15
16
17
18
19
2 39. 730
2 39. 894
2 40. 058
2 40. 222
2 40. 386
2 49. 560
2 49. 724
2 49. 888
2 50.051
2 50. 215
2 59. 389
2 59. 553
2 59. 717
2 59.881
3 0. 045
3 9.219
3 9.383
3 9. 547
3 9. 71C
3 9. 874
3 19.049
3 19. 212
3 19. 376
3 19.540
3 19. 704
3 28.878
3 29. 042
3 29. 206
3 29. 370
3 29. 533
3 38. 708
3 38. 871
3 39.035
3 39. 199
3 39. 363
3 48.537
3 48. 701
3 48. 865
3 49.029
3 49. 193
15
16
17
18
19
.041
.044
.046
.049
.052
20
21
22
23
24
2 40. 549
2 40. 713
2 40. 877
2 41. 041
2 41. 205
2 50. 379
2 50. 543
2 50. 707
2 50. 870
2 51. 034
3 0. 209
3 0.372
3 0. 536
3 0.700
3 0. 864
3. 10. 038
3 10.202
3 10. 366
3 10.530
3 10.693
3 19.868
3 20. 032
3 20. 195
3 20. 359
3 20.523
3 29. 697
3 29. 861
3 30. 025
3 30. 189
3 30. 353
3 39.527
3 39.691
3 39.854
3 40. 018
3 40. 182
3 49. 356
3 49. 520
3 49. 684
3 49. 848
3 50. 012
20
21
22
23
24
.055
.057
.060
.063
.066
25
26
27
28
29
2 41. 369
2 41. 532
2 41. 696
2 41. 860
2 42. 024
2 51. 198
2 51. 362
2 51. 526
2 51. 690
2 51. 853
3 1.028
3 1.192
3 1.355
3 1.519
3 1.683
3 10.857
3 11. 021
3 11. 185
3 11.349
3 11.513
3 20. 687
3 20. 851
3 21.014
3 21. 178
3 21. 342
3 30. 516
3 30. 680
3 30. 844
3 31. 008
3 31. 172
3 40.346
3 40.510
3 40.674
3 40. 837
3 41. 001
3 50. 175
3 50. 339
3 50. 503
3 50. 667
3 50. 831
25
26
27
28
29
.068
.071
.074
.076
.079
30
31
32
33
34
2 42. 188
2 42. 352
2 42. 515
2 42. 679
2 42. 843
2 52. 017
2 52. 181
2 52. 345
2 52. 509
2 52. 673
3 1. 847
3 2.011
3 2. 174
3 2.338
3 2.502
3 11.676
3 11.840
3 12.004
3 12. 168
3 12.332
3 21. 506
3 21.670
3 21.834
3 21. 997
3 22. 161
3 31. 336
3 31. 499
3 31.663
3 31. 827
3 31.991
3 41. 165
3 41. 329
3 41. 493
3 41.657
3 41.820
3 50. 995
3 51. 158
3 51. 322
3 51.486
3 51. 650
30
31
32
33
34
.082
.085
.087
.090
.093
35
36
37
38
39
2 43. 007
2 43. 171
2 43. 334
2 43. 498
2 43. 662
2 52. 836
2 53. 000
2 53. 164
2 53. 328
2 53. 492
3 2. 666
3 2. 830
3 2. 994
3 -3.157
3 3. 321
3 12.496
3 12.659
3 12.823
3 12.987
3 13. 151
3 22. 325
3 22. 489
3 22. 653
3 22. 817
3 22. 980
3 32. 155
3 32. 318
3 32. 482
3 32. 646
3 32. 810
3 41. 984
3 42. 148
3 42. 312
3 42. 476
3 42. 639
3 51.814
3 51.978
3 52. 141
3 52. 305
3 52. 469
35
36
37
38
39
.096
.098
.101
.104
.106
40
41
42
43
44
2 43. 826
2 43. 990
2 44. 154
2 44. 317
2 44. 481
2 53. 656
2 53. 819
2 53. 983
2 54. 147
2 54. 311
3 3.485
3 3.649
3 3.813
3 3. 977
3 4. 140
3 13.315
3 13.478
3 13.642
3 13.806
3 13. 970
3 23. 144
3 23. 308
3 23. 472
3 23. 636
3 23. 800
3 32. 974
3 33.138
3 33. 301
3 33. 465
3 33. 629
3 42. 803
3 42. 967
3 43. 131
3 43. 295
3 43. 459
3 52. 633
3 52. 797
3 52. 961
3 53. 124
3 53. 288
40
41
42
43
44
.109
.112
.115
.117
.120
45
46
47
48
49
2 44. 645
2 44. 809
2 44. 973
2 45. 137
2 45. 300
2 54. 475
2 54. 638
2 54. 802
2 54. 966
2 55. 130
3 4.304
3 4.468
3 4.632
3 4.796
3 4.960
3 14. 134
3 14.298
3 14.461
3 14.625
3 14. 789
3 23.963
3 24. 127
3 24. 291
3 24. 455
3 24. 619
3 33. 793
3 33. 957
3 34. 121
3 34. 284
3 34. 448
3 43.622
3 43. 786
3 43. 950
3 44. 114
3 44. 278
3 53.452
3 53. 616
3 53. 780
3 53. 943
3 54. 107
45
46
47
48
49
.123
.126
.128
.131
.134
50
51
52
53
54
2 45.464
2 45. 628
2 45. 792
2 45. 956
2 46. 120
2 55. 294
2 55. 458
2 55. 621
2 55. 785
2 55. 949
3 5. 123
3 5.287
3 5.451
3 5.615
3 5.779
3 14.953
3 15. 117
3 15.281
3 15.444
3 15.608
3 24. 782
3 24.946
3 25. 110
3 25.274
3 25.438
3 34.612
3 34. 776
3 34.940
3 35. 104
3 35. 267
3 44.442
3 44. 605
3 44. 769
3 44. 933
3 45. 097
3 54. 271
3 54. 435
3 54. 599
3 54. 763
3 54. 926
50
51
52
53
54
.137
.139
.142
.145
.147
55
56
57
58
59
2 46. 283
2 46. 447
2 46. 611
2 46. 755
2 46. 939
2 56. 113
2 56. 277
2 56.441
2 56. 604
2 56. 768 .
3 5. 942
3 6.106
3 6.270
3 6.434
3 6. 598
3 15. 772
3 15. 936
3 16.100
3 16.264
3 16.427
3 25. 602
3 25. 765
3 25.929
3 26. 093
3 26.257
3 35. 431
3 35. 595
3 35. 759
3 35. 923
3 36. 086
3 45.261
3 45.425
3 45.588
3 45. 752
3 45. 916
3 55.090
3 55.254
3 55. 418
3 55. 582
3 55. 746
55
56
57
58
59
.150
.153
.156
.158
0.161
TABLE 9. [Page 645
Mean Solar into Sidereal Time.
g
To be added to a mean time interval.
o
a
Oh ih
Oh
gh 4h
oh 6* 7*>
For seconds.
in.
0
1
2
3
4
m. s. la. s.
0 0. 000 ; 0 9. 856 i
0 0.164 0 10.021 !
0 0.329 0 10.185
0 0. 493 0 10. 349 i
0 0.657 0 10.514
?.-!. S.
0 19. 713
0 19. 877
0 20. 041
0 20.206
0 20. 370
m. s.
0 29. 569
0 29. 734
0 29. 898
0 30.062
0 30. 227
m. s.
0 39. 426
0 39. 590
0 39. 754
0 39. 919
0 40. 083
m. s.
0 49. 282
0 49. 447
0 49.611
0 49. 775
0 49. 939
m. s.
0 59. 139
0 59. 303
0 59. 467
0 59. 632
0 59. 796
m. s.
1 8.995
1 9.160
1 9. 324
1 9. 488
1 9.652
8.
1
2
3
4
s.
0.003
.005
.008
.011
5
6
7
8
9
6 0.821 0 10.678
0 0.986 0 10.842
0 1.150 0 11.006
0 1.314 0 11.171
0 1.478 0 11.335
0 20. 534
0 20. 699
0 20.863
0 21. 027
0 21. 191
0 30.391
0 30. 555
0 30. 719
0 30.884
0 31. 048
0 40. 247
0 40. 412
0 40. 576
0 40. 740
0 40. 904
0 50. 104 0 59. 960
0 50. 268 i 1 0. 124
0 50. 432 s 1 0. 289
0 50. 597 | 1 0. 453
0 50. 761 1 0. 617
1 9.817
1 9. 981
1 10.145
1 10.310
1 10.474
5
6
7
8
9
.014
.016
.019
.022
.025
10
11
12
13
14
0 1. 643 0 11. 499
0 1.807 0 11.663
0 1.971 ! 0 11.828
0 2. 136 0 11. 992
0 2. 300 0 12. 156
0 21. 356
0 21.520
0 21. 684
0 21.849
0 22.013
0 31.212
0 31.376
0 31. 541
0 31. 705
0 31. 869
0 41. 069
0 41. 233
0 41. 397
0 41. 561
0 41. 726
0 50. H25
0 51.089
0 51. 254
0 51.418
0 51. 582
1 0.782
1 0.946
1 1.110
1 1. 274
1 1. 439
1 10.638
1 10.802
1 10.967
1 11. 131
1 11.295
10
11
12
13
14
.027
.030
.033
.036
.038
15
16
17
IS
19
0 2.464 0 12.321
0 2. 628 0 12. 485
0 2. 793 , 0 12. 649
0 2. 957 0 12. 813
0 3. 121 i 0 12. 978
0 22. 177
0 22. 341
0 22. 506
0 22. 670
0 22. 834
0 32.034 0 41.890
0 32. 198 0 42. 054
0 32. 362 0 42. 219
0 32. 526 0 42. 383
0 32. 691 0 42. 547
051.746 1 1.603
0 51. 911 j 1 1. 767
0 52. 075 ! 1 1. 932
0 52. 239 i 1 2. 096
0 52. 404 i 1 2. 260
1 11.459
1 11.624
1 11. 788
1 11.952
1 12.117
15
16
17
18
19
.041
.044
.047
.049
.052
20
21
9->
23
24
0 3. 285 : 0 13. 142
0 3.450 i 0 13.306
0 3. 614 i 0 13. 471
0 3. 778 | 0 13. 635
0 3.943 1 0 13.799
0 22.998
0 23. 163
0 23. 327
0 23. 491
0 23. 656
0 32. 855
0 33.019
0 33. 183
0 33. 348
0 33. 512
0 42. 711
0 42. 876
0 43. 040
0 43. 204
0 43. 368
0 52. 568
0 52.732
0 52. 896
0 53. 061
0 53. 225
1 2.424
1 2.589
1 2.753
1 2.917
1 3.081
1 12.281
1 12.445
1 12.609
1 12. 774
1 12.938
20
21
22
23
24
.055
.057
.060
.063
.066
25
26
27
28
29
0 4. 107 0 13. 963
0 4.271 0 14.128
0 4.435 0 14.292
0 4.600 0 14.456
0 4. 764 ; 0 14. 620
0 23. 820
0 23. 984
0 24. 148
0 24. 313
0 24. 477
0 33. 676
0 33. 841
0 34.005
0 34. 169
0 34. 333
0 43. 533
0 43. 697
0 43. 861
0 44. 026
0 44. 190
0 53.389
0 53. 554
0 53. 718
0 53. 882
0 54. 046
1 3. 246
1 3.410
1 3. 574
1 3. 739
1 3.903
1 13.102
1 13. 266
1 13.431
1 13. 595
1 13. 759
25
26
27
28
29
.068
.071
.074
.077
.079
CO CO CO CO CO j CO CO CO CO CO
0 4. 928 ; 0 14. 785
0 5. 093 , 0 14. 949
0 5. 257 \ 0 15. 113
0 5.421 ' 0 15.278
0 5.585 : 0 15.442
0 24. 641
0 24. 805
0 24. 970
0 25. 134
0 25. 298
0 34.498
0 34. 662
0 34.826
0 34. 990
0 35. 155
0 44. 354 ! 0 54. 211
0 44. 518 0 54. 375
0 44. 683 0 54. 539
0 44. 847 0 54. 703
0 45. Oil 0 54. 868
1 4.067
1 4. 231
1 4.396
1 4.560
1 4. 724
1 13.924
1 14.088
1 14. 252
1 14.416
1 14.581
30
31
32
33
34
.082
.085
.088
.090
.093
0 5.750 i 0 15.606
0 5.914 0 15.770
0 6.078 i 0 15.935
0 6.242 | 0 16.099
0 6.407 0 16.263
0 25. 463
0 25. 627
0 25. 791
0 25.955
0 26. 120
0 35. 319
0 35. 483
0 35. 648
0 35. 812
0 35.976
0 45. 176 0 55. 032
0 45. 340 0 55. 196
0 45. 504 0 55. 361
0 45. 668 0 55. 525
0 45. 833 0 55. 689
1 4.888
1 5.053
1 5.217
1 5. 381
1 5.546
1 14.745
1 14. 909
1 15.073
] 15.238
1 15.402
35
36
37
38
39
.096
.099
.101
.104
.107
40
41
42
43
44
0 6.571 0 16.427
0 6.735 . 0 16.592
0 6. 900 0 16. 756
0 7.064 0 16.920
0 7.228 0 17.085
0 26. 284
0 26. 448
0 26. 612
0 26. 777
0 26. 941
0 36. 140 0 45. 997
0 36. 305 0 46. 161
0 36. 469 0 46. 325
0 36. 633 i 0 46. 490
0 36. 798 i 0 46. 654
0 55. 853 1 5. 710
0 56. 018 1 5. 874
0 56. 182 I 1 6. 038
0 56. 346 1 6. 203
0 56.510 ! 1 6.367
1 15.566
1 15. 731
1 15.895
1 16.059
1 16.223
40
41
42
43
44
.110
.112
.115
.118
.120
45
46
47
48
49
0 7.392 0 17.249
0 7.557 - 0 17.413
0 7. 721 | 0 17. 577
0 7. 885 ! 0 17. 742
0 8.049 0 17.906
0 27. 105
0 27. 270
0 27. 434
0 27.598
0 27. 762
0 36. 962
0 37. 126
0 37. 290
0 37.455
0 37. 619
0 46.818 0 56.675 1 6.531
0 46. 983 i 0 56. 839 i 1 6. 695
0 47. 147 0 57. 003 i 1 6. 860
0 47. 311 , 0 57. 168 i 1 ". 024
0 47. 475 0 57. 332 ! 1 ". 188
1 16. 388
1 16.552
1 16.716
1 16.881
1 17.045
45
46
47
48
49
.123
.126
.129
.131
.134
50
51
52
53
54
0 8.214 0 18.070
0 8.378 0 18.234
0 8. 542 0 18. 399
0 8. 707 ' 0 18. 563
0 8. 871 0 18. 727
0 27. 927
0 28. 091
0 28. 255
0 28.420
0 28.584
i 0 37. 783 0 47. 640
j 0 37. 947 0 47. 804
0 38. 112 I 0 47. 968
; 0 38. 276 i 0 48. 132
i 0 38. 440 0 48. 297
0 57. 496
0 57.660
0 57. 825
0 57.989
0 58. 153
1 7. 353
1 ".517
1 ~. 681
1 ". 845
1 8. 010
1 17.209
1 17.373
1 17.538
1 17.702
1 17.866
50
51
52
53
54
.137
.140
.142
.145
.148
55
56
57
58
59
0 9.035 0 18.892
0 9.199 0 19.056
0 9. 364 0 19. 220
0 9. 528 ; 0 19. 384
0 9. 692 0 19. 549
0 28. 748
0 28. 912
0 29. 077
0 29. 241
0 29. 405
i 0 38.605 0 48r461
0 38. 769 0 48. 625
i 0 38. 933 0 48. 790
! 0 39. 097 0 48. 954
< 0 39. 262 0 49. 118
0 58. 317
0 58. 482
0 58.646
0 58. 810
i 0 58. 975
1 8. 174
1 8. 338
i 1 8.502
1 8. 667
1 8.831
1 18.030
1 18.195
1 18.359
1 18. 523
1 18.688
oo
56
57
58
59
.151
.153
.156
.159
0.162
Page 646] TABLE 9.
Mean Solar into Sidereal Time.
1
X
To be added to a mean time interval.
8*
9h
10*
lib
12h
13*
14h
15h
For seconds.
m.
0
1
2
3
4
m. s.
I 18.852
1 19.016
1 19.180
1 19.345
1 19.509
m. s.
28. 708
28. 873
29. 037
29. 201
29. 365
TO. 8.
1 38.565
1 38. 729
1 38.893
1 39.058
1 39.222
m. s.
1 48.421
1 48.585
1 48.750
1 48.914
1 49.078
m. s.
1 58. 278
1 58. 442
1 58.606
1 58. 771
1 58.935
m. s.
2 8.134
2 8.298
2 8.463
2 8.627
2 8.791
m. s.
2 17.991
2 18. 155
2 18. 319
2 18.483
2 18.648
m. s,
2 27. 847
2 28.011
2 28. 176
2 28. 340
2 28.504
8.
1
2
3
4
8.
0.003
.005
.008
.011
5
6
7
8
9
1 19.673
1 19.837
1 20. 002
1 20. 166
1 20. 330
1 29.530
1 29. 694
1 29. 858
1 30. 022
1 30. 187
1 39. 386
1 39. 550
1 39.715
1 39.879
1 40.043
1 49. 243
1 49. 407
1 49. 571
1 49. 735
1 49. 900
1 59.099
1 59. 263
1 59. 428
1 59. 592
1 59. 756
2 8. 956
2 9. 120
2 9. 284
2 9.448
2 9.613
2 18.812
2 18.976
2 19. 141
2 19. 305
2 19.469
2 28.668
2 28. 833
2 28. 997
2 29. 161
2 29. 326
5
6
7
8
9
.014
.016
.019
.022
.025
10
11
12
13
14
1 20.495
1 20. 659
1 20.823
1 20.987
1 21. 152
1 30.351
1 30.515
1 30.680
1 30.844
1 31. 008
1 40. 207
1 40. 372
1 40. 536
1 40. 700
1 40. 865
1 50.064
1 50.228
1 50.393
1 50. 557
1 50. 721
1 59.920
2 0. 085
2 0.249
2 0.413
2 0.578
2 9. 777
2 9.941
2 10. 105
2 10. 270
2 10.434
2 19.633
2 19. 798
2 19.962
2 20. 126
2 20. 290
2 29.490
2 29. 654
2 29. 818
2 29. 983
2 30. 147
10
11
12
13
14
.027
.030
.033
.036
.038
15
16
17
18
19
1 21.316
1 21.480
1 21.644
1 21.809
1 21.973
1 31.172
1 31.337
31. 501
31. 665
31. 829
1 41.029
1 41. 193
1 41. 357
1 41. 522
1 41. 686
1 50. 885
1 51.050
1 51.214
1 51. 378
1 51. 542
2 0. 742
2 0.906
2 .070
2 .235
2 .399
2 10.598
2 10. 763
2 10. 927
2 11.091
2 11. 255
2 20.455
2 20. 619
2 20. 783
2 20. 948
2 21. 112
2 30.311
2 30.476
2 30. 640
2 30. 804
2 30. 968
15
16
17
18
19
.041
.044
.047
.049
.052
20
21
22
23
24
25
26
27
28
29
1 22. 137
1 22. 302
1 22.466
1 22.630
1 22. 794
31. 994
32. 158
32. 322
1 32.487
1 32.651
1 41.850
1 42.015
1 42. 179
1 42.343
1 42.507
1 51. 707
1 51.871
1 52.035
1 52.200
1 52. 364
2 .563
2 .727
2 .892
2 2.056
2 2.220
2 11.420
2 11.584
2 11. 748
2 11.912
2 12. 077
2 21. 276
2 21.440
2 21. 605
2 21. 769
2 21. 933
2 31. 133
2 31.297
2 31.461
2 31.625
2 31. 790
20
21
22
23
24
.055
.057
.060
.063
.066
1 22. 959
1 23. 123
1 23. 287
1 23. 451
1 23. 616
1 32. 815
1 32. 979
1 33. 144
1 33. 308
1 33.472
1 42.672
1 42.836
1 43.000
1 43.164
1 43. 329
1 52. 528
1 52. 692
1 52.857
1 53.021
1 53. 185
2 2.385
2 2.549
2 2. 713
2 2. 877
2 3. 042
2 12.241
2 12.405
2 12.570
2 12. 734
2 12.898
2 22.098
2 22.262
2 22.426
2 22.590
2 22. 755
2 31. 954
2 32. 118
2 32.283
2 32. 447
2 32. 611
25
26
27
28
29
.068
.071
.074
.077
.079
30
31
32
33
34
1 23. 780
1 23.944
1 24. 109
1 24. 273
1 24. 437
1 33.637
1 33. 801
1 33. 965
1 34. 129
1 34. 294
1 43.493
1 43. 657
1 43. 822
1 43. 986
1 44. 150
1 53. 349
1 53. 514
1 53. 678
1 53. 842
1 54. 007
2 3.206
2 3.370
2 3.534
2 3.699
2 3.863
2 13. 062
2 13. 227
2 13. 391
2 13. 555
2 13. 720
2 22. 919
2 23. 083
2 23. 247
2 23.412
2 23.576
2 32. 775
2 32. 940
2 33. 104
2 33. 268
2 33. 432
30
31
32
33
34
.082
.085
.088
.090
.093
35
36
37
38
39
1 24. 601
1 24.766
1 24.930
1 25.094
1 25. 259
1 34.458
1 34.622
1 34. 786
1 34.951
1 35. 115
1 44.314
1 44.479
1 44. 643
1 44. 807
1 44. 971
1 54. 171
1 54.335
1 54. 499
1 54. 664
1 54. 828
2 4. 027
2 4. 192
2 4.356
2 4.520
2 4.684
2 13.884
2 14. 048
2 14. 212
2 14. 377
2 14.541
2 23. 740
2 23. 905
2 24. 069
2 24. 233
2 24. 397
2 33. 597
2 33. 761
2 33. 925
2 34.090
2 34. 254
35
36
37
38
39
.096
.099
.101
.104
.107
40
41
42
43
44
1 25.423
1 25. 587
1 25.751
1 25.916
1 26.080
1 35. 279
1 35. 444
1 35.608
1 35. 772
1 35.936
1 45. 136
1 45.300
1 45.464
1 45.629
1 45. 793
1 54.992
1 55.156
1 55.321
1 55.485
1 55. 649
2 4.849
2 5.013
2 5.177
2 5.342
2 5.506
2 14.705
2 14.869
2 15. 034
2 15. 198
2 15. 362
2 24.562
2 24. 726
2 24. 890
2 25. 054
2 25.219
2 34. 418
2 34. 582
2 34. 747
2 34.911
2 35. 075
40
41
42
43
44
.110
.112
.115
.118
.120
45
46
47
48
49
1 26. 244
1 26. 408
1 26. 573
1 26. 737
1 26.901
1 36. 101
1 36. 265
1 36.429
1 36.593
1 36.758
1 45. 957
1 46. 121
1 46.286
1 46.450
1 46.614
1 55. 814
1 55.978
1 56. 142
1 56.306
1 56.471
2 5. 670
2 5.834
2 5. 999
2 6. 163
2 6.327
2 15.527
2 15.691
2 15. 855
2 16. 019
2 16. 184
2 25. 383
2 25. 547
2 25. 712
2 25. 876
2 26.040
2 35. 239
2 35. 404
2 35. 568
2 35. 732
2 35. 897
45
46
47
48
49
.123
.126
.129
.131
.134
50
51
52
53
54
1 27. 066
1 27. 230
1 27. 394
1 27. 558
1 27. 723
1 36. 922
1 37.086
1 37.251
1 37.415
1 37.579
1 46, 778
1 46. 943
1 47.107
1 47. 271
1 47.436
1 56.635
1 56. 799
1 56.964
1 57. 128
1 57.292
2 6. 491
2 6. 656
2 6. 820
2 6. 984
2 7. 149
2 16.348
2 16. 512
2 16. 676
2 16. 841
2 17.005
2 26. 204
2 26. 369
2 26. 533
2 26. 697
2 26. 861
2 36.061
2 36. 225
2 36. 389
2 36. 554
2 36. 718
50
51
52
53
54
.137
.140
.142
.145
.148
55
56
57
58
59
1 27.887
1 28. 051
1 28. 215
1 28. 380
1 28.544
1 37. 743
1 37. 908
1 38.072
1 38.236
1 38.400
1 47. 600
1 47. 764
1 47.928
1 48.093
1 48. 257
1 57.456
1 57.621
1 57. 785
1 57.949
1 58. 113
2 7. 313
2 7. 477
2 7. 641
2 7.806
2 7. 970
2 17. 169
2 17. 334
2 17. 498
2 17. 662
2 17.826
2 27. 026
2 27. 190
2 27. 354
2 27.519
2 27. 683
2 36. 882
2 37. 047
2 37. 211
2 37. 375
2 37. 539
55
56
57
58
59
.151
.153
.156
.159
0.162
TABLE 9. [Page 647
Mean Solar into Sidereal time.
-•
l
9
%
To be added to a mean time interval.
16* 17*
IS*
19*
*
21*
22"
23"
For seconds.
m.
0
1
2
3
4
m. f.
2 37. 704
2 37. 868
2 38.032
2 38. 196
2 38. 361
m. s.
2 47. 560
2 47. 724
2 47. 889
: 2 48. 053
2 48. 217
m. s.
2 57.417
2 57. 581
2 57. 745
2 57. 909
2 58. 074
m. g.
3 7.273
3 7.437
3 7. 602
3 7. 766
3 7. 930
TO. t.
3 17.129
3 17.294
3 17.458
3 17. 622
3 17. 787
m. s.
3 26. 986
3 27. 150
3 27.315
3 27. 479
3 27. 643
m. s.
3 36. 842
3 37.007
3 37. 171
3 37. 335
3 37. 500
m. ft.
3 46.699
3 46. 863
3 47. 027
3 47. 192
3 47. 356
s. s.
1 0.003
2 .005
31 .008
4 j .011
5
6
7
8
9
2 38.525
2 38. 689
2 38. 854
2 39. 018
2 39. 182
2 48. 381
2 48. 546
2 48. 710
2 48. 874
2 49. 039
2 58. 238
2 58. 402
2 58. 566
2 58. 731
2 58. 895
3 8.094
3 8. 259
3 8. 423
3 8. 587
3 8.751
3 17.951
3 18.115
3 18. 279
3 18. 444
3 18. 608
3 27. 807
3 27. 972
3 28. 136
3 28. 300
3 28. 464
3 37. 664
3 37. 828
3 37. 992
3 38. 157
3 38. 321
3 47.520
3 47. 685
3 47. 849
3 48. 013
3 48. 177
5| .014
6 .016
7 .019
81 .022
9j .025
10
11
12
13
14
2 39.346
2 39. 511
2 39. 675
2 39. 839
2 40.003
2 49. 203
2 49. 367
2 49. 531
2 40. 696
2 49. 860
2 59. 059
2 59. 224
2 59. 388
2 59.552
2 59. 716
3 8.916 3 18.772
3 9.080 3 18.937
3 9. 244 3 19. 101
3 9.409 3 19.265
3 9.573 3 19.429
3 28. 629
3 28. 793
3 28. 957
3 29. 122
3 29. 286
3 38.485
3 38. 649
3 38. 814
3 38. 978
3 39. 142
3 48.342
3 48.506
3 48. 670
3 48. 834
3 48. 999
10 . 027
11; .030
12 .033
13 .036
14 .038
15
16
17
18
19
2 40. 168
2 40. 332
2 40. 496
2 40. 661
2 40. 825
2 50. 024 2 59. 881 3 9. 737
2 50. 188 ! 3 0. 045 3 9. 901
2 50. 353 ; 3 0. 209 3 10. 066
2 50. 517 ! 3 0. 373 j 3 10. 230
2 50. 681 ; 3 0. 538 3 10. 394
3 19.594
3 19. 758
3 19. 922
3 20.086
3 20.251
3 29. 450
3 29. 614
3 29. 779
3 29. 943
3 30. 107
3 39. 307
3 39.471
3 39. 635
3 39. 799
3 39. 964
3 49. 163
3 49. 327
3 49. 492
3 49. 656
3 49. 820
15 .041
161 .044
17 .047
18 .049
19 .052
20
21
° 2
23
24
2 40. 989
2 41. 153
2 41.318
2 41. 482
2 41. 646
2 50. 846
2 51. 010
2 51. 174
2 51. 338
2 51. 503
3 0. 702
3 0. 866
3 1.031
3 1.195
3 1.359
3 10.559
3 10. 723
3 10.887
3 11.051
3 11.216
3 20. 415
3 20. 579
3 20. 744
3 20.908
3 21.072
3 30.271
3 30.436
3 30. 600
3 30. 764
3 30. 929
3 40. 128
3 40. 292
3 40. 456
3 40. 621
3 40. 785
3 49.984
3 50. 149
3 50. 313
3 50. 477
3 50. 642
20: .055
21 .057
22 .060
23 .063
24' .066
25
26
27
28
29
2 41. 810
2 41. 975
2 42. 139
2 42.303
2 42.468
2 51. 667
2 51. 831
2 51. 995
2 52. 160
2 52. 324
3 1. 523
3 1. 688
3 1.852
3 2.016
3 2.181
3 11.380
3 11.544
3 11. 708
3 11. 873
3 12.037
3 21.236
3 21.401
3 21. 565
3 21. 729
3 21.893
3 31.093
3 31. 257
3 31.421
3 31.586
3 31. 750
3 40.949
3 41.114
3 41. 278
3 41.442
3 41.606
3 50.806
3 50. 970
3 51. 134
3 51. 299
3 51. 463
25 .068
26] .071
27 .074
28 .077
29 . 079
30
31
32
33
34
2 42. 632
2 42. 796
2 42. 960
2 43. 125
2 43. 289
2 52. 488
2 52. 653
2 52. 817
2 52.981
2 53.145
3 2. 345
3 2. 509
3 2.673
3 2.838
3 3.002
3 12.201
3 12.366
3 12. 530
3 12.694
3 12.858
3 22.058
3 99 999
3 31.914
3 32.078
3 32.243
3 32.407
3 32.571
3 41.771
3 41.935
3 42.099
3 42. 264
3 42. 428
3 51. 627
3 51. 791
3 51. 956
3 52. 120
3 52. 284
30 . 082
31 .085
32 .088
33 .090
34! .093
3 22.386
3 22.551
3 22. 715
35
36
37
38
39
2 43.453
2 43. 617
2 43. 782
2 43. 946
2 44. 110
2 53. 310
2 53.474
2 53. 638
2 53. 803
2 53.967
3 3. 166
3 3.330
3 3. 495
3 3.659
3 3. 823
3 13.023
3 13.187
3 13.351
3 13.515
3 13.680
3 22.879
3 23.043
3 23.208
3 23. 372
3 23. 536
3 32. 736
3 32.900
3 33.064
3 33. 228
3 33. 393
3 42.592
3 42. 756
3 42. 921
3 43. 085
3 43. 249
3 52. 449
3 52. 613
3 52. 777
3 52. 941
3 53. 106
35 . 096
36 .099
37 .101
38 i .104
39 . 107
40
41
.0
43
44
2 44. 275
2 44. 439
2 44. 603
2 44. 767
2 44. 932
2 54. 131
2 54. 295
2 54.460
2 54.624
2 54. 788
3 3. 988
3 4.152
3 4. 316
3 4. 480
3 4.645
3 13.844
3 14.008
3 14.173
3 14.337
3 14.501
3 23. 700
3 23. 865
3 24. 029
3 24. 193
3 24.358
3 33. 557
3 33. 721
3 33. 886
3 34. 050
3 34. 214
3 43.413
3 43.578
3 43. 742
3 43. 906
3 44.071
3 53. 270
3 53.434
3 53.598
3 53. 763
3 53. 927
40 . 110
41 . 112
42 .115
43 .118
44 .120
t5
46
47
48
49
2 45. 096
2 45. 260
2 45. 425
2 45. 589
2 45. 753
2 54. 952
2 55.117
2 55. 281
2 55. 445
2 55. 610
3 4.809
3 4. 973
3 5. 137
3 5.302
3 5.466
3 14.665
3 14.830
3 14. 994
3 15. 158
3 15.322
3 24. 522
3 24. 686
3 24. 850
3 25. 015
3 25. 179
3 34. 378
3 34. 543
3 34. 707
3 34. 871
3 35. 035
3 44. 235
3 44. 399
3 44. 563
3 44. 728
3 44. 892
3 54. 091
3 54. 256
3 54. 420
3 54.584
3 54. 748
45! .123
461 .126
47 .129
48 .131
49 . 134
50
51
52
53
54
2 45. 917
2 46. 082
2 46. 246
2 46. 410
2 46. 574
2 55. 774
2 55.938
2 56. 102
2 56. 267
2 56.431
3 5. 630
3 5.795
3 5.959
3 6. 123
3 6. 287
3 15.487
3 15. 651
3 15.815
3 15.980
3 16.144
3 25.343
3 25.508
3 25.672
3 25. 836
3 26.000
3 35. 200
3 35.364
3 35. 528
3 35. 693
3 35. 857
3 45.056
3 45. 220
3 45. 385
3 45. 549
3 45. 713
3 54. 913
3 55.077
3 55. 241
3 55. 405
3 55.570
50 . 137
51 .140
52 . 142
53 . 145
54 . 148
55
56
57
58
59
2 46. 739
2 46. 903
2 47. 067
2 47. 232
2 47. 396
2 56. 595
2 56. 759
2 56. 924
2 57. 088
2 57. 252
3 6.452
3 6. 616
3 6. 780
3 6.944
3 7.109
3 16.308
3 16.472
3 16. 637
3 16. 801
3 16.965
3 26. 165
3 26. 329
3 26. 493
3 26. 657
3 26. 822
3 36.021
3 36. 185
3 36. 350
3 36. 514
3 36.678
3 45. 878
3 46.042
3 46.206
3 46.370
3 46.535
3 55. 734
3 55.898
3 56. 063
3 56. 227
3 56. 391
55 . 151
56 . 153
57 . 156
58 . 159
59 0. 162
Page 648] TABLE !'.».
Mean Time of Son's Visible Rising and Setting.
a
-
2^- -__-___.=;-_*---
•^•^- •_' .
•xojddy £z — x — x^xixsix aix=;a:=ix— xsixpix — x=:xix=:xc;x=:x2ix— x'iixsfix"
*• ^ ='•; :- - £ r- = - r- ~ : ••-••----••--: LJ ~ ~ i: ? - ^ - r - :; = - -
f;
* 5 :^^^~^n:,:"3"^^^r;: /, [S ^s^55S2S2
"" " -c -= - - - -- - -- - - - ------ _ : - - - - - _: j: — ^ — ^ — _; - ^ c -- ^ 00
•li :'i I.. .Inn.- :•:'.
incii.li Mine of NIIII'M vlnlhln Hcl
< - s i|i||i!!!^|^^^^:E522S^^S
— ^.-^.t^-:c-- - -jjj-j^ ---j-^_:^-:%:^-^vr
* ^ ;^G^^::::: ":::::::, :::~:::^:^:::^::^^^-,
~ <i -= ^ ~ - ^ - -- - ~ - ~ - ~ - -: c --. c .; -c -: c -r c .: - -- c -: ,: - _-----_ _-
!x L S;-:-;-^r-r---5_£^-^_^__-^-: :: :^r:r:r;:
Norlli Lnfilllde: 0° to 20°- Mm
1 IIH'IIII l.linc of HIIII'H vlMllilc. rlNlnj.;. !'.- 1 ,<>ni 1
f' i
: ••• = -•-= - - - - -= - = - - ~- = -^ ----- --^---- T~~TI^~???!
-^ — — — — . _
. e e 5-,- = .:= :-^.,5- .5 ^:£;,2.,S^.I£l-£ £_.1^L£ £-_££-£_£ --L-_-
^.= ^^^ ^ ^ ^ ^ ^ ^c^u,c^^^^^c:c
- ^ :-;-=:-;-; -ri-b_-_-_----_^_^___-__-_-^i
I 0 - : cr -^ ^ ^r ^ -: : : -- - - -- ~ ^ - ; - . - . - - - - - q - = - - - ~ - - -
^ =. S i - - = - ; - ; - ;: 5 2 e 2 ----- ---- - - - - - - - - li - ^ - ^ - - -
= = £ = £ = £ = --=- = r. :;. r. r- = x = x - x - ^- r;- .- r; .- r; -^ r; -^ re ==--=--=--;-
r; *^ __-__ . ____.. ... _—---.-- . . . .
^" ^ ^= - -^ -^ c; -r --: ~ - ~~ ~ - - _ _- - - ^ -- ----- - - - : - ----- - _ .- c j; s:
sr __ _ ^ . -._._._._.-_____- _.____._.._.-._.-.-.
r? :_ 5c_-_-_r_r_r_-_;_-_c-r-r- = -c-r-r- = - = - = - = -c-
- ^ =rzrz3 = = = c=H-S = 5 = g-5-S-i = ^ = ^5-5 = = = Si:Srg = gz
">- — — — — ——— —
~ 7 '*-y~*tr"*-r~*-f~*-f ~* -r ** -r "** -r ** -r •** T sL ^ ~* -r ~* rr ~* -r "* -f ~* T' ~* -f "* T' "" -f ** -r ~* -x.
^z : o - c* : ^--*--£ z L £=££-££:?;
TABLE 10. [Page 649
Mean Time of Sun's Visible Rising and Setting.
Ir.srIling.J
__ .
: r \: '-- r F, r, Vl ;'. F • - - r
.3JBp ^ . _ _ _ _ ^ ^ .___. ^ .__.
•xoiddv £* ; ~x x~:r- *-*,-*-*-*-'--'- --r---r--'--f--s. -r.-s.-
z
B
3
5 gS*SS33SS8S|SSSSS8SSS3|S5«2gS3SSS;S33355S3S=2
£
-: i- - .= n re ^ - t- 2 = t rj i - ^ "^ =• x x - ^~^^^xs. -~-.~. -: -c -. -. -c r. r; .- = x
ij - . M — -M .. M
-
: = x S - = ~ - ' * - = -. * * S = - rj - - =;- v: . : r . - - -. - r - - -^'---^^^
-<
r,
S-H-V:----^ §?SSS5SSSS ^^^^-5ii^=^B35r-s£^£
r»
2
^.^^^.j^^j^^^.^. «. _ ^, _ _ — Xl= . _X<N ^.x>_.-^ „_ .j-.....^..^
2
(North Latitude: 21° to 40°— March 21 to Juno 22.
[It-Local mean tlmo of sun'i vlnlblo riding. 8-Looal mean time of BUH'H vinti
OB
= -"• ." r r I- 9 r; L: £- 12 i ^ £ = £ 5 £2 £ z — £ £2 2£ £ S ^ r £; L; — S ^ ^ -= ~ :: ~ ~ • ~. —
.
•e
= -' -- -- -" -' ~ '-" St.". ? I! ! £j .1 :^ S "£ 2£ ~ S ;2 ~ ~ Li ^' Z 2 -£ •= i ~ ? Ir "J » T "•£ '•= '•= ;C
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i. Sr.5-r-J?J?j?lEjr,f, ^fj-r£-L;r4r?;H i^il5-^Z-l:L _^S = g5§.*SS
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5
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^,^« • - ^,« ^^w^,^^. ^i-.^^. _, ^ ^— ^ ^, •.. _
8
^ ^jri'z:*"^--- — "^r-"^ *^ L^ ^ /-, r " r _~ — — . . .•;.-., _j.i* r^: .. zz ^* £ ^r-'^.. — ^ - _
.
9
L gSsj&zsSSlHHrr SjjaSrSrSsSSSSsSjas.Hf.sr.S ?is=;S£.2£-i:?
-
o^ a £ ?, = = 2 - Z :• -j: r- = 3J ^ ^ 2 j= 2 -1- L- ?- -?•= = ?— / L- ^ £ ^ r - ^ r. S S» S r 2
••r ...
~~ ~ ~" •— — 1 . ._-_-_-._. .__ >^ •»
a
a'22^~^?- = -£S- 2245 ?.Er^s^~~ -•:-; = ?. sr:L: = = ==:./::.-- .-.isj 2
C5
-^-, . «__ . _ . . . _ -*-^-^U-w«C^,l fc-^ _*-__w__l »— ^
-
k =££rsz--£:^?£,rzr:£:-£,-x:r ;,r-:-^:-:-.~-? ss!as = = ss.;f;s
X
0^ g$*:!;S: V:. = t.^:.-::-r: _ :: _ : - :-. f; : - r-; : . ::::;.?'H/ -: T ^ S
-
I = = -£-£:-£ -i« o:x£:»H34£ = £- zrz^^r-ijr--r -.-=?2^s-^5?
c
~- • — ———•——•— ^ .iOoio<oic<sie<Dio«a*ctr L-_. . «s »
st
_ ~ t : " r_. -" ? . -c — » — :^ ~ : - c x ~ x ~ * x * x ~ r~ c : ~ — — — " r . ~ - : — — - - — - •
MAitni.
a
^" ;.._..__,-_....- .--.-.---..- _.--.--.....
5
L 5i£_^_ ,_-_-,--_ -:-:t_.-:--r -^5£r^L:5£^i ii^^.-.E-.c?^.--
_^ -. . _ tO
5
Vt
— - ' • — ~ — >— — .— _>_,_.^ . _ . .
IS
o ~ — n — r: — ri — ~- — -: — r; — re — — — — or: er:s — o-r~ — o-r o — — . — r. — r - s. -
«
sS-S-S-^-^-^-S-^-S-S^S^S^S^S^S-'S^S^^^i^I:^
o
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-7 - r, ^ T; - ri s ?; 3 § 2 "="?? K = a ?- '- ?: * 5
-
Page 650]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
to June 22.
ime of sun's
°— March
S=Local m
North Latitude: 41° to
mean time of sun's visible rising.
•8jT?p
•xoaddy
oid
xoiddy
JH
55
s
P5 02 P3 03 f4 02 PH' 02 tf CO Uj CC tf O3 p(? O3 « CC pj OQ
< cc co oo co co co oo
SSS5
«<oNi
iO <£> iO <£> rf <£> •
S Ig
dflj ad 0i «d p4 00(4 0i
coooecoocoooecaoccoo
ecooccooecooeoooeOTD
cooocooocooocooococo COCOCOOOCOOO<NQO^OI
CCaOeCOOINOSIMOiiNO
) CO CO CO CO CO
coooeooocooocoooecao
ccoocooocccocooocooo
> co oo co oo co co
• cot^eooocoooeooo
iO«OiO«OiOWiO<Oi01
iO «D vO «0 10 to -iO tO id (0
ao 0j IB 03 OB PJ ad tt GO
SSSSS888S8
JNW ^J^^^^JocoSscoco
0?Ho2oSo3o3 o3838So5S8iH
P5 co tf ad tf oo p? CB P5 oi
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 651
•9JBP
•TOJddy
<!
- ff
1 5
II
& a
3 I
13 1
§ 3
r5 II
•
— J
North Latitude: 0° to 20°
mean time of sun's visible rising.
o t^ oo o>
OC --O OC W CC ?
OC -C X -C: X
ggggg ggggggss^g'^g?
C^C^l^CC — CO^-'-O-- O iC C5 LC r-. U- r: '-C ?> « X
cCOLCOiCOu-Oi-tO LCO-<rOTO-rOTO f
o. SSo-S§S?32o3g2?
giCCOLCCC'r'JC'^TTO"?' CCiCMiC:^jS'-<'-O — r^Qr~O3C:T>XX?-. OCO t^-Ot^^-iSi-iSSJ^iC'MLCCC
SiCOiCOLCOLCOLCO LC O iC O LC O LC O LC O LCOLCO-^-O^rO'T^- T ~ •^•r^Tftf^rjir-i'Tii-iTri-i
^jiC^iCOiC <Ci
%=iC^ LC^LC^LC^uC^i
•O iC » cC <O
• LC vs --c ^ r-- LC x -^ x re y. « p
: •-£ LC «£ LC -~ LC :c LC -^ LC O O O
5 id«5 iC t£ iC •-£ tC «C ;iC '-C LC tf O O iC •-£ iC -O 10 -O
Sl2S2§^§ — ^2 ^;
ic<cio<ciCs3Lc;e»c» ift;
*!«'
tc o --C « -^ -^ irt v;
•xoaddy
»c o ic o uc -^ LT:
iOOiC«»C«LC«iC!C U3«CiC5£i
± a: si a: tf x' 25 QQ « OQ »5 co
o 1-1 p< ec «*
' I "^"^"^^^"^"g^
I ^H M 1-1 r-t rH C<
Page 652]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
45 .
a*
xoaddv
I*
to September 23.
an time of sun's visi
North Latitude: 21° to 40°— June
mean time of sun's visible rising. S=- Loca
•9^p
oadd
S
rfg lO id iO >
2t--.o
Tf 0
SS 8
$838383838
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CC -* 00 Tj< O5 Tj< OJ C<i CT> CO O O4 O <N r-( r-t ^-( iH (N
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UotOiO«OiO5OU3«OiO«O
JOiOOiOtOid1^) iO<OiO<OiO?OiO
.lOtDiOOiO!
xoaddy
a s
CO«O>O-<*it^<MOJOi-(
HOi-rllOrHiOrHlOr-lO
<N !N iM iM CC
o c^ o eg o^ eo w ^ oo j*
)cdt^I>l>00«OOO«OOJ
iO «O iO O>
SSSS8S8SS
3S; §8 8 8 IS
22 to September
l mean time of sun'
I!
3*
s *
o *
•*-> «-
isi
North Latit
Local mean time of su
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 653
•3}T?P
oid
xoiddy
£3533383838
rf* iO 0 iC SO uC 0 0 0 10 0
si x ^ x ii x — ' x ~ x' ^ x 2J ai 2i x' — x' ^ x d x ^ ! oj ^ x 35 a: c4 oa
r^i^riL-— ut— --O
9O •« o 9o j 9 o
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S-^O^-O^O^O-rC; -r
^ iO O iO 50 O ^ u- v= i-~ ~ iC '
^ CQ r
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^ ri -^ n u- re ut — • — o -o
cr^ ~ — r5^i»^-iiCr-iWi
.- -^ ut — ic •— ic -o i^; o 10
L- -^ L.- is L= %= L~ -o L- -^ L= ~ L= v= ^- v= u~ --o ic -o o -^ u- vs u~ --c o ~ u- vs --: o ic -o ic •
,CJ O 5O ut -O O — L^ "^ iC --O i-t -»S O -^ Lt O u~ -^
i^iM^JCMJi^^co^roc^rc CMcosMio.-icOr-ico.-irc — ^ — =r — ^r — — r
^ lO SO ul «O »C O iC O LC "O 'iS O iC -^ O O O O iC O 'iC «O iO O iC ->3 i-t ••£> LC --C O --S iC O ut -O t2 O O '
-i ut --C i= O O -O Li O u~ vs u- --C LC -^ LC -O iO O iO O 'u
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i^S^SSsSSSSSSls
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S28S8888SS$3393S3S3S38SS
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•xoiddy
s88ssiaS2§5§ ss8a2ass;58tea«a5a
?5^*'^?;McSr?«w^S
t^ -^ M o x tr: re o x u- c^i o is to o ro
F-ciCr-iOoo Or-nc^iu-^Ti-MTrco
,<T}<t^T«t^t-r-Tj<r~-'*t~ •*t>T|t^'^(t^-'«j"t^<q<t^|'»ix-^<XT}<x«xtoxroxcoooMX'MX'C<5i
^•<S<t^T*t^'^t^'«<t^-^<t^:
jccaoccooeo x n x re x re x co x so :
1-1 — — L= S2ooSo2o2^H
isoaocox '«»cocs:
'^-
«a2tfaQ«ad«ad«02 «
61828°— 16 35
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 655
5
<N 2
<M =a
5r *>
Decem
e of sun'
ptember 23
S=Local mean
North Latitude: 21° to 40°
l mean time of sun's visible risi
[R
•ajup
•xojddy
•xoiddy
-^iC <O r- 00
co 06 co cc co
rfjtCiCOi
e* r^ oe Ci r~ ^- L1" *^
g £ p; S T-. ^i — r
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Page 656]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
S
: 41° to
's visible r
North Lati
mean time o
[R=
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T'TTT
TABLE 10.
Mean Time of Sun's Visible Kising and Setting.
[Page 657
er 22 to March 21.
mean time of sun's visible se
itude: 0
sun's visib
£ a
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Page 658]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
a
•xoiddy
ber 22 to
mean tim
de: 21° to
n's visible ri
North L
al mean time
8. 55 S 8
i? 3
tototoototototooto
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 659
21
visible setting.
mber 22 to M
l mean time of
60—
ng. S
e: 41°
s visibl
North L
mean time o
3*
S S S S
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Page 660]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
June 22.
sun's visible
to
time o
h 2
me
South latitude: 0° to 20°—
time of sun's visible rising. S=
•9113P
x caddy
•xojddy
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8S8S8S8S8SSS
tototototototototototoeo
gggggggggg §8§§§§S§
cototototototototototototococototocot
COOCOOMOCOOCOO
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totOtOCOtOtOtOtOtOCO
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OrHOr-IOiHOi-IOi-l
cotocotototototototo
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i-IOi-IOTHOi-IOi-l
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totototototocotoeotototo
TTTTTT
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 661
21 to June 22.
an time of sun's visible
: 21° to 40°
sible rising. 8
•xojddy
r:
! L.C ic is ID o o L£ ic u~
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-. — r~-
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Page 662]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
22.
41° to 60°—
le rising. S—
th
e of
[R
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 663
CO 3
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time of
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South Latitude: 0° to
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S = 15 = ^3:2 S
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Page 664]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
South Latitude: 21° to 40°— June 22 to September 23.
ean time of sun's visible rising. S = Local mean time of sun's visible
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S S 3 8
% %
TABLE 10. [Page 665
Mean Time of Sun's Visible Rising and Setting.
to 60°— June 22 to September 23.
ising. S = Local mean time of sun's visible setting.]
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-c x t- x x cj x tc c» is ' 0 ;r -H r: ^ r-j ~: — is O
^•oio^^f
^O.OI^.O^
vc is -»s is — L- -^ is — is --s is tc is -c is ^ is -^ 10
QO
»
SS^'S^^^-^-?:
sssss&ssas
^ ~ ?5 H ^ a ?i ?= n -. ?5 ?i ?. ?J f. n ~ rl f: Tj
~"~" ----- -—.— .— .— Lft
„
0
„• x y — r^ -N — -,) u*. — u~ -M o — t- 5 -^ — x — r- ~! .- i- -i r x ^ o r-
\"" '•"" " •' " "' ^ -1. ..)...].. -N...!.!...). ..!...) ...J. ..)... 4.. ^ r-l
^,--3u. ^L._._._-(-O w -O.^O^i— O. ._iS .-^._. ^ (OlQ vS_O
-
§0
SSS^SSSSSSetS
HKHSKS
H ?5 r* ?1 = ?5 S fl f 7 Ti - - ? - - ^ - ^ 2 ^
AUGUST.
s
*
K55£?;nr»$?r3£?3
« ?! = s ^ - ? r- = - 4 - s = ;-' S 3 558
§
1
^ — — — -
^.so^^u.^o^^
•
s
o
H
iH
68SS5S8S5S^a
-^^?5^2X^S^
SSS^ggSSgg b'i'SSSSSSSS
•^< r» -^<
s
S
^9898939^93
2252s = 321S2
S§SS2 = 3S:=3 S-^^^^^22^^
0
s
JJJJSJ2S22
SfHSf-teSSooS
[South Latitude: 41°
[R — Local mean time of sun's visible i
1-1
g' ~ ~ ~ y- ~2 ~ ~Z ~ "-5 ^!
S2gSSSS3SS
2SSSaS5355?SS§;? = sS3§S3
_
i ^
s
H
SsS3S§2s;2S
= S5S^?5i??i2 =2SSS = ^S5^S5
0
J
££2S-2^^ZZ2~B^^2Z^^^~^~$^^^~~2
•
0
^^iSg^i^^^^^^^^^^^^^g^S
M
IH
S>SS3 = S = SSg SSSSSSSSS^S^ISiSSS^SSSJ??, 325 = 5SS3 = 5
^^r* -c^*— i>ot>^t^-^ •^*i>^c^^i>,t^'^ir*^i>'^'i> ,t^ ,t^- i> ,r^ .x-^x^xr:
"-9
8
1
SlSS^s-ga&s
?f^?^S2^:£ S^3=:3-:^?
8
1
teS5SSS8SS5
* — -vq^L^i>.— v^-.-^-.-*.
f 3 -r f7 — ri r: Ft rt ^ cc
SsS?§S35g = 3S SSSSSSSiJSSS
j;J|>rt
^X-^- X -X..X..X..XW
«
0
^SSaSS58S598g
ǤSE;S2 = q:s*s
SSSS3 = ss = 5 5SSSS5SS558
s
1
S§85JS§^?S3!5
H
1
^a^assssas
ri
p
s
s
1
aHsag^jgag
^r - TP uv . — .
1(5
1
,5SW
1*
1 I
rtxaSfflflSaDflSxtfx ^rt-djD^^irtrfjrfmP^M^rt. ^x^x^x^dtfd
^ . -rrnrir rrirrr
l 3 S 1 1 If Lf 5 S 3
Page 666]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
ptember 23 to December 22.
S=Local mean time of sun's visi
South latitude: 0° to 20
mean time of sun's visible ri
•9}Bp
•xoaddy
0 0 rH (N CO
•8TBp
•xoid
xoiddy
O i-H <M CO
f4 OQ p4 02 tf 00 p? OQ f4 CC PC? OQ P? CC f4 00 f4 OQ f4 02
vc to ic «ic to in to id to
a 3 §
COiOCOiOCOiOCOO<NO
iCtOiOtOiCtOidtOiCtO
OCOClTt<I^5OiCaOCOCT>(Ni-l
lOtOiOtOiOtOiOtOiOtOiQtO
ss;
iQtOiOOiOteiOtOiOtOiCtO
aCO>r^r-ltO(Ml£>Ttl
r-iOi-li-lrHr-li-liH
OtiiCCOiCCOiCCCiOCOiO
COLOCOiCCOi^COLOCOUO
idtOiCtOvOtOiOtOiOtOiOtO
o o o
COO C^l
16 »Q 09 tQttSMd iQ V9 tOiQ
iCiCiOtOiOtOiCtOiCtOiOtO
Tt*CseOO5CaO(Mr-(^rHr-(OJ
KiiOCOiOCOOCOOCOOcOO
SMl^C^r- r-tt^r^COO'XOOOOOOC
«C l> '~00~' OV
aotoootcootoootoooto
T^iO-^iOT^iO-^lO-^iiO
Pn' 02 P4 02 f*5 03 PH' QQ pi 02 PH' CQ
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 667
22
sibl
ber
ptember 23 to De
*=Local mean time o
South latitude: 21° to
mean time of sun's visible
§3
xoiddy
' •/. -' x =i x ^' /. - •/.
; ic ->c ic -~ ic •— i
r
?'5£g3£S£^2 ^~39S$393g3S!
M ~
H
i -.£ rf O .-* O -f O TT --T- -* -~ •
_;; 1C ^O 1C — 1C ~ -~. — U~ -^ lC
; O iC ^ iC -C: uC ^ iC ti iC "-: iC ~ iC 'O iC -O iC •
6?ss55as9ssas asssssssssteassssssss s^s^--^
^sssasbsss^sssasaBSsasa
^iC^OlCOlCOLC^^^ LCOL-ttCt^'^l-t^L^tC LC^lC^lLC^L^^L^'^ LJt^C^^L^^Tr'O'^J'^O
S-S^^SEZ^^ ^i^-^-iHSS^ S?i5?)o'5S"^g?j
ic --c ic — ic -.c ic — ic -^: |ic « ic -^ ic vs ic — tc '-i "C -o ic «c ic o ic ^> o »
— '^COd— iXMt^rt ;c T ic ic — is ic r>- M ac — rso — 5irii^M«-* '
MOM — -- — — — , r-i — , —i—.—.-^r-., ^,__ — — — ,-i — r^or-iorj
: ic -~o ic -j ic «s o -^ i
^j iC tO iC '-= iC •— iC -^ iC — ,uC — iC -^ i
I <O O <O lO «O >O « iC — iC — iC -~ iC '
?5oj^S^^^-?5^^i;|S3^S^SS^;^;
g^SSs^^H5HS ^S^S^SS
• S S 5 ^ 5 :". o r: - ~ o H S H 2 fc 5 -: c ~
rfjiCiCi
• -OiC i=iC O
•aiup
Oiddy
— X — X— *X— X — X — X. — X.
Page 668]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
22.
De
tember 23 to ember
Local mean time o sun's visible
South Latitude: 41° to
mean time of sun's visible
0
83S83S3S8S8
•9TOD
•xoaddv
JH
•xoiddy
"*(M
-^ O
COGOCOOOCOCOCOXCOOO
sooocooceoocioooecco
§OSOOr-llOlM'^<1-llO
JO 0 •* iC iO ^ 0 CO i-H
COOOCOCOC^OOC-JOliMOl
sfc^ooci*— iic~^f>ioGocc>i'^fooo^o^f(o4Gor-~<
S (N T-C r-< CS r-l C*) ri -.N O CO O CC O •* iO rf iO TI< •<* >
*^'^t^-^t><^i>i^t|i>i^r* j*^ t* ^ r-- c^ c^ co c~- co J
mf*eo aoneoeoaoeo ao J00000990 evcoViaociao
COOOC03CCCOO<MOOC<100
Sit-- 1C ^H C-3 -^" 00 t~- iO O CO
(MOC^Jl-lr-li-lOOMOCO
• 00 flQ |e*S 00 CO 00 CO OOCQ 00 WOO
• co3OJO»cooocoao
^•^o^o-^coTtt^-^t^ •^t^'<i'i>Ttii>T}<i>Ttit^j-^ii>T}n>.Tf<c^cot^eoi>1cot>cot>cot^cot>co30
ift CO CC u-5 O t^ SO C5 '-O -
coiceoiccoioc^o
g^5!5^S^S^S
TfiOTfiOT}<O-^«5^tiO
<X> -^ t^ C<I OO j-t O OS r-H
Jlo « o N o ooSeo
S999!
St^ CO CT> rH l-H Ol CO t> l
SO 10 CO 10 T}< Tt TJ< -H
rH OC-)O3'*l^l»lCr-~7''5C5:TH^C
88S8833383
) <M JC<1 ^t1 rHl
«M i-HN T-I (
coocooioocoocoo
o ^J 5J
M CO C4 O2 pj CC A 'JD tf 02
10 imc 10 10 10 ic id o 10 to
2 S S
2JC»P5 02^02 pi '0503 CO
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 669
•dJBp
oid
xoiddy
.2
3
a I
1!
a o
5 i
? 1
1 1
South Latitude: 0° to 20°—
mean time of sun's visible rising. S
•xoiddy
®a5 tfoisix'^x'six'-'x' sixsixsix'si xsix siadsiai
H
s: -j. ~ x si x 2: x ^
: •— to •— — to •-= to to to to to to to to to to to to to to to to to to to to — to to to to to to to to
: to to to to to tO to to to to to to to to tO to -,O to to to to to to tO to to tO
to o «o o o «
to to to o to to to to to to : to to to to to « to to to to to to
< to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to o
^ to — to to to to to to to to to to «o to to to to to to to to to to to to to to to ;o to to to to to to to to to to to to to
! tC to to tO tO to to tO tO tO tO to to to tO tO to tO tO tO to US tO
tO tO tO to tO to tO to O to to tO to to to to to to to tO tO tO to to to to iS to iC to lO to
; to to to to to o to :to to to to to to to to to to jto to to to to to to to to to
to to to to to to to to to :to to to to to to to to to to
•o -~ u- -^ o to 10 to vo to o o
*3S838S885Stea
; to to to to t^O to to to to tO to to to to tO tO tO tO to
tOOtOtCtOOtOOiOO
e to to to to to to to to to to to to to to to to to to to to to to to to to to ic to ic to !io o i
•i*tOtOtOtOtOtOtOtOtOtO'cO<OtOtOtOtOtOtOtOtO;tOtOtOtOOtOOtOiOtO
: to to to <O tO to to tO to to U7 to O tO i
^ to to to to to to to to to to to to to to to to to to to to
^jtototoototootototo tototovotctototoicto L=to^:tcictomtoisto
' to to to to tO to u- to L£ to
iS to iO tO >O to O «O
^ o r-i M o « cc
^'OtOtOtOtOOtOtOtOtO 'tOtOiOtOiCtOiCtOiOtO
68SSS855SS88
rfjtOOtOtOtOOtOOtOtC
iCtOiCtOOtOOOiCO.iOtOOtOultOiOtOiCOiCtO
LCtOOtOOtOOtOiOtOiOtO
' 'l^ tOi/^tOOtOLC tOi^ttO
: ic <
O tf OQ 25 CO PS QD tf QD tf 02 »j CO « DQ
rinrrir
61828°— 16 36
Page 670]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
•9:pjp
oad
xoaddy
22 to March 21.
n time of sun's visible
South Latitude: 21° to 40°— D
mean time of sun's visible rising. S=
xoiddy
T-I (M CO •*
ec ec c« co
l-^N^<N-^<N^O)^iMiO<NiC>!-li»'-iiarHiOrHiO
>iHOr-IOT-IOi-HO^Oi-IOrHO)-lOr-IOr-IOi-l
i^O^HOrHOrMOrH O T^
Or-IOi-lSr-l8r-l8r-l SrHlOrH
«0 50 tO 50 <0 «0 CO «0 <0 50 0 «5 CO CO iO CO ift CO U3 CO
rCJcOCOcOCOiOCOiOCOiOCO
•<*Tj<Tfl-^-^-^T}<-<^<
IM CD CO •* ^* CO O i-l I>
co to co 10
COiO<NiOCNOCNO<MO
WiOCOiCCOiOC^OiMO
iC^fco«Or-iooajot^i-i
!NOCNOCNOiHr-lr-(iH
C^OrHOrHr-lrHr-lT-li-l
rHOiHrH rH rH rH rH O r-l O rH
O-^OOtOOC55^i-((MCO
CNOT-IOiHOi-lrHr-lrH
CMOOOOt^<NvOiO(NI>
iHOtHrHOiHOi-IOi-l
P^ 02 PH* CO P5 CO ftj 02 p? 02
p? co' P3 02' P5 co tf* 02' PS* GQ
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 671
rf?
1!
ol
1 1
II
>
0) jc
-i2 Sc
'•3 -2
c3 -
H? 2
M
1*
•xojddy
"
o 51
S £ 5 S
^QDtfQDrtcotf odtf ad tf
^^c^-^^^c^.-^--^- -•
•C ~ -~ • '. ~ >-~. '*£ ut <£ i£ CC i
SSSSSSS SSSSSSSSSS SSISS5§55S?
• r. — x "r oc
s = r^s525=5^J5«§«gg5g!§g«b$5§j2g;33aa fisssr.sr.;
aj us « ic •— ^ ••& \z ~ iC •-= u- -^ ir -^ L- vs ^ ^ _~ v: Jt
I ^ I «•*>'
: u- -^ L.- <c L.- %c i
n t- Ci Si r i LC —• ~i -^ z*. ^ t~~ M — L.t o x t> M r? ui o si
T- o^^o^^=:^J^^^LC^t li^vcr-'r-T-Tr-r — —
- re -c - x
•8J*p
•xoadd
<f»oc^u;i>'rt^-^'t>-^<t> •<rt^'ri>T?<r.Tj<t^rrt> -^t^-^t^-^'X'<j<X'3<« -^x-fl<co«3Or:xr;x
\ ^-. -^ -^. c~. r i r i ~. i
: T r: T r: i-v -* ec-
;2;2 '^. '•=.?.>
i- M o i- r^ a n ^ o ui ao
^ ir:?: — rtiCT-rtu-^o
'xccccccxrtx tcxrrxrcxccocicci
>«o w«om«eceao<oe»e4Oke«9
>l> 1C OCCC K M CC M OC CO X « X M X CC 00
eoooccocc^CJC^Oir^o
od
itfodtf oDtfoDrtcctfaDiPJcdtf actf DDtfodrtx
s 5 § § s
Page 672] TABLE 11.
For reducing the Time of the Moon's passage over the Meridian of Greenwich to the Time of its pass
age over any other Meridian. The numbers taken from this Table are to be added to the Time at
Greenwich in West Longitude, subtracted in East Longitude.
Longi
tude.
Daily variation of the moon's passing the meridian.
Longi-
tude.
40m
42m
44m
46m
48m
50m
52m
64m
56m
68m
60m
62m
64m
66m
o
0
5
10
15
20
25
30
m.
0
1
1
2
2
3
3
m.
0
1
1
2
2
3
3
m.
0
1
1
2
2
3
4
m.
0
1
1
3
2
3
4
m.
0
1
1
2
3
3
4
m.
0
1
1
2
3
3
4
m.
0
1
1
2
3
4
4
m.
0
1
1
2
3
4
4
m.
0
1
2
2
3
4
5
m.
0
1
2
2
3
4
5
m.
0
1
2
2
3
4
5
m.
0
1
2
3
3
4
5
m.
0
1
2
3
4
4
5
m.
0
1
2
3
4
5
5
o
0
5
10
15
20
25
30
35
40
45
50
55
4
4
5
6
6
4
5
5
6
6
4
5
5
6
7
4
5
6
6
7
5
5
6
7
7
5
6
6
7
8
5
6
6
7
8
5
6
7
7
8
5
6
7
8
9
6
6
7
8
9
6
7
7
8
9
6
7
8
9
9
6
7
8
9
10
6
7
8
9
10
35
40
45
50
55
60
65
70
75
80
7
7
8
8
9
7
8
8
9
9
7
8
9
9
10
8
8
9
10
10
8
9
9
10
11
8
9
10
10
11
9
9
10
11
12
9
10
10
11
12
9
10
11
12
12
10
10
11
12
13
10
11
12
12
13
10
11
12
13
14
11
12
12
13
14
11
12
13
14
15
60
65
70
75
80
85
90
95
100
105
9
10
11
11
12
10
10
11
12
12
10
11
12
12
13
11
11
12
13
13
11
12
13
13
14
12
12
13
14
15
12
13
14
14
15
13
13
14
15
16
13
14
15
16
16
14
14
15
16
17
14
15
16
17
17
15
15
16
17
18
15
16
17
18
19
16
16
17
18
19
20
21
22
23
24
85
90
95
100
105
110
115
120
125
130
110
115
120
125
130
12
13
13
14
14
13
13
14
15
15
13
14
15
15
16
14
15
15
16
17
15
15
16
17
17
15
16
17
17
18
16
17
17
18
19
16
17
18
19
19
17
18
19
19
20
18
19
19
20
21
18
19
20
21
22
19
20
21
22
22
20
20
21
22
23
135
140
145
150
155
15
16
16
17
17
16
16
17
17
18
16
17
18
18
19
17
18
19
19
20
18
19
19
20
21
19
19
20
21
22
19
20
21
22
22
20
21
22
22
23
21
22
23
23
24
22
23
23
24
25
22
23
24
25
26
23
24
25
26
27
24
25
26
27
28
25
26
27
27
28
135
140
145
150
155
160
165
170
175
180
18
18
19
19
20
19
19
20
20
21
20
20
21
21
22
20
21
22
22
23
21
22
23
23
24
22
23
24
24
25
23
24
25
25
26
24
25
25
26
27
25
26
26
27
28
26
27
27
28
29
27
27
28
29
30
28
28
29
30
31
28
29
30
31
32
29
30
31
32
33
160
165
170
175
180
40m
42m
44m
46m
48m
50m
62m
64m
66m
68m
60m
62m
64-
66-
TABLE 12. [Page 673
For finding the Variation of the Sun's Right Ascension or Decimation, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
1"
2"
3"
4"
6"
V
1"
8"
9"
10"
11"
12"
13"
14"
15"
16"
17"
18"
19"
1
2
3
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
1
1
2
2
2
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
2
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
~2~
2
2
2
3
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
2
3
4
5
6
7
8
9
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
~2"
2
2
2
2
1
1
1
2
2
1
1
2
2
2
1
2
2
2
2
1
2
2
2
2
2
2
2
2
3
2
2
2
3
3
2
2
2
3
3
2
2
3
3
3
6
7
8
9
10
11
12
13
14
15
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
2
2
2
3
3
2
2
3
3
3
2
3
3
3
3
3
3
3
3
4
3
3
3
3
3
3
3
3
4
3
4
4
3
, 4
4
11
12
13
14
15
4
4
4
5
5
16
17
18
19
20
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
3
4
4
4
3
4
4
4
4
4
4
4
4
5
4
4
5
5
5
4
5
5
5
5
5
5
5
5
6
5
5
6
6
5
5
6
6
6
16
17
18
19
20
21
22
23
24
25
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
~Y
2
2
2
3
3
3
3
3
3
2
2
2
2
3
~3~
3
3
3
3
~3~
3
3
3
4
2
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
6
4
4
5
5
5
5
5
5
5
5
5
5
5
6
6
5
6
6
6
6
6
6
6
6
7
6
6
7
7
7
6
7
7
8
/
7
8
8
21
22
23
24
25
26
27
28
29
30
3
3
3
3
4
3
4
4
4
4
4
4
4
4
5
5
5
5
5
5
4
5
5
5
5
5
5
6
6
6
6
6
6
6
7
6
6
7
7
7
7
7
7
7
8
7
7
7
8
8
7
8
8
8
9
8
8
8
9
9
8
9
9
n
10
26
27
28
29
30
31
32
33
34
35
4
4
4
4
4
4
4
4
5
5
5
5
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
8
7
7
8
8
8
8
8
8
9
9
8
9
9
9
9
9
9
9
10
10
9 10
10 10
10 10
10 11
11 11
31
32
33
34
35
36
37
38
39
40
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
~~2~
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
9
8
9
9
9
9
9
9
10
10
10
10
10
10
10
11
10
10
11
11
11
11 11
11 12
11 12
12 12
12 13
36
37
38
39
40
41
42
43
44
45
1
1
1
1
1
1
1
1
1
2
3
3
3
3
3
3
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
6
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
7
7
7
7
8
8
S
8
8
8
8
8
9
9
9
9
9
9
10
10
10
10-
10
10
11
10
11
11
11
11
11
11
11
12
12
12
12
12
12
13
12
13
13
13
14
13
13
14
14
14
41
42
43
44
45
46
47
48
49
50
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
6
5
5
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
8
8
8
8
8
9
9
9
9
9
8
9
9
9
9
9
10
10
10
10
9
9
10
10
10
10
10
11
11
11
10
10
10
11
11
11
11
11
12
12
11
11
11
11
12
12
12
12
13
13
12
12
12
12
13
12
13
13
13
13
13
13
14
14
14
14
14
14
15
15
15
15
15
16
16
16
16
17
17
17
46
47
48
49
50
51
52
53
54
55
1
1
1
1
1
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
13
13
13
14
14
14
14
14
14
15
14
15
15
15
16
15
16
16
16
17
51
52
53
54
55
56
57
58
59
60
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
6
6
6
6
6
7
7
7
7
7
7
8
8
8
o
8
9
9
9
9
9
10
10
10
10
10
10
11
11
11
11
11
12
12
12
12
12
13
13
13
13
13
14
14
14
14
14
15
15
15
15
15
15
16
16
16
16
16
17
17
17
17
17
18
18
18
18
18
19
19
56
57
58
59
60
Page 674] TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
20"
21"
22"
23"
24"
25"
26"
27"
28"
29"
30"
31"
32"
33"
34"
35"
36"
1
2
3
4
5
0
1
1
1
2
0
1
1
1
2
0
1
1
1
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
2
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
2
3
4
5
6
7
8
9
10
2
2
3
3
3
2
2
3
3
4
2
3
3
3
4
2
3
3
3
4
2
3
3
4
4
3
3
3
4
4
3
3
3
4
4
3
3
4
4
5
3
3
4
4
5
3
3
3
4
3
4
3
4
3
4
3
4
5
5
6
4
4
5
5
6
4
4
5
5
6
6
7
8
9
10
4
5
5
5
5
5
5
5
5
6
11
12
13
14
15
4
4
4
5
5
4
4
5
5
5
4
4
5
5
6
4
5
5
5
6
4
5
5
6
6
5
5
5
6
6
5
5
6
6
7
5
5
6
6
7
5
6
6
7
7
5
6
6
7
7
6
6
7
7
8
6
6
7
7
8
6
6
7
7
8
6
7
7
8
8
6
7
7
8
9
6
7
8
8
9
7
7
8
8
9
11
12
13
14
15
16
17
18
19
20
5
6
6
6
7
6
6
6
7
7
6
6
7
7
7
6
7
7
7
8
6
7
7
8
8
7
7
8
8
8
7
7
8
8
9
7
8
8
9
9
7
8
8
9
9
8H
8
9
9
10
8
9
9
10
10
8
9
9
10
10
9
9
10
10
11
9
9
10
10
11
9
10
10
11
11
9
10
11
11
12
10
10
11
11
12
16
17
18
19
20
21
22
23
24
25
7
7
8
8
8
7
8
8
8
9
8
8
8
9
9
10
10
10
11
11
8
8
9
9
10
10
10
11
11
12
8
9
9
10
10
10
11
11
12
12
9
9
10
10
10
9
10
10
10
11
9
10
10
11
11
10
10
11
11
12
10
11
11
12
12
11
11
12
12
13
11
11
12
12
13
11
12
12
13
13
12
12
13
13
14
12
12
13
14
14
12
13
13
14
15
13
13
14
14
15
21
22
23
24
25
26
27
28
29
30
9
9
9
10
10
9
9
10
10
11
11
11
12
12
13
11
12
12
13
13
12
12
13
13
14
12
13
13
14
14
13
13
14
14
15
13
14
14
15
15
13
14
14
15
16
14
14
15
15
16
14
15
15
16
17
15
15
16
16
17
15
16
16
17
18
16
16
17
17
18
26
27
28
29
30
31
32
33
34
35
10
11
11
11
12
11
11
12
12
12
11
12
12
12
13
12
12
13
13
13
14
14
15
15
15
12
13
13
14
14
13
13
14
14
15
13
14
14
15
15
14
14
15
15
16
14
15
15
16
16
15
15
16
16
17
16
16
17
17
18
16
17
17
18
18
17
17
18
18
19
17
18
18
19
19
18
18
19
19
20
18
19
19
20
20
19
19
20
20
21
31
32
33
34
35
36
37
38
39
40
12
12
13
13
13
13
13
13
14
14
13
14
14
14
15
14
15
15
16
16
16
17
17
18
18
15
15
16
16
17
16
16
16
17
17
16
17
17
18
18
17
17
18
18
19
17
18
18
19
19
18
19
19
20
20
19
19
20
20
21
19
20
20
21
21
20
20
21
21
22
20
21
22
22
23
21
22
22
23
23
22
22
23
23
24
36
37
38
39
40
41
42
43
44
45
14
14
14
15
15
14
15
15
15
16
16
16
17
17
18
18
18
19
19
19
15
15
16
16
17
16
16
16
17
17
17
18
18
18
19
18
18
19
19
20
18
19
19
20
20
19
20
20
21
21
20
20
21
21
22
21
21
22
22
23
21
22
22
23
23
22
22
23
23
24
23
23
24
24
25
23
24
24
25
26
24
25
25
26
26
25
25
26
26
27
41
42
43
44
45
46
47
48
49
50
15
16
16
16
17
17
17
18
18
18
17
17
18
18
18
18
18
18
19
19
20
20
20
21
21
21
22
22
23
23
18
19
19
20
20
19
20
20
20
21
20
20
21
21
22
21
21
22
22
23
21
22
22
23
23
22
23
23
24
24
23
24
24
25
25
24
24
25
25
26
25
25
26
26
27
25
26
26
27
28
26
27
27
28
28
27
27
28
29
29
28
28
29
29
30
46
47
48
49
50
51
52
53
54
55
19
19
19
20
20
21
21
21
22
22
20
21
21
22
22
22
23
23
24
24
21
22
22
23
23
22
23
23
23
24
23
23
24
24
25
24
24
25
25
26
25
25
26
26
27
26
26
27
27
28
26
27
27
28
28
27
28
28
29
29
28
29
29
30
30
29
29
30
31
31
30
30
31
32
32
31
31
32
32
33
51
52
53
54
55
56
57
58
59
60
19
19
19
20
20
20
20
20
21
21
23
24
24
25
25
24
25
25
26
26
25
26
26
27
27
26
27
27
28
28
27
28
28
29
29
28
29
29
30
30
29
29
30
30
31
30
30
31
31
32
31
31
32
32
33
32
32
33
33
34
33
33
34
34
35
34
34
35
35
36
56
57
58
59
60
TABLE 12. [Page 675
For finding the Variation of the Sun's Right Ascension or Decimation, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
37"
38"
1
1
2
3
3
39"
40"
1
1
2
3
3
41"
42"
43"
1
1
2
3
4
44"
45"
46"
47"
48"
49"
50"
51"
62"
53"
1
2
3
4
5
1
1
2
2
3
1
1
2
3
3
1
1
2
3
3
1
1
2
3
4
1
1
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
1
2
2
3
1
2
2
3
1
2
3
3
1
2
3
3
1
2
3
3
1
2
3
4
1
2
3
4
5
6
7
8
9
10
4
5
6
6
4
5
6
6
5
5
6
5
5
6
5
5
6
5
6
6
5
6
6
5
6
5
5
6
5
5
6
5
5
6
5
6
6
5
6
7
5
6
7
8
8
5
6
7
8
9
5
6
7
8
9
5
6
7
8
9
6
7
8
9
10
~~7~
8
8
9
10
10
11
12
12
13
14
14
15
16
16
~T
8
9
9
10
11
11
12
13
13
14
15
15
16
17
~8~
8
9
10
10
~T
8
9
10
11
7
8
8
8
8
8
11
12
13
14
15
7
7
8
9
9
7
8
8
9
10
8
9
9
10
11
8
9
10
10
11
8
9
10
11
11
8
9
10
11
12
9
9
10
11
12
9
10
10
11
12
9
10
11
11
12
9
10
11
12
13
9
10
11
12
13
10
10
11
12
13
10
11
11
12
13
11
12
13
14
15
16
17
18
19
20
10
10
11
12
12
10
11
11
12
13
11
12
12
13
14
14
15
16
16
17
11
12
13
13
14
11
12
13
14
14
12
12
13
14
15
12
13
14
14
15
12
13
14
15
15
13
13
14
15
16
13
14
14
15
16
13
14
15
16
16
13
14
15
16
17
14
14
15
16
17
14
15
16
16
17
14
15
16
17
18
16
17
18
19
20
21
22
23
24
25
13
14
14
15
15
13
14
15
15
16
15
15
16
17
18
15
16
16
17
18
15
16
17
18
18
16
17
17
18
19
16
17
18
18
19
16
17
18
19
20
17
18
18
19
20
17
18
19
20
20
18
18
19
20
21
18
19
20
20
21
18
19
20
21
22
19
19
20
21
22
21
22
23
24
25
26
27
28
29
30
16
17
17
18
19
16
17
18
18
19
17
18
18
19
20
20
21
21
22
23
23
24
25
25
26
17
18
19
19
20
18
18
19
20
21
18
19
20
20
21
22
22
23
24
25
19
19
20
21
22
19
20
21
21
22
20
20
21
22
23
20
21
21
22
23
20
21
22
23
24
21
22
22
23
24
21
22
23
24
25
22
23
23
24
25
22
23
24
25
26
23
23
24
25
26
23
24
25
26
27
26
27
28
29
30
31
32
33
34
35
19
20
20
21
22
20
20
21
22
22
23
23
24
25
25
21
21
22
23
23
21
22
23
23
24
25
25
26
27
27
22
23
24
24
25
23
23
24
25
26
23
24
25
26
26
24
25
25
26
27
24
25
26
27
27
25
26
26
27
28
2o
26
27
28
29
26
27
28
28
29
26
27
28
29
30
27
28
29
29
30
27
28
29
30
31
31
32
33
34
35
36
37
38
39
40
22
23
23
24
25
24
25
25
26
27
25
26
27
27
28
26
27
27
28
29
26
27
28
29
29
2/
28
29
29
30
28
28
29
30
31
28
29
30
31
31
29
30
30
31
32
29
30
31
32
33
30
31
32
33
33
31
31
32
33
34
31
32
33
34
35
32
33
34
34
35
36
37
38
39
40
41
42
43
44
45
25
26
27
27
28
26
27
27
28
29
29
30
30
31
32
27
27
28
29
29
30
31
31
32
33
~W
34
34
1 35
i 36
27
28
29
29
30
28
29
29
30
31
31
32
33
33
34
35
36
36
37
38
29
29
30
31
32
32
33
34
34
35
29
30
31
32
32
30
31
32
32
33
31
32
32
33
34
31
32
33
34
35
32
33
34
34
35
33
34
34
35
36
33
34
35
36
37
34
35
36
37
38
35
36
37
37
38
36
36
37
38
39
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
28
29
30
30
31
31
31
32
33
33
33
34
34
35
36
34
34
35
36
37
35
35
36
37
38
35
36
37
38
38
36
37
38
38
39
37
38
38
39
40
38
38
39
40
41
38
39
40
41
42
39
40
41
42
43
40
41
42
42
43
41
42
42
43
44
46
47
48
49
50
51
52
53
54
55
31
32
33
33
34
32
33
34
34
35
35
36
37
37
38
34
35
35
36
37
36
36
37
38
39
37
37
38
39
39
37
38
39
40
40
38
39
40
41
41
39
40
41
41
42
40
41
42
42
43
41
42
42
43
44
42
42
43
44
45
43
43
44
45
46
43
44
45
46
47
44
45
46
47
48
45
46
47
48
49
51
52
53
54
55
56
57
58
59
60
35
35
36
36
37
36
37
38
38
39
37
38
39
39
40
38
39
40
40
41
39
40
41
41
42
40
41
42
42
43
41
4'2
43
43
44
42
43
44
44
45
43
44
44
45
46
44
45
45
46
47
45
46
46
47
48
46
47
47
48
49
47
48
48
49
50
48
48
49
50
51
49
49
50
51
52
49
50
51
52
53
56
57
58
59
60
Page 676] TABLE 12.
For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M
Horary motion.
M.
54"
65"
56"
1
2
3
4
5
67"
1
2
3
4
5
68"
1
2
3
4
5
59"
60"
61"
1
2
3
4
5
62"
63"
64"
65"
66"
67"
68"
69"
70"
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
6
1
2
3
4
6
1
2
3
5
6
1
2
3
5
6
1
2
4
5
6
1
2
3
4
5
6
7
8
9
10
5
6
7
8
9
6
6
7
8
9
6
7
7
8
9
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
11
6
7
9
10
11
8
9
10
11
8
9
10
11
8
9
10
11
8
9
10
11
8
9
10
12
8
9
11
12
6
7
8
9
10
11
12
13
14
15
10
11
12
13
14
10
11
12
13
14
10
11
12
13
14
10
11
12
13
14
11
12
13
14
15
11
12
13
14
15
11
12
13
14
15
11
12
13
14
15
11
12
13
14
16
12
13
14
15
16
12
13
14
15
16
12
13
14
15
16
12
13
14
15
17
12
13
15
16
17
12
14
15
16
17
13
14
15
16
17
13
14
15
16
18
11
12
13
14
15
16
17
18
19
20
14
15
16
17
18
15
16
17
17
18
15
16
17
18
19
15
16
17
18
19
15
16
17
18
19
16
17
18
19
20
16
17
18
19
20
16
17
18
19
20
17
18
19
20
21
17
18
19
20
21
17
18
19
20
21
17
18
20
21
22
18
19
20
21
22
18
19
20
21
22
18
19
20
22
23
18
20
21
22
23
19
20
21
22
23
16
17
18
19
20
21
22
23
24
25
19
20
21
22
23
19
20
21
22
23
20
21
21
22
23
20
21
22
23
24
20
21
22
23
24
21
22
23
24
25
21
22
23
24
25
21
22
23
24
25
22
23
24
25
26
22
23
24
25
26
22
23
25
26
27
23
24
25
26
27
23
24
25
26
28
23
25
26
27
28
24
25
26
27
28
24
25
26
28
29
25
26
27
28
29
21
22
23
24
25
26
27
28
29
30
23
24
25
26
27
24
25
26
27
28
24
25
26
27
28
25
26
27
28
29
25
26
27
28
29
26
27
28
29
30
26
27
28
29
30
26
27
28
29
31
27
28
29
30
31
27
28
29
30
32
28
29
30
31
32
28
29
30
31
33
29
30
31
32
33
29
SO
31
32
34
29
31
32
33
34
30
31
32
33
35
30
32
33
34
35
26
27
28
29
30
31
32
33
34
35
28
29
30
31
32
28
29
30
31
32
29
30
31
32
33
29
30
31
32
33
34
35
36
37
38
30
31
32
33
34
30
31
32
33
34
31
32
33
34
35
32
33
34
35
36
32
33
34
35
36
33
34
35
36
37
33
34
35
36
37
34
35
36
37
38
34
35
36
37
39
35
36
37
38
39
35
36
37
39
40
36
37
38
39
40
36
37
39
40
41
31
32
33
34
35
36
37
38
39
40
32
33
34
35
36
33
34
35
36
37
34
35
35
36
37
35
36
37
38
39
35
36
37
38
39
36
37
38
39
40
37
38
39
40
41
37
38
39
40
41
38
39
40
41
42
38
39
41
42
43
39
40
41
42
43
40
41
42
43
44
40
41
42
44
45
41
42
43
44
45
41
43
44
45
46
42
43
44
46
47
36
37
38
39
.40
41
42
43
44
45
37
38
39
40
41
38
39
39
40
41
38
39
40
41
42
39
40
41
42
43
40
41
42
43
44
40
41
42
43
44
41
42
43
44
45
42
43
44
45
46
42
43
44
45
47
43
44
45
46
47
44
45
46
47
48
44
46
47
48
49
45
46
47
48
50
46
47
48
49
50
46
48
49
50
51
47
48
49
51
52
48
49
50
51
53
41
42
43
44
45
46
47
48
49
50
41
42
43
44
45
42
43
44
45
46
43
44
45
46
47
44
45
46
47
48
44
45
46
47
48
45
46
47
48
49
46
47
48
49
50
47
48
49
50
51
48
49
50
51
52
48
49
50
51
53
49
50
51
52
53
50
51
52
53
54
51
52
53
54
55
51
52
54
55
56
52
53
54
56
57
53
54
55
56
58
54
55
56
57
58
46
47
48
49
50
51
52
53
54
55
46
47
48
49
50
47
48
49
50
50
48
49
49
50
51
48
49
50
51
52
49
50
51
52
53
50
51
52
53
54
51
52
53
54
55
52
53
54
55
56
53
54
55
56
57
54
55
56
57
58
54
55
57
58
59
55
56
57
59
60
56
57
58
59
61
57
58
59
60
61
58
59
60
61
62
59
60
61
62
63
60
61
62
63
64
51
52
53
54
55
56
57
58
59
60
50
51
52
53
54
51
52
53
54
55
52
53
54
55
56
53
54
55
56
57
54
55
56
57
58
55
56
• 57
58
59
56
57
58
59
60
57
58
59
60
61
58
59
60
61
62
59
60
61
62
63
60
61
62
63
64
61
62
63
64
65
62
63
64
65
66
63
64
65
66
67
63
65
66
67
68
64
66
67
68
69
65
67
68
69
70
56
57
58
59
60
TABLE 12. [Page 677
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
71"
72"
73"
14" 1 76"
76"
77"
78"
79"
80"
81"
82"
83"
84"
85"
86"
87"
1
2
3
4
5
1
2
1
2
1
2
1
2
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
1
3
4
6
1
3
4
6
1
3
4
6
7
1
2
3
4
5
5
6
5
6
7
8
10
11
12
5
6
7
9
10
11
12
5
6
5
6
5
6
5
6
5
5
5
5
5
6
6
6
7
8
9
10
7
8
9
11
12
7
9
10
11
12
8
9
10
11
13
14
15
16
18
19
8
9
10
11
13
8
9
10
12
13
8
9
10
12
13
8
9
11
12
13
8
9
11
12
13
8
9
11
12
14
8
10
11
12
14
8
10
11
12
14
8
10
11
13
14
9
10
11
13
14
9
10
11
13
14
9
10
12
13
15
6
7
8
9
10
11
12
13
14
15
13
14
15
17
18
13
14
16
17
18
13
15
16
17
18
14
15
16
17
19
14
15
16
18
19
14
15
17
18
19
~2T
22
23
24
26
14
16
17
18
20
14
16
17
18
20
15
16
17
19
20
15
16
18
19
20
15
16
18
19
21
15
17
18
19
21
15
17
18
20
21
16
17
18
20
21
16
17
19
20
22
16
17
19
20
22
11
12
13
14
15
16
17
18
19
20
19
20
21
22
24
19
20
22
23
24
19
21
22
23
24
20
21
22
23
25
20
21
23
24
25
20
22
23
24
25
21
22
23
25
26
21
22
24
25
26
21
23
24
25
27
22
23
24
26
27
22
23
25
26
27
22
24
25
26
28
22
24
25
27
28
23
24
26
27
28
23
24
26
27
29
23
25
26
28
29
16
17
18
19
20
21
22
23
24
25
25 25
26 26
27 28
28 29
30 30
26
27
28
29
30
26
27
28
30
31
26
28
29
30
31
27
28
29
30
32
27
28
30
31
32
~^3~
35
36
37
39
27
29
30
31
33
28
29
30
32
33
28
29
31
32
33
28
30
31
32
34
29
30
31
33
34
29
30
32
33
35
29
31
32
34
35
30
31
33
34
35
30
32
33
34
36
30
32
33
34
36
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
31
32
34
35
36
37
38
40
41
42
32
33
34
35
37
32
33
35
36
37
33
34
35
36
38
33
34
35
37
38
34
35
36
38
39
34
36
37
38
40
35
36
37
39
40
35
36
38
39
41
36
37
38
40
41
36
37
39
40
42
36
38
39
41
42
37
38
40
41
43
37
39
40
42
43
38
39
41
42
44
26
27
28
29
30
31
32
33
34
35
37
38
39
40
41
38
39
40
41
43
38
39
41
42
43
39
40
41
43
44
39
41
42
43
44
40 40
41 42
42 43
44 44
45 ! 46
41
42
43
45
46
41
43
44
45
47
42
43
45
46
47
42
44
45
46
48
43
44
46
47
48
43
45
46
48
49
44
45
47
48
50
44
46
47
49
50
45
46
48
49
51
31
32
33
34
35
36
37
38
39
40
43
44
45
46
47
43
44
46
47
48
49
50
52
53
54
55
56
58
59
60
61
62
64
65
66
44
45
46
47
49
44
46
47
48
49
45
46
48
49
.50
51
53
54
55
56
58
59
60
61
63
46
47
48
49
51
46
47
49
50
51
47
48
49
51
52
47
49
50
51
53
48
49
51
52
53
49
50
' 51
53
54
49
51
52
53
55
50
51
53
54
55
50
52
53
55
56
51
52
54
55
57
52
53
54
56
57
52
54
55
57
58
36
37
38
39
40
41
42
43
44
45
49
50
51
52
53
50
51
52
54
55
"56"
57
58
60
61
51
52
53
54
56
57
58
59
60
62
52
53
54
56
57
53
54
55
56
58
53
55
56
57
59
54
55
57
58
59
55
56
57
59
60
55
57
58
59
61
56
57
59
60
62
57
58
59
61
62
57
59
60
62
63
58
60
61
62
64
59
60
62
63
65
59
61
62
64
65
41
42
43
44
45
46
47
48
49
50
54
56
57
58
59
58
60
61
62
63
59
60
62
63
64
. 60
61
62
64
65
61
62
63
65
66
61
63
64
65
67
62
63
65
66
68
63
64
66
67
68
64
65
66
68
69
64
66
67
69
70
65
67
68
69
71
66
67
69
70
72
67
68
70
71
73
46
47
48
49
50
51
52
53
54
55
60
62
63
64
65
62
63
64
66
67
63
64
65
67
68
64
65
66
68
69
65
66
67
68
70
65
67
68
69
71
66
68
69
70
72
~73~
74
75
77
78
67
68
70
71
72
68
69
71
72
73
69
70
72
73
74
70
71
72
74
75
71
72
73
75
76
71
73
74
76
77
72
74
75
77
78
73
75
76
77
79
74
75
77
78
80
51
52
53
54
55
56
57
58
59
60
66
67
69
70
71
67
68
70
71
72
68
69
71
72
73
69
70
72
73
74
70
71
73
74
75
71
72
73
75
76
72
73
74
76
77
74
75
76
78
79
Vo
76
77
79
80
76
77
78
80
81
77
78
79
81
82
77
79
80
82
83
78
80
81
83
84
79
81
82
84
85
80
82
83
85
86
81
83
84
86
87
56
57
58
59
60
Page 678] TABLE 12.
For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Eight Ascension, in seconds of time, the motion in one minute being given
at the top and the numbers in the side column being taken for seconds.
Horary motion.
M.
88"
1
3
4
6
7
89"
1
3
4
6
7
90"
2
3
5
6
8
9
11
12
14
15
91"
92"
2
3
5
6
8
9
11
12
14
15
17
18
20
21
23
25
26
28
29
31
93"
94"
95"
96"
97"
98"
99"
100"
101"
102"
103"
104"
1
2
3
4
5
2
3
5
6
8
9
11
12
14
15
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
2
3
5
2
3
5
2
3
5
2
3
5
2
3
5
2
3
5
1
2
3
8
8
8
8
9
9
9
5
6
7
8
9
10
9
10
12
13
15
9
10
12
13
15
9
11
12
14
16
9
11
13
14
16
10
11
13
14
16
10
11
13
14
16
10
11
13
15
16
10
11
13
15
16
10
12
13
15
17
10
12
13
15
17
10
12
13
15
17
10
12
14
15
17
10
12
14
15
17
10
12
14
16
17
6
7
8
9
10
11
12
13
14
15
16
18
19
21
22
16
18
19
21
22
17
18
20
21
23
17
18
20
21
23
24
26
27
29
30
17
19
20
22
23
17
19
20
22
24
17
19
21
22
24
18
19
21
22
24
18
19
21
23
24
18
20
21
23
25
18
20
21
23
25
18
20
22
23
25
19
20
22
24
25
19
20
22
24
26
19
21
22
24
26
19
21
23
24
26
11
12
13
14
15
16
17
18
19
20
23
25
26
28
29
24
25
27
28
30
24
26
27
29
30
25
26
28
29
31
25
27
28
30
31
25
27
29
30
32
26
27
29
30
32
26
27
29
31
32
26
28
29
31
33
26
28
30
31
33
27
28
30
32
33
27
29
30
32
34
27
29
31
32
34
27
29
31
33
34
28
29
31
33
35
16
17
18
19
20
21
22
23
24
25
31
32
34
35
37
31
33
34
36
37
32
33
35
36
38
32
33
35
36
38
32
34
35
37
38
33
34
36
37
39
33
34
36
38
39
33
35
36
38
40
34
35
37
38
40
34
36
37
39
40
34
36
38
39
41
35
36
38
40
41
35
37
38
40
42
35
37
39
40
42
36
37
39
41
43
36
38
39
41
43
36
38
40
42
43
21
22
23
24
25
26
27
28
29
30
38
40
41
43
44
39
40
42
43
45
39
41
42
44
45
39
41
42
44
46
40
41
43
44
46
40
42
43
45
47
41
42
44
45
47
41
43
44
46
48
42
43
45
46
48
42
44
45
47
49
42
44
46
47
49
43
45
46
48
50
43
45
47
48
50
44
45
47
49
51
44
46
48
49
51
45
46
48
50
52
45
47
49
50
52
26
27
28
29
30
31
32
33
34
35
45
47
48
50
51
46
47
49
50
52
47
48
50
51
53
54
56
57
59
60
47
49
50
52
53
55
56
58
59
61
48
49
51
52
54
55
57
58
60
61
48
50
51
53
54
49
50
52
53
55
49
51
52
54
55
50
51
53
54
56
50
52
53
55
57
51
52
54
56
57
51
53
54
56
58
52
53
55
57
58
52
54
56
57
59
53
54
56
58
60
53
55
57
58
60
54
55
57
59
61
31
32
33
34
35
36
37
38
39
40
53
54
56
57
59
53
55
56
58
59
56
57
59
60
62
56
58
60
61
63
57
59
60
62
63
58
59
61
62
64
58
60
61
63
65
59
60
62
64
65
59
61
63
64
66
60
62
63
65
67
61
62
64
66
67
61
63
65
66
68
62
64
65
67
69
62
64
66
68
69
36
37
38
39
40
41
42
43
44
45
60
62
63
65
66
61
62
64
65
67
68
70
71
73
74
62
63
65
66
68
62
64
65
67
68
63
64
66
67
69
64
65
67
68
70
64
66
67
69
71
65
67
68
70
71
66
67
69
70
72
66
68
70
71
73
67
69
70
72
74
68
69
71
73
74
68
70
72
73
75
69
71
72
74
76
70
71
73
75
77
70
72
74
76
77
71
73
75
76
78
41
42
43
44
45
46
47
48
49
50
67
69
70
72
73
69
71
72
74
75
70
71
73
74
76
71
72
74
75
77
71
73
74
76
78
72
74
75
77
78
73
74
76
78
79
74
75
77
78
80
74
76
78
79
81
75
77
78
80
82
76
78
79
81
83
77
78
80
82
83
77
79
81
82
84
78
80
82
83
85
79
81
82
84
86
80
81
83
85
87
46
47
48
49
50
51
52
53
54
55
75
76
78
79
81
76
77
79
80
82
83
85
86
88
89
77
78
80
81
83
77
79
80
82
83
78
80
81
83
84
86
87
89
90
92
79
81
82
84
85
80
81
83
85
86
81
82
84
86
87
82
83
85
86
88
82
84
86
87
89
83
85
87
88
90
84
86
87
89
91
85
87
88
90
92
86
88
89
91
93
87
88
90
92
94
88
89
91
93
94
88
90
92
94
95
51
52
53
54
55
56
57
58
59
60
82
84
85
87
88
84
86
87
89
90
85
86
88
90
91
87
88
90
91
93
88
89
91
92
94
89
90
92
93
95
90
91
93
94
96
91
92
94
95
97
91
93
95
96
98
92
94
96
97
99
93
95
97
98
100
94
96
98
99
101
95
97
99
100
102
96
98
100
101
103
97
99
101
102
104
56
57
58
59
60
TABLE 12. [Page 679
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variatior of the
Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given
at the top and the numbers in the side column being taken for seconds.
M.
Horary motion.
105"
106"
107"
108"
109"
110"
ill"
112"
113"
114"
115"
116"
117"
118"
1
2
3
2
2
2
2
2
2
2
2
2
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
1
2
3
4
5
5
5
5
5
5
6
6
6
6
8
9
5
9
9
9
9
9
9
9
9
6
7
8
9
10
11
12
14
16
18
11
12
14
16
18
11
12
14
16
18
11
13
14
16
18
11
13
15
16
18
11
13
15
17
18
11
13
15
17
19
11
13
15
17
19
11
13
15
17
19
11
13
15
17
19
12
13
15
17
19
12
14
15
17
19
12
14
16
18
20
12
14
16
18
20
6
7
8
9
10
11
12
13
14
15
19
21
23
25
26
19
21
23
25
27
20
21
23
25
27
20
22
23
25
27
20
22
24
25
27
20
22
24
26
28
20
22
24
26
28
21
22
24
26
28
21
23
24
26
28
21
23
25
27
29
21
23
25
27
29
21
23
25
27
29
21
23
25
27
29
22
24
26
28
30
11
12
13
14
15
16
17
18
19
20
28
30
32
33
35
28
30
32
34
35
29
30
32
34
36
29
31
32
34
36
29
31
33
35
36
29
31
33
35
37
30
31
33
35
37
30
32
34
35
37
30
32
34
36
38
30
32
34
36
38
31
33
35
36
38
31
33
35
37
39
31
33
35
37
39
31
33
35
37
39
16
17
18
19
20
21
22
23
24
25
37
39
40
42
44
37
39
41
42
44
37
39
41
43
45
38
40
41
43
45
38
40
42
44
45
39
40
42
44
46
39
41
43
44
46
39
41
43
45
47
40
41
43
45
47
40
42
44
46
48
40
42
44
46
48
41
43
44
46
48
41
43
45
47
49
41
43
45
47
49
21
22
23
24
25
26
27
28
29
30
46
47
49
51
53
46
48
49
51
53
46
48
50
52
54
47
49
50
52
54
47
49
51
53
55
48
50
51
53-
55
48
50
52
54
56
49
50
52
54
56
49
51
53
55
57
49
51
53
55
57
50
52
54
56
58
50
52
54
56
58
51
53
55
57
59
51
53
55
57
59
26
27
28
29
30
31
32
33
34
35
54
56
58
60
61
55
57
58
60
62
55
57
59
61
62
56
58
59
61
63
56
58
60
62
64
57
59
61
62
64
57
59
61
63
65
58
60
62
63
65
58
60
62
64
66
59
61
63
65
67
59
61
63
65
67
60
62
64
66
68
60
62
64
66
68
61
63
65
67
69
31
32
33
34
35
36
37
38
39
40
63
65
67
68
70
64
65
67
69
71
64
66
68
70
71
65
67
68
70
72
65
67
69
71
73
66
68
70
72
73
67
68
70
72
74
67
69
71
73
75
68
70
72
73
75
68
70
72
74
76
69
71
73
75
77
70
72
73
75
77
70
72
74
76
78
71
73
75
77
79
36
37
38
39
40
41
42
43
44
45
72
74
75
77
79
72
74
76
78
80
73
75
77
78
80
74
76
77
79
81
74
76
78
80
82
75
77
79
81
83
76
78
80
81
83
77
78
80
82
84
77
79
81
83
85
78
80
82
84
86
79
81
82
84
86
79
81
83
85
87
80
82
84
86
88
81
83
85
87
89
41
42
43
44
45
46
47
48
49
50
81
82
84
86
88
81
83
85
87
88
82
84
86
87
89
83
85
86
88
90
84
85
87
89
91
84
86
88
90
92
85
87
89
91
93
86
88
90
91
93
87
89
90
92
94
87
89
91
93
95
88
90
92
94
96
89
91
93
95
97
90
92
94
96
98
90
92
94
96
98
46
47
48
49
50
51
52
53
54
55
89
91
93
95
96
90
92
94
95
97
91
93
95
96
98
92
94
95
97
99
93
94
96
98
100
94
95
97
99
101
94
96
98
100
102
95
97
99
101
103
96
98
100
102
104
97
99
101
103
105
98
100
102
104
105
99
101
102
104
106
99
101
103
105
107
100
102
104
106
108
51
52
53
54
55
56
57
58
59
60
98
100
102
103
105
99
101
102
104
106
100
102
103
105
107
101
103
104
106
108
102
104
105
107
109
103
105
106
108
110
104
105
107
109
111
105
106
108
110
112
105
107
109
111
113
106
108
110
112
114
107
109
111
113
115
108
110
112
114
116
109
111
113
115
117
110
112
114
116
118
56
57
58
59
60
Page 680] TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
Horary motion.
M.
119"
120"
121"
122"
123"
124"
125"
126"
127"
128"
129"
130"
131"
132"
1
2
3
4
5
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
3
4
5
6
8
10
6
8
10
6
8
10
6
8
10
6
8
10
6
8
10
6
8
10
6
8
11
6
8
11
6
9
11
6
9
11
7
9
11
7
9
11
7
9
11
6
7
8
9
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
12
14
16
18
21
12
14
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
22
13
15
17
,20
22
13
15
17
20
22
13
15
18
20
22
6
7
8
9
10
11
12
13
14
15
22
24
26
28
30
22
24
26
28
30
22
24
26
28
30
22
24
26
28
31
23
25
27
29
31
23
25
27
29
31
23
25
27
29
31
23
25
27
29
32
23
25
28
30
32
23
26
28
30
32
24
26
28
30
32
24
26
28
30
33
24
26
28
31
33
24
26
29
31
33
11
12
13
14
15
16
17
18
19
20
32
34
36
38
40
32
34
36
38
40
32
34
36
38
40
33
35
37
39
41
33
35
37
39
41
33
35
37
39
41
33
35
38
40
42
34
36
38
40
42
34
36
38
40
42
34
36
38
41
43
34
37
39
41
43
35
37
39
41
43
35
37
39
41
44
35
37
40
42
44
16
17
18
19
20
21
22
23
24
25
42
44
46
48
50
42
44
46
48
50
42
44
46
48
50
43
45
47
49
51
43
45
47
49
51
43
45
48
50
52
44
46
48
50
52
44
46
48
50
53
44
47
49
51
53
45
47
49
51
53
45
47
49
52
54
46
48
50
52
54
46
48
50
52
55
46
48
51
53
55
21
22
23
24
25
26
27
28
29
30
52
54
56
58
60
52
54
56
58
60
52
54
56
58
61
53
55
57
59
61
53
55
57
59
62
54
56
58
60
62
54
56
58
60
63
55
57
59
61
63
55
57
59
61
64
55
58
60
62
64
56
58
60
62
65
56
59
61
63
65
57
59
61
63
66
57
59
62
64
66
26
27
28
29
30
31
32
33
34
35
61
63
65
67
69
62
64
66
68
70
63
65
67
69
71
~T3~
75
77
79
81
63
65
67
69
71
64
66
68
70
72
64
66
68
70
72
65
67
69
71
73
65
67
69
71
74
66
68
70
72
74
66
68
70
73
75
67
69
71
73
75
67
69
72
74
76
68
70
72
74
76
68
70
73
75
77
31
32
33
34
35
36
37
38
39
40
71
73
75
77
79
72
74
76
78
80
73
75
77
79
81
74
76
78
80
82
74
76
79
81
83
75
77
79
81
83
76
78
80
82
84
76
78
80
83
85
77
79
81
83
85
77
80
82
84
86
78
80
82
85
87
79
81
83
85
87
79
81
84
86
88
36
37
38
39
40
41
42
43
44
45
81
83
85
87
89
82
84
86
88
90
83
85
87
89
91
83
85
87
89
92
84
86
88
90
92
85
87
89
91
93
85
88
90
92
94
86
88
90
92
95
87
89
91
93
95
87
90
92
94
96
88
90
92
95
97
89
91
93
95
98
90
92
94
96
98
90
92
95
97
99
41
42
43
44
45
46
47
48
49
50
91
93
95
97
99
92
94
96
98
100
93
95
97
99
101
94
96
98
100
102
94
96
98
100
103
95
97
99
101
103
96
98
100
102
104
97
99
101
103
105
97
99
102
104
106
98
100
102
105
107
99
101
103
105
108
100
102
104
106
108
100
103
105
107
109
101
103
106
108
110
46
47
48
49
50
51
52
53
54
55
101
103
105
107
109
102
104
106
108
110
103
105
107
109
111
104
106
108
110
112
105
107
109
111
113
105
107
110
112
114
106
108
110
113
115
107
109
111
113
116
108
110
112
114
116
109
111
113
115
117
110
112
114
116
118
111
113
115
117
119
111
114
116
118
120
112
114
117
119
121
51
52
53
54
55
56
57
58
59
60
111
113
115
117
119
112
114
116
118
120
113
115
117
119
121
114
116
118
120
122
115
117
119
121
123
116
118
120
122
124
117
119
121
123
125
118
120
122
124
126
119
121
123
125
127
119
122
124
126
128
120
123
125
127
129
121
124
126
128
130
122
124
127
129
131
123
125
128
130
132
56
57
58
59
60
TABLE 12. "Page 681
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
133"
134"
135"
136"
137"
138"
139"
140"
141"
142"
143"
144"
145"
146"
1
2
3
4
5
2
4
7
9
11
2
4
7
9
11
2
5
7
9
11
2
5
7
9
11
2
5
7
9
11
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
2
5
—
i
10
12
1
2
3
4
5
6
7
8
9
10
13
16
18
20
22
13
16
18
20
22
14
16
1*
20
23
14
16
18
20
23
14
16
18
21
23
14
16
18
21
23
14
16
19
21
23
14
16
19
21
23
14
16
19
21
24
14
17
19
21
24
14
17
19
21
24
14
17
19
22
24
15
17
19
22
• 24
15
17
19
22
24
6
7
8
9
10
11
12
13
14
15
24
27
29
31
33
25
27
29
31
34
25
27
29
32
34
25
27
29
32
34
25
27
30
32
34
25
28
30
32
35
25
28
30
32
35
26
28
30
33
35
26
28
31
33
35
26
28
31
33
36
26
29
31
33
36
26
29
31
34
36
27
29
31
34
36
27
29
32
34
37
11
12
13
14
15
16
17
18
19
20
35
38
40
42
44
36
38
40
42
45
36
38
41
43
45
36
39
41
43
45
37
39
41
43
46
37
39
41
44
46
37
39
42
44
46
37
40
42
44
47
38
40
42
45
47
38
40
43
45
47
38
41
43
45
48
38
41
43
46
48
39
41
44
46
48
39
41
44
46
49
16
17
18
19
20
21
22
23
24
25
47
49
51
53
55
47
49
51
54
56
47
50
52
54
56
48
50
52
54
57
48
50
53
55
57
48
51
53
55
58
49
51
53
56
58
49
51
54
56
58
49
52
54
56
59
50
52
54
57
59
50
52
55
57
60
50
53
55
58
60
51
53
56
58
60
51
54
56
58
61
21
22
23
24
25
26
27
28
29
30
58
60
62
64
67
58
60
63
65
67
59
61
63
65
68
59
61
63
66
68
59
62
64
66
69
60
62
64
67
69
60
63
65
67
70
61
63
65
68
70
61
63
66
68
71
62
64
66
69
71
62
64
67
69
72
62
65
67
70
72
63
65
68
70
73
63
66
68
71
73
26
27
28
29
30
31
32
33
34
35
69
71
73
75
78
69
71
74
76
78
70
72
74
77
79
70
73
75
77
79
71
73
75
78
80
71
74
76
78
81
72
74
76
79
81
72
75
77
79
82
73
75
78
80
82
73
76
78
80
83
74
76
79
81
83
74
77
79
82
84
75
77
80
82
85
75
78
80
83
85
31
32
33
34
35
36
37
38
39
40
80
82
84
86
89
80
83
85
87
89
81
83
86
88
90
82
84
86
88
91
82
84
87
89
91
83
85
87
90
92
83
86
88
90
93
84
86
89
91
93
85
87
89
92
94
85
88
90
92
95
86
88
91
93
95
86
89
91
94
96
87
89
92
94
97
88
90
92
95
97
36
37
38
39
40
41
42
43
44
45
91
93
95
98
100
92
94
96
98
101
92
95
97
99
101
93
95
97
100
102
94
96
98
100
103
94
97
99
101
104
95
97
100
102
104
96
98
100
103
105
96
99
101
103
106
97
99
102
104
107
98
100
102
105
107
98
101
103
106
108
99
102
104
106
109
100
102
105
107
110
41
42
43
44
45
46
47
48
49
50
102
104
106
109
111
103
105
107
109
112
104
106
108
110
113
104
107
109
111
113
105
107
110
112
114
106
108
110
113
115
107
109
111
114
116
107
110
112
114
117
108
110
113
115
118
109
111
114
116
118
110
112
114
117
119
110
113
115
118
120
111
114
116
118
121
112
114
117
119
122
46
47
48
49
50
51
52
53
54
55
113
115
117
120
122
114
116
118
121
123
115
117
119
122
124
116
118
120
122
125
116
119
121
123
126
117
120
122
124
127
118
120
123
125
127
119
121
124
126
128
120
122
125
127
129
121
123
125
128
130
122
124
126
129
131
122
125
127
130
132
123
126
128
131
133
124
127
129
131
134
51
52
53
54
55
56
57
58
59
60
124
126
129
131
133
12D
127
130
132
134
126
128
131
133
135
127
129
131
134
136
128
130
132
135
137
129
131
133
136
138
130
132
134
137
139
131
133
135
138
140
132
134
136
139
141
133
135
137
140
142
133
136
138
141
143
134
137
139
142
144
135
138
140
143
145
136
139
141
144
146
56
57
58
59
60
Page 682] TABLE 12.
For finding the Variation of the Sun's Right Ascension, or Declination, or of the Equation of Time in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
147"
148"
149"
160"
151"
152"
153"
154"
155"
156"
167"
168"
159"
160"
1
2
3
4
5
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
1»
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
11
13
3
5
8
11
13
3
5
8
11
13
1
2
3
4
5
6
7
8
9
10
15
17
20
22
25
15
17
20
22
25
15
17
20
22
25
15
18
20
23
25
15
18
20
23
25
15
18
20
23
25
15
18
20
23
26
15
18
21
23
26
16
18
21
23
26
16
18
21
23
26
16
18
21
24
26
16
18
21
24
26
16
19
21
24
27
16
19
21
24
27
6
7
8
9
10
11
12
13
14
* 15
27
29
32
34
37
27
30
32
35
37
27
30
32
35
37
28
30
33
35
38
28
30
33
35
38
28
30
33
35
38
28
31
33
36
38
28
31
33
36
39
28
31
34
36
39
29
31
34
36
39
29
31
34
37
39
29
32
34
37
40
29
32
34
37
40
29
32
35
37
40
11
12
13
14
15
16
17
18
19
20
39
42
44
47
49
39
42
44
47
49
40
42
45
47
50
40
43
45
48
50
40
43
45
48
50
41
43
46
48
51
41
43
46
48
51
41
44
46
49
51
41
44
47
49
52
42
44
47
49
52
42
44
47
50
52
42
45
47
50
53
42
45
48
50
53
43
45
48
51
53
16
17
18
19
20
21
22
23
24
25
51
54
56
59
61
52
54
57
59
62
52
55
57
60
62
53
55
58
60
63
53
55
58
60
63
53
56
58
61
63
54
56
59
61
64
54
56
59
62
64
54
57
59
62
65
55
57
60
62
65
55
58
60
63
65
55
58
61
63
66
56
58
61
64
66
56
59
61
64
67
21
22
23
24
25
26
27
28
29
30
64
66
69
71
74
64
67
69
72
74
65
67
70
72
75
65
68
70
73
75
65
68
70
73
76
66
68
71
73
76
66
69
71
74
77
67
69
72
74
77
67
70
72
75
78
68
70
73
75
78
68
71
73
76
79
68
71
74
76
79
69
72
74
77
80
69
72
75
77
80
26
27
28
29
30
31
32
33
34
35
76
78
81
83
86
76
79
81
84
86
77
79
82
84
87
78
80
83
85
88
78
81
83
86
88
79
81
84
86
89
79
82
84
87
89
80
82
85
87
90
80
83
85
88
90
81
83
86
88
91
81
84
86
89
92
82
84
87
90
92
82
85
87
90
93
83
85
88
91
93
31
32
33
34
35
36
37
38
39
40
88
91
93
96
98
89
91
94
96
99
89
92
94
97
99
90
93
95
98
100
91
93
96
98
101
91
94
96
99
101
92
94
97
99
102
92
95
98
100
103
93
96
98
101
103
94
96
99
101
104
94
97
99
102
105
95
97
100
103
105
95
98
101
103
106
96
99
101
104
107
36
37
38
39
40
41
42
43
44
45
100
103
105
108
110
101
104
106
109
111
102
104
107
109
112
103
105
108
110
113
103
106
108
111
113
104
106
109
111
114
105
107
110
112
115
105
108
110
113
116
106
109
111
114
116
107
109
112
114
117
107
110
113
115
118
108
111
113
116
119
109
111
114
117
119
109
112
115
117
120
41
42
43
44
45
46
47
48
49
50
113
115
118
120
123
113
116
118
121
123
114
117
119
122
124
115
118
120
123
125
116
118
121
123
126
117
119
122
124
127
117
120
122
125
128
118
121
123
126
128
119
121
124
127
129
120
122
125
127
130
120
123
126
128
131
121
124
126
129
132
122
125
127
130
133
123
125
128
131
133
46
47
48
49
50
51
52
53
54
55
125
127
130
132
135
126
128
131
133
136
127
129
132
134
137
128
130
133
135
138
128
131
133
136
138
129
132
134
137
139
130
133
135
138
140
131
133
136
139
141
132
134
137
140
142
133
135
138
140
143
133
136
139
141
144
134
137
140
142
145
135
138
140
143
146
136
139
141
144
147
51
52
53
54
55
56
57
58
59
60
137
140
142
145
147
138
141
143
146
148
139
142
144
147
149
140
143
145
148
150
141
343
146
148
151
142
144
147
149
152
143
145
148
150
153
144
146
149
151
154
145
147
150
152
155
146
148
151
153
156
147
149
152
154
157
147
150
153
155
158
148
151
154
156
159
149
152
155
157
160
56
57
58
59
60
TABLE 13. [Page 683
For finding the Sun's change of Right Ascension for any given number of hours.
Hourly
varia
tion.
Number of hours.
Hourly
varia
tion.
1
2
3
4
5
6
7
8
9
10
11
12
8.50
8.55
8.60
8.65
8.70
«.
8.5
8.6
8.6
8.7
8.7
8.
17.0
17.1
17.2
17.3
17.4
25.5
25.7
25.8
26.0
26.1
34.0
34.2
34.4
34.6
34.8
42.5
42.8
43.0
43.3
43.5
51.0
51.3
51.6
51.9
52.2
52.5
52.8
53.1
53.4
53.7
59.5
59.9
60.2
60.6
60.9
68.0
68.4
68.8
69.2
69.6
76.5
77.0
77.4
77.9
78.3
85.0
85.5
86.0
86.5
87.0
93.5
94.1
94.6
95.2
95.7
102.0
102.6
103.2
103.8
104.4
8.50
8.55
8.60
8.65
8.70
8.75
8.80
8.85
8.90
8.95
8.8
8.8
8.9
8.9
9.0
17.5
17.6
17.7
17.8
17.9
26.3
26.4
26.6
26.7
26.9
27^2
27.3
27.5
27.6
35.0
35.2
35.4
35.6
35.8
43.8
44.0
44.3
44.5
44.8
61.3
61.6
62.0
62.3
62.7
70.0
70.4
70.8
71.2
71.6
78.8
79.2
79.7
80.1
80.6
87.5
88.0
88.5
89.0
89.5
96.3
96.8
97.4
97.9
98.5
105.0
105.6
106.2
106.8
107.4
8.75
8.80
8.85
8.90
8.95
9.00
9.05
9.10
9.15
9.20
9.0
9.1
9.1
9.2
9.2
18.0
18.1
18.2
18.3
18.4
36.0
36.2
36.4
36.6
36.8
45.0
45.3
45.5
45.8
46.0
54.0
54.3
54.6
54.9
55.2
63.0
63.4
63.7
64.1
64.4
72.0
72.4
72.8
73.2
73.6
81.0
81.5
81.9
82.4
82.8
90.0
90.5
91.0
91.5
92.0
99.0
99.6
100.1
100.7
101.2
108.0
108.6
109.2
109.8
110.4
9.00
9.05
9.10
9.15
9.20
9.25
9.30
9.35
9.40
9.45
9.3
9.3
9.4
9.4
9.5
18.5
18.6
18.7
18.8
18.9
27.8
27.9
28.1
28.2
28.4
37.0
37.2
37.4
37.6
37.8
46.3
46.5
46.8
47.0
47.3
55.5
55.8
56.1
56.4
56.7
64.8
65.1
65.5
65.8
66.2
74.0
74.4
74.8
75.2
75.6
83.3
83.7
84.2
84.6
85.1
92.5
93.0
93.5
94.0
94.5
101.8
102.3
102.9
103.4
104.0
111.0
111.6
112.2
112.8
113.4
9.25
9.30
9.35
9.40
9.45
9.50
9.55
9.60
9.65
9.70
9.5
9.6
-9.6
9.7
9.7
19.0
19.1
19.2
19.3
19.4
28.5
28.7
28.8
29.0
29.1
38.0
38.2
38.4
38.6
38.8
47.5
47.8
48.0
48.3
48.5
57.0
57.3
57.6
57.9
58.2
66.5
66.9
67.2
67.6
67.9
76.0
76.4
76.8
77.2
77.6
85.5
86.0
86.4
86.9
87.3
95.0
95.5
96.0
96.5
97.0
104.5
105.1
105.6
106.2
106.7
114.0
114.6
115.2
115.8
116.4
9.50
9.55
9.60
9.65
9.70
9.75
9.80
9.85
9.90
9.95
9.8
9.8
9.9
9.9
10.0
19.5
19.6
19.7
19.8
19.9
29.3
29.4
29.6
29.7
29.9
39.0
39.2
39.4
39.6
39.8
48.8
49.0
49.3
49.5
49.8
58.5
58.8
59.1
59.4
59.7
68.3
68.6
69.0
69.3
69.7
78.0
78.4
78.8
79.2
79.6
87.8
88.2
88.7
89.1
89.6
97.5
98.0
98.5
99.0
99.5
107.3
107.8
108.4
108.9
109.5
117.0
117.6
118.2
118.8
119.4
9.75
9.80
9.85
9.90
9.95
10.00
10.05
10.10
10.15
10.20
10.0
10.1
10.1
10.2
10.2
20.0
20.1
20.2
20.3
20.4
30.0
30.2
30.3
30.5
30.6
40.0
40.2
40.4
40.6
40.8
50.0
50.3
50.5
50.8
51.0
60.0
60.3
60.6
60.9
61.2
70.0
70.4
70.7
71.1
71.4
80.0
80.4
80.8
81.2
81.6
90.0
90.5
90.9
91.4
91.8
100.0
100.5
101.0
101.5
102.0
110.0
110.6
111.1
111.7
112.2
120.0
120.. 6
121.2
121.8
122.4
10.00
10.05
10.10
10.15
10. 20
10.25
10.30
10.35
10.40
10.45
10.3
10.3
10.4
10.4
10.5
20.5
20.6
20.7
20.8
20.9
30.8
30.9
31.1
31.2
31.4
41.0
41.2
41.4
41.6
41.8
51.3
51.5
51.8
52.0
52.3
61.5
61.8
62.1
62.4
62.7
71.8
72.1
72.5
72.8
73.2
82.0
82.4
82.8
83.2
83.6
92.3
92.7
93.2
93.6
94.1
102.5
103.0
103.5
104.0
104.5
112.8
113.3
113.9
114.4
115.0
123.0
123.6
124. 2
124.8
125.4
10.25
10.30
10.35
10.40
10. 45
10.50
10.55
10.60
10.65
10.70
10.5
10.6
10.6
10.7
10.7
21.0
21.1
21.2
21.3
21.4
31.5
31.7
31.8
32.0
32.1
42.0
42.2
42.4
42.6
42.8
52.5
52.8
53.0
53.3
53.5
63.0
63.3
63.6
63.9
64.2
73.5
73.9
74.2
74.6
74.9
84.0
84.4
84.8
85.2
85.6
94.5
95.0
95.4
95.9
96.3
105.0
105.5
106.0
106.5
107.0
115.5
116.1
116.6
117.2
117. 7
126.0
126.6
127.2
127.8
128.4
10.50
10.55
10.60
10.65
10.70
10.75
10.80
10.85
10.90
10.95
10.8
10.8
10.9
10.9
11.0
21.5
21.6
21.7
21.8
21.9
32.3
32.4
32.6
32.7
32.9
43.0
43.2
43.4
43.6
43.8
53.8
54.0
54.3
54.5
54.8
64.5
64.8
65.1
65.4
65.7
75.3
75.6
76.0
76.3
76.7
86.0
86.4
86.8
87.2
87.6
96.8
97.2
97.7
98.1
98.6
107.5
108.0
108.5
109.0
109.5
118.3
118.8
119.4
119.9
120. 5
129.0
129.6
130.2
130.8
131.4
10.75
10.80
10.85
10.90
10.95
11.00
11.05
11.10
11.15
11.20
11.0
11.1
11.1
11.2
11.2
22.0
22.1
22.2
22.3
22.4
33.0
33.2
33.3
33.5
33.6
44.0
44.2
44.4
44.6
44.8
55.0
55.3
55.5
55.8
56.0
66.0
66.3
66.6
66.9
67.2
77.0
77.4
77.7
78.1
78.4
88.0
88.4
88.8
89.2
89.6
99.0
99.5
99.9
100.4
100.8
110.0
110.5
111.0
111.5
112.0
121.0
121.6
122.1
122.7
123.2
132.0
132.6
133.2
133.8
134.4
11.00
11.05
11.10
11.15
11.20
11.25
11.30
11.35
11.40
11.45
11.3
11.3
11.4
11.4
11.5
22.5
22.6
22.7
22.8
22.9
33.8
33.9
34.1
34.2
34.4
45.0
45.2
45.4
45.6
45.8
56.3
56.5
56.8
57.0
57.3
67.5
67.8
68.1
68.4
68.7
78.8
79.1
79.5
79.8
80.2
90.0
90.4
90.8
91.2
91.6
101.3
101.7
102.2
102.6
103.1
112.5
113.0
113.5
114.0
114.5
123.8
124.3
124.9
125.4
126.0
135.0
135.6
136.2
136.8
137.4
11.25
11.30
11.35
11.40
11.45
Page 684] TABLE 13.
For finding the Sun's change of Right Ascension for any given number of hours.
Hourly
Number of hours.
Hourly
varia
tion.
tion.
13
14
15
16|
17
18
19
20
21
22
23
24
204. 0
205.2
206.4
207.6
208.8
8.' 50
8.55
8.60
8.65
8.70
110. 5
111.2
111.8
112.5
113.1
119. 0
119.7
120.4
121.1
121.8
127. 5
128.3
129.0
129.8
130.5
136. 0
136.8
137.6
138.4
139.2
144. 5
145.4
146.2
147.1
147.9
153.0
153.9
154.8
155.7
156.6
161. 5
162.5
163.4
164.4
165.3
170. 0
171.0
172.0
173.0
174.0
178. 5
179.6
180.6
181.7
182.7
187.0
188.1
189.2
190.3
191.4
195. 5
196.7
197.8
199.0
200.1
8.50
8.55
8.60
8.65
8.70
8.75
8.80
8.85
8.90
8.95
113.8
114.4
115.1
115.7
116.4
122.5
123.2
123.9
124.6
125.3
131.3
132.0
132.8
133. 5
134.3
140.0
140.8
141.6
142.4
143.2
148.8
149.6
150.5
151.3
152.2
157.5
158,4
159.3
160.2
161.1
166.3
167.2
168.2
169.1
170.1
175.0
176.0
177.0
178.0
179.0
183.8
184.8
185.9
186.9
188.0
192.5
193.6
194.7
195.8
196.9
201.3
202.4
203.6
204.7
205.9
210.0
211.2
212.4
213.6
214.8
8.75
8.80
8.85
8.90
8.95
9.00
9.05
9.10
9.15
9.20
117.0
117.7
118.3
119.0
119.6
126.0
126.7
127.4
128.1
128.8
135. 0
135.8
136.5
137.3
138.0
144.0
144.8
145.6
146.4
147.2
153.0
153.9
154.7
155.6
156.4
162.0
162.9
163.8
164.7
165.6
171.0
172.0
172.9
173.9
174.8
180.0
181.0
182.0
183.0
184.0
189.0
190.1
191.1
192.2
193.2
198.0
199.1
200.2
201.3
202.4
207.0
208.2
209.3
210.5
211.6
216.0
217.2
218.4
219.6
220.8
9.00
9.05
9.10
9.15
9.20
9.25
9.30
9.35
9.40
9.45
120.3
120.9
121.6
122.2
122.9
129.5
130.2
130.9
131.6
132.3
138.8
139.5
140.3
141.0
141.8
148.0
148.8
149.6
150.4
151.2
157.3
158.1
159.0
159.8
160.7
166. 5
167.4
168.3
169.2
170.1
175.8
176.7
177.7
178.6
179.6
185.0
186.0
187.0
188.0
189.0
194.3
195.3
196.4
197.4
198.5
203.5
204.6
205.7
206.8
207.9
209.0
210.1
211.2
212.3
213.4
212.8
213.9
215.1
216.2
217.4
222.0
223.2
224.4
225.6
226.8
9.25
9.30
9.35
9.40
9.45
9.50
9.55
9.60
9.65
9.70
123.5
124.2
124.8
125.5
126.1
133.0
133.7
134.4
135.1
135.8
142.5
143.3
144.0
144.8
145.5
152.0
152.8
153.6
154.4
155.2
161.5
162.4
163.2
164.1
164.9
171.0
171.9
172.8
173.7
174.6
180.5
181.5
182.4
183.4
184.3
190.0
191.0
192.0
193.0
194.0
199.5
200.6
201.6
202.7
203.7
218.5
219.7
220.8
222.0
223.1
228.0
229.2
230.4
231.6
232. 8
9.50
9.55
9.60
9.65
9.70
9.75
9.80
9.85
9.90
9.95
126.8
127.4
128.1
128.7
129.4
130.0
130.7
131.3
132.0
132. 6
136.5
137.2
137.9
138.6
139.3
146.3
147.0
147.8
148.5
149.3
156.0
156.8
157.6
158.4
159.2
165.8
166.6
167.5
168.3
169.2
175.5
176.4
177.3
178.2
179.1
185.3
186.2
187.2
188.1
189.1
195.0
196.0
197.0
198.0
199.0
204.8
205.8
206.9
207.9
209.0
214.5
215.6
216.7
217.8
218.9
224.3
225.4
226.6
227.7
228.9
234.0
235.2
236.4
237.6
238. 8
9.75
9.80
9.85
9.90
9.95
10.00
10.05
10.10
10.15
10.20
140.0
140.7
141.4
142.1
142.8
150.0
150.8
151.5
152.3
153.0
160.0
160.8
161.6
162.4
163.2
170.0
170.9
171. 7
172.6
173.4
180.0
180.9
181.8
182.7
183.6
190.0
191.0
191.9
192.9
193.8
200.0
201.0
202.0
203.0
204.0
210.0
211.1
212.1
213.2
214.2
220.0
221.1
222.2
223.3
224.4
230.0
231.2
232.3
233.5
234.6
240.0
241.2
242.4
243.6
244.8
10.00
10.05
10.10
10.15
10.20
10.25
10.30
10.35
10.40
10.45
133.3
133.9
134.6
135.2
135.9
143.5
144.2
144.9
145.6
146.3
153.8
154.5
155.3
156.0
156.8
164.0
164.8
165.6
166.4
167.2
174.3
175.1
176.0
176.8
177.7
184.5
185.4
186.3
187.2
188.1
194.8
195.7
196.7
197.6
198.6
205. 0
206.0
207.0
208.0
209.0
215.3
216.3
217.4
218.4
219.5
225.5
226.6
227.7
228.8
229.9
235. 8
236.9
238.1
239.2
240.4
241.5
242.7
243.8
245.0
246.1
246.0
247.2
248.4
249.6
250.8
10.25
10.30
10.35
10.40
10.45
10.50
10.55
10.60
10.65
10.70
136.5
137.2
137.8
138.5
139.1
147.0
147.7
148.4
149.1
149.8
157.5
158. 3
159.0
159.8
160.5
168.0
168.8
169.6
170.4
171.2
178.5
179.4
180.2
181.1
181.9
189.0
189.9
190.8
191.7
192.6
199.5
200.5
201.4
202.4
203.3
210.0
211.0
212.0
213.0
214.0
220.5
221.6
222.6
223.7
224.7
231.0
232.1
233.2
234.3
235.4
252.0
253.2
254.4
255.6
256.8
10.50
10.55
10.60
10.65
10.70
10.75
10.80
10.85
10.90
10.95
139.8
140.4
141.1
141.7
142.4
150.5
151.2
151.9
152.6
153.3
161.3
162.0
162.8
163.5
164.3
172.0
172.8
173.6
174.4
175.2
182.8
183.6
184.5
185.3
186.2
193.*
194.4
195.3
196.2
197.1
204.3
205. 2
206.2
207.1
208.1
215.0
216.0
217.0
218.0
219.0
225.8
226.8
227.9
•228.9
230.0
236.5
237.6
238.7
239.8
240.9
247.3
248.4
249.6
250.7
251.9
258.0
259.2
260.4
261.6
262. 8
10.75
10.80
10.85
10.90
10. 95
11.00
11.05
11.10
11.15
11.20
143.0
143.7
144.3
145.0
145.6
154.0
154.7
155.4
156.1
156.8
165.0
165.8
166.5
167.3
168.0
176.0
176.8
177.6
178.4
17*. 2
187.0
187.9
188.7
189.6
190.4
198.0
198.9
199.8
200.7
201.6
209.0
210.0
210.9
211.9
212.8
220.0
221.0
222.0
223.0
224.0
231.0
232.1
233.1
234.2
235.2
242.0
243.1
244.2
245.3
246.4
253.0
254.2
255.3
256.5
257.6
264.0
265.2
266.4
267.6
268.8
11.00
11.05
11.10
11.15
11.20
11.25
11.30
11.35
11.40
11.45
146.3
146.9
147.6
148.2
148.9
157. 5
158.2
158.9
159.6
160.3
168.8
169.5
170.3
171.0
171.8
180.0
180.8
181.6
182.4
183.2
191.3
192.1
193.0
193.8
194.7
202.5
203.4
204.3
205.2
206.1
213.8
214.7
215.7
216.6
217.6
225.0
226.0
227.0
228.0
229.0
236. 3
237.3
238.4
239.4
240.5
247.5
248.6
249.7
250.8
251.9
258. 8
259.9
261.1
262.2
263.4
270.0
271.2
272.4
273.6
274. 8
11.25
11.30
11.35
11.40
11.45
TABLES 14, 15, 16.
[Page 685
TABLE 14.
Dip of the Sea
Horizon.
TABLE 15.
Dip of the Sea at different Distances from the Observer.
Height of
the Eye.
Dip of the
Horizon.
Dist. of
Height of the Eye above the Sea in Feet.
Sea Miles. 5 10
15 20
25
30
35
40
Feet.
1
2
3
4
5
6
7
8
9
10
11
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45
50
55
60
65
70
75
80
85
90
95
100
0 59
1 23
1 42
1 58
2 11
2 24
2 36
2 46
2 56
3 06
3 15
3 24
3 32
3 40
3 48
3 55
4 02
4 09
4 16
4 23
4 29
4 36
4 42
4 48
4 54
5 00
5 06
5 11
5 17
5 22
5 27
5 33
5 38
5 43
5 48
5 53
5 58
6 02
6 07
6 12
6 36
6 56
7 16
7 35
7 54
8 12
8 29
8 46
9 02
9 18
9 33
9 48
I 11 23
* 6 12
f 4 8
136
34 45
17 23
12 15
9 12
/
57
28
19
15
/
68
34
23
17
79
40
27
20
91
45
30
23
H 3 5
1J 3 4
224
2* 2 3
7 10
6 8
5 7
4 6
12
10
8
7
14
12
9
8
16
14
11
9
19
16
12
10
3 3
3J 2 3
4" 2
4 5
4 5
4 5
4 4
6
6
5
5
7
6
6
6
8
7
7
6
9
8
7
7
5 2 ' '3"
623
4 4
5
5
6
6
NOTE TO TABLE 15.
are the same as are g
to those heights not 1
— The numbers of this Table below the black lines
iven in Table 14, the visible horizon corresponding
)eing so far distant as the land.
-
TABLE 16.
The Sun's Parallax
in Altitude.
Altitude.
Parallax.
o
0
10
20
30
40
50
55
60
65
70
75
80
85
90
//
9
9
8
8
7
6
5
4
4
3
2
2
1
0
61828°— 16 37
TABLES 18, 19. [Page 687
TABLE 18.
Augmentation of the Moon's Semidiameter.
TABLE 19.
Augmentation of the Moon's
Horizontal Parallax.
s-c
22 -
eS — p*
^ ^
0,flO
<
})'s Semidiameter.
oi
0 >
£§§
3)'sHor. Parallax.
14 15' 16' 17'
30" 0" SO" 0"
30"
0"
|ol
53'
57' 61'
o
0
2
4
6
8
0.1
0.6
1.0
1.5
2.0
„
0.1
0.6
1.1
1.6
2.1
n
o. i
0.7
1.2
1.7
2.3
//
0.1
-0.7
1.3
1.9
2.4
0.2
0.8
1.4
2.0
2.6
//
0.2
0.8
1.5
2.1
2.7
0
0
2
4
6
8
n
0.0
0.0
0.1
0.1
0.2
//
0.0
0.0
0.1
0.1
0.2
H
0.0
0.0
0.1
0.1
0.2
10
12
14
16
18
2.4
2.9
3.4
3.8
4.3
2.6
3.1
3.6
4.1
4.6
2.8
3.3
3.9
4.4
4.9
3.0
3.6
4.1
4.7
5.2
3.2
3.8
4.4
5.0
5.6
3.4
4.0
4.7
5.3
5.9
10
12
14
16
18
0.3
0.5
0.6
0.8
1.0
0.3
0.5
0.7
0.9
1.1
0.4
0.5
0.7
0.9
1.1
20
22
24
26
28
* 4.7
5.2
5.6
6.0
6.5
5.1
5. 5
6.0
6.5
6.9
5.4
5.9
6.4
6.9
7.4
5.8
6.3
6.8
7.4
7.9
6.1
6.7
7.3
7.8
8.4
6.5
7.1
7.7
8.3
8.9
20
22
24
26
28
1.2
1.5
1.7
2.0
2.3
1.3
1.6
1.9
2.2
2.5
1.4
1.7
2.0
2.3
2.6
30
32
34
36
38
6.9
7.3
7.7
8.1
8.4
7.3
7.8
8.2
8.6
9.0
7.9
8.3
8.8
9.2
9.7
8.4
8.9
9.4
9.8
10.3
8.9
9.4
10.0
10.5
10.9
9.5
10.0
10.6
11.1
11.6
30
32
34
36
38
2.6
2.9
3.3
3.6
4.0
2.8
3.1
3.5
3.9
4.3
3.0
3.4
3.8
4.1
4.6
40
42
44
46
48
8.8
9.2
9.5
9.8
10.2
9.4
9.8
10.2
10.5
10.9
10.1
10.5
10.9
11.3
11.6
10.7
11.2
11.6
12.0
12.4
11.4
11.9
12.3
12.8
13.2
12.1
12.6
13.1
13.6
14.0
40
42
44
46
48
4.3
4.7
5.0
5.4
5.8
4.6
5.0
5.4
5.8
6.2
5.0
5.4
5.8
6.2
6.6
50
52
54
56
58
10.5
10.8
11.1
11.3
11.6
11.2 I 12.0
11.5 i 12.3
11. 8 ! 12. 7
12.1 13.0
12.4 i 13.3
12.8
13.1
13.5
13.8
14.1
13.6
14.0
14.4
14.7
15.1
14.4
14.9
15.3
15.6
16.0
50
52
54
56
58
6.1
6.5
6.8
7.2
7.5
6.6
7.0
7.4
7.7
8.1
7.1
7.5
7.9
8.3
8.6
60
62
64
66
68
11.8
12.1
12.3
12.5
12.7
12.7
12.9
13.2
13.4
13.6
13.5
13.8
14.1
14.3
14.5
14.4
14.7
15.0
15.2
15.5
15.4
15.7
16.0
16.2
16.5
16.3
16.6
16.9
17.2
17.5
60
62
64
66
68
7.8
8.1
8.4
8.7
9.0
8.4
8.8
9.1
9.4
9.7
9.0
9.4
9.7
10.0
10.3
70
72
74
76
78
12.9
13.0
13.1
13.3
13.4
13.8
13.9
14.1
14.2
14.3
14.7
14.9
15.0
15.2
15.3
15.7
15.9
16.0
16.2
16.3
16.7
16.9
17.1
17.2
17.4
17.7
17.9
18.1
18.3
18.4
70
72
74
76
78
9.2
9.5
9.7
9.8
10.0
9.9
10.2
10.4
10.6
10.8
10.6
10.9
11.1
11.3
11.5
80
82
84
86
88
13.5 i
13.5
13.6
13.6
13.7 1
14.4
14.5
14.6
14.6
14.6
15.4
15.5
15.6
15.6
15.6
16.4
16.5
16.6
16.6
16.7
17.5
17.6
17.6
17.7
17.7
18.6
18.7
18.7
18.8
18.8
80
82
84
86
88
10.1
10.3
10.3
10.4
10.4
10.9
11.0
11.1
11.2
11.2
11.7
11.8
11.9
12.0
12. 0
90
13.7 i 14.6 15.6 16.7
17.7
18.8
90
10.5
11.3
12.0
Page 688] TABLE 20A.
Mean Refraction.
[Barometer, 30 inches. Fahrenheit's Thermometer, 50°.J
Apparent
Altitude.
Mean Re
fraction.
Apparent
Altitude.
Mean Re
fraction.
Apparent
Altitude.
Mean Re
fraction.
Apparent
Altitude.
Mean Re
fraction.
Apparent
Altitude.
Mean Re
fraction.
o /
0 00
1 00
2 00
3 00
4 00
36 29. 4
24 53. 6
18 25.5
14 25. 1
11 44.4
0 /
9 30
35
40
45
50
55
5 35.1
5 32.4
5 29.6
5 27.0
5 24.3
5 21.7
o /
15 00
10
20
30
40
50
f a
3 34. 1
3 31.7
3 29.4
3 27.1
3 24.8
3 22.6
0 /
25 00
10
20
30
40
50
/ it
2 4.4
2 3.4
2 2.5
2 1.6
2 0.7
1 59.8
o /
42 00
20
40
43 00
20
'40
1 04.7
1 03.9
1 03.2
1 02.4
1 01.7
1 01.0
5 00"
05
10
15
20
•25
9 52.0
9 44.0
9 36.2
9 28.6
9 21.2
9 14.0
10-00
05
10
15
20
25
5 19.2
5 16.7
5 14.2
5 11.7
5 9.3
5 6.9
16 00
10
20
30
40
50
3 20.5
3 18.4
3 16.3
3 14.2
3 12.2
3 10.3
26 00
10
20
30
40
50
58.9
58.1
57.2
56.4
55.5
54.7
44 00
20
40
45 00
20
40
1 00.3
0 59.6
0 58.9
0 58.2
0 57.6
0 56.9
5 30' 1 9 7.0
35 9 0. 1
40 8 53. 4
4\ L 8 46. 8
50 \ 8 40. 4
55 I\JS 34. 2
10 30
35
40
45
50
55
5 4.6
5 2.3
5 0.0
4 57.8
4 55.6
4 53.4
17 00
10
20
30..
40
50
* 3 8.3
3 6.4
3 4.6
3 2.8
3 1.0
2 59. 2'
27 00
10
20
30
40
50
53/9
53.1
52.3
51.5
50.7
50.0
46 00^
. 20-
40,
47 00«
20*
40
0 56.2
0 55.6
0 55. (X
* o 54:3
0 53.7
0 53.1
6 00
05
10
15
20
25
\8 28.0
Y* 22.1
a, i6. 2
8 10. 5
8 4.8
7 59.3
11 00
05
10
15
20
25
4 51.2
4 49.1
4 47.0
4 44.9
4 42.9
4 40.9
18 00
10
20
30
40
50
2 57.5
2 55.8
2 54. 1
2 52.4
2 50.8
2 49.2
28 00
20
40
29 00
20
40
49.2
47.7
46.2
44.8
43.4
42.0
48 00
49 00
50 00
"51 00
52 00
53 00
0 52.5
0 50.6
0 48.9
0 47.2
0 45.5
0 43.9
6 30
35
40
45
50
55
7 53.9
7 48.7
7 43. 5
7 38.4
7 33.5
7 28.6
11 30
35
40
45
50
55
4 38.9
4 36.9
4 35.0
4 33.1
4 31.2
4 29.4
19 00
10
20
30
40
50
2 47.7
2 46.1
2 44. 6
2 43.1
2 41.6
2 40.2
30 00
20
40
31 00
20
40
40.6
39.3
38.0
36.7
35.5
34.2
54 00
55 00
56 00
57 00
58 00
59 00
0 42.3
0 40.8
0 39.3
0 37.8
0 36.4
0 35. 0
7 00
05
10
15
20
25
7 23.8
7 19. 2
7 14.6
7 10.1
7 5. 7
7 1.4
12 00
05
10
15
20
25
4 27.5
4 25.7
4 23.9
4 22.2
4 20.4
4 18.7
20 00
10
20
30
40
50
2 38.8
2 37.4
2 36. 0
2 34.6
2 33.3
2 32.0
32 00
20
40
33 00
20
40
1 33. 0
1 31. ff
1 30.7
1 29. 5
1 28.4
1 27.3
60 00
61 00
62 00
63 00
64 00
65 00
0 33. 6
0 32.3
0 31.0
0 29.7
0 28.4
0 27.2
7 30
35
40
45
50
55
6 57.1
6 53. 0
6 48.9
6 44.9
6 41.0
6 37.1
12 30
35
40
45
50
55
4 17.0
4 15.3
4 13.6
4 12.0
4 10.4
4 8.8
21 00
10
20
30
40
50
2 30.7
2 29.4
2 28.1
2 26.9
2 25.7
2 24.5
34 00
20
40
35 00
20
40
1 26.2
1*25.1
1 24.1
1 23. 1
1 22.0
1 21.0
66 00
67 00
68 00
69 00
70 00
71 00
0 25.9
0 24.7
0 23.6
0 22.4
0 21.2
0 20.1
8 00
05
10
15
20
25
6 33.3
6 29.6
6 25.9
6 22.3
6 18. 8
6 15.3
13 00
05
10
15
20
25
4 7.2
4 5.6
4 4.1
4 2.6
4 1.0
3 59.6
22 00
10
20
30
40
50
2 23.3
2 22.1
2 20.9
2 19.8
2 18.7
2 17.5
36 00
20
40
37 OO
20.
40
1 20.1
1 19.1
1 18.2
1 tf.2
1 16.3
: i j 7 7
1 ii-,9
1 11.0
1 10.2
72 00
73 00
74 00
75 00
76 00
77 00
0 18.9
0 17.8
0 16.7
0 15.6
0 14.5
0 13.5
8 30
35
40
45
50
55
6 11.9
6 8.5
6 5.2
6 2.0
5 58.8
5 55.7
13 30
35
40
45
50
55
3 58.1
3 56.6
3 55.2
3 53.7
3 52.3
3 50. 9
23 00
10
20
30
40
50
2 16.4
2 15.4
2 14.3
2 13.3'
2 12.2
2 11.2
t'
:;'.) 0.0'
20
40
78 00
-. 79 00
80 00
X81 00
82 00
83 00
0 12.4
0 11.3
0 10.3
0 9.2
0 8.2
0 7.2
9 00
05
10
15
20
25
5 52.6
5 49.6
5 46.6
5 43.6
5 40.7
5 37.9
14 00
10
20
30
40
50
3 49.5
3 46.8
3 44.2
3 41.6
3 39.0
3 36.5
24 00
10
20
30
40
50
2 10.2
2 9.2
2 8.2
2 7.2
2 6. 2
2 5.3
40 00
20
40
41 00
20
40
1 9. 4
1 8.6
1 7.8
1 7.0
1 6. 2
1 5.4
84 00
85 00
86 00
87 00
88 00
89 00
0 6.1
0 5.1
0 4.1
0 3.1
0 2.0
0 1.0
9 30
5 35.1
15 00
3 34.1
25 00
V
2 4.4
42 00
1 4.f
90 00 0 0. 0
TABLE 20B. [Page 689
Correction of the Sun's Apparent Altitude for Refraction and Parallax.
[Barometer, 30 inches. Fahrenheit's Thermometer, 50°.]
Apparent
Altitude.
Mean Re
fraction am
Parallax 0
Apparent
Altitude.
Mean Re
fraction and
Parallax 0.
Apparent
Altitude.
Mean Re
fraction am
Parallax 0
Apparent
Altitude.
Mean Re
fraction am
Parallax ©
Apparent
Altitude.
Mean Re
fraction am
Parallax 0.
o /
0 00
1 00
2 00
3 00
4 00
/ //
36 20
24 45
18 17
14 16
11 35
9 30
35
40
45
50
55
i n
5 26
5 23
5 21
5 18
5 15
5 13
o /
15 00
10
20
30
40
50
/ //
3 25
3 24
3 21
3 19
3 17
3 15
o /
25 00
10
20
30
40
50
/ //
1 56
1 55
1 55
54
53
52
o /
42 00
20
40
43 00
20
40
/ //
0 58
0 57
0 56
0 55
0 55
0 54
5 00
05
10
15
20
25
9 43
9 35
9 27
9 20
9 12
9 5
10 00
05
10
15
20
25
5 10
5 8
5 5
5 3
5 0
4 58
16 00
10
20
30
40
50
3 13
3 10
3 8
3 6
3 4
3 2
26 00
10
20
30
40
50
51
50
49
48
48
47
44 00
20
40
45 00
20
40
0 53
0 53
0 52
0 52
0 52
0 51
5 30
35
40
45
50
55
8 58
8 51
8 44
8 38
8 31
8 25
10 30
35
40
45
50
55
4 56
4 53
4 51
>: 49
4 47
4 44
17 00
10
t 20
30
40
50
3 0
2 58
2 57
2 55
2 53
2 51
27 00
10
20
30
40
50
46
45
1 44
1 44
1 43
1 42
46 00
20
40
47 00
20
40
0 50
0 50
0 49
0 48
0 48
0 47
6 00
05
10
15
20
25
8 19
8 13
8 7
8 2
7 56
7 50
11 00
05
10
15
20
25
4 42
4 40
4 38
4 36
4 34
4 32
18 00
1 o
30
40
50
2 50
2 48
2 46
2 44
2 43
2 41
28 00
20
40
29 00
20
40
1 41
1 40
1 38
1 37
1 35
1 34
48 00
49 00
50 00
51 00
52 00
53 00
0 47
0 45
0 43
0 41
0 40
0 39
6 30
35
4Q
45
50
55
7 45
7 40
7 35
7 29
7 25
7 20
11 30
35
40
45
50
55
4 30
4 28
4 26
4 24
4 22
4 20
19 00
10
20
30
40
50
2 40
2 38
2 37
2 35
2 34
2 32
30 00
20
40
31 00
20
40
1 33
1 31
1 30
1 29
1 28
1 26
54 00
55 00
56 00
57 00
58 00
59 00
0 37
0 36
0 34
0 33
0 32
0 31
7 00
05
10
15
20
25
7 15
7 10
7 6
7 1
. 6 57
6 52
12 00
05
10
15
20
25
4 19
4 17
4 15
4 13
4 11
4 10
20 00
10
20
30
40
50
2 31
2 29
2 28
2 27
2 25
2 24
32 00
20
40
33 00
20
40
1 25
1 24
1 23
1 22
1 20
1 19
60 00
61 00
62 00
63 00
64 00
65 00
0 30
0 28
0 27
0 26
0 24
0 23
7 30
35
40
45
50
55
6 48
6 44
6 40
6 36
6 32
6 28
12 30
35
40
So
50
55
48 21 00
4 C , 10
4 5 J 20
4 ^ ; 30
41 40
4 0 1 50
2 23
2 21
2 20
2 19
2 18
2 17
34 00
20
40
35 00
20
40
1 18
1 17
1 16
1 15
1 15
1 14
66 00 0 22
67 00 0 21
68 00 0 21
69 00 0 19
70 00 0 18
71 00 0 17
8 00
05
10
15
20
25
6 24
6 21
6 17
6 13
6 10
6 6
13 00
05
10
15
20
25
3 58 ,
3 57
3 55
3 54
3 52
3 51
22 00
10
20
30
40
50
2 15
2 14
2 13
2 12
2 11
2 10
36 00
20
40
37 00
20
40
1 13
1 12
1 11
1 10
1 9
1 8
72 00 0 16
73 00 0 16
74 00 0 15
75 00 0 14
76 00 i 0 13
77 00 j 0 12
8 30
35
40
45
50
55
6 '3
6 0
5 56
5 53
5 50
5 47
13 30
35
40
45
50-
55
3 49
3 48
3 46
3 45
3 43
3 42
23 00
10
20
30
40
* 50
2 8
2 7
2 6.
2 5
2 4
2 3
38 00
20
40
39 00
20
40
1 8
1 7
1 6
1 5
1 4
1 3
78 00
79 00
80 00
81 00
82 00
83 00
0 10
0 9
0 8
0 7
0 6
0 6
9 00
05
10
35
20
25
5 44
5 41
5 38
5 35
5 32
5 29
14 00
10
20
30
40
A 50
3 41
3 38
3 35
3 33
3 30
3 28
24 00
10
20
30
40
50
2 2
2 1
2 0
1 59
1 58
1 57
40 00
20
40
41 00
20
40
1 2
1 2
1 1
1 0
0 59
0 58
84 00
85 00
86 00
87 00
88 00
89 00
0 5
0 4
0 3
0 2
0 2
0 1
9 30
*5 26
15 00
3 25
25 00
1 56
42 00 : 0 58
90 00 : 00
Page 690] TABLE 21.
Correction of the Mean Refraction for the Height of the Barometer.
Barom.
Subtract.
Mean refraction.
Barom.
Add.
0'
V
2'
3'
4'
5'
6'
1'
8'
9'
10'
0"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
27.50
27.55
27.60
27.65
27.70
0
0
0
0
0
2
2
2
2
2
5
5
5
5
5
4
4
4
4
4
4
4
4
4
4
3
3
3
3
3
7
7
7
7
7
10
10
10
9
9
9
9
9
8
8
12
12
12
12
11
15
15
14
14
14
13
13
13
13
12
17
17
17
16
16
20
20
19
19
18
23
22
22
21
21
25
25
24
24
23
28
27
27
26
25
30
30
29
28
28
33
32
31
31
30
35
35
34
33
32
38
37
36
36
35
40
40
39
38
37
43
42
41
40
39
45
45
44
43
42
48
47
46
45
44
43
42
41
40
39
38
37
36
36
35
34
33
32
31
30
29
28
27
26
25
51
50
49
48
47
27.75
27.80
27.85
27.90
27.95
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
7
7
6
6
6
6
6
6
6
5
11
11
11
10
10
16
15
15
15
14
18
18
17
17
16
20
20
19
19
18
23
22
22
21
21
25
24
24
23
23
27
27
26
25
25
29
29
28
27
27
26
25
25
24
24
32
31
30
30
29
34
33
32
32
31
30
29
29
28
27
36
35
35
34
33
32
31
31
30
29
39
38
37
36
35
41
40
39
38
37
46
45
44
43
42
28.00
28.05
28.10
28.15
28.20
0
0
0
0
0
8
8
8
7
7
10
10
9
9
9
12
12
11
11
11
14
14
13
13
13
16
16
15
15
y
18
18
17
17
16
20
20
19
19
18
22
22
21
20
20
24
24
23
22
22
~2T
21
20
19
19
18
17
17
16
16
28
27
27
26
25
34
33
33
32
31
36
35
34
34
33
32
31
30
29
28
27
26
25
25
24
41
39
38
37
36
28.25
28.30
28.35
28.40
28.45
0
0
0
0
0
2
2
2
2
2
5
5
5
5
5
7
7
7
6
6
6
6
6
5
5
9
8
8
8
8
10
10
10
10
9
9
9
8
8
8
12
12
12
11
11
14
14
13
13
12
16
15
15
14
14
18
17
17
16
16
15
15
14
14
13
19
19
18
18
17
17
16
15
15
14
23
22
22
21
20
25
24
23
23
22
26
26
25
24
23
23
22
21
20
20
28
27
27
26
25
30
29
28
27
27
35
34
33
32
31
28.50
28.55
28.60
28.65
28.70
0
0
0
0
0
1
1
1
1
1
3
3
3
3
3
4
4
4
4
4
7
7
7
7
6
10
10
10
9
9
12
12
11
11
10
14
13
13
12
12
20
19
18
18
17
21
20
20
19
18
24
23
23
22
21
26
25
24
23
22
30
29
28
27
26
31.50
31.45
31.40
31.35
31.30
28.75
28.80
28.85
28.90
28.95
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
4
4
3
3
3
5
5
5
4
4
6
6
6
5
5
7
7
7
7
6
6
6
5
5
5
9
8
8
8
7
10
10
9
9
8
11
11
10
10
9
13
12
12
11
11
10
10
9
9
8
14
13
13
12
12
15
14
14
13
13
16
16
15
14
14
13
12
12
11
10
18
17
16
16
15
14
13
13
12
11
19
18
17
17
16
20
19
19
18
17
16
15
15
14
13
21
21
20
19
18
23
22
21
20
19
24
23
22
21
20
19
18
17
16
15
25
24
23
22
21
31.25
31.20
31.15
31.10
31.05
29.00
29.05
29.10
29.15
29.20
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
3
3
3
3
2
4
4
4
3
3
5*
5
4
4
4
7
7
6
6
6
8
8
7
7
6
9
9
8
8
7
11
11
10
9
9
12
11
11
10
10
15
14
14
13
12
17
16
15
15
14
18
17
16
15
15
20
19
18
17
16
31.00
30.95
30.90
30.85
30.80
29.25
29.30
29.35
29.40
29.45
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
~0~
0
0
0
0
2
2
2
2
2
3
3
3
2
2
4
3
3
3
3
4
4
4
4
3
3
3
2
2
2
1
1
1
1
0
5
5
5
4
4
6
6
5
5
4
7
6
6
5
5
8
7
7
6
6
5
5
4
4
3
8
8
7
7
6
9
8
8
7
7
10
9
9
8
7
11
10
9
8
8
11
11
10
9
8
12
11
10
10
9
13
12
11
10
9
14
13
12
11
10
9
8
7
6
5
5
4
3
2
1
14
13
13
12
11
15
14
13
12
11
30.75
30.70
30.65
30.60
30.55
29.50
29.55
29.60
29.65
29.70
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
2
2
2
1
1
1
1
1
0
0
2
2
2
2
1
1
1
1
0
0
3
3
3
2
2
2
1
1
1
0
4
4
3
3
2
2
2
1
1
0
5
4
4
3
3
6
5
4
4
3
6
5
5
4
4
~3~
2
2
1
1
7
6
5
5
4
7
6
6
5
4
8
7
6
5
5
8
7
6
6
5
4
3
2
2
1
9
8
7
6
5
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
30.50
30.45
30.40
30.35
30.30
29.75
29.80
29.85
29.90
29.95
0
0
0
0
0
0
0
0
^0
0
2
2
1
1
0
3
2
2
1
1
3
2
2
1
1
3
3
2
1
1
4
3
2
1
1
4
3
2
2
1
4
3
3
2
1
5
4
3
2
1
30.25
30.20
30.15
30.10
30.05
30.00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
o//
0
30"
0
0
0
0
0
30.00
Subtract.
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
i
30"
V
0"
30"
0"
30"
0"
80"
0"
Add.
Barom.
0'
1'
2'
3'
4'
6'
7' | 8'
9'
10'
Mean refraction.
TABLE 22. [Page 691
Correction of the Mean Refraction for the Height of the Thermometer.
Ther.
Add.
Mean refraction.
Ther.
Add.
0'
I'
at
3'
4'
5' 6'
7' 8' 9'
10'
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0'
30"
0"
30"
0"
30"
0"
30"
0"
//
41
40
38
37
35
ii
46
44
42
41
39
ii
50
48
47
45
43
n
55
53
51
49
47
//
60
58
55
53
51
n
65
62
60
57
55
53
50
48
46
43
n
70
67
64
62
59
—10
— 8
— 6
— 4
— 2
0
0
0
0
0
4
4
4
4
3
8
8
7
7
7
7
6
6
6
5
12
12
11
11
10
16
15
15
14
14
20
19
19
18
17
24
23
22
22
21
28
27
26
25
24
33
31
30
29
28
37
36
34
33
31
75
72
69
66
64
80
77
%
68
85
82
79
76
72
69
66
63
60
57
90
87
84
80
77
-10
- 8
- 6
4.
- 2
0
2
4
6
8
0
0
0
0
0
3
3
3
3
3
10
9
9
8
8
13
12
12
11
11
16
16
15
14
14
20
19
18
17
16
23
22
21
20
19
27
25
24
23
22
30
29
28
26
25
34
32
31
29
28
37
36
34
32
31
41
39
37
36
34
45
43
41
39
37
49
47
44
42
40
57
54
52
49
47
61
58
55
53
50
65
62
59
56
54
74
70
67
64
61
0
2
4
6
8
10
11
12
13
14
0
0
0
0
0
3
2
2
2
2
5
5
5
5
5
8
7
7
7
7
10
10
10
9
9
13
13
12
12
11
15
15
15
14
14
18
18
17
17
16
21
20
20
19
19
24
23
22
22
21
26
26
25
24
24
29
28
28
27
26
32
31
30
30
29
35
34
33
32
31
38
37
36
35
34
41
40
39
38
37
44
43
42
41
40
48
46
45
44
42
51
49
48
47
45
54
53
51
50
48
58
56
54
53
i 51
10
11
12
13
14
15
16
17
18
19
0
0
0
0
0
2
2
2
2
2
4
4
4
4
4
4
4
3
3
3
7
6
6
6
6
9
9
8
8
8
8
7
7
7
6
11
11
10
10
10
13
13
13
12
12
16
15
15
14
14
13
13
12
12
11
18
18
17
16
16
15
15
14
14
13
20
20
19
19
18
23
22
21
21
20
19
19
18
17
17
25
25
24
23
22
22
21
20
19
18
28
27
26
25
24
30
29
29
28
27
33
32
31
30
29
28
27
26
25
24
36
35
33
32
31
38
37
36
35
34
41
40
39
37
36
44
43
41
40
39
47
45
44
43
41
50
48
47
45
44
15
16
17
18
19
20
21
22
23
24
0
0
0
0
0
2
2
2
2
2
6
5
5
5
5
9
9
9
8
8
11
11
11
10
10
17
17
16
15
15
24
23
22
21
20
26
25
24
23
22
30
29
28
27
26
33
31
30
29
28
35
34
32
31
30
37
36
35
33
32
40
38
37
36
34
42
41
39
38
36
20
21
22
23
24
25
26
27
28
29
0
0
0
0
0
2
3
3
3
3
3
T
2
2
2
2
5
4
4
4
4
6
6
6
5
5
~6
5
4
4
4
8
7
7
7
6
~6~
6
6
5
5
9
9
9
8
8
11
11
10
10
9
13
12
12
11
11
14
14
13
12
12
16
15
15
14
13
18
17
16
15
15
19
19
18
17
16
21
20
19
19
18
23
22
21
20
19
25
24
23
22
21
27
26
25
23
22
29
28
26
25
24
31
29
28
27
26
33
31
30
29
27
35
33
32
30
29
25
26
27
28
29
30
31
32
33
34
0
0
0
0
0
4
3
3
3
3
7
7
7
6
6
T
5
5
4
4
9
8
8
If
i
7
10
9
9
8
8
11
11
10
10
9
13
12
11
11
10
14
13
13
12
11
~w
10
9
8
8
7
6
5
5
4
15
15
14
13
12
17
16
15
14
13
18
17
16
15
14
20
19
18
17
16
21
20
19
18
17
23
22
20
19
18
24
23
22
21
19
26
25
23
22
21
28
26
25
23
22
30
31
52
33
34
35
36
37
38
39
0
0
0
0
0
2
2
2
1
1
3
3
2
2
2
4
3
3
3
3
5
4
4
4
3
6
6
6
5
5
7
7
6
6
5
5
4
4
3
3
8
8
7
7
6
9
9
8
7
7
6
6
5
4
4
11
11
10
9
8
8
7
6
5
4
4
3
2
13
12
11
10
9
8
7
7
6
5
4
3
2
2'
1
14
13
12
11
10
9
8
7
6
5
4
4
3
2
1
0
15
14
13
12
11
10
9
8
7
6
16
15
14
13
11
17
16
15
13
12
11
10
9
8
7
18
17
16
14
13
19
18
17
15
14
13
11
10
9
8
20
19
18
16
15
35
36
37
38
39
40
41
42
43
44
0
0
0
0
0
0
0
0
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
3
3
2
2
2
4
3
3
3
2
4
4
3
3
3
6
5
4
4
3
10
9
8
7
6
12
11
S
8
7
13
12
11
9
8
40
41
42
43
44
45
46
47
48
49
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
2
1
2
2
2
2
3
2
2
3
2
2
3
2
2
5
4
3
2
1
5
4
3
2
1
6
4
3
2
1
6
5
4
2
1
6
5
4
2
1
7
5
4
3
1
45
46
47
48
49
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
~0
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
Add.
Ther.
0"
30"
0"
30"
0"
30"
0"
80"
0"
30"
0"
30"
0"
30"
0"
30"
0"
80"
0"
30"
0"
Add.
Ther.,
w
1'
2'
3'
4'
5'
6'
7' 8'
9'
10'
Mean refraction.
Page-692] TABLE 22.
Correction of the Mean Refraction for the Height of the Thermometer.
Ther.
Subt.
Mean refraction.
Ther.
Subt.
0'
V
2'
3'
4'
5'
6'
V
8'
9'
10'
0"
SO"
0"
30"
0"
30"
0"
30"
0"
30"
0"
30"
0"
80"
0"
80"
0"
80"
0"
30"
0"
o
50
51
52
53
54
//
0
0
0
0
0
It
0
0
0
0
0
//
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
it
0
0
0
1
1
n
0
0
0
1
1
1
1
2
2
2
~2~
3
3
3
3
n
0
0
1
1
1
II
0
0
1
1
1
2
2
2
3
3
n
0
0
1
1
2
it
0
0
1
1
2
2
3
3
4
4
T
5
6
6
7
~7
7
8
8
9
n
0
n
0
H
0
II
0
H
0
II
0
1
2
2
3
n
0
1
2
3
4
n
0
1
2
3
4
T
6
7
8
9
10
11
12
13
14
H
0
1
2
3
4
T
6
8
9
10
n
0
1
2
3
5
6
7
8
9
10
11
12
14
15
16
n
0
1
2
4
5
6
7
8
10
11
12
13
15
16
17
II
0
1
3
4
5
o
50
51
52
53
54
1
2
2
1
2
2
1
2
3
1
2
3
4
4
5
6
6
7
8
9
9
10
2
2
3
55
56
57
58
59
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
2
2
2
3
2
2
3
3
4
3
3
4
4
5
~F
6
6
7
7
3
4
4
5
5
"6"
7
7
8
8
3
4
5
5
6
~T
7
8
8
9
4
5
6
6
7
4
5
6
7
8
9
9
10
11
12
5
6
6
7
8
9
10
11
12
13
6
8
9
10
12
13
14
15
17
18
55
56
57
58
59
60
61
62
63
64
60
61
62
63
64
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
3
3
3
4
4
3
4
4
5
5
4
4
5
5
6
8
9
9
10
11
11
12
13
14
15
65
66
67
68
69
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
8
3
3
4
4
4
4
5
5
5
5
5
4
5
5
5
5
6
6
6
7
7
5
6
6
6
7
6
6
7
7
8
8
8
9
9
10
8
8
9
9
10
9
9
10
11
11
12
12
13
13
14
10
10
11
11
12
12"
13
14
14
15
11
11
12
13
13
14
15
16
16
17
12
12
13
14
15
16
16
17
18
18
13
14
14
15
16
17
18
18
19
20
14
15
16
16
17
15
16
17
18
19
20
20
21
22
23
16
17
18
19
20
21
22
23
24
25
17
18
19
20
21
18
19
20
22
23
19
20
22
23
24
65
66
67
68
69
70
71
72
73
74
0
0
0
0
0
~0~
0
0
0
0
1
1
1
1
1
3
4
4
4
4
7
7
8
8
8
9
10
10
11
11
10
11
11
12
12
18
19
20
21
22
22
23
25
26
27
24
25
26
27
28
25
27
28
29
30
70
71
72
73
74
75
76
77
78
79
1
1
1
2
2
3
3
3
3
3
4
4
5
5
5
6
6
6
6
6
7
7
7
7
8
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
13
13
13
]3
14
14
15
14
15
16
16
17
16
16
17
18
18
18
18
19
20
20
19
20
21
21
22
21
22
22
23
24
22
23
24
25
26
24
25
26
27
28
26
27
28
29
30
28
29
30
31
32
29
31
32
33
34
31
32
34
35
36
75
76
77
78
79
80
81
82
83
84
0
0
0
0
0
2
2
2
2
2
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
6
8
9
9
9
9
10
10
10
10
11
10
10
11
11
11
12
12
13
13
13
14
14
14
15
15
15
16
16
17
17
17
18
18
19
19
19
20
20
21
21
21
21
22
23
23
23
24
24
25
26
25
26
26
27
28
27
28
28
29
30
29
30
31
31
32
31
32
33
34
35
33
34
35
36
37
35
36
37
38
39
40
42
43
44
45
37
38
40
41
42
80
81
82
83
84
85
86
87
88
89
85
86
87
88
89
0
0
0
0
0
2
2
2
2
2
6
6
6
6
6
8
8
8
8
9
12
12
12
13
13
14
14
14
15
15
16
16
17
17
17
18
18
19
19
19
18
18
19
19
20
20
20
21
21
22
22
23
23
24
24
24
25
25
26
27
26
27
28
28
29
29
29
30
31
32
31
32
32
33
34
35
36
37
37
38
33
34
35
36
37
36
37
38
38
39
40
41
42
43
44
38
39
40
41
42
43
44
45
46
48
90
91
92
93
94
0
0
0
0
0
2
2
2
2
2
7
7
7
7
7
7
7
8
8
8
9
9
9
9
10
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
16
16
16
17
17
20
21
21
22
22
23
23
24
24
25
25"
26
26
27
27
25
25
26
27
27
27
28
29
29
30
30
31
31
32
33
32
33
34
35
35
38
39
39
40
41
43
44
45
46
47
46
47
48
49
50
51
52
53
54
55
49
50
51
52
53
54
55
56
58
59
90
91
92
93
94
95
96
97
98
99
0
0
0
0
0
2
2
3
3
3
5
5
5
5
5
15
15
15
16
16
17
18
18
18
19
20
20
21
21
21
22
23
23
24
24
28
28
29
29
30
30
31
32
32
33
33
34
35
35
36
36
37
38
38
39
39
40
41
41
42
42'
43
44
44
45
45
46
47
48
49
48
49
50
51
52
95
96
97
98
99
100
0
3
30"
5
8
SO"
11
0"
13
30"
16
0"
19
30"
22
0"
25
30"
28
0"
31
30"
34
0"
37
40
43
46
50
53
56
60
100
Subt.
Ther.
0"
0"
30"
0"
30"
7'
0"
30"
0"
30"
0"
Subt.
Ther.
0'
i'
2'
3'
4'
5'
6'
8'
9'
10'
Mean refraction.
TABLES 23, 24.
[Page 693
TABLE 23.
Correction of the Moon's Altitude for parallax and re
fraction corresponding to a mean value of the hori
zontal parallax, 57' 30".
Moon's
alt.
Corr.
Moon's
alt.
Corr.
Moon's
alt.
Corr.
Moon's /-.__,
alt. Corr'
o
10
11
12
13
14
15
16
17
18
19
20
r
51
52
52
52
52
52
52
52
52
52
51
o
31
32
33
34
35
36
37
38
39
40
/
48
47
47
46
46
45
45
44
44
43
o
51
52
53
54
55
56
57
58
59
60
35
35
34
33
32
32
31
30
29
28
0
71
72
73
74
75
76
77
78
79
80
18
17
17
16
15
14
13
12
11
10
21
22
23
24
25
26
27
28
29
30
51
51
51
50
50
50
49
49
49
48
41
42
43
44
45
46
47
48
49
50
42
42
41
40
40
39
38
38
37
36
61
62
63
64
65
66
67
68
69
70
27
26
26
25
24
23
22
21
20
19
81
82
83
84
85
86
87
88
89
90
9
8
7
6
5
4
3
2
1
0
TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and
[Barometer, 30 inches.— Fahrenheit's Thermometer, 50°.]
Refraction.
Moon's
Horizontal parallax.
~ •*,
y: ^
S g
il
-s.
Correction for seconds of
parallax.— Add.
Corr. for
minutes
of alt.
app. alt.
54'
00'
56'
67'
58'
59'
60'
61'
0"
•» I 4* I •" 1 8*
c /
5 0
10
20
30
40
50
II
0
10
20
30
40
50
0
10
20
30
40
50
•
0
10
20
30
40
50
10
20
30
40
50
//
2
12
22
32
42
52
2
12
22
32
42
52
a
4
14
24
34
44
54
4
14
24
34
44
54
H
6
16
26
36
46
56
n
8
18
28
38
48
58
Add.
!/ !//
2 1
3 2
4 2
5 3
6 4
7 4
8 5
9 5
43 56
44 11
25
39
52
45 4
44 56
45 11
25
39
51
46 3
45 56
46 11
25
38
51
47 3
46 56
47 11
25
38
51
48 3
47 56
48 11
25
38
51
49 3
48 55
49 10
24
38
51
50 3
49 55
50 10
24
37
51
51 3
5055
51 10
24
37
51
52 3
6 0
10
20
30
40
50
45 15
26
36
46
55
46 4
46 15
26
36
46
55
47 3
47 14
25
36
45
55
48 3
48 14
25
35
45
54
49 3
49 14
25
35
45
54
50 3
50 13
25
34
44
54
51 2
51 13
25
34
44
53
52 1
5213
25
34
44
53
53 1
6
16
26
36
46
56
6
16
26
36
46
56
8
18
28
38
48
58
8
18
28
38
48
58
7 0
10
20
30
40
50
46 12
21
29
36
43
50
47 2
8
13
19
24
47 12
20
28
36
42
49
48 12
20
28
35
42
48
49 12
20
27
35
41
48
50 12
19
27
34
41
48
50 54
51 0
6
11
16
21
51 11
18
26
34
40
47
52 11
18
25
34
40
46
53 10
18
25
33
40
46
0
10
20
30
40
50
0
10
20
30
40
50
2
12
22
32
42
52
4
14
24
34
44
54
8 0
10
20
30
40
50
47 56
48 2
7
13
18
23
48 55
49 1
7
12
17
22
49 54
50 0
6
11
' 17
22
51 54
59
52 5
10
16
20
52 53
59
53 4
10
15
19
5353
58
54 4
9
14
19
0
10
20
30
40
50
0
10
20
30
40
50
2
12
22
32
42
52
4
14
24
34
44
54
6
16
26
36
46
56
6
16
26
36
46
55
8
18
28
38
48
58
8
18
28
38
48
57
9 0
10
20
30
40
50
47 28
33
37
41
45
49
48 27
32
36
41
44
48
49 26
31
35
40
43
47
50 26
30
34
39
43
46
51 25 ! 52 24
30 29
34 33
38 37
42 | 41
46 45
53 24
28
32
37
40
44
5423
27
32
36
39
44
0
10
20
30
40
50
0
10
20
30
40
49
2
12
22
32
42
51
4
14
24
34
44
53
Page 694] TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt
Horizontal parallax.
2a
ll
!&
Correction for seconds oJ
parallax.— Add.
Corr.
for
minutes
of alt.
54'
55'
56'
57'
58'
69'
60'
61'
0"
n
0
10
20
29
39
49
2"
n
2
12
22
31
41
51
4"
6"
8"
o /
10 0
10
20
30
40
50
* //
47 53
56
59
48 2
5
7
f n
48 52
55
58
49 1
4
6
i H
49 51
54
57
50 0
2
5
1 H
50 50
53
56
59
51 2
4
i n
51 50
52
55
58
52 1
4
f n
52 48
51
55
57
53 0
2
t n
53 48
50
54
56
59
54 1
/ //
54 47
50
53
55
58
55 0
n
0
10
20
30
40
50
n
4
14
24
33
43
53
n
6
16
26
35
45
55
8
18
28
37
47
57
Add.
V 0"
2 1
3 1
4 1
5 2
6 2
7 2
8 2
9 3
11 0
10
20
30
40
50
48 10
12
15
17
19
21
49 9
11
14
16
18
20
50 8
10
12
14
17
18
51 7
9
12
13
15
17
52 7
9
11
13
15
17
53 5
7
9
11
13
15
54 4
6
8
10
12
14
55 3
fa
7
9
11
13
0
10
20
30
40
50
0
10
20
30
40
50
0
10
20
29
39
49
2
12
22
31
41
51
4
14
24
33
43
53
4
14
24
33
43
53
6
16
26
35
•45
55
8
18
28
37
47
57
12, 0
10
20
30
40
50
48 22
24
26
27
28
29
49 21
23
25
26
27
28
50 19
21
23
24
25
26
51 18
20
22
23
24
25
52 17
19
21
22
23
24
53 17
18
20
20
21
22
54 15
16
18
19
20
21
55 14
15
17
18
19
20
0
10
20
29
39
49
0
10
19
29
39
49
2
12
22
31
41
51
6
16
25
35
45
55
8
18
27
37
47
57
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
Sub.
V 0"
2 0
3 0
4 0
5 1
6 1
7 1
8 1
9 1
13 0
10
20
30
40
50
48 30
31
32
33
34
35
49 29
30
31
32
32
33
50 27
28
29
30
30
31
51 26
27
27
28
29
30
52 25
26
26
27
28
28
53 23
24
24
25
26
26
54 22
22
23
23
24
25
55 20
21
21
22
22
23
0
10
20
30
40
50
2
12
21
31
41
51
4
14
23
33
43
53
6
16
25
35
45
55
8
18
27
37
47
57
14 0
10
20
30
40
50
48 35
35
36
36
36
36
49 33
34
34
34
34
34
50 31
32
32
32
32
32
51 30
30
30
30
30
30
52 28
28
29
29
29
29
53 26
26
27
27
27
27
54 25
25
25
25
25
25
55 23
23
24
23
23
23
0
10
20
30
40
50
0
10
19
29
39
49
2
12
21
31
41
51
4
14
23
33
43
53
4
14
23
33
43
53
6
16
25
35
45
55
8
18
27
37
47
57
15 0
10
20
30
40
50
48 36
36
36
36
36
35
49 35
35
35
34
34
33
50 33
32
32
31
31
30
51 31
30
30
29
29
28
52 29
28
28
28
27
26
53 27
26
26
25
25
24
54 25
24
24
23
23
21
55 23
22
22
21
21
19
0
10
20
30
40
50
0
10
19
29
39
49
2
12
21
31
41
51
6
16
25
35
45
55
6
15
25
35
44
54
8
18
27
37
47
57
16 0
10
20
30
40
50
48 35
34
34
33
33
32
49 32
32
32
31
31
30
50 29
29
29
28
28
27
51 27
27
27
26
25
24
52 25
25
25
24
23
22
53 23
23
22
21
21
20
54 20
20
20
19
18
17
55 18
18
17
16
16
15
0
10
20
30
40
50
0
10
19
29
38
48
2
12
21
31
40
50
4
13
23
33
42
52
8
17
27
36
46
56
17 0
10
20
30
40
50
48 31
30
28
27
26
26
49 29
28
26
25
24
23
50 26
25
23
22
21
20
51 23
22
20
19
18
17
52 21
20
18
17
16
15
53 18
17
15
14
13
12
54 16
14
12
11
10
9
55 13
12
10
9
7
6
0
10
20
30
40
50
0
10
19
29
38
48
2
12
21
31
40
50
4
13
23
33
42
52
6
15
25
34
44
53
8
17
27
36
46
55
18 0
10
20
30
40
50
48 24
23
22
21
20
18
49 21
20
19
18
17
15
49 13
12
10
8
6
5
50 18
17
16
15
14
12
51 15
14
13
12
10
9
52 13
12
11
10
8
6
53 10
9
8
6
4
2
54 7
6
5
3
1
53 59
55 4
3
2
0
54 58
56
0
10
20
30
40
50
0
10
19
29
38
48
2
11
21
30,
40
50
4
13
23
32
42
51
6
15
25
34
44
53
8
17
27
36
46
55
8
17
27
36
46
55
19 0
10
20
30
40
50
48 16
15
13
12
10
9
50 10
8
6
5
3
2
51 7
5
3
2
0
50 58
52 4
2
0
51 58
56
55
53 0
52 59
57
55
53
51
53 57
55
53
51
49
48
54 55
53
51
49
47
45
0
10
20
30
40
50
0
10
19
29
38
48
2
11
21
30
40
50
4
13
23
32
42
51
6
15
25
34
44
53
TABLE 24. [Page 695
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
li
i!
3*
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
54'
55'
56'
57'
58'
59'
607
61'
0"
2"
4"
6"
n
6
15
24
34
43
53
8"
of alt.
o /
20 0
10
20
30
40
50
48 6
5
3
1
59
57
f n
49 3
2
0
48 58
56
54
f n
49 59
58
56
53
52
50
50 56
55
52
50
48
46
' N
51 52
51
49
46
44
42
52 49
47
45
42
40
38
/ //
53 45
43
41
38
36
34
i it
5442
40
37
35
33
30
n
0
10
20
30
40
50
n
0
9
19
28
38
47
-Q-
9
19
28
37
47
ii
2
11
21
30
39
49
2
11
21
30
39
49
n
4
13
23
32
41
51
8
17
26
36
45
54
Sub.
V 0"
2 0
3 1
4 1
5 1
6 1
21 0
10
20
30
40
50
47 55
53
51
48
46
43
48 51
49
47
44
42
39
49 47
45
43
40
38
35
50 43
41
39
36
33
31
51 39
37
35
32
29
27
52 35
33
31
28
25
22
53 31
29
27
24
21
18
5428
26
23
20
17
14
0
10
20
30
40
50
4
13
22
32
41
50
4
13
22
31
41
50
4
13
22
31
40
50
4
13
22
30
40
49
6
15
24
34
43
52
7
17
26
35
45
54
7
17
26
35
45
54
7 1
8 1
9 2
1 0
2 1
3 1
4 1
5 2
6 2
7 2
8 2
9 3
1 0
2 1
3 1
4 1
5 2
6 2
7 3
8 3
9 3
22 0
10
20
30
40
50
47 42
40
37
34
32
29
48 37
35
32
30
27
25
49 33
30
27
25
22
20
50 29
26
23
20
18
15
51 25
22
19
16
13
11
52 20
17
14
11
9
6
53 16
13
10
7
4
1
5411
8
5
3
0
5357
0
10
20
30
40
50
0
9
19
28
37
46
2
11
20
30
39
48
2
11
20
29
39
48
2
11
20
29
38
47
6
15
24
33
43
52
6
15
24
33
42
51
5
15
24
32
42
51
5
14
24
33
42-
51
23 0
10
20
30
40
50
47 27
25
22
19
16
13
48 22
20
17
14
11
8
49 17
15
12
9
6
3
50 13
10
7
4
1
49 58
51 8
5
2
0
50 57
54
52 3
0
51 57
54
51
48
52 58
55
52
49
46
43
5354
51
48
45
42
38
0
10
20
30
40
50
0
9
18
28
37
46
7
17
26
35
44
53
7
16
26
34
44
53
24 0
10
20
30
40
50
47 10
8
5
2
46 59
56
48 5
3
0
47 57
54
51
49 0
48 57
54
51
48
45
49 55
52
49
46
43
40
50 50
47
44
41
38
35
51 45
42
39
35
32
29
52 40
37
33
30
27
23
5335
32
28
24
21
18
0
10
20
30
40
50
0
9
18
27
36
46
25 0
10
20
30
40
50
46 53
50
46
43
40
37
47 48
45
41
38
34
31
48 42
39
35
32
28
25
49 37
33
29
26
23
19
50 31
28
24
20
17
14
51 26
22
18
14
11
7
52 20
16
12
8
5
1
53 14
10
6
3
5259
56
0
10
20
30
40
50
0
9
18
27
36
45
2
11
20
29
38
47
4
13
22
31
40
49
7
16
25
34
43
52
26 0
10
20
30
40
50
46 34
31
27
24
20
17
47 28
25
21
18
14
11
48 22
19
15
12
8
4
49 16
13
9
6
2
48 58
50 10
7
3
49 59
55
51
51 4
1
50 57
53
49
45
51 58
54
50
46
42
38
5252
48
44
40
36
32
0
10
20
30
40
50
0
9
18
27
36
45
2
11
20
29
38
47
4
13
22
31
39
48
5
14.
23
32
41
50
7
16
25
34
43
52
27 0
10
20
30
40
50
46 14
11
7
3
45 59
56
47 7
4
1
46 57
53
49
48 1
47 58
54
50
46
42
48 54
51
47
43
39
35
49 48
44
40
36
32
28
50 41
37
33
29
25
21
51 35
31
27
23-
19
15"
5228
24
20
16
12
8
0
10
20
30
40
50
0
10
20
30
40
50
0
9
18
27
36
44
0
9
18
26
35
44
2
11
20
28
37
46
2
11
19
28
37
46
4
12
21
30
39
48
5
14
23
32
41
50
7
16
25
34
43
52
28 0
K)
20
30
40
50
45 53
49
45
41
37
34
46 46
42
38
34
30
26
47 38
34
30
26
23
19
48 31
27
23
19
15
11
49 24
20
16
12
8
4
50 17
13
9
5
1
49 57
51 11
6
2
50 57
54
49
52 4
5159
55
50
46
42
4
12
21
30
39
48
5
14
23
32
41
49
7
16
25
33
42
51
29 0
10
20
30
40
50
45 30
26
22
18
14
11
46 22
18
14
10
6
3
47 15
11
7
2
46 58
55
48 7
3
47 59
55
51
47
49 0
48 56
52
47
43
39
49 53
49
44
39
35
31
50 45
40
36
31
27
23
5138
34
29
24
20
15
0
10
20
30
40
50
0
9
17
26
35 i
44
2
10
19
28
37
45
4
12
21
30
38
47
5
14
23
31
40
49
/
16
24
33
42
51
Page 696] TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
15 M
%&
I!
Correction for seconds of
parallax. — A dd.
Corr.
for
minutes
of alt.
54'
55'
56'
67'
58'
69'
60'
61'
0"
2"
4"
6"
8"
o /
30 0
10
20
30
40
50
/ //
45 6
2
44 58
54
50
45
/ //
45 57
54
50
46
42
38
/ //
46 50
46
42
37
33
29
/ rt
47 42
38
34
29
25
21
/ //
48 34
30
26
21
17
12
/ //
49 26
22
18
13
8
4
r n
50 18
13
9
4
0
49 55
t n
51 10
6
1
50 56
52
47
a
0
10
20
30
40
50
//
0
9
17
26
35
43
//
2
10
19
28
36
45
n
3
12
21
29
38
47
n
5
14
23
31
40
49
a
1
16
24
33
42
50
Sub.
V 0"
2 1
3 1
4 2
5 2
6 3
7 3
8 4
9 4
1 0
2 1
3 1
4 2
5 2
6 3
7 3
8 4
9 4
1 1
2 1
3 2
4 2
5 3
6' 3
7 4
8 4
9 5
1 1
2 1
3 2
4 2
5 3
31 0
10
20
30
40
50
44 41
37
33
28
24
20
45 33
29
24
20
16
11
46 24
20
15
11
7
2
47 16
12
7
2
46 58
53
48 7
2
47 58
54
49
44
48 59
54
49
45
40
35
49 50
45
40
36
31
26
50 42
37
32
27
22
17
0
10
20
30
40
50
0
9
17
26
34
43
2
10
19
27
36
44
2
10
19
27
35
44
2
10
18
27
35
43
3
12
21
29
38
46
3
12
20
29
37
46
3
12
20
28
37
45
5
14
22
31
39
48
5
14
22
30
39
47
5
13
22
30
38
47
5
13
21
30
38
46
7
15
24
32
41
50
7
15
24
32
41
49
7
15
23
32
40
48
32 0
10
20
30
40
50
44 15
11
7
3
43 58
54
45 7
3
44 58
53
48
44
45 58
53
48
44
39
34
46 49
44
39
34
29
24
47 40
35
30
25
20
15
48 31
26
21
16
11
6
49 22
17
11
6
1
48 56
50 13
8
2
49 57
52
47
0
10
20
30
40
50
0
8
17
25
34
42
0
8
17
25
33
42
33 0
10
20
30
40
50
43 48
44
40
35
30
25
44 39
34
30
25
20
15
45 29
25
20
15
10
5
46 19
15
10
5
0
45 55
47 10
5
0
46 55
50
45
48 0
47 55
50
45
40
35
48 50
45
40
35
30
24
49 41
36
31
25
20
14
0
10
20
30
40
50
34 0
10
20
30
40
50
43 21
16
11
6
1
42 56
44 11
6
1
43 56
51
46
45 0
44 55
50
45
40
35
45 50
45
40
35
30
24
46 40
34
29
24
19
14
47 30
24
19
13
8
3
48 19
14
9
3
47 58
52
49 9
3
48 58
52
47
42
0
10
20
30
40
50
0
8
17
25
33
41
2
10
18
26
35
43
3
12
20
28
36
44
7
15
23
31
40
48
7
15
23
31
39
47
6
14
23
31
39
47
6
14
22
30
38
46
6
14
22
30
38
46
35 0
10
20
30
40
50
42 52
47
42
37
32
27
43 41
36
31
26
21
16
44 30
25
20
15
10
4
45 19
14
9
3
44 58
53
46 9
3
45 58
52
47
42
46 58
52
47
41
36
30
47 47
41
36
30
25
19
48 36
30
25
19
14
8
0
10
20
30
40
50
0
8
16
24
33
41
2
10
18
26
34
42
3
11
20
28
36
44
5
13
21
29
38
46
36 0
10
20
30
40
50
42 22
17
12
7
1
41 56
43 11
5
0
42 55
50
44
43 59
54
48
43
38
32
44 48
42
37
31
26
20
45 37
31
25
. 20
14
8
46 25
19
14
8
2
45 56
47 14
8
2
46 56
50
44
48 2
47 56
50
44
39
33
0
10
20
30
40
50
0
8
16
24
32
40
2
10
18
26
34
42
3
11
19
27
35
43
5
13
21
29
37
45
37 0
10
20
30
40
50
41 51
46
41
35
30
25
42 39
34
29
23
18
12
43 27
21
16
11
5
42 59
44 15
9
4
43 58
53
47
45 3
44 57
52
46
40
34
45 51
45
40
34
28
22
46 39
33
27
21
15
9
47 27
21
15
9
3
46 57
0
10
20
30
40
50
0
8
16
24
32
40
2
10
17
25
33
41
3
11
19
27
35
43
5
13
21
29
37
45
38 0
10
20
30
40
50
41 19
14
8
3
40 58
52
42 7
2
41 56
51
45
39
42 54
49
43
38
32
26
43 41
36
30
24
18
13
44 29
23
17
12
6
0
45 16
10
4
44 58
52
46
46 3
45 57
51
45
39
33
46 51
45
38
32
26
20
0
10
20
30
40
50
0
8
16
23
31
39
2
9
17
25
33
41
3
11
19
27
35
42
5
13
20
28
36
44
5
12
20
28
36
43
39 0
10
20
30
40
50
40 47
42
36
30
25
19
41 33
28
23
17
11
5
42 20
15
9
3
41 57
51
43 7
1
42 55
49
43
37
43 54
48
42
36
30
23
44 40
34
28
22
16
9
45 27
21
15
8
2
44 55
46 13
7
1
45 54
48
42
0
10
20
30
40
50
0
8
15
23
31
39
2
9
17
25
32
40
3
11
19
26
34
42
6
14
22
29
37
45
TABLE 24. [Page 697
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
Is
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
of alt.
54'
55'
56'
57'
58'
59'
60'
61'
ft
-jj
0"
2"
4"
n
3
11
18
26
34
41
V
n
5
12
20
27
35
43
5
12
20
27
35
42
8"
o /
40 0
10
20
30
40
50
/ //
40 14
8
2
39 56
50
45
/ n
41 0
40 54
48
42
36
30
t n
41 46
39
33
28
22
16
/ //
42 32
25
19
13
7
1
/ n
43 18
11
5
42 59
53
47
/ //
44 4
43 57
50
44
38
32
/ //
44 50
43
36
30
24
18
/ n
45 36
29
22
16
9
3
n
0
10
20
30
40
50
//
0
8
15
23
30
38
it
2
9
17
24
32
40
6
14
21
29
37
44
6
14
21
29
36
44
Sub.
6' 3"
7 4
8 5
9 5
1 1
2 1
3 2
4 2
5 3
6 4
7 4
8 5
9 5
1 1
2 1
3 2
4 3
5 3
6 4
7 5
8 5
9 6
1 1
2 1
3 2
4 3
5 3
6 4
7 5
8 5
9 6
41 0
10
20
30
40
50
39 39
33
27
21
16
10
40 24
18
12
6
0
39 54
41 10
4
40 58
51
45
39
41 55
49
43
36
30
24
42 41
34
28
22
16
9
42 2
41 56
50
43
36
30
43 26
19
13
7
0
42 53
44 11
4
43 58
51
45
38
44 56
49
43
37
30
23
0
10
20
30
40
50
0
8
15
23
30
38
2
9
17
24
32
39
3
11
18
26
33
41
42 0
10
20
30
40
50
39 4
38 58
52
46
40
34
39 48
42
36
30
24
18
40 33
27
21
1
2
41 17
11
5
40 58
52
46
42 47
41
34
27
21
14
43 31
25
18
11
5
42 58
44 16
10
3
43 56
49
42
0
10
20
30
40
50
0
7
15
22
30
37
1
9
16
24
31
38
1
9
16
23
31
38
3
10
18
25
33
40
4
12
19
27
34
41
6
13
21
28
36
43
43 0
10
20
30
40
50
38 28
22
16
10
4
37 57
39 12
6
38 59
53
47
41
39 56
50
43
37
30
24
40 40
34
27
20
14
7
41 24
18
11
5
40 58
51
42 8
1
41 54
48
41
34
42 52
45
38
31
24
17
43 36
29
22
15
8
1
0
10
20
30
40
50
0
7
15
22
29
37
3
10
18
25
32
39
3
10
17
24
31
39
4
12
19
26
34
41
6
13
20
28
35
42
6
13
20
27
34
41
44 0
10
20
30
40
50
37 51
45
38
32
26
20
38 35
28
21
15
9
2
39 18
11
4
38 58
51
44
40 1
39 54
47
41
34
27
40 44
37
30
24
17
10
41 27
20
13
7
0
40 53
42 10
3
41 56
49
42
35
42 54
46
39
32
25
18
0
10
20
30
40
50
0
7
14
21
29
36
1
9
16
23
30
37
4
11
19
26
33
40
45 0
10
20
30
40
50
37 14
7
0
36 54
48
41
37 56 i 38 38
49 31
43 25
37 i 18
30 11
23 4
39 21
14
7
1
38 54
47
40 3
39 56
49
43
36
29
40 46
39
32
25
18
11
41 28
21
14
7
0
40 52
42 11
3
41 56
49
42
34
0
10
20
30
40
50
0
7
14
21
28
35
1
8
15
23
30
37
3
10
17
24
31
38
4
11
18
25
32
39
6
13
20
27
34
41
46 0
10
20
30
40
50
36 35
29
22
16
9
2
37 17 '• 37 58
10 51
3 44
36 57 i 38
50 ' 32
43 25
38 40
33
26
20
13
6
39 22
15
8
1
38 54
47
40 4
39 57
49
42
35
28
40 45
38
31
24
17
9
41 27
20
12
5
40 58
50
0
10
20
30
40
50
0
7
14
21
28
35
1
8
15
22
29
36
3
10
17
23
30
37
4
11
18
25
32
39
6
12
19
26
33
40
47 0
10
20
30
40
50
35 56
49
42
36
30
23
36 37
30
23
17
10
o
37 18
11
4
36 57
50
43
37 59
52
45
38
31
24
38 40
34
26
19
12
5
39 21
14
6
38 59
52
45
40 2
39 55
47
40
32
25
40 43
36
28
21
13
5
0
10
20
30
40
50
0
7
14
20
27
34
1
8
15
22
29
35
1
8
15
21
28
35
3
10
16
23
30
37
3
9
16
23
29
36
4
11
18
24
31
38
4
11
17
24
31
37
5
12
19
26
33
39
5
12
19
25
32
39
5
12
18
25
31
38
48 0
10
20
30
40
50
35 16
10
3
34 56
49
42
35 56
50
43
36
29
22
36 36
30
23
16
9
1
37 17
10
2
36 55
48
41
37 57
50
43
35
28
21
38 37
30
22
15
8
0
39 17
10
2
38 55
48
40
39 58
50
42
34
27
19
0
10
20
30
40
50
0
7
13
20
27
33
49 0
10
20
30
40
50
34 35
29
22
15
8
1
35 15
8
1
34 54
47
40
35 54
47
.40
33
26
19
36 34
27
20
12
5
35 58
37 13
6
36 59
51
44
36
37 53
46
38
30
23
15
38 32
25
17
9
2
37 54
39 11
4
38 56
48
41
33
0
10
20
30
40
50
0
fj
i
13
20
26
33
1
8
14
21
27
34
3
9
16
22
29
35
4
10
17
23
30
36
Page 698] TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches. — Fahrenheit's Thermometer 50°.]
Moon's
app. alt
Horizontal parallax.
OM
%3
Correction for seconds of
parallax. — Add.
Corr.
for
minutes
of alt.
54'
55'
56'
67'
68'
59'
60'
61'
£2
3&
0"
2"
4"
6"
8"
O '
50 0
10
20
30
40
50
' //
33 54
47
40
33
26
19
• it
34 33
26
19
11
4
33 57
35 11
4
34 57
49
42
35
35 50
43
36
28
20
13
36 29
21
14
6
35 58
51
' //
37 8
0
36 53
45
37
29
' n
37 46
38
31
23
15
7
/ //
3825
17
9
1
3753
45
n
0
10
20
30
40
50
0
10
20
30
40
50
//
0
6
13
19
26
32
ii
1
8
14
20
27
33
1
8
14
20
26
33
1
7
13
20
26
32
ii-
3
9
15
22
28
35
3
9
15
21
28
34
2
9
15
21
27
33
2
8
14
20
26
32
2
8
14
20
26
32
n
4
10
17
23
29
36
n
5
12
18
24
31
37
Sub.
V V
2 1
3 2
4 3
5 4
6 4
7 5
8 6
9 6
1 1
2 2
3 2
4 3
5 4
6 5
7 5
8 6
9 7
51 0
10
20
30
40
50
33 12
5
32 58
51
44
37
33 50
43
36
29
22
14
34 28
21
13
6
33 59
51
35 6
34 58
50
43
36
28
35 44
36
28
21
14
6
36 22
14
6
35 58
50
42
36 59
51
43
36
28
20
3737
29
21
13
5
3657
0
6
13
19
25
31
4
10
16
23
29
35
4
10
16
22
28
34
4
10
16
22
28
34
4
9
15
21
27
33
3
9
15
20
26
32
3
9
14
20
25
31
3
9
14
19
25
30
5
11
18
24
30
36
52 0
10
20
30
40
50
32 30
23
15
8
1
31 54
33 7
0
32 52
45
38
31
33 44
36
29
21
14
7
34 21
13
6
33 58
50
43
34 58
50
43
35
27
19
35 35
27
19
11
3
34 55
36 12
4
35 56
48
40
32
3649
41
33
24
16
8
0
10
20
30
40
50
0
6
12
18
24
31
5
11
17
23
29
35
53 0
10
20
30
40
50
31 47
39
32
25
17
10
32 23
15
8
0
31 53
46
32 59
51
44
36
28
21
33 35
27
20
12
4
32 57
34 11
3
33 56
48
40
32
34 47
39
31
23
15
7
35 24
15
7
34 59
51
43
36 0
3551
43
35
27
19
0
10
20
30
40
50
0
6
12
18
24
30
1
7
13
19
25
31
5
11
17
23
29
35
54 0
10
20
30
40
50
31 3
30 55
48
40
31 38
30
22
15
8
0
32 13
5
31 57
49
42
35-
32 49
41
33
25
17
9
33 24
16
8
0
32 52
44
33 59
51
43
35
27
19
34 35
26
18
10
1
33 53
3510
1
3453
45
37
28
0
10
20
30
40
50
0
6
12
18
23
29
0
6
11
17
23
28
0
6
11
17
22
28
1
7
13
19
25
30
1
7
13
18
24
30
1
7
12
18
23
29
1
6
12
17
23
28
5
11
16
22
28
34
55 0
10
20
30
40
50
30 18
10
3
29 55
48
40
30 52
45
38
30
22
14
31 27
19
12
4
30 56
48
32 1
31 53
46
38
30
22
32 36
28
20
12
4
31 55
33 10
2
32 54
46
37
29
33 45
36
28
20
11
3
3419
11
3
3354
45
37
0
10
20
30
40
50
2
8
14
19
25
31
5
10
16
22
27
33
56 0
10
20
30
40
50
29 33
25
18
10
3
28 55
30 7
29 59
51
43
36
28
30 40
32
24
16
9
1
31 14
6
30 58
50
42
34
31 47
39
31
23
15
7
32 21
13
4
31 56
48
40
32 55
46
37
29
21
12
3328
20
11
2
3254
45
0
10
20
30
40
50
0
10
20
30
40
50
2
8
13
19
24
30
2
7
13
18
24
29
4
10
16
21
27
32
4
10
15
21
26
31
57 0
10
20
30
40
50
28 47
39
32
24
17
9
29 20
12
5
28 57
49
41
29 53
45
37
29
21
13
30 25
17
9
1
29 53
45
30 58
50
42
33
25
17
31 31
22
14
6
30 57
49
32 3
31 55
47
38
29
21
3236
27
19
10
1
3152
0
5
11
16
22
27
58 0
10
20
30
40
50
28 1
27 53
45
38
30
22
28 33
25
17
9
1
27 53
29 5
28 57
49
41
33
24
29 37
28
20
12
4
28 55
30 9
0
29 52
44
35
27
30 41
32
23
15
6
29 58
31 12
4
30 55
46
38
29
3144
35
26
17
9
0
0
10
20
30
40
50
0
5
10
16
21
26
1
6
12-
17
22
27
2
7
13
18
23
28
3
8
14
19
24
29
4
9
15
20
25
30
59 0
10
20
30
40
50
27 14
6
26 58
51
43
35
27 45
37
29
21
13
5
28 16
7
27 59
51
43
35
28 47
38
30
22
14
5
29 18
9
1
28 53
44
36
29 49
40
31
23
14
6
30 20
11
2
29 54
45
36
3051
42
33
24
15
6
0
10
20
30
40
50
0
5
10
15
20
25
1
6
,11
16
21
26
2
7
12
17
22
27
3
8
13
18
23
29
4
9
14
19
24
30
TABLE 24. [Page 699
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
Horizontal parallax.
ll
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
of alt.
app. alt.
54'
55'
56'
57'
58'
59'
60'
61'
H
0"
911
4"
6»
8"
o /
60 0
10
20
30
40
50
t ii
26 26
19
11
3
25 55
47
t n
26 57
49
41
32
24
16
f n
27 27
19
11
2
26 53
45
' //
27 57
49
40
31
23
14
i n
28 27
19
10
1
27 53
44
' //
28 57
49
40
1 31
22
13
' //
29 27
18
9
0
28 51
42
/ //
29 57
48
39
30
21
12
Sub.
V V
2 2
3 3
4 4
5 5
6 '5
7 6
8 7
9 8
0
10
20
30
40
50
0
5
10
15
20
25
I
6
11
16
21
26
2
7
12
17
22
27
3
8
13
18
23
28
4
9
14
19
24
29
61 0
10
20
30
40
50
25 39
31
23
15
7
24 59
26 8
0
25 52
43
35
27
26 37
29
20
12
4
25 55
27 6
26 58
49
40
32
24
27 36
27
18
10
1
26 52
28 5
27 56
47
38
29
20
28 34
25
16
7
27 58
49
29 3
28 54
45
35
26
17
0
10
20
30
40
50
0
5
10
14
19
24
1
6
11
15
20
25
1
6
10
15
19
24
2
7
12
16
21
26
3
8
12
17
22
27
4
9
13
18
23
28
62 0
10
20
30
40
50
24 50
42
34
26
18
10
25 19
10
2
24 54
46
37
25 47
38
29
21
13
4
26 15
6
25 57
49
41
32
26 43
34
25
17
8
25 59
27 11
2
26 53
45
36
27
27 40
30
21
12
3
26 54
28 8
27 58
49
40
31
21
0
10
20
30
40
50
0
5
9
14
19
23
2
6
11
16
20
25
3
7
12
17
21
26
3
7
12
16
21
25
3
7
11
16
20
24
4
8
12
18
22
27
63 0
10
20
30
40
50
24 2
23 54
46
37
29
20
24 29
21
13
4
23 55
47
24 56
48
39
31
22
13
25 23
15
6
24 58
49
40
25 51
42
33
24
15
6
26 18
9
0
25 51
42
33
26 45
36
27
18
8
25 59
27 12
3
26 54
45
35
26
0
10
20
30
40
50
0
4
9
13
18
22
0
4
9
13
17
22
1
5
10
14
19
23
1
5
10
14
18
23
2
6
11
15
20
24
2
6
10
15
19
23
4
8
13
17
22
26
3
8
12
16
21
25
64 0
10
20
30
40
50
23 12
4
22 56
47
39
31
23 39
31
22
13
5
22 57
24 5
23 57
48.
39
30
22
24 32
23
14
5
23 56
48
24 58
49
40
31
22
13
25 24
15
6
24 57
48
39
25 50
41
32
22
13
4
26 17
8
25 58
48
39
30
0
10
20
30
40
50
0
10
20
30
40
50
65 0
10
20
30
40
50
22 23
14
6
21 58
49
41
22 48
40
31
23
14
6
23 13
5
22 56
48
39
30
23 39
30
21
13
4
22 55
24 4
23 55
46
37
28
19
24 30
20
11
2
23 53
44
24 55
46
36
27
18
8
25 21
11
1
24 52
43
.33
0
4
8
13
17
21
1
5
9
13
18
22
2
6
10
14
18
23
2
6
10
14
18
22
2
5
9
13
17
21
1
5
9
13
16
20
2
7
11
15
19
23
3
7
12
16
20
24
3
7
11
16
20
24
66 0
10
20
30
40
50
21 32
24
15
7
20 59
50
21 57
48
39
31
22
14
22 21
• 12
3
21 55
46
37
22 46
37
28
19
10
1
23 10
1
22 52
43
34
25
23 35
25
15
6
22 57
48
23 59
49
40
31
21
12
24 23
14
4
23 55
45
36
0
10
20
30
40
50
0
4
8
12
16
20
1
5
9
13
17
21
1
5
8
12
16
20
1
4
8
12
16
19
2
7
11
15
19
23
67 0
10
20
30
40
50
20 41
33
25
16
8
19 59
21 5
20 56
48
39
30
21
21 28
19
11
2
20 53
44
21 52
43
34
25
16
7
22 15
6
21 57
48
39
30
22 39
29
20
11
2
21 52
23 2
22 52
43
34
24
15
23 26
16
7
22 57
47
37
0
10
20
30
40
50
0
4
8
12
15
19
0
4
7
11
15
18
2
6
10
14
18
22
2
6
9
13
17
21
2
6
9
13
16
20
3
7
11
15
18
22
3
7
10
14
18
21
68 0
10
20
30
40
50
19 50
42
33
25
16
7
20 13
4
19 56
47
38
29
20 35
27
18
9
0
19 51
20 58
49
40
31
22
13
!21 21
12
2
20 53
44
34
21 43
34
24
15
5
20 56
22 5
21 56
47
37
27
17
22 28
19
9
21 59
49
39
0
10
20
30
40
50
69 0
10
20
30
40
50
18 59
50
42
33
24
. 16
19 21
12
3
18 54
45
37
19 42
33
24
15
6
18 57
20 4
19 55
45
36
27
18
20 25
16
7
19 57
48
39
20 47
37
28
18
9
0
21 8
20 59
49
39
29
20
21 30
20
10
0
20 50
41
0
10
20
30
40
50
0
4
7
11
14
18
1
4
8
11
15
18
1
5
8
12
15
19
3
6
10
13
17
20
V
Page 700] TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
II
§s
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
of alt.
54'
55'
56'
57'
58'
59'
60'
61'
IB,
0"
2"
4"
n
1
5
8
11
15
18
6"
8"
70 0
10
20
30
40
50
/ //
18 7
17 58
50
41
32
24
> n
18 28
19
10
1
17 53
44
/ n
18 48
39
30
21
12
3
/ //
19 9
0
18 50
41
32
23
/ n
19 30
20
11
1
18 52
43
/ //
19 50
41
31
21
12
3
t n
20 11
1
19 51
41
32
22
t n
20 31
21
11
1
19 52
42
n
0
10
20
30
40
50
ii
0
3
7
10
13
17
0
3
6
10
13
16
a
1
4
7
11
14
17
n
2
5
9
12
15
19
it
3
6
9
13
16
19
Sub.
V V
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
71 0
10
20
30
40
50
17 15
6
16 57
48
. 40
31
17 35
26
17
8
16 59
50
17 54
45
36
27
18
9
18 14
5
17 55
46
37
28
18 34
24
14
5
17 56
47
18 53
43
33
24
15
5
19 12
3
18 53
43
34
24
19 32
22
12
2
18 52
42
0
10
20
30
40
50
1
4
7
10
13
17
1
4
8
11
14
17
2
5
8
12
15
18
3
6
9
12
15
19
2
5
8
11
14
18
72 0
10
20
30
40
50
16 22
13
5
15 57
48
39
16 41
32
23
14
5
15 56
17 0
16 50
41
32
23
14
17 18
9
16 59
50
41
32
17 37
27
18
9
16 59
50
17 55
46
36
27
17
7
18 14
4
17 54
45
35
25
18 32
22
12
3
17 53
43
0
10
20
30
40
50
0
3
6
9
12
15
1
4
7
10
13
16
i
4
7
10
13
16
2
5
8
11
14
17
2
5
7
10
13
16
2
4
7
10
12
15
73 0
10
20
30
40
50
15 30
21
12
3
14 54
45
15 47
38
29
20
11
2
16 5
15 56
47
37
28
19
16 22
13
4
15 55
45
35
16 40
30
21
12
2
15 52
16 58
48
39
29
19
9
17 15
5
16 56
46
36
26
17 33
23
13
3
16 53
42
0
10
20
30
40
50
0
3
6
9
11
14
1
3
6
9
12
15
1
4
7
10
13
15
1
4
6
9
12
14
2
5
8
11
14
17
74 0
10
20
30
40
50
14 36
28
19
10
1
13 52
14 53
44
35
26
17
8
15 9
0
14 51
42
33
23
15 26
17
8
14 58
49
39
15 42
33
24
14
5
14 55
15 59
49
40
30
20
10
16 16
6
15 56
46
36
26
16 32
22
12
2
15 52
42
0
10
20
30
40
50
0
3
5
8
11
13
1
3
6
9
11
14
1
3
6
8
11
13
2
5
8
11
13
16
75 0
10
20
30
40
50
13 43
34
25
16
7
12 58
13 59
50
41
32
22
13
14 14
5
13 56
46
37
28
14 29
20
11
1
13 52
42
14 45
36
27
17
7
1£ 57
15 1
14 52
42
32
22
12
15 16
7
14 57
47
37
27
15 32
22
12
2
14 51
41
0
10
20
30
40
50
0
3
5
8
10
13
1
4
6
9
11
14
2
4
7
9
12
14
2
5
7
10
12
15
76 0
10
20
30
40
50
12 49
41
32
23
14
5
13 4
12 55
46
37
27
18
13 18
9
0
12 51
41
32
13 33
24
14
5
12 55
45
13 47
38
28
19
9
12 59
14 2
13 53
43
33
23
13
14 17
7
13 57
47
36
26
14 31
21
11
1
13 50
40
0
10
20
30
40
50
0
2
5
7
9
12
0
3-
5
8
10
12
1
3
6
8
10
13
1
4
6
8
11
13
2
4
7
9
11
14
77 0
10
20
30
40
50
11 56
47
38
29
19
10
12 9
0
11 51
42
32
23
12 22
13
4
11 55
45
35
12 36
27
17
8
11 58
48
12 49
40
30
21
11
1
13 3
12 53
43
33
23
13
13 16
7
12 57
47
36
26
13 30
20
10
0
12 49
39
0
10
20
30
40
50
0
2
4
7
9
11
0
3
5
7
9
11
1
3
5
7
9
12
1
3
5
7
9
11
1
3
4
6
8
10
1
4
6
8
10
12
2
4
6
8
10
13
78 0
10
20
30
40
50
11 1
10 52
43
34
25
16
11 14
5
10 55
46
37
28
11 26
17
8
10 58
48
39
11 39
30
20
10
0
10 51
11 52
42
32
22
12
3
12 4
11 54
44
34
24
15
12 16
6
11 56
46
36
26
12 39
19
8
11 58
48
38
0
10
20
30
40
50
0
2
4
6
8
10
0
2
4
6
8
10
1
3
5
7
9
11
1
3
5
7
8
10
2
4
6
8
10
12
79 0
10
20
30
40
50
10 7
9 58
49
40
31
22
10 19
9
0
9 50
41
32
10 30
21
11
1
9 52
43
10 42
32
22
12
3
9 54
10 53
43
33
23
13
4
11 5
10 55
44
34
24
15
11 16
6
10 56
45
35
25
11 28
17
7
10 56
46
36
0
10
20
30
40
50
0
2
4
6
7
9
0
2
4
6
8
10
1
3
5
7
9
11
TABLE 24. [Page 701
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
O J
*d
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
of alt.
54'
55'
56'
57'
58'
59'
6<y
61'
52
*» $
-ji
0"
2"
it
0
2
4
5
7
9
"0"
2
3
5
6
8
4»
II
1
2
4
6
7
9
6"
8*
0 /
80 0
10
20
30
40
50
/ it
9 13
3
8 54
45
36
27
f it
9 23
14
4
8 55
46
37
/ //
9 34
24
14
5
8 55
46
. > //
9 44
34
24
15
5
8 56
/ //
9 55
45
35
25
15
6
i a
10 5
9 55
45
35
25
15
/ n
10 15
5
9 55
45
35
25
i n
10 26
15
5
9 54
44
34
it
0
10
20
30
40
50
//
0
2
3
5
7
8
H
1
3
4
6
8
9
H
1
3
5
6
8
10
Sub.
V V'
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
81 0
10
20
30
40
50
8 18
9
7 59
50
41
32
8 27
18
8
7 59
50
41
8 37
27
17
8
7 59
49
8 46
36
26
17
8
7 58
8 56
46
36
26
17
7
9 5
8 55
45
35
25
15
9 14
4
8 54
44
34
24
9 24
13
3
8 52
42
32
0
10
20
30
40
50
0
1
3
4
6
7
1
2
4
5
6
8
1
2
4
5
7
8
1
2
3
5
6
7
1
3
4
6
7
9
1
2
4
5
6
8
82 0
10
20
30
40
50
7 23
14
4
6 55
46
37
7 31
22
12
3
6 54
45
7 40
30
20
11
2
6 52
7 48
38
28
19
10
0
7 57
47
37
27
17
7
8 5
7 55
45
35
25
15
8 13
3
7 52
42
32
22
8 22
11
0
7 50
40
30
U
10
20
30
40
50
0
1
3
4
5
7
0
2
3
4
6
7
1
2
3
5
6
7
83 0
10
20
30
40
50
6 28
19
9
0
5 51
42
6 35
26
16
7
5 58
49
6 43
33
23
13
4
5 55
6 50
40
30
20
11
1
6 57
47
37
27
18
8
7 5
6 54
44
34
24
14
• 7 12
2
6 51
41
31
21
7 20
9
6 58
48
38
27
0
10
20
30
40
50
0
1
2
3
5
6
0
1
3
4
5
6
0
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
6
7
84 0
10
20
30
40
50
5 33
23
14
5
4 56
47
5 39
30
20
10
1
4 52
5 45
36
26
16
7
4 58
5 52
42
32
22
13
3
5 58
48
38
28
18
8
6 4
5 54
44
34
24
14
6 10
0
5 50
39
29
19
6 17
6
5 55
45
35
25
0
10
20
30
40
50
0
1
2
3
4
5
0
1
2
2
3
4
0
1
1
2
3
3
0
1
2
3
4
5
0
1
2
3
3
4
0
1
1
2
3
3
0
1
1
1
2
2
0
0
1
1
1
1
0
1
2
3
4
5
0
1
2
3
4
4
~0"
1
2
2
3
3
1
2
3
3
4
5
1
2
3
4
5
6
85 0
10
20
30
40
50
4 37
28
18
9
0
3 51
4 43
33
24
14
5
3 56
4 48
38
28
19
10
0
4 53
43
33
23
14
5
4 58
48
38
28
19
9
5 4
4 53
43
33
23
13
5 9
4 58
48
38
28
18
5 14
3
4 53
43
33
22
0
10
20
30
40
50
0
1
2
3
4
5
0
1
2
2
3
4
0
1
1
2
2
3
1
1
2
3
4
5
1
1
2
2
3
4
0
1
1
2
2
3
86 0
10
20
30
40
50
3 42
33
23
14
5
2 56
3 46
37
27
18
9
2 59
3 50
41
31
21
12
3
3 55
45
35
25
16
6
3 59
49
39
29
19
9
4 3
3 53
43
33
23
13
4 7
3 57
46
36
26
16
4 11
1
3 50
40
30
19
0
10
20
30
40
50
87 0
10
20
30
40
50
2 47
37
28
19
10
1
2 50
40
31
21
12
3
2 53
43
33
24
15
5
2 56
46
36
26
17
7
2 59
49
39
29
19
9
3 2
2 52
42
32
22
12
3 5
2 55
45
34
24
14
3 9
2 58
47
37
27
16
0
10
20
30
40
50
0
0
1
1
2
2
0
1
1
2
2
2
88 0
10
20
30
40
50
1 51
42
32
23
14
5
1 53
43
34
25
15
6
1 55
45
36
26
16
7
1 57
47
38
28
19
9
1 59
49
39
29
20
10
2 2
1 51
41
31
21
11
2 4
1 53
43
32
22
12
2 6
1 55
44
34
24
13
0
10
20
30
40
50
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
2
0
0
0
0
0
1
89 0
10
20
30
40
50
0 56
46
37
28
19
9
0 57
47
37
28
19
10
0 58
48
38
28
19
10
0 59
49
39
29
19
10
1 0
0 50
40
30
20
10
1 1
0 51
40
30
20
10
1 2
0 51
41
31
21
10
1 3
0 52
42
31
21
10
0
10
20
30
40
50
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
61828°— 16 38
Page 702] TABLE 25.
Table showing the variation of the altitude of an object arising from a change of 100 seconds in the
declination. Unmarked quantities in the Table are positive. If the change move the body toward
the elevated pole, apply the correction to the altitude with the signs in the Table; otherwise,
change the signs.
Declination.
1
4->
3
Latitude of same name as declination. Latitude of different name from declination.
•j
5j
fl
«
70°
60°
60°
40°
80°
20°
10°
0°
10°
20°
30°
40°
50°
60°
70°
o
0
0
0
10
20
30
40
50
60
70
0
0
10
20
30
40
50
60
70
0
0
2
94
95
100
87
88
92
100
76
78
82
88
100
64
65
68
74
84
100
50
51
53
57
65
78
100
34
35
36
39
45
53
68
100
17
18
18
20
22
27
35
51
0
0
0
0
0
0
0
0
17
18
18
20
22
27
35
51
34
35
36
39
45
53
68
100
50
51
53
57
65
78
100
64
65
68
74
84
100
76
78
82
88
100
87
88
92
100
94
95
100
2
4
0
10
20
30
40
50
60
70
94
95
99
107
87
87
91
98
111
77
77
81
87
98
116
64
65
67
73
82
97
124
50
50
52
56
63
74
95
139
34
34
35
38
42
50
64
92
17
17
17
18
20
24
30
43
0
— 1
- 1
2
— 2
3
- 5
- 8
17
18
19
22
25
30
40
59
34
35
37
41
47
57
73
108
50
51
54
59
68
81
103
64
66
69
76
86
103
77
78
83
90
102
87
88
93
102
94
96
101
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
94
94
98
105
87
87
90
96
107
77
77
79
85
94
111
64
64
66
70
78
92
117
50
50
51
54
59
70
88
127
34
34
34
36
39
45
56
81
17
16
16
16
17
19
23
32
' 0
— 1
- 3
— 4
— 6
— 8
—12
—19
17
19
21
24
29
35
47
70
34
36
39
44
51
62
81
119
50
52
56
62
71
86
112
64
67
71
78
90
109
77
79
84
93
106
87
89
95
104
94
97
103
0
10
20
30
40
50
60
70
4
6
0
10
20
30
40
50
60
70
94
94
97
103
87
87
89
94
105
77
76
78
83
92
107
65
64
65
69
76
88
111
50
49
50
52
57
66
82
118
34
33
33
34
36
41
51
72
17
16
15
14
14
15
17
22
0
- 2
— 4
- 6
- 9
—13
—18
-29
17
20
22
26
32
40
53
80
34
37
40
46
54
66
87
129
50
53
57
64
74
91
119
65
67
73
81
93
113
77
80
86
95
109
87
90
96
107
94
98
104
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
6
8
0
10
20
30
40
50
60
70
95
94
96
101
87
86
88
93
102
77
76
77
81
89
104
65
63
64
67
73
84
105
50
49
49
50
54
62
77
109
35
33
32
32
33
37
45
62
18
15
14
12
11
11
11
13
0
- 3
- 5
- 8
—12
-17
—24
-39
18
20
24
28
35
44
59
90
35
38
40
48
57
70
93
140
50
54
59
66
78
95
125
65
68
74
83
97
118
77
81
87
97
113
87
91
98
109
95
99
106
8
10
12
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
95
94
95
100
88
86
87
91
100
78
75
76
80
87
100
65
63
63
65
70
81
100
51
48
48
49
51
58
71
100
35
32
31
30
31
33
39
53
18
15
12
10
8
6
5
3
0
3
- 6
-10
-15
-21
-31
—48
18
21
25
30
38
48
66
100
35
38
43
50
60
75
100
51
55
60
69
81
100
65
69
76
86
100
78
82
89
100
88
92
100
95
100
0
10
20
30
40
50
60
70
10
96
94
94
99
108
89
86
86
90
98
112
78
76
76
78
84
97
120
66
63
62
64
68
77
95
134
51
48
47
47
49
54
65
91
35
32
29
28
28
29
33
44
18
14
11
8
5
2
—1
-6
0
- 4
- 8
-12
-18
—25
-37
-58
18
22
27
33
41
53
72
110
35
39
45
53
63
80
107
51
56
62
71
85
105
66
70
78
88
104
78
83
91
103
89
94
102
96
101
0
10
20
30
40
50
60
70
o3
c
_g
<5
12
1 Declination.
flj
T3
<5
70°
60°
50°
40°
30°
20°
10°
0°
10°
20°
30°
40°
50°
60°
70°
§
1
"o
0
Latitude of same name as declination. Latitude of different name from declination.
TABLE 25. [Page 703
Table showing the variation of the altitude of an object arising from a change of 100 seconds in the
declination. Unmarked quantities in the Table are positive. If the change move the body toward
the elevated pole, apply the correction to the altitude with the signs in the Table; otherwise,
change the signs.
Declination.
05
3
Latitude of same name as declination.
Latitude of different name from declination.
•
•c
S
3
G
.2
70°
60°
50°
40°
30°
20°
10°
0°
10°
20°
30°
40°
50°
60°
70°
1
o
14
O
0
10
20
30
40
50
60
70
//
97
94
94
97
106
ii
89
86
86
89
96
109
n
79
76
75
77
82
93
115
//
66
63
61
62
66
73
89
125
n
52
48
46
45
46
50
60
82
52
48
45
44
44
47
54
73
n
35
31
27
26
25
25
27
35
II
18
14
10
6
2
- 2
— 7
-16
II
0
— 4
- 9
— 14
— 21
- 30
- 43
- 69
n
18
23
28
35
44
58
79
121
n
35
40
45
55
67
85
114
n
52
57
64
74
88
110
66
72
80
91
107
79
85
93
106
89
95
104
97
103
0
10
20
30
40
50
60
70
14
16
18
0
10
20
30
40
50
60
70
98
94
94
96
104
90
86
85
87
94
106
80
76
74
75
80
90
110
67
63
61
61
63
70
84
117
36
31
27
25
22
21
21
25
18
13
9
4
0
- 6
-14
-26
0
— 5
— 10
— 17
- 24
- 34
- 50
— 79
18
23
30
37
48
62
86
132
36
41
48
58
70
90
121
52
58
66
77
92
115
67
73
82
94
111
80
86
95
109
90
97
106
98
104
0
10
20
30
40
50
60
70
16
0
10
20
30
40
50
60
70
99
95
93
95
102
91
87
85
86
92
103
81
76
74
74
78
87
105
68
63
60
59
61
66
79
108
53
48
44
42
41
43
49
64
53
48
43
40
39
39
43
56
36
31
26
23
20
17
16
16
18
13
8
2
3
—10
-20
-36
0
— 6
- 12
- 19
— 27
— 39
— 56
— 89
18
24
31
40
51
67
93
143
36
42
50
60
74
95
128
53
59
68
79
96
121
68
74
84
97
116
81
88
98
112
91
98
109
99
106
0
10
20
30
40
50
60
70
18
20
20
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
100
95
93
94
100
92
87
85
85
90
100
82
76
74
73
76
83
100
68
63
60
58
59
63
74
100
36
31
25
21
17
13
10
6
18
12
6
0
— 6
-15
-26
-46
0
— 6
- 13
— 21
- 31
- 43
- 63
-100
18
25
33
42
55
72
100
36
43
52
63
78
100
53
60
70
82
100
68
76
86
100
82
89
100
92
100
100
0
10
20
30
40
50
60
70
22
96
93
94
98
110
93
88
85
85
88
97
117
83
77
73
72
74
80
95
131
69
63
59
57
57
60
68
92
54
48
43
39
36
36
38
47
37
30
25
19
14
9
4
3
19
12
5
- 2
— 9
—19
-33
-56
0
7
- 15
- 23
- 34
— 48
- 70
—111
19
26
35
45
58
77
107
37
45
54
66
82
106
54
62
72
86
104
69
78
88
103
83
91
103
93
102
101
0
10
20
30
40
50
60
70
22
24
0
10
20
30
40
50
60
70
97
93
93
97
107
95
88
85
84
86
93
112
84
77
73
71
72
77
91
123
70
64
59
56
54
56
64
83
55
48
42
38
34
32
32
38
37
30
24
18
12
5
- 2
-13
19
11
4
4
—12
-23
-39
-67
0
Q
O
- 16
- 26
— 37
- 53
— 77
-122
19
27
36
48
•62
83
115
37
46
56
69
86
111
55
63
74
89
109
70
79
91
107
84
93
105
95
104
103
0
10
20
30
40
50
60
70
24
26
0
10
20
30
40
50
60
70
98
95
93
96
105
96
89
85
83
85
92
108
85
78
73
70
70
74
86
115
72
64
59
54
52
53
58
75
56
48
41
36
32
28
27
29
38
30
23
16
9
1
g
-23
19
11
3
— 6
—16
-28
-46
—78
0
- 9
- 18
- 28
- 41
- 58
- 84
—134
19
28
38
50
66
88
123
38
47
58
72
91
117
56
65
77
92
114
72
81
94
111
85
95
108
96
106
105
0
10
20
30
40
50
60
70
26
1 Declination.
6
•0
3
<
70°
60°
50°
40°
30°
20°
10°
0°
10°
20°
30°
40°
60°
60°
70°
•j
•o
_3
5
^
d
1
(3
1
Latitude of same name as declination.
Latitude of different name from declination.
Page 704] TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of the same name as the latitude; upper transit; reduction additive.
Lati
0°
1°
2°
3°
40
5°
6°
7°
8°
9°
10°
11°
tude.
0
0
1
2
3
4
//
28.1
ft
tt
tt
rt
28.1
tt
22.4
28.0
tt
18.7
22.4
28.0
it
16.0
18.6
22.3
27.9
ft
14.0
16.0
18.6
22.3
27.8
ft
12.4
13.9
15.9
18.5
22.2
rt
11.1
12.4
13.9
15.8
18.5
rt
10.1
11.1
12. 3
13.8
15.8
o
0
1
2
3
4
5
6
7
8
9
22.4
18.7
16.0
14.0
12.4
28.0
22.4
18.6
16.0
13.9
28.0
22.3
18.6
15.9
27.9
22.3
18.5
27.8
22.2
27.7
27.7
22.1
27.6
18.4
22.0
27.4
5
6
7
8
9
10
11
12
13
14
11.1
10.1
9.2
8.5
7.9
12.4
11.1
10.1
9.2
8.5
13.9
12.3
11.1
10.0
9.2
15.8
13.8
12.3
11.0
10.0
18.5
15.8
13.8
12.2
10.9
22.1
18.4
15.7
13.7
12.1
27.6
22.0
18.3
15.6
13.6
27.4
21.9
18.2
15.5
27.3
21.7
18.0
27.1
21.6
26.9
10
11
12
13
14
15
16
17
18
19
7.3
6.8
6.4
6.0
5.7
7.8
7.3
6.8
6.4
6.0
8.4
7.8
7.2
6.8
6.3
9.1
8.4
7.8
7.2
6.7
9.9
9.1
8.3
7.7
7.2
10.9
9.8
9.0
8.3
7.6
12.1
10.8
9.8
8.9
8.2
13.5
12.0
10.7
9.7
8.9
15.4
13.4
11.9
10.6
9.6
17.9
15.3
13.3
11.8
10.6
21.4
17.8
15.2
13.2
11.7
26.7
21.3
17.6
15.0
13.1
15
16
17
18
19
20
21
22
23
24
5.4
5.1
4.9
4.6
4.4
5.7
5.4
5.1
4.8
4.6
6.0
5.6
' 5.3
5.0
4.8
6.3
5.9
5.6
5.3
5.0
6.7
6.3
5.9
5.5
5.2
7.1
6.6
6.2
5.8
5.5
7.6
7.0
6.6
6.1
5.8
8.1
7.5
7.0
6.5
6.1
8.8
8.1
7.5
6.9
6.4
9.5
8.7
8.0
7.4
6.8
6.4
6.0
5.6
5.3
5.0
10.5
9.5
8.6
7.9
7.3
11.6
10.4
9.4
8.5
7.8
20
21
22
23
24
25
26
27
28
29
4.2
4.0
3.9
3.7
3.5
4.4
4.2
4.0
3.8
3.7
4.6
4.3
4.1
4.0
3.8
4.7
4.5
4.3
4.1
3.9
5.0
4.7
4.5
4.3
4.1
5.2
4.9
4.7
4.4
4.2
5.4
5.1
4.9
4.6
4.4
5.7
5.4
5.1
4.8
4.6
6.0
5.7
5.3
5.0
4.7
6.8
6.3
5.9
5.5
5.2
7.2
6.7
6.2
5.8
5.5
*25
26
27
28
29
30
31
32
33
34
3.4
3.3
3.1
3.0
2.9
3.5
3.4
3.2
3.1
3.0
3.6
3.5
3.3
3.2
3.1
3.7
3.6
3.4
3.3
3.2
3.9
3.7
3.5
3.4
3.2
4.0
3.8
3.7
3.5
3.3
4.2
4.0
3.8
3.6
3.4
4.3
4.1
3.9
3.7
3.6
4.5
4.3
4.1
3.9
3.7
4.7
4.4
4.2
4.0
3.8
4.9
4.6
4.4
4.2
3.9
5.1
4.8
4.6
4.3
4.1
30
31
32
33
34
35
36
37
38
39
2.8
2.7
2.6
2.5
2.4
2.9
2.8
2.7
2.6
2.5
3.0
2.8
2.7
2.6
2.5
3.0
2.9
2.8
2.7
2.6
3.1
3.0
2.9
2.8
2.7
3.2
3.1
2.9
2.8
2.7
3.3
3.2
3.0
2.9
2.8
3.4
3.3
3.1
3.0
2.9
3.5
3.4
3.2
3.0
2.9
3.6
3.5
3.3
3.2
3.0
3.7
3.6
3.4
3.2
3.1
3.9
3.7
3.5
3.3
3.2
35
36
37
38
39
40
41
42
43
44
2.3
2.3
2.2
2.1
2.0
2.4
2.3
2.2
2.1
2.1
2.4
2.4
2.3
2.2
2.1
2.5
2.4
2.3
2.2
2.1
2.6
2.5
2.4
2.3
2.2
2.6
2.5
2.4
2.3
2.2
2.7
2.6
2.5
2.4
2.3
2.7
2.6
2.5
2.4
2.3
2.8
2.7
2.6
2.5
2.4
2.9
2.8
2.6
2.5
2.4
3.0
2.8
2.7
2.6
2.5
3.0
2.9
2.8
2.7
2.5
40
41
42
43
44
45
46
47
48
49
2.0
1.9
1.8
1.8
1.7
2.0
1.9
1.9
1.8
1.7
2.0
2.0
1.9
1.8
1.8
2.1
2.0
1.9
1.9
1.8
2.1
2.0
2.0
1.9
1.8
2.2
2.1
2.0
1.9
1.8
2.2
2.1
2.0
2.0
1.9
2.2
2.2
2.1
2.0
1.9
2.3
2.2
2.1
2.0
.9
2.3
2.2
2.1
2.1
2.0
2.4
2.3
2.2
2.1
2.0
2.4
2.3
2.2
2.1
2.1
45
46
47
48
49
50
51
52
53
54
1.6
.6
.5
.5
.4
1.7
1.6
1.6
1.5
1.4
1.7
1.6
1.6
1.5
1.5
1.7
1.7
1.6
1.5
1.5
1.8
1.7
1.6
1.6
1.5
1.8
1.7
1.6
1.6
1.5
1.8
1.7
1.7
1.6
1.5
1.8
1.8
1.7
1.6
1.6
.9
.8
.7
.7
.6
1.9
1.8
1.8
1.7
1.6
1.9
.9
.8
.7
.6
2.0
1.9
1.8
1.7
1.7
50
51
52
53
54
55
56
57
58
59
60
.4
.3
.3
.2
.2
1.1
1.4
1.3
1.3
1.2
1.2
1.1
1.4
1.4
1.3
1.3
1.2
1.2
1.4
1.4
1.3
1.3
1.2
1.2
1.5
1.4
1.3
1.3
1.2
1.2
1.5
1.4
1.4
1.3
1.3
1.2
1.5
1.4
1.4
1.3
1.8
1.2
1.5
1.4
1.4
1.3
1.3
1.2
.5
.5
.4
.3
1.3
1.2
1.6
1.5
1.4
1.4
1.3
1.2
.6
.5
1.4
1.4
1.3
1.3
1.6
1.5
1.5
1.4
1.3
1.3
55
56
57
58
59
60
0°
1°
2°
3°
4°
5°
6°
7°
8°
9°
10°
11°
Declination of the same name as the latitude; upper transit; reduction additive.
TABLE 26. [Page 705
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of the same name as the latitude; upper transit; reduction additive.
Lati
tude.
12°
13°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
o
0
1
2
3
4
a
9.2
10.1
11.1
12.3
13.8
8.5
9.2
10.0
11.0
12.2
o
0
1
2
3
4
7.9
8.5
9.2
10.0
10.9
7.3
7.8
8.4
9.1
9.9
6.8
7.3
7.8
8.4
9.1
6.4
6.8
7.2
7.8
8.3
6.0
6.4
6.8
7.2
7.7
5.7
6.0
6.3
6.7
7.2
5.4
5.7
6.0
6.3
6.7
5.1
5.4
5.6
5.9
6.3
4.9
5.1
5.3
5.6
5.9
4.6
4.8
5.0
5.3
5.5
4.4
4.6
4.8
5.0
5.2
5
6
7
8
9
15.7
18.3
21.9
27.3
13.7
15.6
18.2
21.7
27.1
12.1
13.6
15.5
18.0
21.6
10.9
12.1
13.5
15.4
17.9
9.8
10.8
12.0
13.4
15.3
9.0
9.8
10.7
11.9
13.3
8.3
8.9
9.7
10.6
11.8
7.6
8.2
8.9
9.6
10.6
7.1
7.6
8.1
8.8
9.5
6.6
7.0
7.5
8.1
8.7
6.2
6.6
7.0
7.5
8.0
5.8
6.1
6.5
6.9
7.4
5.5
5.8
6.1
6.4
6.8
5
6
7
8
9
10
11
12
13
14
26.9
21.4
26.7
17.8
21.3
26.5
15.2
17.6
21.1
26.2
13.2
15.0
17.5
20.9
26.0
11.7
13.1
14.9
17.3
20.7
10.5
11.6
13.0
14.8
17.1
9.5
10.4
11.5
12.8
14.6
8.6
9.4
10.3
11.3
12.7
7.9
8.5
9.3-
10.1
11.2
7.3
7.8
8.4
9.2
10.0
10
11
12
13
14
15
16
17
18
19
26.5
21.1
17.5
14.9
26.2
20.9
17.3
26.0
20.7
25.7
25.7
20.4
25.4
16.9
20.2
25.1
14.4
16.7
20.0
24.8
12.5
14.3
16.5
19.7
24.5
11.1
12.4
14.1
16.3
19.5
15
16
17
18
19
20
21
22
23
24
13.0
11.5
10.3
9.3
8.4
14.8
12.8
11.3
10.1
9.2
17.1
14.6
12.7
11.2
10.0
20.4
16.9
14.4
12.5
11.1
25.4
20.2
16.7
14.3
12.4
25.1
20.0
16.5
14.1
24.8
19.7
16.3
24.5
19.5
24.2
24.2
20
21
22
23
24
25,
26
27
28
29
7.7
7.1
6.6
6.2
5.7
8.3
7.6
7.0
6.5
6.1
9.0
8.2
7.5
7.0
6.4
9.9
8.9
8.1
7.4
6.9
10.9
9.8
8.8
8.0
7.3
12.2
10.8
9.6
8.7
7.9
13.9
12.1
10.6
9.5
8.6
16.1
13.7
11.9
10.5
9.4
19.2
15.9
13.5
11.7
10.3
23.8
18.9
15.6
13.3
11.5
23.5
18.6
15.4
13.1
23.1
18.3
15.1
22.7
18.0
25
26
27
28
29
30
31
32
33
34
5.4
5.1
4.8
4.5
4.3
5.7
5.3
5.0
4.7
4.4
6.0
5.6
5.2
4.9
4.6
6.4
5.9
5.5
5.1
4.8
6.8
6.3
5.8
5.4
5.1
7.2
6.7
6.2
5.7
5.3
7.8
7.1
6.5
6.1
5.6
8.4
7.7
7.0
6.4
5.9
9.2
8.3
7.5
6.9
6.3
10.1
9.0
8.1
7.4
6.8
11.3
10.0
8.9
8.0
7.3
12.8
11.1
.9.8
8.7
7.8
14.9
12.6
10.9
9.6
8.6
30
31
32
33
34
35
36
37
38
39
4.0
3.8
3.6
3.4
3.3
4.2
4.0
3.8
3.6
3.4
4.4
4.1
3.9
3.7
3.5
4.5
4.3
4.0
3.8-
3.6
4.7
4.5
4.2
- 4.0
3.8
5.0
4.7
4.4
4.1
3.9
5.2
4.9
4.6
4.3
4.0
5.5
5.1
4.8
4.5
4.2
5.8
5.4
5.0
4.7
4.4
6.2
5.7
5.3
4.9
4.6
6.6
6.1
5.6
5.2
4.8
7.1
6.5
6.0
5.5
5.1
7.7
7.0
6.4
5.8
5.4
35
36
37
38
39
40
41
42
43
44
3.1
3.0
2.9
2.7
2.6
5.2
3.1
2.9
2.8
2.7
3.3
3.2
3.0
2.9
2.7
3.4
3.3
3.1
3.0
2.8
3.6
3.4
3.2
3.0
2.9
3.7
3.5
3.3
3.1
3.0
3.8
3.6
3.4
3.2
3.1
4.0
3.7
3.5
3.3
3.2
4.1
3.9
3.7
3.5
3.3
4.3
4.0
3.8
3.6
3.4
4.5
4.2
4.0
3.7
3.5
4.7
4.4
4.1
3.9
3.6
5.0
4.6
4.3
4.0
3.8
40
41
42
43
44
45
46
47
48
49
2.5
2.4
2.3
2.2
2.1
2.6
2.4
2.3
2.2
2.1
2.6
2.5
2.4
2.3
2.2
2.7
2.6
2.4
2.3
2.2
2.8
2.6
2.5
2.4
2.3
2.8
2.7
2.6
2.4
2.3
2.9
2.8
2.6
2.5
2.4
3.0
2.8
2.7
2.6
2.4
3.1
2.9
2.8
2.6
2.5
3.2
3.0
2.9
2.7
2.6
3.3
3.1
2.9
2.8
2.6
3.4
3.2
3.0
2.9
2.7
3.5
3.3
3.1
3.0
2.8
45
46
47
48
49
50
51
52
53
54
2.0
1.9
1.8
1.8
1.7
2.0
2.0
1.9
1.8
1.7
2.1
2.0
1.9
1.8
.7
2.1
2.0
.9
.9
.8
2.2
2.1
2.0
1.9
1.8
2.2
2.1
2.0
1.9
1.8
2.3
2.2
2.1
2.0
1.9
2.3
2.2
2.1
2.0
1.9
2.4
2.3
2.1
2.0
1.9
2.4
2.3
2.2
2.1
2.0
2.5
2.4
2.2
2.1
2.0
2.6
2.4
2.3
2.2
2.1
2.6
2.5
2.4
2.2
2.1
50
51
52
53
54
55
56
57
58
59
60
oo
56
57
58
59
60
1.6
1.5
1.5
1.4
1.4
1.3
1.6
1.6
1.5
1.4
1.4
1.3
.7
.6
.5
.5
1.4
1.3
.7
.6
1.5
1.5
1.4
1.3
1.7
1.6
1.6
1.5
1.4
1.4
1.8
1.7
1.6
1.5
1.5
1.4
1.8
1.7
1.6
1.5
1.5
1.4
1.8
1.7
1.6
1.6
1.5
1.4
1.9
1.8
1.7
1.6
1.5
1.4
1.9
1.8
1.7
1.6
1.5
1.5
.9
.8
.7
.6
.6
.5
2.0
1.9
1.8
1.7
1.6
1.5
2.0
1.9
1.8
1.7
1.6
1.5
12°
13°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
Declination of the same name as the latitude; upper transit; reduction additive .
Page 706] TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of the same name as the latitude; upper transit; reduction addltlTC.
Lati
tude.
25°
26°
27°
28°
29°
30°
31°
32°
33°
34°
35°
36°
37°
0
0
1
2
3
4
it
3.0
3.1
3.2
3.3
3.4
2.9
3.0
3.1
3.2
3.3
2.8
2.9
3.0
3.0
3.1
2.7
2.8
2.8
2.9
3.0
2.6
2.7
2.7
2.8
2.9
o
0
1
2
3
4
4.2
4.4
4.6
4.7
5.0
4.0
4.2
4.3
4.5
4.7
3.9
4.0
4.1
4.3
4.5
3.7
3.8
4.0
4.1
4.3
3.5
3.7
3.8
3.9
4.1
3.4
3.5
3.6
3.7
3.9
3.3
3.4
3.5
3.6
3.7
3.1
3.2
3.3
3.4
3.5
5
6
7
8
9
5.2
5.4
5.7
6.0
6.4
4.9
5.1
5.4
5.7
6.0
4.7
4.9
5.1
5.3
5.6
4.4
4.6
4.8
5.0
5.3
4.2
4.4
4.6
4.8
5.0
4.0
4.2
4.3
4.5
4.7
3.8
4.0
4.1
4.3
4.4
3.7
3.8
3.9
4.1
4.2
3.5
3.6
3.7
3.9
4.0
3.3
3.5
3.6
3.7
3.8
3.2
3.3
3.4
3.5
3.6
3.1
3.2
3.3
3.4
3.5
3.0
3.0
3.1
3.2
3.3
5
6
7
8
9
10
11
12
13
14
6.8
7.2
7.7
8.3
9.1
6.3-
6.7
7.1
7.6
8.2
5.9
6.2
6.6
7.1
7.6
5.5
5.8
6.2
6.5
7.0
5.2
5.5
5.8
6.1
6.4
4.9
5.1
5.4
5.7
6.0
4.6
4.8
5.1
5.3
5.6
4.4
4.6
4.8
5.0
5.2
4.2
4.3
4.5
4.7
4.9
3.9
4.1
4.3
4.4
4.6
3.8
3.9
4.0
4.2
4.4
3.6
3.7
3.8
4.0
4.1
3.4
3.5
3.6
3.8
3.9
10
11
12
13
14
15
16
17
18
19
9.9
10.9
12.2
13.9
16.1
8.9
9.8
10.8
12.1
13.7
8.1
8.8
9.6
10.6
11.9
7.4
8.0
8.7
9.5
10.5
6.9
7.3
7.9
8.6
9.4
6.4
6.8
7.2
7.8
8.4
5.9
6.3
6.7
7.1
7.7
5.5
5.8
6.2
6.6
7.0
5.2
5.4
5.7
6.1
6.4
4.8
5.1
5.3
5.6
6.0
4.5
4.8
5.0
5.2
5.5
4.3
4.5
4.7
4.9
5.1
4.0
4.2
4.4
4.6
4.8
15
16
17
18
19
20
21
22
23
24
19.2
23.8
15.9
18.9
23.5
13.5
15.6
18.6
23.1
11.7
13.3
15.4
18.3
22.7
10.3
11.5
13.1
15.1
18.0
9.2
10.2
11.3
12.8
14.9
8.3
9.1
10.0
11.1
12.6
7.5
8.2
8.9
9.8
10.9
6.9
7.4
8.0
8.7
9.6
6.3
6.8
7.3
7.9
8.6
5.8
6.2
6.6
7.1
7.7
5.4
5.7
6.1
6.5
7.0
5.0
5.3
5.6
6.0
6.4
20
21
22
23
24
25
26
27
28
29
22.3
22.3
17.7
21.9
14.6
17.4
21.5
12.4
14.3
17.0
21.1
10.7
12.1
14.0
16.7
20.6
9.4
10.5
11.9
13.8
16.3
8.4
9.2
10.3
11.7
13.5
7.5
8.2
9.1
10.1
11.4
6.8
7.4
8.1
8.9
9.9
25
26
27
28
29
30
31
32
33
34
17.7
14.6
12.4
10.7
9.4
21.9
17.4
14.3
12.1
10.5
21.5
17.0
14.0
11.9
21.1
16.7
13.8
20.6
16.3
20.2
20.2
16.0
19.8
13.2
.15.6
19.3
11.1
12.9
15.3
18.9
30
31
32
33
34
35
36
37
38
39
8.4
7.5
6.8
6.2
5.7
9.2
8.2
7.4
6.7
6.1
10.3
9.1
8.1
7.2
6.5
11.7
10.1
8.9
7.9
7.1
13.5
11.4
9.9
8.7
7.7
16.0
13.2
11.1
9.6
8.5
19.8
15.6
12.9
10.9
9.4
19.3
15.3
12.6
10.6
18.9
14.9
12.2
18.4
14.5
17.9
35
36
37
38
39
40
41
42
43
44
5.3
4.9
4.5
4.2
3.9
5.6
5.2
4.8
4.4
4.1
6.0
5.5
5.0.
4.6
4.3
6.4
5.8
5.3
4.9
4.5
6.9
6.2
5.7
5.2
4.8
7.5
6.7
6.1
5.5
5.1
8.2
7.3
6.6
5.9
5.4
9.2
8.0
7.1
6.4
5.8
10.4
8.9
7.8
6.9
6.2
11.9
10.1
8.7
7.6
6.7
14.1
11.6
9.8
8.5
7.4
17.4
13.8
11.3
9.5
8.2
17.0
13.4
11.0.
9.3
40
41
42
43
44
45
46
47
48
49
3.7
3.5
3.3
3.1
2.9
3.8
3.6
3.4
3.2
3.0
4.0
3.7
3.5
3.3
3.1
4.2
3.9
3.6
3.4
3.2
4.4
4.1
3.8
3.5
3.3
4.7
4.3
4.0
3.7
3.4
4.9
4.5
4.2
3.9
3.6
5.2
4.8
4.4
4.0
3.7
5.6
5.1
4.6
4.3
3.9
6.0
5.4
4.9
4.5
4.1
6.6
5.9
5.3
4.8
4.4
7.2
6.4
5.7
5.1
4.6
8.0
7.0
6.2
5.5
5.0
45
46
47
48
49
50
51
52
53
54
2.7
2.6
2.4
2.3
2.2
2.8
2.6
2.5
2.3
2.2
2.9
2.7
2.6
2.4
2.3
3.0
2.8
2.6
2.5
2.3
3.1
2.9
2.7
2.5
2.4
3.2
3.0
o £>
2^6
2.5
3.3
3.1
2.9
2.7
2.5
3.5
3.2
3.0
2.8
2.6
3.6
3.4
3.1
2.9
2.7
3.8
3.5
3.2
3.0
2.8
4.0
3.7
3.4
3.1
2.9
4.2
3.9
3.6
3.3
3.0
4.5
4.1
3.7
3.4
3.2
50
51
52
53
54
55
56
57
58
59
60
2.0
1.9
1.8
1.7
1.6
1.6
2.1
2.0
1.9
1.8
1.7
1.6
2.1
2.0
1.9
1.8
1.7
1.6
2.2
2.1
2.0
1.8
1.7
1.6
2.3
2.1
2.0
1.9
1.8
1.7
2.3
2.2
2.0
1.9
1.8
1.7
2.4
2.2
2.1
2.0
1.9
1.7
2.4
2.3
2.2
2.0
1.9
1.8
2.5
2.4
2.2
2.1
1.9
1.8
2.6
2.4
2.3
2.1
2.0
1.9
2.7
2.5
2.3
2.2
2.0
1.9
2.8
2.6
2.4
2.3
2.1
2.0
2.9
2.7
2.5
2.3
2.2
2.0
55
56
57
58
59
60
25°
26°
27°
28°
29°
30°
31°
32°
33°
34°
35°|
36°
37°
Declination of the same name as the latitude; upper transit; reduction additive.
TABLE 26. [Page 707
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of the same name as the latitude; upper transit; reduction additive.
Lati
tude.
38°
39°
40°
41°
4oo 430
44°
45°
46°
47° 48°
49°
50°
• o
0
1
2
3
4
2.5
2.6
2.6
2.7
2.8
1.8
1.8
1.8
1.9
1.9
1.7
1.7
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.8
o
0
1
2
3
4
2.4
2.5
2.5
2.6
2.7
2.3
2.4
2.4
2.5
2.6
2.3
2.3
2.4
2.4
2.5
2.2
2.2
2.3
2.3
2.4
2.1
2.2
2.2
2.2
2.3
2.0
2.1
2.1
2.2
2.2
2.0
2.0
2.0
2.1
2.1
1.9
1.9
2.0
2.0
2.0
1.8
1.9
1.9
1.9
2.0
5
6
7
8
9
2.8
2.9
3.0
3.1
3.2
2.7
2.8
2.9
2.9
3.0
2.6
2.7
2.7
2.8
2.9
2.5
2.6
2.6
2.7
2.8
2.4
2.5
2.5
2.6
2.7
2.3
2.4
2.4
2.5
2.5
2.2
2.3
2.3
2.4
2.4
2.2
2.2
2.2
2.3
2.3
2.1
2.1
2.2
2.2
2.2
2.0
2.0
2.1
2.1
2.2
1.9
2.0
2.0
2.0
2.1
1.9
1.9
1.9
1.9
2.0
1.8
1.8
1.8
1.9
1.9
5
6
7
8
9
10
11
12
13
14
3.3
3.4
3.5
3.6
3.7
3.1
3.2
3.3
3.4
3.5
3.0
3.1
3.1
3.2
3.3
2.8
2.9
3.0
3.1
3.2
2.7
2.8
2.9
2.9
3.0
2.6
2.7
2.7
2.8
2.9
2.5
2.6
2.6
2.7
2.7
2.4
2.4
2.5
2.6
2.6
2.3
2.3
2.4
2.4
2.5
2.2
2.2
2.3
2.3
2.4
2.1
2.1
2.2
2.2
2.3
2.0
2.1
2.1
2.1
2.2
1.9
2.0
2.0
2.0
2.1
10
11
12
13
14
15
16
17
18
19
3.8
4.0
4.1
4.3
4.5
3.6
3.8
3.9
4.1
4.2
3.4
3.6
3.7
3.8
4.0
3.3
3.4
3.5
3.6
3.7
3.1
3.2
3.3
3.4
3.5
3.0
3.0
3.1
3.2
3.3
2.8
2.9
3.0
3.1
3.2
2.7
2.8
2.8
2.9
3.0
2.6
2.6
2.7
2.8
2.8
2.4
2.5
2.6
2.6
2.7
2.3
2.4
2.4
2.5
2.6
2.2
2.3
2.3
2.4
2.4
2.1
2.2
2.2
2.3
2.3
15
16
17
18
19
20
21
22
23
24
4.7
4.9
5.2
5.5
5.8
4.4
4.6
4.8
5.1
5.4
4.1
4.3
4.5
4.7
5.0
3.9
4.0
4.2
4.4
4.6
3.7
3.8
4.0
4.1
4.3
3.5
3.6
3.7
3.9
4.0
3.3
3.4
3.5
3.6
3.8
3.1
3.2
3.3
3.4
3.5
2.9
3.0
3.1
3.2
3.3
2.8
2.9
2.9
3.0
3.1
2.6
2.7
2.8
2.9
3.0
2.5
2.6
2.6
2.7
2.8
2.4
2.4
2.5
2.6
2.6
20
21
22
23
24
25
26
27
28
29
6.2
6.7
7.2
7.9
8.7
5.7
6.1
6.5
7.1
7.7
5.3
5.6
6.0
6.4
6.9
4.9
5.2
5.5
5.8
6.2
4.5
4.8
5.0
5.3
5.7
4.2
4.4
4.6
4.9
5.2-
3.9
4.1
4.3
4.5
4.8
3.7
3.8
4.0
4.2
4.4
3.5
3.6
3.7
3.9
4.1
3.3
3.4
3.5
3.6
3.8
3.1
3.2
3.3
3.4
3.5
2.9
3.0
3.1
3.2
3.3
2.7
2.8
2.9
3.0
3.1
25
26
27
28
29
30
31
32
33
34
9.6
10.9
12.6
14.9
18.4
8.5
9.4
10.6
12.2
14.5
7.5
8.2
9.2
10.4
11.9
6.7
7.3
8.0
8.9
10.1
6.1
6.6
7.1
7.8
8.7
5.5
5.9
6.4
6.9
7.6
5.1
5.4
5.8
6.2
6.7
4.7
4.9
5.2
5.6
6.0
4.3
4.5
4.8
5.1
5.4
4.0
4.2
4.4
4.6
4.9
3.7
3.9
4.0
4.3
4.5
3.4
3.6
3.7
3.9
4.1
3.2
3.3
3.5
3.6
3.8
30
31
32
33
34
35
36
37
38
39
17.9
14.1
17.4
11.6
13.8
17.0
9.8
11.3
13.4
16.5
8.5
9.5
11.0
13.0
16.0
7.4
8.2
9.3
10.7
12.6
6.6
7.2
8.0
9.0
10.3
5.9
6.4
7.0
7.7
8.7
5.3
5.7
6.2
6.8
7.5
4.8
5.1
5.5
6.0
6.5
4.4
4.6
5.0
5.3
5.8
4.0
4.2
4.5
4.8
5.1
35
36
37
38
39
40
41
42
43
44
16.5
13.0
10.7
16.0
12.6
15.5
15. 5
12.2
15.0
10.0
11.8
14.5
8.4
9.7
11.4
14.0
7.2
8.1
9.3
11.0
13.6
6.3
7.0
7.9
9.0
10.6
5.6
6.1
6.7
7.6
8.7
40
41
42
43
44
45
46
47
48
49
9.0
7.7
6.8
6.0
5.3
10.3
8.7
7.5
6.5
5.8
12.2
10.0
8.4
7.2
6.3
15.0
11.8
9.7
8.1
7.0
14.5
11.4
9.3
7.9
14.0
11.0
9.0
13.6
10.6
13.1
13.1
10.2
12.6
45
46
47
48
49
50
51
52
53
54
4.8
4.3
3.9
3.6
3.3
5.1
4.6
4.2
3.8
3.5
5.6
5.0
4.5
4.0
3.7
6.1
5.4
4.8
4.3
3.9
6. 7
5.9
5.2
4.6
4.1
7.6
6.5
5.7
5.0
4.4
8.7
7.3
6.3
5.4
4.8
10.2
8.4
7.0
6.0
5.2
12.6
9.9
8.0
6.7
5.8
12.1
9.5
7.7
6.5
11.6
9.1
7.4
11.1
8.7
10.6
50
51
52
53
54
55
56
57
58
59
60
3.0
2.8
2.6
2.4
2.2
2.1
3.2
2.9
2.7
2.5
2.3
2.1
3.3
3.1
2.8
2.6
2.4
2.2
3.5
3.2
2.9
2.7
2.5
2.3
3.7
3.4
3.1
2.8
2.6
2.4
4.0
3.6
3.2
2.9
2.7
2.5
4.3
3.8
3.4
3.1
2.8
2.6
4.6
4.1
3.6
3.3
3.0
2.7
5.0
4.4
3.9
3.5
3.1
2.8
5.5
4.8
4.2
3.7
3.3
3.0
6.2
5.3
4.6
4.0
3.6
3.2
7.1
5.9
5.0
4.4
3.8
3.4
8.3
6.8
5.6
4.8
4.2
3.6.
55
56
57
58
59
60
38°
39°
40°
41°
42°
43°
44°
45°
46°
47®
48°
49°
60°
Declination of the same name as the latitude; upper transit; reduction additive.
Page 708] TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of the same name as the latitude; upper transit; reduction additive.
Lati
tude.
61°
62°
53°
54°
65°
56°
57°
68°
69°
60°
61°
62°
63°
o
0
1
2
3
4
//
1.6
1.6
1.6
1.7
1.7
ii
1.5
1.6
1.6
1.6
1.6
ii
1.5
1.5
1.5
1.5
1.6
n
1.4
1.4
1.5
1.5
1.5
u
1.4
1.4
1.4
1.4
1.5
n
1.3
1.3
1.4
1.4
1.4
n
1.3
1.3
1.3
1.3
1.3
n
1.2
1.2
1.3
1.3
1.3
//
1.2
1.2
1.2
1.2
1.2
n
1.1
1.2
1.2
1.2
1.2
II
1.1
1.1
1.1
1.1
1.1
n
1.0
1.1
1.1
1.1
1.1
n
1.0
1.0
1.0
1.0
1.0
o
0
1
2
3
4
5
6
7
8
9
.7
.7
.8
.8
.8
1.7
. 1.7
1.7
1.7
1.8
1.6
1.6
1.6
1.7
1.7
1.5
1.5
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.6
.4
.4
.4
.5
.5
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.3
1.1
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
5
6
7
8
9
10
11
12
13
14
1.9
1.9
1.9
2.0
2.0
1.8
1.8
1.8
1.9
1.9
1.7
1.7
1.8
1.8
1.8
1.6
1.7
.7
.7
.7
1.6
1.6
1.6
1.6
1.7
.5
.5
.6
.6
.6
1.4
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.5
1.3
1.3
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
.2
.2
.2
.3
.3
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.2
10
11
12
13
14
15
16
17
18
19
2.0
2.1
2.1
2.2
2.2
1.9
2.0
2.0
2.1
2.1
1.9
1.9
1.9
2.0
2.0
.8
.8
.8
1.9
1.9
1.7
1.7
1.8
1.8
1.8
.6
.6
.7
1.7
1.7
1.5
1.6
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.6
1.4
1.4
1.5
1.5
1.5
1.3
1.4
1.4
1.4
1.4
.3
.3
.3
.3
.4
1.2
1.2
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
15
16
17
18
19
20
21
22
23
24
2.3
2.3
2.4
2.4
2.5
2.1
2.2
2.2
2.3
2.4
2.0
2.1
2.1
2.2
2.2
1.9
2.0
2.0
2.1
2.1
1.9
1.9
1.9
2.0
2.0
1.8
1.8
1.8
1.9
1.9
1.7
.7
.7
.8
.8
1.6
1.6
1.6
1.7
1.7
1.5
1.5
1.6
1.6
1.6
1.4
1.5
1.5
1.5
1.5
.4
.4
.4
1.4
1.5
1.3
1.3
1.3
1.4
1.4
1.2
1.2
1.3
1.3
1.3
20
21
22
23
24
25
26
27
28
29
2.6
2.6
2.7
2.8
2.9
2.4
2.5
2.6
2.6
2.7
2.8
2.9
3.0
3.1
3.2
2.3
2.3
2.4
2.5
2.5
2.2
2.2
2.3
2.3
2.4
2.0
2.1
2.1
2.2
2.3
1.9
2.0
2.0
2.1
2.1
.8
1.9
1.9
2.0
2.0
1.7
1.8
1.8
1.8
1.9
1.6
1.7
1.7
1.7
1.8
1.6
1.6
1.6
1.6
1.7
1.5
1.5
1.5
1.5
1.6
1.4
1.4
1.4
1.5
1.5
1.3
1.3
1.4
1.4
1.4
25
26
27
28
29
30
31
32
33
34
3.0
3.1
3.2
3.4
3.5
2.6
2.7
2,8
2.9
3.0
2.5
2.5
2.6
2.7
2.8
2.3
2.4
2.4
2.5
2.6
2.2
2.2
2.3
2.4
2.4
2.0
2.1
2.2
2.2
2.3
1.9
2.0
2.0
2.1
2.1
1.8
1.9
1.9
1.9
2.0
1.7
1.7
1.8
1.8
1.9
1.6
1.6
1.7
1.7
1.7
1.5
1.5
1.6
1.6
1.6
1.4
1.4
1.5
1.5
1.5
30
31
32
33
34
35
36
37
38
39
3.7
3.9
4.1
4.3
4.6
3.4
3.6
3.7
3.9
4.2
3.1
3.3
3.4
3.6
3.8
2.9
3.0
3.2
3.3
3.5
2.7
2.8
2.9
3.0
3.2
2.5
2.6
2.7
2.8
2.9
2.3
2.4
2.5
2.6
2.7
2.2
2.3
2.3
2.4
2.5
2.0
2.1
2.2
2.2
2.3
1.9
2.0
2.0
2.1
2.1
1.8
1.8
1.9
1.9
2.0
1.7
1.7
1.7
1.8
1.8
1.6
1.6
1.6
1.7
1.7
35
36
37
38
39
40
41
42
43
44
5.0
5.4
5.9
6.5
7.3
4.5
4.8
5.2
5.7
6.3
4.0
4.3
•1.6
5.0
5.4
3.7
3.9
4.1
4.4
4.8
3.3
3.5
3.7
4.0
4.3
3.1
3.2
3.4
3.6
3.8
2.8
2.9
3.1
3.2
3.4
2.6
2.7
2.8
2.9
3.1
2.4
2.5
2.6
2.7
2.8
2.2
2.3
2.4
2.5
2.6
2.0
2.1
2.2
2.3
2.3
1.9
1.9
2.0
2.1
2.2
1.8
1.8
1.9
1.9
2.0
40
41
42
43
44
45
46
47
48
49
8.4
9.9
H
7.0
8.0
-JfcS
6.0
6.7
7.7
9.1
11.1
5.2
5.8
6.5
7.4
8.7
4.6
5.0
5.5
6.2
7.1
4.1
4.4
4.8
5.3
5.9
3.6
3.9
4.2
4.6
5.0
3.3
3.5
3.7
4.0
4.4
3.0
3.1
3.3
3.6
3.8
2.7
2.8
3.0
3.2
3.4
2.4
2.6
2.7
2.8
3.0
2.2
2.3
2.4
2.6
2.7
2.0
2.1
2.2
2.3
2.4
45
46
47
48
49
50
51
52
53
54
10.6
8.3
10.2
6.8
7.9
9.7
5.6
6.4
7.6
9.2
4.8
5.4
6.1
7.2
8.8
4.2
4.6
5.1
5.9
6.8
3.6
4.0
4.3
4.9
5.5
3.2
3.5
3.8
4.1
4.6
2.9
3.0
3.3
3.6
3.9
2.6
2.7
2.9
3.1
3.4
50
51
52
53
54
55
56
57
58
59
60
10.2
7.9
6.4
5.4
4.6
4.0
9.7
7.6
6.1
5.1
4.3
9.2
7.2
5.9
4.9
8.8
6.8
5.5
8.3
6.5
7.9
8.3
6.5
7.9
5.3
6.1
7.4
4.3
5.0
5.8
7.0
3.7
4.1
4.7
5.4
6.6
55
56
57
58
59
60
51°
52°
53°
54°
55°
56°
67°
58°
69°
60°
61°
62°
63°
Declination of the same name as the latitude; upper transit; reduction additive.
TABLE 26. [Page 709
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of a different name from the latitude; upper transit; reduction additive.
Lati
tude.
0°
1°
2°
3°
4°
6°
6°
7°
8°
9°
10°
11°
a
22.4
18.7
16.0
14.0
12.5
ii
18.7
16.0
14.0
12.5
11.2
u
16.0
14.0
12.5
11.2
10.2
14.0
12.4
11.2
10.2
9.3
ii
12.4
11.2
10.2
9.3
8.6
11.1
10.1
9.3
8.6
8.0
10.1
9.3
8.6
8.0
7.4
o
0
1
2
3
4
0
1
2
3
4
28.1
28.1
22.4
28.1
22.4
18.7
28.1
22.4
18.7
16.0
28.1
22.4
18.7
16.0
14.0
5
6
7
8
9
22.4
18.7
16.0
14.0
12.4
18.7
16.0
14.0
12.4
11.2
16.0
14.0
12.4
11.2
10.2
14.0
12.5
11.2
10.2
9.3
12.5
11.2
10.2
9.3
8.6
11.2
10.2
9.3
8.6
8.0
10.2
9.3
8.6
8.0
7.5
9.3
8.6
8.0
7.5
7.0
8.6
8.0
7.5
7.0
6.6
8.0
7.5
7.0
6.6
6.2
7.4
7.0
6.6
6.2
5.9
7.0
6.6
6.2
5.9
5.6
5
6
7
8
9
10
11
12
13
14
11.1
10.1
9.2
8.5
7.9
10.1
9.3
8.5
7.9
7.4
9.3
8.6
7.9
7.4
6.9
8.6
8.0
7.4
6.9
6.5
8.0
7.4
7.0
6.5
6.2
7.4
7.0
6.5
6.2
5.8
7.0
6.6
6.2
5.8
5.5
6.6
6.2
5.9
5.6
5.3
6.2
5.9
5.6
5.3
5.0
5.9
5.6
5.3
5.0
•4.8
5.6
5.3
5.0
4.8
4.6
5.3
5.1
4.8
4.6
4.4
10
11
12
13
14
15
16
17
18
19
7.3
6.8
6.4
6.0
5.7
6.9
6.5
6.1
5.7
5.4
6.5
6.1
5.8
5.5
5.2
6.1
5.8
5.5
5.2
4.9
5.8
5.5
5.2
5.0
4.7
5.5
5.2
5.0
4.8
4.5
5.3
5.0
4.8
4.6
4.4
5.0
4.8
4.6
4.4
4.2
4.8
4.6
4.4
' 4.2
4.0
4.6
4.4
4.2
4.1
3.9
4.4
4.2
4.1
3.9
3.8
4.2
4.1
3.9
3.8
3.6
15
16
17
18
19
20
21
22
23
24
5.4
5.1
4.9
5.1
4.9
4.7
4.9
4.7
4.5
4.7
4.5
4.3
4.5
4.3
4.1
4.3
4.2
4.0
3.8
3.7
4.2
4.0
3.9
3.7
3.6
4.0
3.9
3.7
3.6
3.5
3.9
3.7
3.6
3.5
3.4
3.8
3.6
3.5
3.4
3.3
3.6
3.5
3.4
3.3
3.2
3.5
3.4
3.3
3.2
3.1
20
21
22
23
24
4.4
4.2
4.1
3.9
3.8
25
26
27
28
29
4.2
4.0
3.9
3.7
3.5
4.1
3.9
3.7
3.6
3.4
3.9
3.8
3.6
3.5
3.3
3.8
3.6
3.5
3.4
3.2
3.7
3.5
3.4
3.3
3.1
3.5
3.4
3.3
3.2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.8
3.1
3.0
2.9
2.8
2.8
3.1
3.0
2.9
2.8
2.7
3.0
2.9
2.8
2.7
2.6
25
26
27
28
29
30
31
32
33
34
3.4
3.3
3.2
3.0
2.9
3.3
3.2
3.1
2.9
2.8
3.2
3.1
3.0
2.9
2.8
3.1
3.0
2.9
2.8
2.7
3.0
2.9
2.8
2.7
2.6
3.0
2.9
2.8
2.7
2.6
2.9
2.8
2.7
2.6
2.5
2.8
2.7
2.6
2.5
2.5
2.7
2.6
2.6
2.5
2.4
2.7
2.6
2.5
2.4
2.4
2.6
2.5
2.5
2.4
2.3
2.5
2.5
2.4
2.3
2.3
30
31
32
33
34
35
36
37
38
39
2.8
2.7
2.6
2.5
2.4
2.7
2.6
2.5
2.5
2.4
2.7
2.6
2.5
2.4
2.3
2.6
2.5
2.4
2.4
2.3
2.5
2.5
2.4
2.3
2.2
2.5
2.4
2.3
2.3
2.2
2.4
2.4
2.3
2.2
2.1
2.4
2.3
2.2
2.2
2TT
2.3
2.3
2.2
2.1
2.1
2.3
2.2
2.2
2.1"
2.0
1.9
.9
.8
.7
2.2
2.2
2.1
2.1
2.0
2.2
2.1
2.1
2.0
2.0
35
36
37
38
39
40
41
42
43
44
2.3
2.3
2.2
2.1
2.0
2.3
2.2
2.1
2.1
2.0
2.2
2.2
2.1
2.0
2.0
2.2
2.1
2.1
2.0
.9
2.2
2.1
2.0
2.0
1.9
2.1
2.1
2.0
1.9
1.9
2.1
2.0
2.0
.9
.8
2.0
2.0
1.9
1.9
1.8
2.0
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1.8
1.7
1.9
1.8
1.8
1.7
1.7
40
41
42
43
44
45
46
47
48
49
2.0
1.9
.8
.8
. 7
1.9
1.9
1.8
1.7
1.7
.9
.8
.8
.7
.7
.9
.8
.7
.7
.6
1.8
1.8
1.7
1.7
1.6
1.8
1.7
1.7
1.6
1.6
.8
.7
.7
.6
.6
1.7
1.7
1.6
1.6
1.5
1.7
1.7
1.6
1.6
1.5
.7
.6
.6
.6
1.5
1.7
1.6
1.6
1.5
1.5
1.6
1.6
• 1.6
1.5
1.5
45
46
47
48
49
50
51
52
53
54
.6
.6
.5
.5
.4
1.6
1.6
1.5
1.5
1.4
.6
.6
.5
.4
.4
.6
.5
.5
.4
1.4
1.6
1.5
1.5
1.4
1.4
.5
.5
.4
A
.3
.5
.5
.4
1.4
1.3
1.5
1.5
1.4
1.4
1.3
1.5
1.4
1.4
1.3
1.3
1.5
1.4
1.4
1.3
1.3
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
50
51
52
53
54
55
56
57
58
59
60
1.4
1.3
1.3
1.2
1.2
1.1
1.4
1.3
1.3
1.2
1.2
1.1
.3
.3
.3
.2
1.2
1.1
1.3
1.3
1.2
1.2
1.2
1.1
1.3
1.3
1.2
1.2
1.1
1.1
.3
.3
.2
2
!i
.1
1.3
1.2
1.2
1.2
1.1
1.1
1.3
1.2
1.2
1.1
1.1
1.1
1.3
1.2
1.2
1.1
1.1
1.0
1.2
1.2
1.2
1.1
1.1
1 0
9°
1.2
1.2
1.1
1.1
1.1
1.0
1.2
1.2
1.1
1.1
1.1
1.0
55
56
57
58
59
60
0°
1°
2°
3°
4°
6°
6°
7°
8°
10°
11°
Declination of a different name from the latitude; upper transit; reduction additive.
Page 710] TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of a different name from the latitude; upper transit; reduction additive.
Lati
tude.
12°
13°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
0
0
1
2
3
4
9.2
8.5
7.9
7.4
7.0
n
8.5
7.9
7.4
6.9
6.5
H
7.9
7.4
6.9
6.5
6.2
n
7.3
6.9
6.5
6.1
5.8
6.8
6.5
6.1
5.8
5.5
n
6.4
6.1
5.8
5.5
5.2
n
6.0
5.7
5.5
5.2
5.0
n
5.7
5.4
5.2
4.9
4.7
II
5.4
n
5.1
n
4.9
n
4.6
4.4
o
0
1
2
4J
6
H
9j
4.9
4.7
4.5
4.7
4.5
4.3
4.5
4.3
4.1
4.3
4.1
4.0
4.1
3.9
3.8
5
6
7
8
9
6.5
6.2
5.9
5.6
5.3
6.2
5.8
5.6
5.3
5.0
5.8
5.5
5.3
5.0
4.8
5.5
5.3
5.0
4.8
4.6
5.2
5.0
4.8
4.6
4.4
5.0
4.8
4.6
4.4
4.2
4.8
4.6
4.4
4.2
4.1
4.5
4.4
4.2
4.0
3.9
4.3
4.2
4.0
3.9
3.8
4.2
4.0
3.9
3.7
3.6
4.0
3.9
3.7
3.6
3.5
3.8
3.7
3.6
3.5
3.4
3.7
3.6
3.5
3.4
3.3
10
11
12
13
14
5.0
4.8
4.6
4.4
4.2
4.8
4.6
4.4
4.3
4.1
4.6
4.4
4.3
4.1
3.9
4.4
4.2
4.1
3.9
3.8
4.2
4.1
3.9
3.8
3.7
4.1
3.9
3.8
3.7
3.5
3.9
3.8
3.7
3.5
3.4
3.8
3.6
3.5
3.4
3.3
3.6
3.5
3.4
3.3
3.2
3.5
3.4
3.3
3.2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.8
10
11
12
13
14
15
16
17
18
19
4.1
3.9
3.8
3.7
3.5
3.9
3.8
3.7
3.5
3.4
3.8
3.7
3.5
3.4
3.3
3.7
3.5
3.4
3.3
3.2
3.5
3.4
3.3
3'. 2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.9
3.1
3.0
2.9
2.9
2.8
3.0
2.9
2.8
2.8
2.7
2.9
2.8
2.8
2.7
2.6
2.8
2.8
2.7
2.6
2.6
2.8
2.7
2.6
2.5
2.5
15
16
17
18
19
20
21
22
23
24
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.8
3.1
3.0
2.9
2.8
2.8
3.0
2.9
2.8
2.8
2.7
2.9
2.8
2.8
2.7
2.6
2.9
2.8
2.7
2.6
2.5
2.8
2.7
2.6
2.6
2.5
2.7
2.6
2.6
2.5
2.4
2.6
2.6
2.5
2.4
2.4
2.6
2.5
2.4
2.4
2.3
2.5
2.4
2.4
2.3
2.3
2.4
2.4
2.3
2.3
2.2
20
21
22
23
24
25
26
27
28
29
2.9
2.8
2.7
2.6
2.6
2.8
2.7
2.7
2.6
2.5
2.7
2.7
2.6
2.5
2.4
2.7
2.6
2.5
2.5
2.4
2.6
2.5
2.5
2.4
2.3
2.5
2.5
2.4
2.3
2.3
2.5
2.4
2.4
2.3
2.2
2.4
2.4
2.3
2.2
2.2
2.4
2.3
2.2
2.2
2.1
2.3
2.3
2.2
2.1
2.1
2.3
2.2
2.1
2.1
2.0
2.2
2.1
2.1
2.1
2.0
2.2
2.1
2.1
2.0
2.0
25
26
27 1
28 1
29
30
31
32
33
34
2.5
2.4
2.3
2.3
2.2
2.4
2.4
2.3
2.2
2.2
2.4
2.3
2.2
2.2
2.1
2.3
2.3
2.2
2.1
2.1
2.3
2.2
2.2
2.1
2.0
2.2
2.2
2.1
2.1
2.0
2.2
2.1
2.1
2.0
2.0
2.1
2.1
2.0
2.0
1.9
2.1
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.9
2.0
2.0
1.9
1.9
1.8
2.0
1.9
1.9
1.8
1.8
1.9
1.9
1.8
'1.8
1.8
30
31
32
33
34
35
36
137
38
39
2.2
2.1
2.0
2.0
1.9
2.1
2.1
2.0
1.9
1.9
2.1
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.8
2.0
.9
.9
.8
.8
2.0
1.9
1.9
1.8
1.8
.9
.9
.8
.8
.7
1.9
1.8
1.8
1.8
1.7
1.8
1.8
1.8
1.7
1.7
1.8
1.8
1.7
1.7
1.6
1.8
1.7
1.7
1.7
1.6
1.7
1.7
1.7
1.6,
1.6
1.7
1.7
1.6
1.6
1.6
35
36
37
38
39
40
41
42
43
44
1.9
1.8
1.8
1.7
1.7
1.8
1.8
1.7
1.7
1.6
1.8
1.8
1.7
1.7
1.6
1.8
1.7
1.7
1.6
1.6
.7
.7
.7
.6
.6
1.7
1.7
1.6
1.6
1.5
.7
.6
.6
.6
.5
1.7
1.6
1.6
1.5
1.5
1.6
1.6
1.6
1.5
1.5
1.6
1.6
1.5
1.5
1.5
1.6
1.5
1.5
1.5
1.4
1.6
1.5
1.5
1.4
1.4
1.5
1.5
1.5
1.4
1.4
40
41
42
43
44 1
45
46
47
48
49
1.6
1.6
1.5
1.5
1.4
1.6
1.6
1.5
1.5
1.4
1.6
1.5
1.5
1.4
1.4
1.5
1.5
1.5
1.4
1.4
.5
.5
.4
.4
.4
1.5
1.5
1.4
1.4
1.3
.5
.4
.4
.4
.3
1.5
1.4
1.4
1.4
1.3
1.4
1.4
1.4
1.3
1.3
.4
.4
.3
.3
.3
1.4
1.4
1.3
1.3
1.3
1.4
.3
.3
.3
.2
1.4
1.3
1.3
1.3
1.2
45
46
47
48
49
50
51
52
53
54
~55~1
56
57
58
59
60
50
51
52
53
54
1.4
1.4
1.3
1.3
1.2
1.4
1.3
1.3
1.3
1.2
1.4
1.3
1.3
1.3
1.2
1.3
1.3
1.3
1.2
1.2
.3
.3
1.3
1.2
1.2
1.3
1.3
1.3
1.2
1.2
.3
.3
.2
.2
1.2
1.3
1.2
1.2
1.2
1.1
1.3
1.2
1.2
1.2
1.1
.3
.2
.2
.2
.1
1.2
1.2
1.2
1.1
1.1
.2
.2
.1
.1
.1
1.2
1.2
1.1
1.1
1.1
55
56
57
58
59
60
1.2
1.2
1.1
1.1
1.1
1.0
.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
.1
.1
.0
.0
.0
0.9
1.1
1.0
1.0
1.0
1.0
0.9
.1
.0
.0
.0
0.9
0.9
1.1
1.0
1.0
1.0
0.9
0.9
.1
.1
.0
.0
1.1
1.1
1.0
1.0
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
1.0
1.0
1.0
0.9
12°
13°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
1
Declination of a different name from the latitude; upper transit; reduction additive.
TABLE 26. [Page 711
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of a different name from the latitude; upper transit; reduction additive.
Lati
tude.
25°
26°
27°
28°
29°
30°
31°
32°
83°
34°
86°
36°
87°
0
0
1
2
3
4
//
4.2
4.1
3.9
3.8
3.7
H
4.0
3.9
3.8
3.6
3.5
H
3.9
3.7
3.6
3.5
3.4
n
3.7
3.6
3.5
3.4
3.3
//
3.5
3.4
3.3
3.2
3.2
H
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
u
3.1
3.1
3.0
2.9
2.8
3.0
2.9
2.9
2.8
2.7
2.9
2.8
2.8
2.7
2.6
n
2.8
2.7
2.7
2.6
2.6
n
2.7
2.6
2.6
2.5
2.5
n
2.6
2.6
2.5
2.4
2.4
o
0
1
2
3
4
5
6
7
8
9
3.6
3.4
3.3
3.2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.9
3.1
3.0
2.9
2.8
2.8
3.0
2.9
2.8
2.7
2.7
2.9
2.8
2.7
2.7
2.6
2.8
2.7
2.6
2.6
2.5
2.7
2.6
2.5
2.5
2.4
2.6
2.5
2.5
2.4
2.4
2.5
2.4
2.4
2.3
2.3
2.4
2.4
2.3
2.3
2.2
2.3
2.3
2.2
2.2
2.2
5
6
7
8
9
10
11
12
13
14
3.1
3.0
2.9
2.8
2.7
3.0
2.9
2.8
2.7
2.7
2.9
2.8
2.7
2.7
2.6
2.8
2.7
2.6
2.6
2.5
2.7
2.6
2.6
2.5
2.4
2.6
2.5
2.5
2.4
2.4
2.5
2.5
2.4
2.4
2.3
2.5
2.4
2.3
2.3
2.3
2.4
2.3
2.3
2.2
2.2
2.3
2.3
2.2
2.2
2.1
2.2
2.2
2.2
2.1
2.1
2.2
2.1
2.1
2.1
2.0
2.1
2.1
2.0
2.0
2.0
10
11
12
13
14
15
16
17
18
19
2.7
2.6
2.5
2.5
2.4
2.6
2.5
2.5
2.4
2.4
2.5
2.5
2.4
2.4
2.3
2.5
2.4
2.3
2.3
2.2
2.4
2.3
2.3
2.2
2.2
2.3
2.3
2.2
2.2
2.1
2.3
2.2
2.2
2.1
2.1
2.2
2.2
2.1
2.1
2.0
2.1
2.1
2.1
2.0
2.0
2.1
2.0
2.0
2.0
1.9
2.0
2.0
2.0
1.9
1.9
2.0
1.9
1.9
1.9
1.8
1.9
1.9
1.9
1.8
1.8
15
16
17
18
19
20
21
22
23
24
2.4
2.3
2.3
2.2
2.2
2.3
2.3
2.2
2.2
2.1
2.3
2.2
2.2
2.1
2.1
2.2
2.1
2.1
2.1
2.0
2.1
2.1
2.1
2.0
2.0
2.1
2.0
2.0
2.0
1.9
2.0
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.8
1.9
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1.8
1.8
1.9
1.8
1.8
1.8
.7
1.8
1.8
1.7
1.7
1.7
1.8
1.7
1.7
1.7
1.6
20
21
22
23
24
25
26
27
28
29
2.1
2.1
2.0
2.0
1.9
2.1
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.9
2.0
1.9
1.9
1.9
1.8
1.9
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1.8
1.7
1.8
1.8
1.8
1.7
1.7
.8
.8
1. 7
.7
.7
1.8
.7
.7
.7
.6
1.7
1.7
1.7
1.6
1.6
.7
.7
.6
.6
.6
1.6
1.6
1.6
1.6
1.5
1.6
1.6
1.6
1.5
1.5
25
26
27
28
29
30
31
32
33
34
1.9
1.8
1.8
1.8
1.7
1.8
1.8
1.8
1.7
1.7
1.8
1.8
1.7
1.7
1.7
1.8
1.7
.7
.7
.6
1.7
1.7
1.7
1.6
1.6
1.7
1.7
1.6
1.6
1.6
1.7
1.6
1.6
1.6
1.5
.6
.6
.6
.5
.5
.6
.6
.5
.5
.5
1.6
1.5
1.5
1.5
1.5
.5
.5
.5
.5
1.4
1.5
1.5
1.5
1.4
1.4
1.5
1.5
1.4
1.4
1.4
30
31
32
33
34
35
36
37
38
39
1.7
1.6
1.6
1.6
1.5
1.7
1.6
1.6
.5
.5
1.6
1.6
1.6
1.5
1.5
.6
.6
.5
1.5
1.5
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.4
.5
1.5
1.4
1.4
.5
.4
.4
.4
1.4
•1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.4
1.3
1.3
1.3
1.3
35
36
37
38
39
40
41
42
43
44
1.5
1.5
1.4
1.4
1.4
.5
.4
.4
1.4
.4
1.5
1.4
1.4
1.4
1.3
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.4
1.3
1.3
1.3
1.3
.3
.3
.3
.3
.2
.3
.3
.3
.2
1.2
TT"
1.2
1.1
1.1
1.1
1.3
1.3
1.2
1.2
1.2
1.3
1.3
1.2
1.2
1.2
.3
.2
.2
.2
.2
1.2
1.2
1.2
1.2
1.2
40
41
42
43
44
45
46
47
48
49
1.3
1.3
.3
.2
.2
.3
.3
.3
.2
.2
1.3
1.3
1.2
1.2
1.2
1.3
1.3
1.2
1.2
1.2
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.2
1.2
1.2
.1
.1
.2
.2
.2
.1
.1
1.2
1.2
1.1
1.1
1.1
1.2
1.1
1.1
1.1
1.1
.1
.1
.1
1.1
1.1
1.1
1.1
45
46
47
48
49
50
51
52
53
54
.2
.2
.1
1.1
1.1
.2
1.1
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
.1
.1
.0
.0
.1
.1
1.0
1.1
1.0
1.1
50
51
52
53
54
1.1
1.0
1.1
1.0
1.1
1.0
1.0
1.0
55
56
57
58
59
60
1.0
1.0
1.0
1.0
0.9
1.0
1.0
1.0
0.9
1.0
1.0
1.0
1.0
1.0
1.0
HO"
OO
56
57
58
59
60
0.8
0.8
25°
26°
27°
28°
29°
80°
31°
32°
33°
34°
85°
36°
37°
Declination of the same name as the latitude; lower transit; reduction subtractlye.
Page 712] TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati
tude.
Declination of a different name from thedatitude; upper transit; reduction additive.
Lati
tude.
38°
39°
40°
41°
42°
43°
it ! 45°
46°
47°
48°
49°
50°
0
0
1
2
3
4
//
2.5
2.5
2.4
2.4
2.3
n
2.4
2.4
2.3
2.3
2.2
n
2.3
2.3
2.3
2.2
2.2
n
2.3
2.2
2.2
2.1
2.1
n
2.2
2.1
2.1
2.1
2.0
n
2.1
2.1
2.0
2.0
2.0
m
-A 2.0
2.0 1.9
2.0 1.9
1.9 1.9
~~1,9 | i.S
1.8 1.8
:.8 1.8
1.8 1.7
imii.7
l.flll.7
l.Bh.6
1.1H1.6
1.6*1.6
1.6~1.6
n
1.9
1.9
1.8
1.8
1.8
//
1.8
1.8
1.8
1.8
1.7
n
1.8
1.7
1.7
1.7
1.7
n
1.7
1.7
1.7
1.6
1.6
II
1.7
1.6
1.6
1.6
1.6
0
0
1
2
3
4
5
6
7
8
9
2.3
2.2
2.2
2.1
2.1
2.2
2.2
2.1
2.1
2.0
2.1
2.1
2.0
2.0
2.0
2.1
2.0
2.0
.9
.9
2.0
2.0
1.9
1.9
1.9
.9
.9
.9
1.8
.8>
1.8
1.7
1.7
1.7
1.6
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
5
6
7
8
9
10
11
12
13
14
2.1
2.0
2.0
1.9
1.9
2.0
2.0
.9
.9
.9
1.9
1.9
1.9
1.8
1.8
.9
.8
.8
.8
.8
1.8
1.8
1.8
1.7
1.7
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.5
1.6
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.4
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
10
11
12
13
14
15
16
17
18
19
1.9
1.8
1.8
1.8
1.7
.8
.8
.8
.7
.7
1.8
1.7
1.7
1.7
1.7
1.7
1.7
1.7
1.6
1.6
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.6
1.6
1.5
1.6
1.6
1.5
1.5
1.5
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.4
1.3
1.3
1.3
1.3
15
16
17
18
19
20
21
22
23
24
1.7
.7
.7
.6
.6
1.7
1.6
1.6
1.6
1.6
1.6
.6
.6
.6
.5
1.6
1.6
1.5
1.5
1.5
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.3
1.3
1.2
1.2
1.2
20
21
22
23
24
25
26
27
28
29
.6
.6
.5
.5
.5
1.5
1.5
1.5
1.5
1.4
.5
.5
.5
.4
.4
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.-2
1.2
1.1
1.1
25
26
27
28
29
30
31
32
33
34
30
31
32
33
34
.5
.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.3
.4
.4
1.3
.3
.3
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
35
36
37
38
39
1.3
.3
.3
.3
.2
1.3
1.3
1.3
1.2
1.2
.3
.3
.2
.2
.2
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.2
1.2
1.2
1.1
1.1
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
35
36
37
38
39
40
41
42
43
44
.2
.2
.2
.2
.1
1.2
1.2
1.2
1.1
1.1
.2
.2
1.1
1.1
1.1
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
40
41
42
43
44
45
46
47
48
49
.1
.1
1.1
"oT
45
46
47
48
49
0.9
0.9
0.9
0.8
0.9
0.9
0.9
0.9
0.9
50
51
52
53
54
-09-
0.9
0.9
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.8
0.8
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
50
51
52
53
54
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.9
55
56
57
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.8
0.8
0.7
0.7
0.8
0.8
0.8
0.8
0.7
0.7
0.8
0.8
0.8
0.7
0.7
0.7
0.8
0.8
0.7
0.7
0.7
0.7
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
55
56
57
58
59
60
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
58
59
60
0.8
0.8
0.8
38°
39°
40°
41°
42°
43°
44°
45°
46°
47°
48°
49°
50°
Declination of the same name as the latitude; lower transit; reduction snbtractive.
TABLE 26. [Page 713
Variation of Altitude in one minute from meridian passage.
Lati
Declination of a different name from the latitude; upper transit; reduction additive.
Lati
tude.
tude.
51°
62°
53°
54°
55°
56°
57°
58°
59°
60°
61°
62°
63°
0
0
1
2
3
4
//
1.6
.6
.5
.5
.5
//
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.4
ft
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
.3
//
1.3
1.3
1.3
1.3
1.3
n
1.3
1.3
1.3
1.2
1.2
H
1.2
1.2
.2
.2
.2
rt
1.2
1.2
1.2
1.1
1.1
n
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0
0
1
2
3
4
5
6
7
8
9
.5
.5
.4
.4
.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
.3
.3
.3
.3
.2
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
.2
.2
.1
.1
.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
5
6
7
8
9
10
11
12
13
14
.4
.4
.4
.3
.3
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
.2
.2
.2
1.2
.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
.1
.1
.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
10
11
12
13
14
15
16
17
18
19
.3
.3
.3
.3
.2
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
.2
.2
.1
.2
1.1
.1
.1
.1
1.1
1.1
1.1
1.1
1.1
.1
!i
1.1
1.0
1.1
.0
.0
.0
.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
15
16
17
18
19
20
21
22
23
24
.2
.2
.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.2
1.2
1.1
1.1
1.1
I.
.1
1.1
.1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
.0
.0
.0
.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.9
0.8
0.8
20
21
22
23
24
25
26
27
28
29
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
25
26
27
28
29
30
31
32
33
34
1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
30
31
32
33
34
0.8
0.7
0.8
35
36
37
38
39
-as"
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
35
36
37
38
39
0.8
0.8
0.8
0.8
0.8
0.8
0.8
40
41
42
43
44
~O"
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
40
41
42
43
44
0.9
0.8
0.8
0.8
0.9
0.9
0.8
0.9
0.9
45
46
47
48
49
0.9
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.8
0.7
0.7
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.7
0.7
0.6
0.6
0.6
45
46
47
48
49
50
51
52
53
54
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.8
0.7
0.7
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.7
0.7
0.7
0.6
0.6
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
50
51
52
53
54
55
56
57
58
59
60
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.7
0.7
0.7
0.7
0.6
0.6
0.7
0.7
0.7
0.7
0.6
0.6
0.7
0.7
0.7
0.6
0.6
0.6
0.7
0.7
0.6
0.6
0.6
0.6
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
0.5
55
56
57
58
59
60
51°
52°
53°
54°
65°
56°
57°
58°
69°
60°
61°
62°
63°
Declination of the same name as the latitude; lower transit; reduction subtractlve.
Page 714] TABLE 27.
Reduction to be applied to Altitudes near the Meridian.
Var.
1 min.
(Table
26.)
Time from meridian passage.
Var.
1 min.
(Table
26.)
m. s.
0 30
ra. s.
1 0
m. s.
1 30
m. s.
2 0
m. s.
2 30
m. a.
3 0
m. 8.
3 30
m. s.
4 0
m. s.
4 30
m. 8.
5 0
m. s.
5 30
m. s.
6 0
m. s.
6 30
//
0.1
0.2
0.3
0.4
t n
00
0 0
0 0
0 0
t n
0 0
0 0
0 0
0 0
f n
0 0
0 0
0 1
0 1
t n
0 0
0 1
0 1
0 2
r n
0 1
0 1
0 2
0 2
r n
0 1
0 2
0 3
0 4
t n
0 1
0 3
0 4
0 5
i n
0 2
0 3
0 5
0 6
t n
0 2
0 4
0 6
0 8
0 2
0 5
0 7
0 10
e II
0 3
0 6
0 9
0 12
f n
0 4
0 7
0 11
0 14
r n
0 4
0 8
0 13
0 17
it
0.1
0.2
0. §
0.4
0.5
0.6
0.7
0.8
0.9
0 0
0 0
0 0
0 0
0 0
0 0
0 1
0 1
0 1
0 1
0 1
0 1
0 2
0 2
0 2
0 2
0 2
0 3
0 3
0 4
0 3
0 4
0 4
0 5
0 6
0 4
0 5
0 6
0 7
0 8
0 6
0 7
0 9
0 10
0 11
0 8
0 10
0 11
0 13
0 14
0 10
0 12
0 14
0 16
0 18
0 12
0 15
0 17
0 20
0 22
0 15
0 18
0 21
0 24
0 27
0 18
0 22
0 25
0 29
0 32
0 21
0 25
0 30
0 34
0 38
0.5
0.6
0.7
0.8
0.9
1.0
2.p
3.0
4.0
5.0
0 0
0 0
0 1
0 1
0 1
0 1
0 2
0 3
0 4
0 5
0 2
0 4
0 7
0 9
0 11
0 4
0 8
0 12
0 16
0 20
0 6,
0 12
0 19
0 25
0 31
0 U
0 18
0 27
0 36
0 45
0 12
0 24
0 37
0 49
1 1
0 16
0 32
0 48
1 4
1 20
0 20
0 41
1 1
1 21
1 41
0 25
^§
1 40
2 5
0 30
1 0
1 31
2 1
2 31
0 36
1 12
1 48
2 24
3 0
0 42
1 24
. 2 6
2 49
3 31
r.o
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0 1
0 2
0 2
0 2
0 2
0 6
0 7
0 8
0 9
0 10
0 13
0 16
0 18
0 20
0 22
0 24
0 28
0 32
0 36
0 40
0 37
0 44
0 50
0 56
1 2
0 54
1 3
1 12
1 21
1 30
1 13
1 26
1 38
1 50
2 3
1 36
1 52
2 8
2 24
2 40
2 56
3 12
3 28
3 44
4 0
2 1
2 22
2 42
3 2
3 23
2 30
2 55
3 20
3 45
4 10
3 1
3 32
4 2
4 32
5 2
3 36
4 12
4 48
5 24
6 0
4 13
4 56
5 3&
6 20
7 2
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
0 3
0 3
0 3
0 3
0 4
0 11
0 12
0 13
0 14
0 15
0 25
0 27
0 29
0 31
0 34
0 44
0 48
0 52
0 56
1 0
1 9
1 15
1 21
1 27
1 34
1 39
1 48
1 57
2 6
2 15
2 15
2 27
2 39
2 51
3 4
3 43
4 3
4 23
4 43
5 3
4 35
5 0
5 25
5 50
6 15
5 32
6 3
6 33
7 4
7 34
6 36
7 12
7 48
8 24
9 0
7 45
8 27
9 9
9 51
10 34
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
0 4
0 4
0 4
0 5
0 5
0 16
0 17
0 18
0 19
0 20
0 36
0 38
0 40
0 43
0 45
1 4
1 8
1 12
1 16
1 20
1 40
1 46
1 52
1 59
2 5
2 24
2 33
2 42
2 51
3 0
3 16
3 28
3 40
3 53
4 5
4 16
4 32
4 48
5 4
5 20
5 24
5 44
6 4
6 25
6 45
6 4b
7 5
7 30
7 55
8 20
8 4
8 34
9 4
9 35
10 5
9 36
10 12
10 48
11 24
12 0
11 16
11 58
12 40
13 23
14 5
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
25.0
21.0
22.0
23.0
24.0
25.0
G 5
0 5
0 6
0 6
0 6
0 21
0 22
0 23
0 24
0 25
0 47
0 49
0 52
0 54
0 56
1 24
1 28
1 32
1 36
1 40
2 11
2 17
2 24
2 30
2 36
3 9
3 18
3 27
3 36
3 45
4 17
4 30
4 42
4 54
5 6
5 36
5 52
6 8
6 24
6 40
7 5
7 25
7 46
8 6
8 26
8 45
9 10
9 35
10 0
10 25
10 35
11 5
11 36
12 6
12 36
12 36
13 12
13 48
14 24
15 0
14 47
15 29
16 12
16 54
26.0
27.0
28.0
0 6
0 7
0 7
0 26
0 27
0 28
0 58
1 1
1 3
1 44
1 48
1 52
2 42
2 49
2 55
3 54
4 3
4 12
5 18
5 30
5 43
6 56
7 12
7 28
8 46
9 7
9 27
10 50
11 15
11 40
13 6
26.0
27.0
28.0
TABLE 27. [Page 715
Reduction to be applied to Altitudes near the Meridian.
Var.
Imin.
(Table
26.)
Time from meridian passage.
Var.
1 min.
(Table
26.)
m. s.
7 0
m. s.
1 30
m. a.
8 0
m. s.
8 30
m. s.
9 0
m. s.
9 30
m. s.
10 0
m. s.
10 30
m. s.
11 0
m. s.
11 30
m. &.
12 0
TO. s.
12 30
TO. t.
13 0
H
0.1
0.2
0.3
0.4
i ii
0 5
0 10
0 15
0 20
/ //
0 6
0 11
0 17
0 23
0 6
0 13
0 19
0 26
it
0.1
0.2
0.3
0.4
0 7
0 14
0 22
0 29
0 8
0 16
0 24
0 32
0 9
0 18
0 27
0 36
0 10
0 20
0 30
0 40
0 11
0 22
0 33
0 44
0 12
0 24
0 36
0 48
0 13
0 26
0 40
0 53
0 14
0 29
0 43
0 58
0 16
0 31
0 47
1 2
0 17
0 34
0 51
1 8
0.5
0.6
0.7
0.8
0.9
0 24
0 29
0 34
0 39
0 44
0 28
0 34
0 39
0 45
0 51
0 32
0 38
0 45
0 51
0 57
0 36
0 43
0 51
0 58
1 5
0 40
0 49
0 57
1 5
1 13
0 45
0 54
1 3
1 12
1 21
0 50
1 0
1 10
1 20
1 30
0 55
1 6
1 17
1 28
1 39
1 0
1 13
1 25
1 37
1 49
1 6
1 19
1 33
1 46
1 59
1 12
1 26
1 41
1 55
2 10
1 18
1 34
1 49
2 5
2 21
1 24
1 41
1 58
2 15
2 32
0.5
0.6
0.7
0.8
0.9
,1:4)
§3
3.0
4.0
5.0
0 49
1 38*
2 27
3 16
4 5
0 56
1 52
2 49
3 45
4 41
1 4
2 8
3 12
4 16
5 20
1 12
2 24
3 37
4 49
6 1
1 21
2 42
4 3
5 24
6 45
1 30
3 0
4 30
6 1
7 31
1 40
3 20
5~0
6 40
8 20
1 50
3 40
5 31
7 21
9 11
2 1
4 2
6 3
8 4
10 5
2 12
4 24
6 37
8 49
11 1
2 24
4 48
7 12
9 36
12 0
2 36
5 12
7 49
10 25
13 1
2 49
5 38
8 27
11 16
14 5
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
4 54
5 43
6 32
7 21
8 10
5 37
6 34
7 30
8 26
9 22
6 24
7 28
8 32
9 36
10 40
7 14
8 26
9 38
10 50
12 2'
8 6
9 27
10 48
12 9
13 30
9 1
10 32
12 2
13 32
15 2
10 0
11 40
13 20
15 0
16 40
11 1
12 52
14 42
16 32
18 22
12 6
14 7
16 8
18 9
20 10
13 13.
15 26
17 38
19 50
22 2
14 24
16 48
19 12
21 36
24 0
15 37
18 14
20 50
23 26
26 2
16 54
19 43
22 32
25 21
28 10
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
8 59
9 48
10 37
11 26
12 15
10 19
11 15
12 11
13 7
14 4
11 44
12 48
13 52
14 56
16 0
13 15
14 27
15 39
16 51
18 14
14 51
16 12
17 33
18 54
20 15
16 33
18 3
19 33
21 3
22 34
18 20
20 0
21 40
23 20
25 0
20 13
22 3
23 53
25 43
27 34
22 11
24 12
26 13
28 14
24 15
26 27
28 39
26 24
28 48
28 39
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
13 4
13 53
14 42
15 31
16 20
15 0
15 56
16 52
17 49
18 45
17 4
18 8
19 12
20 16
19 16
20 28
21 40
21 36
22 57
24 18
24 4
25 34
26 40
16.0
17.0
18.0
19.0
20.0
21.0
17 9
21.0
Page 716] TABLE 27.
Reduction to be applied to Altitudes near the Meridian
Var.
Time from meridian passage.
Var.
1 min.
(Table
26.)
(Table
26.)
m. e.
13 30
m. s.
14 0
m. 8.
14 30
m. s.
15 0
m. s.
15 30
TO. s.
16 0
TO. 8.
16 30
TO. 8.
17 0
TO. 8.
17 30
TO. 8,
18 0
TO. S.
18 30
TO. 8.
19 0
TO. 8.
19 30
f ii
038
116
154
232
,n
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
018
036
055
113
020
039
059
1 18
021
042
1 3
124
022
045
1 7
130
024
048
1 12
136
026
051
117
142
027
054
122
149
029
058
127
156
031
1 1
132
2 2
032
1 5
137
210
034
1 8
143
217
036
1 12
148
224
0.5
0.6
0.7
0.8
0.9
131
149
2 8
226
244
138
158
217
237
256
145
2 6
227
248
3 9
152
215
237
3 0
322
2 0
224
248
312
336
2 8
234
259
325
350
216
243
311
338
4 5
224
253
322
351
420
233
3 4
334
4 5
436
242
314
347
419
452
251
325
4 0
434
5 8
3 1
337
413
449
525
310
348
426
5 4
542
0.5
0.6
0.7
0.8
0.9
1.0
2.0
3.0
4.0
5.0
3 2
6 4
9 7
12 9
1511
316
632
948
1314
1620
330
7 0
1030
14 1
1731
345
730
1115
15 0
1845
4 0
8 0
12 1
16 1
20 1
416
832
1248
17 4
2120
432
9 4
1338
18 9
2241
449
938
1427
1916
24 5
5 6
1012
1519
2025
2531
524
1048
1612
2136
27 0
542
1124
17 7
2249
2831
6 1
12 2
18 3
24 4
620
1240
19 1
2521
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
1813
2116
2418
2720
1936
2252
26 8
21 2
2432
28 2
2230
2615
24 1
28 1
2536
2713
6.0
7.0
8.0
9.0
Var.
Time from meridian passage.
Var.
(Table
26.)
m. s.
20 0
m. 8.
20 30
m. s.
21 0
TO. 8.
21 30
TO. S.
22 0
TO. 8.
22 30
TO. S.
23 0
TO. 8.
23 30
TO. 8.
24 0
TO. 8.
24 30
TO. 8.
25 0
TO. 8.
25 30
TO. 8.
26 0
(Table
26.)
0.1
0.2
0.3
0.4
040
1 20
2 0
240
042
124
2 6
248
044
128
212
256
046
132
219
3 5
048
137
225
314
051
141
232
322
053
146
239
332
055
150
246
341
058
155
253
350
1 0
2 0
3 0
4 0
1 2
2 5
3 7
410
1 6
210
315
420
1 8
215
323
430
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
320
4 0
440
520
6 0
330
412
454
536
618
341
425
5 9
553
637
351
437
524
610
656
4 2
450
539
627
716
413
5 4
554
645
736
424
517
610
7 3
756
436
531
627
722
817
448
546
643
741
838
5 0
6 0
7 0
8 0
9 0
512
615
717
820
922
525
630
735
840
945
538
646
753
9 1
10 8
0.5
0.6
0.7
0.8
0.9
1.0
2.0
3.0
4.0
640
1320
20 0
2640
7 0
14 0
21 0
28 1
721
1442
22 3
2924
742
1524
23 7
8 4
16 8
2412
826
1652
2519
849
1738
2627
912
1824
2737
936
1912
2848
10 0
20 0
30 0
1025
2050
1050
2140
11 16
2232
1.0
2.0
3.0
4.0
Note. — The pages formerly occupied with Tables 28A, 28B, 28C, and 28D have been dropped, and
consecutive page numbering is thereby broken.
TABLE 29. [Page 725
Conversion Tables for Nautical and Statute Miles.
Xautical miles into statute miles.
Statute miles into nautical miles.
1 nautical mile or knot= 6,080.20 feet.
1 statute mile = 5,280 feet
1 statute mile =5,2SO feet.
1 nautical mile or knot= 6,080.20 feet.
Nautical
Statute
Nautical
Statute
Statute
Nautical
Statute
Nautical
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
1
1.15
51
58. 729
1
0.87
51
44.288
2
2.30
52
59. 881
2
1.74
52
45. 156
3
3.45
53
61.032
3
2.61
53
46. 025
4
4.61
54
62.184
4
3.47
54
46. 893
5
5.76
55
63.335
5
4.34
55
47. 762
6
6.91
56
64.487
6
5.21
56
48. 630
7
8.06
57
65. 639
7
6.08
57
49. 498
8
9.21
58
66. 790
8
6.95
58
50. 367
9
10.36
59
67. 942
9
7.82
59
51. 235
10
11.52
60
69. 093
10
8.68
60
52. 104
11
12. 667
61
70. 245
11
9.552
61
52. 972
12
13. 819
62
71.396
12
10.421
62
53.840
13
14. 970
63
72.548
13
11. 289
63
54.709
14
16. 122
64
73. 699
14
12. 158
64
55. 577
15
17. 273
65
74. 851
15
13. 026
65
56.445
16
18. 425
66
76.003
16
13.894
66
57.314
17
19. 576
67
77.154
17
14. 763
67
58. 182
18
20. 728
68
78. 306
18
15. 631
68
59. 051
19
21. 880
69
79.457
19
16.499
69
59. 919
20
23. 031
70
80. 609
20
17. 368
70
60. 787
21
24. 183
71
81. 760
21
18. 236
71
61. 656
22
25. 334
72
82. 912
22
19. 105
72
62. 524
23
26. 486
73
84.063
23
19. 973
73
63. 393
24
27. 637
74
85. 215
24
20.841
74
64.261
25
28. 789
75
86. 366
25
21. 710
75
65. 129
26
29. 940
76
87.518
26
22. 578
76
65.998
27
31. 092
77
88. 670
27
23.447
77
66. 866
28
32. 243
78
89. 821
28
24. 315
78
67. 735
29
33. 395
79
90.973
29
25.183
79
68. 603
30
34. 547
80
92. 124
30
26.052
80
69. 471
31
35. 698
81
93. 276
31
26. 920
81
70. 340
32
36. 850
82
94.427
32
27. 789
82
71. 208
33
38. 001
83
95. 579
33
28. 657
83
72. 077
34
39. 153
84
96. 730
34
29.525
84
72. 945
35
40.304
85
97.882
35
30.394
85
73. 813
36
41.456
86
99. 034
36
31. 262
86
74. 682
37
42.607
87
100. 185
37
32. 131
87
75. 550
38
43.759
88
101. 337
38
32. 999
88
76.419
39 44. 911
89
102.488
39
33. 867
89
77. 287
40 ; 46. 062
90
103. 640
40
34. 736
90
78. 155
41 ! 47. 214
91
104. 791
41
35. 604
91
79. 024
42 | 48.365
92
105. 942
42
36.473
92
79. 892
43
49. 517
93
107. 094 •
43
37.341
93
80.760
44
50.668
94
108. 246
44
38. 209
94
81. 629
45
51. 820
95
109. 397
45
39. 078
95
82. 497
46
52. 971
96
110. 549
46
39.946
96
83. 366
47
54.123
97
111. 701
47
40. 814
97
84.234
48
55. 275
98
112. 852
48
41. 683
98
85.102
49
56. 426
99
114.004
49
42. 551
99
85. 971
50
57. 578
100
115. 155
50
43. 420
100
86. 839
61828°— 16 39
Pago 726] TABLE 30.
Conversion Tables for Metric and English Linear Measure.
Metric to English.
Meters.
Feet.
Yards.
Statute miles.
Nautical miles.
I
2
3
4
3.280 833 3
6. 561 666 7
9.842 500 0
13. 123 333 3
1.093 611 1
2.187 222 2
3. 280 833 3
4.374 444 4
0.000 621 369
.001 242 738
. 001 864 106
.002 485 475
0.000 539 593
. 001 079 185
.001 618 778
.002 158 370
5
6
7
8
9
16. 404 166 7
19.685 000 0
22.965 833 3
26. 246 666 7
29.527 500 0
5.468 055 6
6.561 666 7
7.655 277 8
8.748 888 9
9.842 500 0
. 003 106 844
.003 728 213
.004 ,349 582
.004 970 950
. 005 592 319
. 002 697 963
. 003 237 556
.003 777 148
.004 316 741
.004 856 333
English to metric.
No.
Feet to meters.
Yards to meters.
Statute miles to meters.
Nautical miles to meters.
1
2
3
4
0. 304 800 6
0. 609 601 2
0.914 401 8
1.219 202 4
0.914 401 8
1. 828 803 7
2.743 205 5
3.657 607 3
1, 609. 35
3, 218. 70
4, 828. 05
6, 437. 40
1, 853. 25
3, 706. 50
5, 559. 75
7,413.00
5
6
7
8
9
1.524 003 0
1. 828 803 7
2.133 604 3
2.438 404 9
2.743 205 5
4. 572 009 1
5.486 411 0
6. 400 812 8
7.315 214 6
8.229 616 5
8, 046. 75
9, 656. 10
11, 265. 45
12, 874. 80
14, 484. 15
9, 266. 25
11, 119. 50
12, 972. 75
14,826.00
16, 679. 25
TABLE 31.
Conversion Tables for Thermometer Scales.
[F°=Fahrenheit temperature; C°= Centigrade temperature; R°=Re"aumur temperature.'
[Page 727
Equivalent temperatun
R°=4 C°=
C°=|R°=
's—Fahr., Cent., Riau
r>.
Co.
R°.
F°.
c°.
RO.
Equivalent temperature*— Centigrade and Fahrenheit,
F°=f C°+32°.
i
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
-17.2
16.7
16.1
15.6
15.0
14.4
13.9
13.3
12.8
12 2
1L7
11.1
10.6
10.0
9.4
8.9
8.3
7.8
7.2
6.7
6.1
5.6
5.0
4.4
3.9
3.3
2.8
2.2
1.7
1.1
- 0.6
0.0
+ 0.6
1.1
1.7
2.2
2.8
3.3
3.9
4.4
5.0
5.6
6.1
6.7
7.2
7.8
8.3
8.9
9.4
+10.0
—13.8
13.3
12.9
12.4
12.0
11.6
11.1
10.7
10.2
9.8
9.3
8.9
8.4
8.0
7.6
7.1
6.7
6.2
5.8
5.3
4.9
4.4
4.0
3.6
3.1
2.7
2.2
1.8
1.3
0.9
-0.4
0.0
+ 0.4
0.9
1.3
1.8
2.2
2.7
3.1
3.6
4.0
4.4
4.9
5.3
5.8
6.2
6.7
7.1
7.6
+ 8.0
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
i
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
+10.6
11.1
11.7
12.2
12.8
13.3
13.9
14.4
15.0
15.6
16.1
16.7
17.2
17.8
18.3
18.9
19.4
20.0
20.6
21.1
21.7
22.2
22.8
23.3
23.9
24.4
25.0
25.6
26.1
26.7
27.2
27.8
28.3
28.9
29.4
30.0
30.6
31.1
31.7
32.2
32.8
33.3
33.9
34.4
35.0
35.6
36.1
36.7
37.2
+37.8
+ 8.4
8.9
9.3
9.8
10.2
10.7
C°. FO.
Co.
F°.
Co.
FO.
GO.
FO.
GO.
PO.
11.1
11.6
12.0
12.4
12.9
13.3
13.8
14.2
14.7
15.1
15.6
16.0
-10 14.0
- 9 15. 8
- 8 17.6
- 7 19.4
— 6 21.2
— 5 23.0
— 4 24.8
- 3 26.6
- 2 28.4
- 1 30.2
0
1
2
3
4
5
6
7
8
9
32.0
33.8
35.6
37.4
39.2
41.0
42.8
44.6
46.4
48.2
10
11
12
13
14
15
16
17
18
19
50.0
51.8
53.6
55.4
57.2
59.0
60.8
62.6
64.4
66.2
20
21
22
23
24
25
26
27
28
29
68.0
69.8
71.6
73.4
75.2
77.0
78.8
80.6
82.4
84.2
30
31
32
33
34
35
36
37
38
39
86.0
87.8
89.6
91.4
93.2
95.0
96.8
98.6
100.4
102.2
16.4
16.9
17.3
17.8
18.2
18.7
19.1
19.6
20.0
20.4
20.9
21.3
21.8
22.2
22.7
23.1
23.6
24.0
24.4
24.9
25.3
25.8
26.2
26.7
27.1
27.6
28.0
28.4
28.9
29.3
29.8
+30.2
Equivalent temperature*— Reaumur and Fahrenheit.
F°=| R°+32°.
RO. po.
R°.
P°.
RO.
PO.
RO.
po.
—10 9. 5
— 9 11.8
— 8 14.0
- 7 16. 2
- 6 18.5
- 5 20.8
- 4 23. 0
— 3 25.2
- 2 27. 5
- 1 29.8
0
1
2
3
4
5
6
7
8
9
32.0
34.2
36.5
38.8
41.0
43.2
45.5
47.8
50.0
52.2
10
11
12
13
14
15
16
17
18
19
54.5
56.8
59.0
61.2
63.5
65.8
68.0
70.2
72.5
74.8
20
21
22
23
24
25
26
27
28
29
77.0
79.2
81.5
83.8
86.0
88.2
90.5
92.8
95.0
97.2
Page 728]
TABLE 32.
To obtain the True Force and Direction of the Wind from its Apparent Force and Direction on a
Moving Vessel.
c<icoiocoTj<iO'^iuitoioi»t^i£>t>oo
t»aOOOOOOOO»aOOlOO»Or-IOrHrH
rH rH <N (M <M >M <N O* <M
•Avoq 9qi no s^uiod 'uorpaaip 9mx
•9[BOS jiojnuag; 'OOJQJ aiux
•Avoq aqj jjo sjuiod 'uopoaaip atux
lOiOtOiOiCiCOiOiO
'80JOJ 9UJI,
t> 00 CO 00 00 0> 00 01 O 01 O O O rH rH rH r-l
'JA-OqeqUJO SJUtOd 'UOrpaiJP OtUX 3 S S rH rH rH rH S rH rH rH rH rH rH 5 rHrHrHrHrHrHrHrHrHrHrHrHrHrHrH prHrHrHrHrHrHrHrH
'aojoj atux
OOOi-iI-li-l1HCqC^C<lOJC<lCk)iM
"ALOq 9q^ HO S^UIOd ' UOl}O9JJP 9U IX rHrHrHrHr^SrHrHrHrHrHrHrHr^rH
rHrHrHrHi-lrHrHrHrHrHrHi-Hi-lrHrH rHr-(rHrHrHrHrHrHr-(
'aojoj anix
)rHrHrHlN<NCM'N(M(N<
•Avoq 9q* no s^uiod 'uop09Jtp an^x 33333^33333333
eo-*Tj< co eo-* eo co co coco coco coco
'90IOJ 9HJX
«Ot>QOI>000000000>010»0000
•M.oq 9q;so s^uiod '
•A4.oq 9q^ go s^utod '
to ic irt ^* ^ ic c
rH rH rH rH rH rH ,
A\.oq 9q^ uo si mod 'uopooatp 9tu,i
(OrHrHOOrHOOrHOOOOOO
'90ioj 9nix
^ic^iOioWi
Avoq aqj 50 s^utod 'uopoaiip 9nix
a> CT> o o> 01 o a» 01 os
'90JOJ 9UJX
•h
eNeO-^fNCO-^COCO^CO-^iC-^lOlOlOlOtOCOtOt-t^t^t^aOCOQOOlOlOO OOOrHrHrH<M<NC^
•M.oq8q; so s^urod
ooco
1
'aojoj gnij,
•h
10 10 «3 «3 «0 l> <£> t~ 00 00 00 0> 00 00 OOJOlrHrHOfNINiN
Moq aq^ no sjuiod 'uopoaatp anij,
'9DJOJ 9UJJ,
Avoq 9q^ uo s^uiod '
•81BDS ^jojutrag 'aojoj anai
01 01 00 0 0 0 rH r- rH
M.Oq aq'J UO SJUTOd 'UOpOaitp 9UIX 333rH33°'rHrHGOrHrHl>COrH
'90JOJ 901,1
1
OlOOOOOOOlrHrHrH
•Moq 9q^ go srjuiod
'SS'
| >«««>>
'90JOJ 9UIX
O10OOOOO>O>rHrHO
Aioqaq^ no ejuiod 'uopoaiip anix
<M co eo c^ e« eo IN IN co
'90JOJ 9UJX
01 00 t- 0 0> 0> rH rH O
M.oq 9q; jjo s^utod '
0> 00 l> O 0> 01 rH rH
OOlOlr-JrHO
TABLE 33.
Distance by Vertical Angle.
[Page 729
I
1
c
1
1
-sssss
?SS^S
SS38-3
ooooo
ooooo
ooooo
?i?l?,~.?5
ooooo
oooooo
o
o ^«o^ cc
SS525
iHrHfHf-10
ooooo
ooooo
ooooo
ooooo
oooooo
1
-0-880-
KS^SSSi
ooooo
ooooo
SJOC^Og
^CO£JOO
oooooo
ooooo
ooooo
s
-S833
ss^ss
ooooo
ooooo
ooooo
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t^JOjOjO^J^J
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*
0
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1
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8
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0 0 0» OC 00
t-OiO^-cc
CO <M C« r-t r-l O
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8
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£SS8S
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3S°.£3
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8
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o
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o
8
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s
0
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0
§
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0
o
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0
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0
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3 •••••*•
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Page 730]
TABLE 33.
Distance by Vertical Angle.
1
-*<CM OOiOO
- SSSSSSrl^
CMOI co
Q !>• QO lC "
o jo
-£838
Q lO t> lO M*
-38SS
o ^t^ioco
i!
00 COiO •»* (
CSr-10001
0010500
0»0>COQOI>
rHOOOOCO
O>COCOOOI>
'•O CO CO SO CO
COCN C^ CM O»
r-lTHrHrHO
SS8SS
85S3S3
rHOOOO
3SSSS
CM CM CM CM CM
M CN C< CM i-l
t^ -^1 r-H O» t-
iG> i£> iQ •<& if
OOOOO
OOOOO
OOOOO
OOOOO
f ^r coco
OOOOO
CMCMCMCMi-t
OOOOO
OOOOO
OOOOO
OOOOO
co eocoeococo
SS823S
N CM rH i-H r-l r -<
S33SS
oooooo
OOOOO
oooooo
OOOOO
OOOOO
OOOOO
OOOOO
oooooo
oooooo
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oooooo
oooooo
TABLE 34. [Page 731 !
For finding the distance of an object by an angle, measured from an elevated position, between the
object and the horizon beyond.
Dist.,
yards.
Height of the Eye Above the Level of the Sea, in Feet.
Dist.,
yards.
2O
30
40
50
60
70
80
90
100
no
120
100
200
300
400
500
o /
3 44
1 50
1 12
52
41
o /
5 37
2 46
1 49
1 21
1 03
o /
7 29
3 43
2 26
1 48
1 25
100
200
300
400
500
9 21
4 39
3 04
2 16
1 48
11 11
5 35
3 41
2 44
2 10
13 00
6 31
4 19
3 12
2 32
14 47
7 27
4 56
3 40
2 54
16 34
8 23
5 33
4 08
3 17
18 16
9 18
6 11
4 3d
3 39
19 58
10 13
6 48
5 04
4 01
21 37
11 08
7 25
5 32
4 24
600
700
800
900
1,000
34
28
24
21
18
52
44
38
33
29
1 10
1 01
51
45
40
1 29
1 15
1 05
57
50
1 47
1 31
1 18
1 09
1 01
2 05^
1 46
1 32
1 22
1 12
2 24
2 01
1 46
1 33
1 23
2 42
2 18
2 00
45
34
3 01
2 34
2 13
57
45
3 20
2 50
2 27
2 10
1 56
3 38
3 05
2 41
2 22
2 07
600
700
800
900
1,000
1,100
1,200
1,300
1,400
1,500
16
15
13
12
11
26
23
21
19
18
35
32
29
27
24
45
41
37
34
31
55
50
45
41
38
1 05
59
53
49
45
1 15
1 08
1 02
57
52
24
17
10
04
59
34
26
18
12
07
1 44
1 35
1 27
1 20
1 14
1 54
1 44
1 35
1 27
1 21
1,100
1,200
1,300
1,400
1,500
1,600
1,700
1,800
1,900
2,000
10
16
15
14
13
12
22
21
19
18
17
29
27
25
23
22
35
33
31
29
27
42
39
36
34
32
48
45
42
39
37
55
51
48
45
42
1 02
58
54
50
47
1 08
1 04
1 00
56
53
1 15
1 10
1 06
1 02
58
1,600
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
2,500
11
10
16
15
14
13
12
20
19
18
17
16
25
24
22
21
20
30
28
27
25
24
35
33
31
29
28
40
38
36
34
32
45
42
40
38
36
50
47
45
42
40
55
52
49
47
44
2,100
2,200
2,300
2,400
2,500
2,600
2,700
2,800
2,900
3,000
11
11
10
15
14
14
13
12
19
18
17
16
15
23
22
20
19
19
26
25
24
23
22
30
29
28
26
25
34
33
31
30
28
38
36
35
33
32
42
40
38
37
35
2,600
2,700
2,800
2,900
3,000
3,100
3,200
3,300
3,400
3,500
12
11
10
15
14
13
13
12
18
17
16
15
15
21
20
19
18
17
24
23
22
21
20
27
26
25
24
23
30
29
28
27
26
34
32
31
30
29
3,100
3,200
3,300
3,400
3,500
3,600
3,700
3,800
3,900
4,000
12
11
11
10
14
13
13
12
12
17
16
15
15
14
19
19
18
17
16
22
21
20
20
19
25
24
23
22
21
27
26
25
25
24
3,600
3,700
3,800
3,900
4,000
4,100
4,200
4,300
4,400
4,500
11
11
10
14
13
13
12
12
16
15
15
14
14
18
17
17
16
16
20
20
19
18
18
23
22
21
21
20
4,100
4,200
4,300
4,400
4,500
4,600
4,700
4,800
4,900
5,000
11
11
10
13
13
12
12
11
15
15
14
14
13
17
17
16
15
15
19
19
18
17
17
4,600
4,700
4,800
4,900
5,000
Page 732] TABLE 35.
Speed in knots per hour developed by a vessel traversing a measured nautical mile in any given
number of minutes and seconds.
Sec.
0
1
2
3
4
Number of minutes.
1
2
3
4
5
6
7
8
9
10
11
1 1*
Knots.
60. 000
59. 016
58. 065
57, 143
56. 250
Knots.
30. 000
29. 752
29. 508
29. 268
29. 032
Knots.
20. 000
19. 890
19. 780
19. 672
19. 565
Knots.
15. 000
14. 938
14. 876
14. 815
14. 754
14. 694
14. 634
14. 575
14. 516
14. 458
Knots.
12. 000
11. 960
11.920
11.880
11. 841
Knots.
10. 000
9.972
9.944
9, 917
9.890
Knots.
8.571
8.551
8.530
8.510
8.490
Knots.
7.500
7.484
7.468
7.453
7.438
Knots.
6.666
6.654
6.642
6.629
6, 617
Knots.
6.000
5.990
5.980
5.970
5.960
Knots.
5.455
5.446
5.438
5.429
5.421
Knots.
5.000
4.993
4.986
4.978
4,972
0
1
2
3
4
5
6
7
8
9
55. 385
54, 545
53, 731
52. 941
52. 174
28. 800
28. 571
28. 346
28. 125
27. 907
19. 460
19. 355
19. 251
19. 149
19. 048
11. 803
11.764
11. 726
11.688
11. 650
9.863
9.836
9.809
9.783
9.756
a 470
8. 450
8.430
8.411
8.392
7.422
7.407
7.392
7.377
7.362
6.605
6.593
6.581
6.569
6.557
5.950
5.940
5.930
5.921
5.911
5.413
5.405
5.397
5.389
5.381
4.965
4.958
4.951
4.945
4.938
5
6
7
8
9
10
11
12
13
14
51. 429
50. 704
50. 000
49. 315
48. 649
27. 692
27. 481
27. 273
27. 068
26. 866
18. 947
18. 848
18. 750
18. 652
18. 556
14. 400
14. 342
14. 286
14. 229
14. 173
11.613
11.575
11. 538
11.501
11. 465
9.729
9.703
9.677
9.651
9.625
8.372
8. 353
8.334
8.315
8.295
7.346
7.331
7.317
7.302
7.287
6.545
6.533
6.521
6.509
6.498
5.902
5.892
5.882
5.872
5.863
5.373
5.365
5.357
5.349
5.341
4.932
4.924
4.918
4.911
4.904
10
11
12
13
14
15
16
17
18
19
48. 000
47. 368
46. 753
46. 154
45. 570
26. 667
26. 471
26. 277
26. 087
25. 899
18. 461
18. 367
18. 274
18. 182
18. 090
14. 118
14. 063
14. 008
13. 953
13. 900
11. 428
11. 392
11. 356
11. 321
11. 285
9.600
9.574
9.549
9.524
9.499
8.276
8.257
8.238
8.219
8.200
7.272
7.258
7. 243
7.229
7.214
6.486
6.474
6.463
6.451
6.440
5.853
5.844
5.834
5.825
5.815
5.333
5.325
5.317
5.309
5.301
4.897
4.891
4.884
4.878
4.871
15
16
17
18
19
20
21
22
23
24
45.000
44. 444
43. 902
43. 373
42. 857
25. 714
25. 532
25. 352
25. 175
25. 000
18. 000
17. 910
17. 822
17. 734
17. 647
13. 846
13. 793
13. 740
13. 688
13. 636
11. 250
11. 214
11. 180
11. 146
11.111
9.473
9.448
9.424
9.399
9.375
8.181
8.163
8.144
8.126
8.108
7.200
7.185
7.171
7.157
7.142
6.428
6.417
6.405
6.394
6.383
5. 806
5.797
5.787
5.778
5.769
5.294
5.286
5.278
5.270
5.263
4.865
4.858
4.851
4.845
4.838
20
21
22
23
24
25
26
27
28
29
42. 353
41. 860
41. 379
40. 909
40. 449
24. 828
24. 658
24. 490
24. 324
24. 161
17. 560
17. 475
17. 391
17. 307
17. 225
13.584
13. 533
13. 483
13.433
13. 383
11. 077
11. 043
11. 009
10. 975
10. 942
9.350
9.326
9.302
9.278
9.254
8.090
8.071
8.053
8.035
8.017
7.128
7.114
7.100
7.086
7.072
6.371
6.360
6.349
6.338
6.327
5.760
5. 750
5.741
5.732
5. 723
5. 255
5.247
5.240
5.232
5.224
4.832
4.825
4.819
4.812
4.806
25
26
27
28
29
30
31
32
33
34
40. 000
39. 560
39. 130
38. 710
38. 298
24. 000
23. 841
23. 684
23. 529
23. 377
17. 143
17. 061
16. 981
16. 901
16. 822
13. 333
13. 284
13. 235
13. 186
13. 138
10. 909
10. 876
10. 843
10.810
10. 778
9.230
9.207
9. 183
9.160
9.137
8.000
7.982
7.964
7.947
7.929
7.059
7.045
7.031
7.017
7.004
6.315
6.304
6.293
6.282
6.271
5.714
5.705
5.696
5.687
5.678
5.217
5.210
5.202
5.195
5.187
4.800
4.793
4.787
4.780
4.774
30
31
32
33
34
35
36
37
38
39
37. 895
37. 500
37. 113
36. 735
36. 364
23. 226
26. 077
22. 930
22. 785
22.642
16. 744
16. 667
16. 590
16.514
16. 438
13. 091
-13. 043
12. 996
12. 950
12. 903
10. 746
10. 714
10. 682
10. 651
10. 619
9.113
9.090
9.068
9.045
9.022
7.912
7.895
7.877
7.860
7.843
6.990
6.977
6.963
6.950
6.936
6.260
6.250
6.239
6.228
6.217
5.669
5.660
5.651
5.642
5.633
5.179
5.172
5.164
5.157
5.150
4.768
4.761
4.755
4.749
4.743
35
36
37
38
39
40
41
42
43
44
36. 000
35. 644
35. 294
34. 951
34. 615
22. 500
22. 360
22. 222
22! 086
21. 951
16. 363
16. 289
16. 216
16. 143
16.071
12. 857
12. 811
12. 766
12. 721
12. 676
10. 588
10. 557
10. 526
10. 495
10. 465
9.000
8.977
8.955
8. 933
8.911
7.826
7.809
7.792
7.775
7.758
6.923
6.909
6.896
6.883
6. 870
6.207
6.196
6.185
6.174
6.164
5.625
5.616
5.607
5.598
5.590
5.143
5.135
5.128
5.121
5.114
4.737
4.731
4.724
4.718
4.712
40
41
42
43
44
45
46
47
48
49
34.286
33. 962
33. 645
33. 333
33. 028
21.818
21. 687
21. 557
21. 429
21. 302
16. 000
15. 929
15. 859
15. 789
15. 721
12. 631
12. 587
12. 543
12. 500
12. 456
10.434
10. 404
10. 375
10. 345
10. 315
8.889
8.867
8. 845
8. 823
8.801
7.741
7.725
7.708
7.692
7. 675
6.857
6.844
6.831
6.818
6.805
6.153
6.143
6.132
6.122
6.112
5.581
5.572
5.564
5.555
5.547
5.106
5.099
5.091
5.084
5.077
4.706
4.700
4.693
4.687
4.681
45
46
47
48
49
50
51
52
53
54
32. 727
32. 432
32. 143
31. 858
31. 579
21. 176
21. 053
20. 930
20. 809
20. 690
15. 652
15. 584
15. 517
15. 450
15. 384
12. 413
12. 371
12. 329
12. 287
12. 245
10. 286
10. 256
10. 227
10. 198
10. 169
8.780
8.759
8.737
8.716
8.695
7.659
7.643
7.627
7.611
7.595
6.792
6.779
6.766
6.754
6.741
6.101
6.091
6.081
6.071
6.060
5.538
5.530
5.521
5.513
5.504
5.070
5.063
5.056
5.049
5.042
4.675
4.669
4.663
4.657
4.651
50
51
52
53
54
55
56
57
58
59
31.304
31. 034
30. 769
30. 508
30. 252
20. 571
20. 455
20. 339
20. 225
20. 112
15.319
15. 254
15. 190
15. 126
15. 062
12. 203
12. 162
12. 121
12. 080
12. 040
10. X40
10. 112
10. 084
10. 055
10. 027
8.675
8.654
8.633
8.612
8.591
7.579
7.563
7.547
7.531
7.515
6.739
6.716
6.704
6.691
6.679
6.050
6.040
6.030
6.020
6.010
5.496
5.487
5.479
5.471
5.463
5. 035
5.028
5.020
5.013
5.006
4.645
4.639
4.633
4.627
4.621
55
56
57
58
59
Sec.
l
2
3
4
0
6
7
8
9
10
11
12
Sec.
TABLE 36. [Page 733
Reduction of Local Mean Time to Standard Meridian Time, and the reverse.
[If local meridian is east of standard meridian, subtract from local mean time, or add to standard meridian time. If local
meridian is west of standard meridian, add to local mean time, or subtract from standard meridian time.]
Difference of longitude be
tween local meridian and
standard meridian.
Reduction to
be applied
to local mean
time.
Difference of longitude be
tween local meridian and
standard meridian.
Reduction to
be applied
to local mean
time.
0 / 0 /
Minutes.
o / o /
Minutes.
0 00 to 0 07
0
7 23 to 7 37
30
0 08 to 0 22
1
7 38 to 7 52
31
0 23 to 0 37
2
7 53 to 8 07
32
0 38 to 0 52
3
8 08 to 8 22
33
0 53 to 1 07
4
8 23 to 8 37
34
1 08 to 1 22
5
8 38 to 8 52
35
1 23 to 1 37
6
8 53 to 9 07
36
1 38 to 1 52
7
9 08 to 9 22
37
1 53 to 2 07
8
9 23 to 9 37
38
2 08 to 2 22
9
9 38 to 9 52
39
2 23 to 2 37
10
9 53 to 10 07
40
2 38 to 2 52
11
10 08 to 10 22
41
2 53 to 3 07
12
10 23 to 10 37
42
3 08 to 3 22
13
10 38 to 10 52
43
3 23 to 3 37
14
10 53 to 11 07
44
3 38 to 3 52
15
11 08 to 11 22
45
3 53 to 4 07
16
11 23 to 11 37
46
4 08 to 4 22
17
11 38 to 11 52
47
4 23 to 4 37
18
11 53 to 12 07
48
4 38 to 4 52
19
12 08 to 12 22
49
4 53 to 5 07
20
12 23 to 12 37
50
5 08 to 5 22
21
12 38 to 12 52
51
5 23 to 5 37
22
12 53 to 13 07
52
5 38 to 5 52
23
13 08 to 13 22
53
5 53 to 6 07
24
13 23 to 13 37
54
6 08 to 6 22
25
13 38 to 13 52
55
6 23 to 6 37
26
13 53 to 14 07
56
6 38 to 6 52
27
14 08 to 14 22
57
6 53 to 7 07
28
14 23 to 14 37
58
7 08 to 7 22
29
14 38 to 14 52
59
Note. — Tlie pages formerly occupied with. Tables 37 and 37 A have been dropped, and consecutive page
numbering is thereby broken.
TABLE 38. [Page 739
Error in Longitude due to one minute Error of Latitude.
si o
OQ
f|
Is
Latitude.
i
£ 3
z~
Is «
x-O
"=5
do
0°
5°
10°
15°
20°
25°
30°
85°
40°
45°
60°
65°
60°
65°
70°
75°
10
20
30
40
50
60
110
.4
.4
.4
.5
.7
.9
.4
.4
.5
.6
.9
.4
.5
.6
.8
1.2
.5
.6
.7
1.0
.5
.7
.9
1.3
.6
.8
1.1
. 7
1.0
1.5
.8
1.2
2.3
1.0
1.6
1.3
2.6
T9~
1.6
1.8
L2~
2.7
2.9
I78~
110
10
20
30
40
50
60
10
20
30
40
50
60
10
20
30
40
50
60
105
.3
.3
.3
.4
.4
.6
.3
.3
.4
.5
.6
.9
.3
.4
.5
.6
.8
.3
.4
.6
.7
1.2
.4
.5
.7
1.0
.4
.6
.8
1.3
.5
.7
1.1
.6
.9
1.5
.8
1.2
2.4
3.0
105
15
20
30
40
50
60
100
.2
.2
.2
.2
.3
.3
.2
.2
.3
.3
.4
.6
.2
.3
.3
.4
.6
.9
.3
.3
.4
.6
.8
.3
.4
.5
.7
1.2
.4
.5
.6
.9
.4
.5
.8
1.3
.5
r*
. I
1.1
2.1
.6
.9
1.5
.8
1.1
2.4
1.1
1.6
1.6
2.7
2.9
100
15
20
30
40
50
60
15
20
30
40
50
60
95
.1
.1
.1
.1
.1
.2
.1
.1
.2
.2
.3
.3
.1
.2
.2
.3
.4
.6
.2
.2
.3
.4
.6
.9
.2
.3
.4
.5
.8
.3
.3
.5
.7
1.1
.3
.4
.6
.9
.4
.5
.8
1.3
.5
.6
1.0
2.1
T4~
.7
1.3
73~
.5
.9
.6
.8
1.5
T6"
1.0
2.2
T3~
. 7
1.3
.8
1.1
2.5
TY"
1.5
.5
1.0
2.3
1.1
1.6
ITT
2.7
1.7
2.8
r<r
3.0
j£F
95
15
20
30
40
50
60
20
30
40
50
60
70
20
30
40
50
60
70
90
.0
.0
.0
.0
.0
.0
.0
.1
.1
.1
.2
.2
.1
.1
.2
.2
.3
.6
.1
.2
.3
.4
.5
1.1
.1
.2
.3
.5
.9
.2
.3
.5
.8
.2
.4
.6
1.1
.3
.5
.9
72~
.4
.6
1.1
90
20
30
40
50
60
70
85
.1*
.1*
.1*
.1*
.2*
.3*
.1*
.0
.0
.0
.0
.0
.0
.0
.0
.1
.1
.2
.0
.1
.1
.2
.3
.6
.0
.1
.2
.3
.5
1.1
.1
.2
.3
.5
.9
.1
.2
.4
.7
.7
1.5
1.0
2.7
1.6
3.1
I75~
Te~
3.0
3TT
L2~
85
20
30
40
50
60
70
20
30
40
50
60
70
80
. 2*
.*2*
.2*
.3*
.4*
.6*
.2*
.2*
.2*
.2*
.2*
.3*
.1*
.1*
.1*
.1*
.0
.0
.1*
.0
.0
.1
.1
.2
.1*
.0
.1
.2
.3
.6
.0
.1
.2
.3
.5
1.2
.0
.1
.3
.5
.9
.0
.2
.4
.7
TI*
.1
.2
.5
.9
.1
.3
.6
1.1
"71*
.1
.4
.7
T2*
.0
.2
.4
.9
.1
.4
.9
~7o~
.2
.5
1.1
.2
.6
1.3
7(T
.4
.8
.4
.9
2.4
.5
1.5
.9
2.8
80
20
30
40
50
60
70
20
30
40
50
60
70
20
30
40
50
60
70
75
.3*
.3*
.4*
.4*
.6*
1.2*
.3*
.3*
.3*
.3*
.4*
.6*
.2*1 .2*
.2* .2*
.2* .1*
.2* .1*
.2* .1*
.3* .0
.2*
.1*
.1*
.0
.1
.2
.1*
.1*
.0
.1
.3
.6
.1*
.0
.1
.3
.5
1.2
.1
.6
1.3
.2
.9
2.5
.3
1.5
75
20
30
40
50
60
70
70
.4*
.4*
.5*
.6*
.9*
.4*
.4*
.4*
.5*
.6*
1.2*
.3*
.3*
.3*
.3*
.4*
.6*
.3*
.3*
.3*
.2*
.3*
3*
.3*
.2*
.2*
.2*
.1*
.1*
.3*
.2*
.1*
.0
.1
.2
.2*
.1*
.0
.1
.2
.6
.2*
.1*
.1
.3
.5
1.2
.2*
.0
.3
.7
.2*
.1
.5
1.1
.2*
.2
.8
.2*
.6
1.3
.2*
.8
2.6
2*
1.5
.2*
3.1
70
20
30
40
50
60
70
Is
i
Si
li
0°
5°
10°
15°
20°
25°
80°
85°
40°
4o°
50°
55°
60°
66°
70°
75°
A .
P
2
1i 0
p
Latitude.
Page 740] TABLE 39.
Amplitudes.
Lati
tude.
Declination.
Lati
tude.
o°.o
0°.5
1°.0
1°.5
2c.O
2°. 5
8°.0
3°. 5
4°.0
4°. 5
6°.0
5°. 5
6°.0
o
0
10
15
20
25
o
0.0
0.0
0.0
0.0
0.0
o
0.5
0.5
0.5
0.5
0.5
o
1.0
1.0
1.0
1.1
1.1
o
1.5
1.5
1.5
1.6
1.6
0
2.0
2.0
2.1
2.1
2.2
o
2.5
2.5
2.6
2.7
2.8
o
3.0
3.0
3.1
3.2
3.3
0
3.5
3.5
3.6
3.7
3.8
0
4.0
4.1
4.2
4.3
4.4
0
4.5
4.6
4.7
4.8
5.0
o
5.0
5.1
5.2
5.3
5.5
o
5.5
5.6
5.7
5.8
6.0
0
6.0
6.1
6.2
6.4
6.6
o
0
10
15
20
25
30
32
34
36
38
0.0
0.0
0.0
0.0
0.0
0.6
0.6
0.6
0.6
0.6
1.2
1.2
1.2
1.2
1.3
1.7
1.8
1.8
1.8
1.9
2.3
2.4
2.4
2.5
2.5
2.9
2.9
3.0
3.1
3.2
3.4
3.5
3.6
3.7
3.8
4.0
4.1
4.2
4.3
4.4
4.6
4.7
4.8
4.9
5.1
5.2
5.3
5.4
5.6
5.7
5.8
5.9
6.0
6.1
6.3
6.3
6.5
6.6
6.8
7.0
6.9
7.0
7.2
7.4
7.6
7.8
8.0
8.3
8.6
9.0
30
32
34
36
38
40
42
44
46
48
0.0
0.0
0.0
0.0
0.0
0.7
0.7
0.7
0.7
0.7
1.3
1.3
1.4
1.4
1.5
2.0
2.0
2.1
2.2
2.2
2.6
2.7
2.8
2.9
3.0
3.3
3.4
3.5
3.6
3.7
3.9
4.0
4.2
4,3
4.5
4.6
4.7
4.9
5.0
5.2
5.2
5.4
5.6
5.8
6.0
5.9
6.1
6.3
6.5
6.7
6.5
6.7
6.9
7.2
7.5
7.2
7.4
7.6
7.9
8.2
40
42
44
46
48
50
51
52
53
54
0.0
0.0
0.0
0.0
0.0
0.8
0.8
0.8
0.8
0.9
1.5
1.6
1.6
1.6
1.7
2.3
2.4
2.4
2.5
2.5
3.1
3.2
3.3
3.3
3.4
3.9
4.0
4.1
4.2
4.3
4.7
4.8
4.9
5.0
5.1
5.4
5.6
5.7
5.8
6.0
6.2
6.4
6.5
6.7
6.8
7.0
7.2
7.3
7.5
7.7
7.8
8.0
8.1
8.3
8.5
8.6
8.8
9.0
9.2
9.4
9.3
9.5
9.7
10.0
0.2
50
51
52
53
54
55
56
57
58
59
0.0
0.0
0.0
0.0
0.0
0.9
0.9
0.9
0.9
1.0
1.7
1.8
1.8
1.9
1.9
2.6
2.7
2.7
2.8
2.9
3.5
3.6
3.7
3.8
3.9
4.4
4.5
4.6
4.7
4.9
5.2
5.4
5.5
5.7
5.8
6.1
6.3
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
7.9
8.1
8.3
8.5
8.8
8.7
9.0
9.2
9.5
9.7
9.6
9.9
10.1
0.4
0.7
10.5
0.8
1.1
1.4
1.7
55
56
57
58
59
60
61
62
63
64
0.0
0.0
0.0
0.0
0.0
1.0
1.0
1.1
1.1
1.1
2.0
2.1
2.1
2.2
2.3
3.0
3.1
3.2
3.3
3.4
4.0
4.1
4.3
4.5
4.6
5.0
5.2
5.3
5.5
5.7
6.0
6.2
6.4
6.6
6.9
7.0
7.2
7.5
7.7
8.0
8.0
8.3
8.5
8.8
9.2
9.0
9.3
9.6
9.9
10.3
10.0
0.3
0.7
1.1
1.5
11.0
1.4
1.8
2.2
2.6
12.1
2.5
2.9
3.4
3.9
60
61
62
63
64
65.0
5.5
6.0
6.5
7.0
0.0
0.0
0.0
0.0
0.0
1.2
1.2
1.2
1.2
1.3
2.4
2.4
2.5
2.5
2.6
3.5
3.6
3.7
3.8
3.8
4.8
4.8
4.9
5.0
5.1
5.9
6.0
6.1
6.3
6.4
7.1
7.2
7.4
7.5
7.7
8.3
8.5
8.6
8.8
9.0
9.5
9.7
9.9
10.1
0.3
10.7
0.9
1.1
1.3
1.6
11.9
2.1
2.4
2.6
2.9
13.1
3.4
3.6
3.9
4.2
14.4
4.6
4.9
5.2
5.5
65.0
5.5
6.0
6.5
7.0
67.5
8.0
8.5
9.0
9.5
0.0
0.0
0.0
0.0
0.0
1.3
1.3
1.4
1.4
1.4
2.6
2.7
2.7
2.8
2.9
3.9
4.0
4.1
4.2
4.3
5.2
5.3
5.4
5.5
5.7
6.5
6.7
6.8
7.0
7.2
7.9
8.0
8.2
8.4
8.6
9.2
9.4
9.6
9.8
10.0
10.5
0.7
1.0
1.2
1.5
11.8
2.1
2.4
2.6
2.9
13.2
3.5
3.8
4.1
4.4
14.5
4.8
5.2
5.5
5.9
15.9
6.2
6.6
7.0
7.4
67.5
8.0
8.5
9.0
9.5
70.0
0.5
1.0
1.5
2.0
0.0
0.0
0.0
0.0
0.0
1.5
1.5
1.5
1.6
1.6
2.9
3.0
3.1
3.2
3.2
4.4
4.5
4.6
4.7
4.9
5.8
6.0
6.2
6.3
6.5
7.3
7.5
7.7
7.9
8.1
8.8
9.0
9.3
9.5
9.8
10.3
0.5
0.8
1.1
1.4
11.8
2.1
2.4
2.7
3.0
13.3
3.6
3.9
4.3
4.7
14.8
5.1
5.5
5.9
6.4
16.3
6.7
7.1
7.8
8.1
17.8
8.2
8.7
9.2
9.8
70.0
0.5
1.0
1.5
2.0
72.5
3.0
3.5
4.0
4.5
0.0
0.0
0.0
0.0
0.0
1.7
1.7
1.8
1.8
1.9
3.3
3.4
3.5
3.6
3.7
5.0
5.1
5.2
5.4
5.6
6.7
6.9
7.1
7.3
7.5
8.3
8.6
8.8
9.1
9.4
10.0
0.3
0.6
0.9
1.3
11.7
2.0
2.4
2.8
3.2
13.4
3.8
4.2
4.6
5.1
15.1
5.5
6.0
6.5
7.1
16.9
7.4
7.9
8.4
9.0
18.6
9.1
9.7
20.3
1.0
20.3
0.9
1.6
2.3
3.0
72.5
3.0
3.5
4.0
4.5
75.0
5.5
6.0
6.5
7.0
0.0
0.0
0.0
0.0
0.0
1.9
2.0
2.1
2.1
2.2
3.8
3.9
4.0
4.2
4.4
5.8
6.0
6.2
6.4
6.6
7.7
8.0
8.3
8.6
8.9
9.7
10.0
0.4
0.8
1.2
11.7
2.1
2.5
3.0
3.5
13.6
4.1
4.6
5.2
5.8
15.6
6.2
6.8
7.4
8.1
17.7
8.3
8.9
9.6
20.4
19.7
20.4
1.1
1.9
2.8
21.7
2.5
3.3
4.2
5.2
23.8
4.7
5.6
6.6
7.7
75.0
5.5
6.0
6.5
7.0
TABLE 39. [Page 741
Amplitudes.
Lati
tude.
Declination.
Lati
tude.
6°.0
6°. 5
7°.0
7°.5
8°.0
8°. 5
9°.0
9°. 5
10°.0
10°. 5
11°.0
11°.5
12°.0
o
0
10
15
20
25
o
6.0
6.1
6.2
6.4
6.6
0
6.5
6.6
6.7
6.9
7.1
0
7.0
7.1
7.2
7.4
7.7
7.5
7.6
7.8
8.0
8.3
8.0
8.1
8.3
8.5
8.8
8.5
8.6
8.8
9.1
9.4
9.0
9.1
9.3
9.6
9.9
9.5
9.7
9.8
10.1
0.5
10.0
0.1
0.4
0.7
1.1
10.5
0.7
0.9
1.2
1.6
11.0
1.2
1.4
1.7
2.2
11.5
1.7
1.9
2.3
2.8
12.0
2.2
2.5
2.8
3.3
0
10
15
20
25
30
32
34
36
38
6.9
7.0
7.2
7.4
7.6
7.5
7.7
7.8
8.0
8.2
8.1
8.3
8.5
8.7
8.9
8.7
8.8
9.0
9.3
9.5
9.3
9.5
9.7
9.9
10.2
9.8
10.0
0.3
0.5
0.8
10.4
0.6
0.8
1.1
1.4
11.0
1.2
1.5
1.8
2.1
11.5
1.8
2.1
2.4
2.7
12.1
2.4
2.7
3.0
3.4
12.7
3.0
3.3
3.6
4.0
13.3
3.6
3.9
4.3
4.7
13.9
4.2
4.5
4.9
5.3
30
32
34
36
38
40
42
44
46
48
7.8
8.0
8.3
8.6
9.0
8.5
8.8
9.1
9.4
9.7
9.1
9.4
9.7
10.1
0.5
9.8
10.1
0.5
0.8
1.2
10.5
0.8
1.1
1.5
2.0
11.1
1.5
1.9
2.3
2.8
11.7
2.1
2.5
3.0
3.5
12.4
2.8
3.3
3.8
4.3
13.1
3.5
4.0
4.5
5.0
13.8
4.2
4.7
5.2
5.8
14.4
4.8
5.3
5.9
6.6
15.1
5.6
6.1
6.7
7.3
15.7
6.2
6.8
7.4
8.1
40
42
44
46
48
50
51
52
53
54
9.3
9.5
9.7
10.0
0.2
10.1
0.4
0.6
0.8
1.1
10.9
1.2
1.4
1.7
2.0
11.7
2.0
2.2
2.5
2.8
12.5
2.8
3.1
3.4
3.7
13.3
3.6
3.9
4.2
4.6
14.1
4.4
4.7
5.1
5.4
14.9
5.2
5.6
5.9
6.3
15.7
6.0
6.4
6.8
7.2
16.5
6.8
7.2
7.6
8.1
17.3
7. 7
8.1
8.5
8.9
18.1
8.5
8.9
9.4
9.8
18.9
9.3
9.7
20.2
0.7
50
51
52
53
54
55
56
57
58
59
10.5
0.8
1.1
1.4
1.7
11.4
1.7
2.0
2.3
2.7
12.3
2.6
2.9
3.3
3.7
13.1
3.5
3.9
4.3
4.7
14.0
4.4
4.8
5.2
5.7
14.9
5.3
5.8
6.2
6.7
15.8
6.2
6.7
7.2
7.7
16.7
7.2
7.7
8.2
8.7
17.6
8.1
8.6
9.1
9.7
18.5
9.0
9.6
20.1
0.7
19.4
9.9
20.5
1.1
1.7
20.3
0.9
1.5
2.1
2.8
21.2
1.8
2.4
3.1
3.8
oo
56
57
58
59
60
61
62
63
64
12.1
2.5
2.9
3.4
3.9
13.1
3.5
3.9
4.4
5.0
14.1
4.6
5.1-
5.6
6.2
15.1
5.6
6.1
6.7
7.3
16.2
6.7
7.3
7.9
8.5
17.2
7.8
8.4
9.0
9.7
18.2
8.8
9.4
20.1
0.9
19.3
9.9
20.6
1.3
2.1
20.3
1.0
1.7
2.5
3.3
21.4
2.1
2.9
3.7
4.6
22.4
3.1
3.9
4.8
5.7
23.5
4.3
5.2
6.1
7.1
24.6
5.4
6.3
7.2
8.3
60
61
62
63
64
65.0
5.5
6.0
6.5
7.0
14.4
4.6
4.9
5.2
5.5
15.5
5.8
6.2
6.5
6.8
16.8
7.1
7.4
7.8
8.2
18.0
8.3
8.7
9.1
9.5
19.3
9.6
20.0
0.4
0.9
20.5
0.9
1.3
1.8
2.2
21.7
2.2
2.6
3.1
3.6
23.0
3.5
3.9
4.4
5.0
24.2
4.7
5.3
5.8
6.4
25.6
6.1
6.6
7.2
7.8
26.8
7.4
8.0
8.6
9.2
28.2
8.7
9.3
30.0
0.7
29.5
30.1
0.7
1.4
2.1
65.0
5.5
6.0
6.5
7.0
67.5
8.0
8.5
9.0
9.5
15.9
6.2
6.6
7.0
7.4
17.2
7.6
8.0
8.4
8.9
18.6
9.0
9.4
9.9
20.4
19.9
20.4
0.9
1.4
1.9
21.3
1.8
2.3
2.8
3.4
22.7
3.2
3.8
4.4
5.0
24.1
4.7
5.3
5.9
6.5
25.5
6.1
6.8
7.4
8.1
27.0
7.6
8.3
9.0
9.7
28.4
9.1
9.8
30.6
1.4
29.9
30.6
1.4
2.2
3.0
31.4
2.2
3.0
3.8
4.7
32.9
3.7
4.6
5.5
6.4
67.5
8.0
8.5
9.0
9.5
70.0
0.5
1.0
1.5
2.0
17.8
8.2
8.7
9.2
9.8
19.3
9.8
20.3
0.9
1.5
20.9
1.4
2.0
2.6
3.2
22.4
3.0
3.6
4.3
5.0
24.0
4.6
5.3
6.0
6.8
25.6
6.3
7.0
7.8
8.6
27.2
7.9
8.7
9.5
30.4
28.8
9.6
30.5
1.4
2.3
30.5
1.3
2.2
3.2
4.2
32.2
3.1
4.0
5.0
6.1
33.9
4.9
5.9
7.0
8.1
35.7
6.7
7.8
8.9
40.2
37.4
8.5
9.7
40.9
2.3
70.0
0.5
1.0
1.5
2.0
72.5
3.0
3.5
4.0
4.5
20.3
0.9
1.6
2.3
3.0
22.1
2.8
3.5
4.3
5.1
23.9
4.6
5.4
6.2
7.1
25.7
6.5
7.4
8.3
9.3
27.6
8.4
9.3
30.3
1.4
29.5
30.4
1.4
2.5
3.6
31.4
2.4
3.4
4.6
5.8
33.3
4.4
5.5
6.8
8.2
35.3
6.5
7.7
9.1
40.5
37.3
8.6
9.9
41.4
3.0
39.4
40.8
2.2
3.8
5.6
41.5
3.0
4.6
6.3
8.2
43.7
5.3
7.0
8.9
51.1
72.5
3.0
3.5
4.0
4.5
75.0
5.5
6.0
6.5
7.0
23.8
4.7
5.6
6.6
7.7
26.0
6.9
7.9
9.0
30.2
28.1
9.1
30.2
1.4
2.8
30.3
1.4
2.6
4.0
5.5
32.5
3.8
5.1
6.6
8.2
34.8
6.2
7. 7
9.3
41.1
37.2
8.7
40.3
2.1
4.1
39.6
41.2
3.0
5.0
7.2
42.1
3.9
5.9
8.1
50.5
44.8
6.7
8.9
51.3
4.1
47.5
9.6
52.1
4.8
8.0
50.4
2.8
5.5
8.7
62.4
53.5
6.2
9.3
63.0
7.6
75.0
5.5
6.0
6.5
7.0
Page 742] TABLE 39.
Amplitudes.
Lati
Declination.
Lati
tude.
j
tude.
12°. 0
12°. 5
13°. 0
13°. 5
14°. 0
14°. 6
15°.0
15°. 5
16°. 0 \16°.6
17°.0
17°. 5
18°. 0
o
0
10
15
20
25
0
12.0
2.2
2.5
2.8
3.3
c
12.5
2.7
2.9
3.3
3.8
0
13.0
3.2
3.5
3.8
4.4
0
13.5
3.7
4.0
4.4,
4.9
0
14.0
4.2
4.5
4.9
5.5
0
14.5
4.7
5.0
5.5
6.1
0
15.0
5.3
5.6
6.0
6.6
0
15.5
5.8
6.1
6.5
7.1
16.0
6.3
6.6
7.1
7.7
o
16.5
6.8
7.1
7.6
8.3
0
17.0
7.3
7.7
8.1
8.8
o
17.5
7.9
8.2
8.7
9.4
o
18.0
8.3
8.7
9.2
9.9
f" "~
0
0
10
15
20
25
30
32
34
36
38
13.9
4.2
4.5
4.9
5.3
14.5
4.8
5.1
5.5
6.0
15.0
5.3
5.7
6.1
6.6
15.6
6.0
6.4
6.8
7.2
16.2
6.6
7.0
7.4
7.9
16.8
7.2
7.6
8.0
8.5
17.4
7.8
8.2
8.7
9.2
18.0
8.4
8.8
9.3
9.8
18.6
9.0
9.5
20.0
0.5
19.2
9.6
20.0
0.5
1.1
19.7
20.2
0.7
1.2
1.8
20.3
0.8
1.3
1.8
2.4
20.9
1.4
1.9
2.5
3.1
30
32
34
36
38
40
41
42
43
44
15.7
6.0
6.2
6.5
6.8
16.4
6.7
6.9
7.2
7.5
17.1
7.3
7.6
7.9
8.2
17.8
8.0
8.3
8.6
8.9
18.4
8.7
9.0
9.3
9.6
19.1
9.4
9.7
20.0
0.4
19.7
20.0
0.4
0.7
1.1
20.4
0.8
1.1
1.4
1.8
21.1
1.4
1.8
2.2
2.6
21.8
2.1
2.5
2.9
3.3
22.4
2.8
3.2
3.6
4.0
23.1
3.5
3.9
4.3
4.7
23.8
4.2
4.6
5.0
5.4
40
41
42
43
44
45
46
47
48
49
17.1
7.4
'7.7
8.1
8.5
17.8
8.2
8.5
8.9
9.3
18.5
8.9
9.3
9.7
20.1
19.3
9.6
20.0
0.4
0.8
20.0
0.4
0.8
1.2
1.6
20.7
1.1
1.5
2.0
2.4
21.5
1.9
2.3
2.8
3.2
22.2
2.6
3.1
3.6
4.1
23.0
3.4
3.8
4.3
4.9
23.7
4.1
4.6
5.1
5.7
24.4
4.9
5.4
5.9
6.5
25.2
5.7
6.2
6.7
7.3
25.9
6.4
6.9
7.5
8.1
45
46
47
48
49
50
51
52
53
54
18.9
9.3
9.7
20.2
0.7
19.7
20.1
0.6
1.1
1.6
20.5
0.9
1.4
1.9
2.5
21.3
1.8
2.3
2.8
3.4
22.1
2.6
3.1
3.7
4.3
22.9
3.5
4.0
4.6
5.2
23.7
4.3
4.9
5.5
6.1
24.6
5.1
5.7
6.4
7.1
25.4
6.0
6.6
7.3
8.0
26.2
6.8
7.5
8.2
8.9
27.0
7.6
8.3
9.0
9.8
27.9
8.5
9.2
30.0
0.8
28.7
9.4
30.1
0.9
1.7
50
51
52
53
54
55
56
57
58
59
21.2
1.8
2.4
3.1
3.8
22.2
2.8
3.4
4.1
4.8
23.1
3.7
4.4
5.1
5.9
24.0
4.7
5.4
6.1
6.9
24.9
5.6
6.4
7.2
8.0
25.9
6.6
7.4
8.2
9.1
26.8
7.6
8.4
9.2
30.2
27.8
8.6
9.4
30.3
1.3
28.7
9.5
30.4
1.3
2.3
29.7
30.5
1.4
2.4
3.5
30.6
1.5
2.5
3.5
4.6
31.6
2.5
3.5
4.6
5.7
32.6
3.6
'4.6
5.7
6.9
55
56
57
58
59
60
61
62
63
64
24.6
5.4
6.3
7.2
8.3
25.6
6.5
7.5
8.5
9.6
26.7
7.6
8.6
9.7
30.9
27.8
8.8
9.8
31.0
2.2
28.9
9.9
31.0
2.2
3.5
30.1
1.1
2.2
3.5
4.8
31.2
2.2
3.4
4.7
6.2
32.3
3.5
4.7
6.1
7.6
33.4
4.6
5.9
7.4
9.0
34.6
5.8
7.2
8.7
40.4
35.8
7.1
8.5
40.1
1.8
36.9
8.3
9.8
41.5
3.3
38.2
9.6
41.2
2.9
4.8
t
62
63
64
65.0
5.5
6.0
6.5
7.0
29.5
30.1
0.7
1.4
2.1
30.8
1.5
2.2
2.9
3.6
32.2
2.9
3.6
4.3
5.1
33.5
4.3
5.0
5.8
6.7
34.9
5.7
6.5
7.3
8.2
36.3
7.1
8.0
8.9
9.8
37.8
8.6
9.5
40.5
1.5
39.2
40.1
1.1
2.1
3.2
40.7
1.6
2.7
3.8
4.9
42.2
3.2
4.3
5.4
6.6
43.8
4.8
5.9
7.1
8.4
45.4
6.5
7.7
8.9
50.3
47.0
8.2
9.4
50.8
2.3
65.0
5.5
6.0
6.5
7.0
67.5
8.0
8.5
9.0
9.5
32.9
3.7
4.6
5.5
6.4
34.4
5.3
6.2
7.2
8.2
36.0
6.9
7.9
8.9
40.0
37.6
8.6
9.6
40.7
1.8
39.2
40.2
1.3
2.5
3.7
40.8
1.9
3.1
4.3
5.6
42.6
3.7
4.9
6.2
7.6
44.3
5.5
6.8
8.2
9.7
46.1
7.4
8.8
50.3
1.9
47.9
9.3
50.8
2.4
4.2
49.8
51.3
2.9
4.6
6.5
51.8
3:4
5.1
7.0
9.1
53.9
5.6
7.5
9.6
61.9
67.5
8.0
8.5
9.0
9.5
70.0
0.5
1.0
1.5
2.0
37.4
8.5
9.7
40.9
2.3
39.3
40.4
1.7
3.0
4.4
41.1
2.4
3.7
5.1
6.7
43.0
4.4
5.8
7.4
9.1
45.0
6.4
8.0
9.7
51.5
47.0
8.6
50.3
2.1
4.1
49.2
50.8
2.6
4.6
6.9
51.4
3.2
5.2
7.4
9.9
53.7
5.7
7.9
60.3
3.1
56.1
8.3
60.7
3.5
6.8
58.7
61.1
3.9
7.1
71.1
61.5
4.3
7.5
71.4
6.7
64.6
7/8
71.7
6.9
90.0
70.0
0.5
1.0
1.5
2.0
72.5
3.0
3.5
4.0
4.5
43.7
5.3
7.0
8.9
51.1
46.0
7.7
9.6
51.7
4.1
48.4
50.3
2.3
4.7
7.3
50.9
3.0
5.3
7.9
60.9
53.6
5.9
8.4
61.4
4.9
56.4
8.9
61.8
5.3
9.5
59.4
62.2
5.6
9.8
75. 5
62.7
6.1
70.3
75.9
90.0
66.4
70.6
6.1
90.0
70.9
6.3
90.0
76.5
90.0
90.0
72.5
3.0
3.5
4.0
4.5
TABLE 39. [Page 743
Amplitudes.
Lati
Declination.
Lati
tude.
tude.
1S°.0
18°. 5 j 19°.0
19°. 6
20°. 0
20°. 5
21°.0
21°. 5
22°. 0
22°. 5
23°. 0
23°. 5
24°. 0
o
0
10
15
20
25
18.0
8.3
8.7'
9.2
9.9
0
18.5
8.8
9.2
9.7
20.5
o
19.0
9.3
9.7
20.3
1.1
o
19.5
9.8
20.2
0.8
1.6
20.0
0.3
0.7
1.4
2.2
o
20.5
0.8
1.3
1.9
2.7
o
21.0
1.3
1.8
2.4
3.3
o
21.5
1.8
2.3
3.0
3.9
o
22.0
2.3
2.8
3.5
4.4
o
22.5
2.9
3.3
A.Q
5.0
o
23.0
3.4
3.9
4.6
5.5
o
23.5
3.9
4.4
5.1
6.1
o
24.0
4.4
4.9
5.7
6.7
o
0
10
15
20
25
30
32
34
36
38
20.9
1.4
1.9
2.5
3.1
21.5
2.0
2.5
3.1
3.8
22,1
2.6
3.1
3.7
4.4
22.7
3.2
3.8
4.4
5.1
23.3
3.8
4.4
5.0
5.7
23.8
4.4
5.0
5.7
6.4
24.4
5.0
5.6
6.3
7.0
25.0
5.6
6.2
6.9
7.7
25.6
6.2
6.9
7.6
8.4
26.2
6.8
7.5
8.2
9.1
26.8
7.4
8.1
8.9
9.7
27.4
8.0
8.7
9.5
30.4
28.0
8.7
9.4
30.2
1.1
30
32
34
36
38
40
41
42
43
44
23.9
4.2
4.6
5.0
5.4
24.4
4.8
5.3
5.7
6.2
25.1
5.5
6.0
6.4
6.9
25.8
6.2
6.7
7.2
7.7
26.5
6.9
7.4
7.9
8.4
27.2
7.7
8.1
8.6
9.1
27.9
8.3
8.8
9.3
9.8
28.6
9.1
9.6
30.1
0.6
29.3
9.8
30.3
0.8
1.4
30.0
0.5
1.0
1.6
2.2
30.7
1.2
1.7
2.3
2.9
31.3
1.8
2.4
3.0
3.6
32.1
2.6
3.2
• 3.8
4.4
40
41
42
43
44
45
46
47
48
49
25.9
6.4
6.9
7.5
8.1
26.7
7.2
7.7
8.3
8.9
27.4
7.9
8.5
9.1
9.7
28.2
8.7
9.3
9.9
30.6
28.9
9.5
30.1
0.7
1.4
29.7
30.3
0.9
1.6
2.3
30.4
1.0
1.7
2.4
3.1
31.2
1.8
2.5
3.2
4.0
32.0
2.6
3.3
4.0
4.8
32.8
3.4
4.1
4.9
5.7
33.5
4.2
4.9
5.7
6.5
34.3
5.0
5.7
6.5
7.4
35.1
5.8
6.6
7.4
8.3
45
46
47
48
49
50
51
52
53
54
28.7
9.4
30.1
0.9
1.7
29.6
30.3
1.0
1.8
2.7
30.4
1.1
1.9
2.7
3.6
31.3
2.0
2.8
3.7
4.6
32.1
2.9
3.7
4.6
5.6
33.0
3.8
4.7
5.6
6.6
33.9
4.7
5.6
6.6
7.6
34.8
5.6
6.5
7.5
8.6
35.6
6.5
7. 5
8.5
9.6
36.5
7.4
8.4
9.5
40.6
37.4
8.4
9.4
40.5
1.7
38.3
9.3
40.3
1.4
2.6
39.2
40.2
1.3
2.5
3.8
50
51
52
53
54
55
56
57
58
59
32.6
3.6
4.6
5.7
6.9
33.6
4.6
5.6
6.8
8.0
34.6
5.6
6.7
7.9
9.2
35.6
6.7
7.8
9.1
40.4
36.6
7.7
8.9
40.2
1.6
37.6
8.8
40.0
1.4
2.8
38.7
9.8
41.1
2.5
4.1
39.7
41.0
2.3
3.8
5.4
40.8
2.1
3.5
5.0
6.7
41.9
3.2
4.6
6.2
8.0
42.9
4.3
5.8
7.5
9.3
44.0
5.4
7.0
8.8
50.7
45.2
6.7
8.3
50.1
2.2
55
56
57
58
59
60.0
0.^
1.5
2.0
38.2
8.9
9.6
40.4
1.2
39.4
40.1
0.9
1.7
2.5
40.6
1.4
2.2
3.0
3.9
41.9
2.7
3.5
4.4
5.3
43.2
4.0
4.9
5.8
6.8
44.5
5.4
6.3
7.3
8.3
45.8
6.7
7.7
8.7
9.8
47.2
8.1
9.1
50.2
1.3
48.6
9.6
50.6
1.7
2.9
49.9
51.0
2.1
3.3
4.6
51.4
2.5
3.7
5.0
6.3
52.9
4.1
5.3
6.7
8.1
54.4
5.7
7.0
8.5
60.0
60.0
0.5
1.0
1.5
2.0
62.5
3.0
3.5
4.0
4.5
42.0
2.9
3.8
4.8
5.9
43.4
4.3
5.3
6.4
7.5
44.9
5.9
6.9
8.0
9.2
46.3
7.4
8.5
9.7
50.9
47.8
8.9
50.1
1.3
2.6
49.4
50.5
1.7
3.0
4.5
51.0
2.2
3.5
4.9
6.4
52.6
3.9
5.3
6.7
8.4
54.2
5.6
7.1
8.7
60.5
56.0
7.5
9.1
60.7
2.8
57.8
9.4
61.1
3.0
5.2
59.7
61.4
3.4
5.5
7.8
61.7
3.6
5.7
8.1
70.9
62.5
3.0
3.5
4.0
4.5
65.0
5.5
6.0
6.5
7.0
47.0
8.2
9.4
50.8
2.3
48.7
50.0
1.3
2.7
4.3
50.4
1.8
3.2
4.7
6.4
52.2
3.6
5.1
6.8
8.7
54.0
5.6
7.3
9.1
61.1
56.0
7.6
9.4
61.4
3.7
58.0
9.8
61.8
4.0
6.5
60.2
2.2
4.4
6.8
9.8
62.5
4.7
7.1
70.0
3.5
64.9
7.3
70.2
3.7
8.3
67.6
70.4
3.8
8.4
90.0
70.6
4.1
8.6
90.0
74.4
8.9
90.0
65.0
5.5
6.0
6.5
7.0
67.5
8.0
8.5
9.0
9.5
53.9
5.6
7.5
9.6
61.9
56.0
7.9
60.0
2.3
5.0
58.3
60.3
2.6
5.3
8.4
60.7
3.0
5.6
8.7
72.4
63.4
5.9
8.9
72.7
7.6
66.2
9.2
72.8
7.7
90.0
69.5
73.0
7.9
90.0
73.3
8.1
90.0
78.2
90.0
90.0
67.5
8.0
8.5
9.0
9.5
70.0
0.5
1.0
1.5
2.0
64.6
7.8
71.7
6.9
90.0
69.1
71.9
7.1
90.0
72.2
7.2
90.0
77.4
90.0
90.0
70.0
0.5
1.0
1.5
2.0
Page 744] TABLE 39. j
Amplitudes. '
Lati
tude.
Declination.
Lati
tude.
24°. 0
24°. 6
25°.0
25°. 5
26°. 0
26°. 5
27°.0
27°.5
28°. 0
28°. 6
29°. 0
29°.5
30°. 0
0
0
4
8
12
16
24.0
4.1
4.3
4.6
5.0
o
24.5
4.6
4.8
5.1
5.6
25.0
5.1
5.3
5.6
6.1
0
25.5
5.6
5.8
6.1
6.6
0
26.0
6.1
6.3
6.6
7.1
0
26.5
6.6
6.8
7.1
7.6
0
27.0
7.1
7.3
7.6
8.2
o
27.5
7.6
7.8
8.1
8.7
o
28.0
8.1
8.3
8.7
9.2
o
28.5
8.6
8.8
9.2
9.8
o
29.0
9.1
9.3
9.7
30.3
o
29.5
9.6
9.8
30.2
0.8
0
30.0
0.1
0.3
0.7
1.3
o
0
4
8
12
16
20
22
24
26
28
25.7
6.0
6.4
6.9
7.4
26.2
6.6
7.0
7.5
8.0
26.7
7.1
7.6
8.1
8.6
27.3
7.7
8.1
8.6
9.2
27.8
8.2
8.7
9.2
9.8
28.3
8.8
9.2
9.7
30.3
28.9
9.3
9.8
30.3
0.9
29.4
9.9
30.4
0.9
1.5
30.0
0.4
0.9
1.5
2.1
30.5
1.0
1.5
2.1
2.7
31.1
1.5
2.0
2.6
3.3
31.6
2.1
2.6
3.2
3.9
32.1
2.6
3.2
3.8
4.5
20
22
24
26
28
30
31
32
33
34
28.0
8.3
8.7
9.0
9.4
28.6
8.9
9.3
9.6
30.0
29.2
9.5
9.9
30.2
0.6
29.8
30.1
0.5
0.9
31.3
30.4
0.8
1.1
L5
1.9
31.0
1.4
1.7
2.1
2.6
31.6
2.0
2.4
2.8
3.2
32.2
2.6
3.0
3.4
3.8
32.8
3.2
3.6
4.0
4.5
33.4
3.8
4.2
4.7
5.1
34.0
4.5
4.9
5.3
5.8
34.7
5.1
5.5
6.0
6.4
35.3
5.7
6.1
6.6
7.1
30
31
32
33
34
35
36
37
38
39
29.8
30.2
0.6
1.1
1.6
30.4
0.8
1.3
1.7
2.2
31.1
1.5
1.9
2.4
2.9
31.7
2.1
2.6
3.1
3.6
32.3
2.8
3.3
3.8
4.3
33.0
3.5
4.0
4.5
5.0
33.6
4.1
4.6
5.2
5.7
34.3
4.8
5.3
5.9
6.5
35.0
5.5
6.0
6.6
7.2
35.6
6.1
6.7
7.3
7.9
36.3
6.8
7.4
8.0
8.6
36.9
7.5
8.1
8.7
9.3
37.6
8.2
8.8
9.4
40.0
35 |
36 1
37 i
38 i
39 !
40
41
42
43
44
32.1
2.6
3.2
3.8
4.4
32.8
3.3
3.9
4.5
5.2
33.5
4.1
4.7
5.3
6.0
34.2
4.8
5.4
6.1
6.8
34.9
5.5
6.1
6.8
7.5
35.6
6.2
6.9
7.6
8.3
36.3
7.0
7.7
8.4
9.1
37.1
7.7
8.4
9.2
40.0
37.8
8.5
9.2
9.9
40.7
38.5
9.2
9.9
40.7
1.6
39.3
40.0
0.7
1.5
2.4
40.0
0.7
1.5
2.3
3.2
40.7
1.5
2.3
3.1
4.0
40 .
41
42
43
44
45
46
47
48
49
35.1
5.8
6.6
7.4
8.3
35.9
6.6
7.4
8.3
9.2
36.7
7.5
8.3
9.2
40.1
37.5
8.3
9.1
40.0
1.0
38.3
9.1
40.0
0.9
1.9
39.1
40.0
0.9
1.8
2.8
39.9
40.8
1.7
2.7
3.8
40.8
1.7
2.6
3.6
4.7
41.6
2.5
3.5
4.6
5.7
42.5
3.4
4.4
5.5
6.7
43.3
4.3
5.3
6.4
7.6
44.1
5.1
6.2
7.4
8.6
45.0
6.0
7.1
8.3
9.6
45 I
46
47
48
49
50
51
52
53
54
39.2
40.2
1.3
2.5
3.8
40.2
1.2
2.3
3.5
4.9
41.1
2.2
3.3
4.6
6.0
42.0
3.2
4.4
5.7
7.1
43.0
4.1
5.4
6.7
8.2
43.9
5.1
6.4
7.8
9.4
51.1
2.0
2.9
3.9
5.0
44.9
6.2
7.5
9.0
50.6
45.9
7.2
8.6
50.1
1.8
46.9
8.2
9.7
51.3
3.0
47.9
9.3
50.8
2.5
4.3
48.9
50.4
2.0
3.7
5.6
50.0
1.5
3.1
4.9
6.9
51.1
2.6
4.3
6.2
8.3
50
51
52
53 i
54
55.0
5.5
6.0
6.5
7.0
45.2
5.9
6.7
7.5
8.3
46.3
7.1
7.9
8.8
9.6
47.5
8.3
9.1
50.0
0.9
48.6
9.5
50.4
1.3
2.2
49.8
50.7
1.6
2.6
3.6
52.3
3.3
4.3
5.4
6.5
53.6
4.6
5.7
6.8
8.0
54.9
6.0
7.1
8.3
9.5
56.3
7.4
8.6
9.9
61.2
57.7
8.9
60.1
1.5
2.9
59.1
60.4
1.7
3.2
4.7
60.7
2.0
3.4
5.0
6.6
55.0
5.5
6.0
6.5
7.0
57.5
8.0
8.5
9.0
9.5
57.5
8.0
8.5
9.0
9.5
49.2
50.1
1.1
2.2
3.3
50.5
1.5
2.5
3.6
4.8
51.9
2.9
4.0
5.1
6.4
53.2
4.3
5.5
6.7
8.0
54.7
5.8
7.0
8.3
9.7
56.2
7.4
8.6
60.0
1.5
57.7
8.9
60.3
1.8
3.4
59.3
60.6
2.1
3.7
5.5
60.9
2.4
3.9
5.7
7.7
62.6
4.2
6.0
7.9
70.1
64.5
6.2
8.1
70.3
2.8
66.4
8.3
70.4
3.0
5.9
68.5
70.7
3.1
6.2
80.1
60.0
0.5
1.0
1.5
2.0
54.4
5.7
7.0
8.5
60.0
56.0
7.4
8.8
60.3
2.0
57.7
9.1
60.7
2.3
4.2
59.4
61.0
2.6
4.4
6.5
61.2
2.9
4.7
6.7
9.0
63.2
5.0
7.0
9.2
71.9
65.2
7.2
9.5
72.0
5.2
67.4
9.6
72.3
5.4
9.6
69.9
72.4
5.5
9.7
90.0
72.6
5.8
9.8
90.0
75.8
9.9
90.0
80.0
90.0
90.0
60.0
0.5
1.0
1.5
2.0
62.5
3.0
3.5
4.0
4.5
62.5
3.0
3.5
4.0
4.5
61.7
3.6
5.7
8.1
70.9
63.9
6.0
8.3
71.1
4.4
66.2
8.6
71.3
4.6
9.0
68.8
71.5
4.8
9.2
90.0
71.7
4.9
9.3
90.0
75.1
9.4
90.0
9.5
90.0
90.0
TABLE 40. [Page 745
Correction of the Amplitude as observed on the Apparent Horizon.
Lati
tude.
Declination.
Lati
tude.
0°
5°
10°
12°
14°
16° 18°
20°
22°
24°
26°
28°
30°
o
0
5
10
15
20
o
0.0
.1
.1
.2
.2
o
0.0
.1
.1
.2
.2
0
0.0
.1
.1
.2
.2
0
0.0
.1
.1
.2
.2
0
0.0
.1
.1
.2
.2
0
0.0
.1
.1
.2
.2
0
0.0
.1
.2
.3
o
0.0
.1
.1
.2
.3
o
0.0
.1
.1
.2
.3
o
0.0
.1
.1
. 2
'.3
0
0.0
.1
.1
.2
.3
o
0.0
.1
.1
.2
.3
o
0.0
.1
.1
.2
.3
0
0
5
10
15
20
24
28
32
36
38
0.3
.3
.4
.5
.5
0.3
.4
.4
.5
.5
0.3
.4
.4
.5
.5
0.3
.4
.4
.5
.5
0.3
.4
.4
.5
.6
0.3
.4
.4
.5
.6
0.3
.4
.4
g
!e
0.3
.4
.5
.5
.6
0.3
.4
.5
.6
.6
0.3
.4
.5
.6
.6
0.3
.4
.5
.6
.6
0.4
.4
.5
.6
.7
0.4
.4
.5
.6
.7
24
28
32
36
38
40
42
44
46
48
0.6
.6
.6
.7
.7
0.6
.6
.6
.7
.8
0.6
.6
.7
.7
.8
0.6
.6
.7
.7
.8
0.6
.6
.7
.7
.8
0.6
.7
.7
.8
.8
0.6
.7
. 7
.8
.8
0.6
.7
. 7
.8
.9
0.6
.7
.8
.8
.9
0.7
.7
.8
.9
1.0
0.7
.8
.8
.9
1.0
0.7
.8
.9
.9
1.0
0.7
.8
.9
1.0
.1
40
42
44
46
48
50
52
54
56
58
0.8
.8
.9
1.0
.1
0.8
.9
.9
1.0
.1
0.8
.9
1.0
.1
.2
0.8
.9
1.0
.1
.2
0.9
.9
1.0
.1
.2
0.9
1.0
.1
.2
.3
0.9
1.0
.1
.2
.3
0.9
1.0
.1
.2
.4
1.0
.1
.2
.3
.5
1.1
.2
.3
.5
.7
1.1
.2
.4
.6
.9
1.1
.3
.5
.8
2.3
1.3
.5
.8
2.2
3.2
50
52
54
56
58
60
62
64
66
68
1.2
.3
.4
.5
.6
1.2
.3
.4
.5
.7
1.3
.4
.5
.7
.9
1.3
.4
.5
.7
2.0
1.3
.4
.6
.9
2.2
1.4
.6
.8
2.0
.4
1.5
.7
.9
2.3
.9
1.6
.8
2.2
.8
4.0
1.7
2.1
.6
3.8
2.0
.5
3.7
2.4
3.5
3.4
60
62
64
66
68
70
72
74
76
78
1.8
2.0
.2
.6
3.1
1.9
2.1
.5
3.0
.6
2.1
.5
3.0
.8
5.7
2.3
.8
3.5
5.2
2.6
3.3
4.8
3.1
4.6
4.3
70
72
74
76
78
80
3.8
4.4
80
61828°— 16 40
Page 746] TABLE 41.
Natural Sines and Cosines.
Prop.
parts
29
0°
1°
2°
3°
4°
Prop,
parts
2
M.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine
N. cos.
0
0
1
1
2
2
3
0
1
2
3
4
5
6
00000
00029
00058
00087
00116
00145
00175
100000
100000
100000
100000
100000
100000
100000
01745
01774
01803
01832
01862
01891
01920
99985
99984
99984
99983
99983
99982
99982
03490
03519
03548
03577
03606
03635
03664
99939
99938
99937
99936
99935
99934
99933
05234
05263
05292
05321
05350
05379
05408
99863
99861
99860
99858
99857
99855
99854
06976
07005
07034
07063
07092
07121
07150
99756
99754
99752
99750
99748
99746
99744
60
59
58
57
56
55
54
2
2
2
2
2
2
2
3
4
4
5
5
6
7
8
9
10
11
12
00204
00233
00262
00291
00320
00349
100000
100000
100000
100000
99999
99999
01949
01978
02007
02036
02065
02094
99981
99980
99980
99979
99979
99978
03693
03723
03752
03781
03810
03839
99932
99931
99930
99929
99927
99926
05437
05466
05495
05524
05553
05582
99852
99851
99849
99847
99846
99844
07179
07208
07237
07266
07295
07324
99742
99740
99738
99736
99734
99731
53
52
51
50
49
48
2
2
2
2
2
2
6
7
7
8
8
9
13
14
15
16
17
18
00378
00407
00436
00465
00495
00524
99999
99999
99999
99999
99999
99999
02123
02152
02181
02211
02240
02269
99977
99977
99976
99976
99975
99974
03868
03897
03926
03955
03984
04013
99925
99924
99923
99922
99921
99919
05611
05640
05669
05698
05727
05756
99842
99841
99839
99838
99836
99834
07353
07382
07411
07440
07469
07498
99729
99727
99725
99723
99721
99719
47
46
45
44
43
42
2
2
2
1
1
1
9
10
10
11
11
12
19
20
21
22
23
24
00553
00582
00611
00640
00669
00698
99998
99998
99998
99998
99998
99998
02298
02327
02356
02385
02414
02443
99974
99973
99972
99972
99971
99970
04042
04071
04100
04129
04159
04188
99918
99917
99916
99915
99913
99912
05785
05814
05844
05873
05902
05931
99833
99831
99829
99827
99826
99824
07527
07556
07585
07614
07643
•07672
99716
99714
99712
99710
99708
99705
41
40
39
38
37
36
1
1
1
1
1
1
12
13
13
14
14
15
25
26
27
28
29
30
00727
00756
00785
00814
00844
00873
99997
99997
99997
99997
99996
99996
02472
02501
02530
02560
02589
02618
99969
99969
99968
99967
99966
99966
04217
04246
04275
04304
04333
04362
99911
99910
99909
99907
99906
99905
05960
05989
06018
06047
06076
06105
99822
99821
99819
99817
99815
99813
07701
07730
07759
07788
07817
07846
99703
99701
99699
99696
99694
99692
35
34
33
32
31
30
1
1
1
1
1
1
15
15
16
16
17
17
31
32
33
34
35
36
37
38
39
40
41
42
00902
00931
00960
00989
01018
01047
99996
99996
99995
99995
99995
99995
02647
02676
02705
02734
02763
02792
99965
99964
99963
99963
99962
99961
04391
04420
04449
04478
04507
04536
99904
99902
99901
99900
99898
99897
06134
06163
06192
06221
06250
06279
99812
99810
99808
99806
99804
99803
07875
07904
07933
07962
07991
08020
99689
99687
99685
99683
99680
99678
29
28
27
26
25
24
1
1
1
1
1
1
18
18
19
19
20
20
01076
01105
01134
01164
01193
01222
99994
99994
99994
99993
99993
99993
02821
02850
02879
02908
02938
02967
99960
99959
99959
99958
99957
99956
04565
04594
04623
04653
04682
04711
99896
99894
99893
99892
99890
99889
06308
06337
06366
06395
06424
06453
99801
99799
99797
99795
99793
99792
08049
08078
08107
08136
08165
08194
99676
99673
99671
99668
99666
99664
23
22
21
20
19
18
1
1
1
1
1
1
21
21
22
22
23
23
43
44
45
46
47
48
01251
01280
01309
01338
01367
01396
99992
99992
99991
99991
99991
99990
02996
03025
03054
03083
03112
03141
999o5
99954
99953
99952
99952
99951
04740
04769
04798
04827
04856
04885
99888
99886
99885
99883
99882
99881
06482
06511
06540
06569
06598
06627
99790
99788
99786
99784
99782
99780
08223
08252
08281
08310
08339
08368
99661
99659
99657
99654
99652
99649
17
16
15
14
13
12
1
1
1
0
0
0
24
24
25
25
26
26
49
50
51
52
53
54
01425
01454
01483
01513
01542
01571
99990
99989
99989
99989
99988
99988
03170
03199
03228
03257
03286
03316
99950
99949
99948
99947
99946
99945
04914
04943
04972
05001
05030
05059
99879
99878
99876
99875
99873
99872
06656
06685
06714
06743
06773
06802
99778
99776
99774
99772
99770
99768
08397
08426
08455
08484
08513
08542
99647
99644
99642
99639
99637
99635
11
10
9
8
7
6
0
0
0
0
0
0
27
27
28
28
29
29
55
56
57
58
59
60
01600
01629
01658
01687
01716
01745
99987
99987
99986
99986
99985
99985
03345
03374
03403
03432
03461
03490
99944
99943
99942
99941
99940
99939
05088
05117
05146
05175
05205
05234
99870
99869
99867
99866
99864
99863
06831
06860
06889
06918
06947
06976
99766
99764
99762
99760
99758
99756
08571
08600
08629
08658
08687
08716
99632
99630
99627
99625
99622
99619
5
4
3
2
1
0
0
0
0
0
0
0
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
M.
89°
88°
87°
86°
86°
TABLE 41. [Page 747
Natural Sines and Cosines.
Prop,
parts
29
5°
6°
7°
8°
9°
Prop,
parts
4
M.
N.sine. N.cos.
N. sine.
N.cos.
N.sine.
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
60
59
58
57
56
55
54
0
0
1
1
2
2
3
0
1
2
3
4
5
6
08716
08745
08774
08S03
08831
08860
08889
99619
99617
99614
99612
99609
99607
99604
10453
10482
10511
10540
10569
10597
10626
99452
99449
99446
99443
99440
99437
99434
12187
12216
12245
12274
12302
12331
12360
99255
99251
99248
99244
99240
99237
99233
13917
13946
13975
14004
14033
14061
14090
99027
99023
99019
99015
99011
99006
99002
15643
15672
15701
15730
15758
15787
15816
98769
98764
98760
98755
98751
98746
98741
4
4
4
4
4
4
4
3
4
4
5
5
6
7
8
9
10
11
12
08918
08947
08976
09005
09034
09063
99602
99599
99596
99594
99591
99588
10655
10684
10713
10742
10771
10800
99431
99428
99424
99421
99418
99415
99412
99409
99406
99402
99399
99396
12389
12418
12447
12476
12504
12533
99230
99226
99222
99219
99215
99211
14119
14148
14177
14205
14234
14263
98998
98994
98990
98986
98982
98978
15845
15873
15902
15931
15959
15988
98737
98732
98728
98723
98718
98714
53
52
51
50
49
48
4
3
3
3
3
3
6
7
7
8
8
9
13
14
15
16
17
18
09092
09121
09150
09179
09208
09237
99586
99583
99580
99578
99575
99572
10829
10858
10887
10916
10945
10973
12562
12591
12620
12649
12678
12706
99208
99204
99200
99197
99193
99189
14292
14320
14349
14378
14407
14436
98973
98969
98965
98961
98957
98953
16017
16046
16074
16103
16132
16160
98709
98704
98700
98695
98690
98686
47
46
45
44
43
42
3
3
3
3
3
3
9
10
10
11
11
12
12
13
13
14
14
15
19
20
21
22
23
24
09266
09295
09324
09353
" 09382
09411
99570
99567 .
99564
99562
99559
99556
11002
11031
11060
11089
11118
11147
99393
99390
99386
99383
99380
99377
12735
12764
12793
12822
12851
12880
99186
99182
99178
99175
99171
99167
14464
14493
14522
14551
14580
14608
98948
98944
98940
98936
98931
98927
16189
16218
16246
16275
16304
16333
98681
98676
98671
98667
98662
98657
41
40
39
38
37
36
3
3
3
3
2
2
25
26
27
28
29
30
09440
09469
09498
09527
09556
09585
99553
99551
99548
99545
99542
99540
11176
11205
11234
11263
11291
11320
99374
99370
99367
99364
99360
99357
12908
12937
12966
12995
13024
13053
99163
99160
99156
99152
99148
99144
14637
14666
14695
14723
14752
14781
98923
98919
98914
98910
98906
98902
16361
16390
16419
16447
16476
16505
98652
98648
98643
98638
98633
98629
35
34
33
32
31
30
2
2
2
2
2
2
15
15
16
16
17
17
31
32
33
34
35
36
09614
09642
09671
09700
09729
09758
99537
99534
99531
99528
99526
99523
11349
11378
11407
11436
11465
11494
99354
99351
99347
99344
99341
99337
99331
99327
99324
99320
99317
13081
13110
13139
13168
13197
13226
99141
99137
99133
99129
99125
99122
14810
14838
14867
14896
14925
14954
98897
98893
98889
98884
98880
98876
16533
16562
16591
16620
16648
16677
98624
98619
98614
98609
98604
98600
29
28
27
26
25
24
2
2
2
2
2
2
18
18
19
19
20
20
21
21
22
22
23
23
37
38
39
40
41
42
09787
09816
09845
09874
09903
09932
99520
99517
99514
99511
99508
99506
11523
11552
11580
11609
11638
11667
13254
13283
13312
13341
13370
13399
99118
99114
99110
99106
99102
99098
14982 | 98871
15011 ! 98867
15040 98863
15069 98858
15097 1 98854
15126 1 98849
16706
16734
16763
16792
16820
16849
98595
98590
98585
98580
98575
98570
23
22
21
20
19
18
2
1
1
1
1
1
43
44
45
46
47
48
09961
09990
10019
10048
10077
10106
99503
99500
99497
99494
99491
99488
11696 j 99314
11725 i 99310
11754 99307
11783 99303
11812 99300
11840 ! 99297
13427
13456
13485
13514
13543
13572
99094
99091
99087
99083
99079
99075
15155
15184
15212
15241
15270
15299
98845
98841
98836
98832
98827
98823
16878 1 98565
16906 i 98561
16935 i 98556
16964 j 98551
16992 : 98546
17021 I 98541
17
16
15
14
13
12
1
1
1
1
1
1
24
24
25
25
26
26
49
50
51
52
53
54
10135
10164
10192
10221
10250
10279
99485
99482
99479
99476
99473
99470
11869 99293
11898 : 99290
11927 ; 99286
11956 99283
11985 , 99279
12014 99276
13600
13629
13658
13687
13716
13744
99071
99067
99063
99059
99055
99051
15327
15356
15385
15414
15442
15471
98818
98814
98809
98805
98800
98796
17050
17078
17107
17136
17164
17193
98536
98531
98526
98521
98516
98511
11
10
9
8
7
6
1
1
1
1
0
0
27
27
28
28
29
29
55
56
57
58
59
60
10308
10337
10366
10395
10424
10453
99467
99464
99461
99458
99455
99452
12043
12071
12100
12129
12158
12187
99272
99269
99265
99262
99258
99255
13773
13802
13831
13860
13889
13917
99047
99043
99039
99035
99031
99027
15500
15529
15557
15586
15615
15643
98791
98787
98782
98778
98773
98769
17222
17250
17279
17308
17336
17365
98506
98501
98496
98491
98486
98481
5
4
3
2
1
0
0
0
0
0
0
0
N. cos.
N.sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos. N. sine.
M.
84°
83°
82°
81°
80°
Page 748] TABLE 41.
Natural Sines and Cosines.
Prop,
parts
28
M.
10°
11°
12°
13°
14°
Prop,
parts
6
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
0
0
1
1
2
2
3
0
1
2
3
4
5
6
17365
17393
17422
17451
17479
17508
17537
98481
98476
98471
98466
98461
98455
98450
19081
19109
19138
19167
19195
19224
19252
98163
98157
98152
98146
98140
98135
98129
20791
20820
20848
20877
20905
20933
20962
97815
97809
97803
97797
97791
97784
97778
22495
22523
22552
22580
22608
22637
22665
97437
97430
97424
97417
97411
97404
97398
24192
24220
24249
24277
24305
24333
24362
97030
97023
97015
97008
97001
96994
96987
60
59
58
57
56
55
54
6
6
6
6
6
6
5
3
4
4
5
5
6
V
8
9
10
11
12
17565
17594
17623
17651
17680
17708
98445
98440
98435
98430
98425
98420
19281
19309
19338
19366
19395
19423
98124
98118
98112
98107
98101
98096
20990
21019
21047
21076
21104
21132
97772
97766
97760
97754
97748
97742
22693
22722
22750
22778
22807
22835
97391
97384
97378
97371
97365
97358
24390
24418
24446
24474
24503
24531
96980
96973
96966
96959
96952
96945
53
52
51
50
49
48
5
5
5
5
5
5
6
7-
7
7
8
8
13
14
15
16
17
18
17737
17766
17794
17823
17852
17880
98414
98409
98404
98399
98394
98389
19452
19481
19509
19538
19566
19595
98090
98084
98079
98073
98067
98061
21161
21189
21218
21246
21275
21303
97735
97729
97723
97717
97711
97705
22863
22892
22920
22948
22977
23005
97351
97345
97338
97331
97325
97318
24559
24587
24615
24644
24672
24700
96937
96930
96923
96916
96909
96902
47
46
45
44
43
42
5
5
5
4
4
4
9
9
10
10
11
11
19
20
21
22
23
24
17909
17937
17966
17995
18023
18052
98383
98378
98373
98368
98362
98357
19623
19652
19680
19709
19737
19766
98056
98050
98044
98039
98033
98027
21331
21360
21388
21417
21445
21474
97698
97692
97686
97680
97673
97667
23033
23062
23090
23118
23146
23175
97311
97304
97298
97291
97284
97278
24728
24756
24784
24813
24841
24869
96894
96887
96880
96873
96866
96858
41
40
39
38
37
36
4
4
4
4
4
4
12
12
13
13
14
14
25
26
27
28
29
30
18081
18109
18138
18166
18195
18224
98352
98347
98341
98336
98331
98325
19794
19823
19851
19880
19908
19937
98021
98016
98010
98004
97998
97992
21502
21530
21559
21587
21616
21644
97661
97655
97648
97642
97636
97630
97623*
97617
97611
97604
97598
97592
23203
23231
23260
23288
23316
23345
97271
97264
97257
97251
97244
97237
24897
24925
24954
24982
25010
25038
96851
96844
96837
96829
96822
96815
35
34
33
32
31
30
4
3
3
3
3
3
14
15
15
16
16
17
31
32
33
34
35
36
18252
18281
18309
18338
18367
18395
98320
98315
98310
98304
98299
98294
19965
19994
20022
20051
20079
20108
97987
97981
97975
97969
97963
97958
21672
21701
21729
21758
21786
21814
23373
23401
23429
23458
23486
23514
97230
97223
97217
97210
97203
97196
25066
25094
25122
25151
25179
25207
96807
96800
96793
96786
96778
96771
29
28
27
26
25
24
3
3
3
3
3
2
17
18
18
19
19
20
37
38
39
40
41
42
18424
18452
18481
18509
18538
18567
98288
98283
98277
98272
98267
98261
20136
20165
20193
20222
20250
20279
97952
97946
97940
97934
97928
97922
21843
21871
21899
21928
21956
21985
97585
97579
97573
97566
97560
97553
23542
23571
23599
23627
23656
23684
97189
97182
97176
97169
97162
97155
25235
25263
25291
25320
25348
25376
96764
96756
96749
96742
96734
96727
23
22
21
20
19
18
2
2
2
2
2
2
20
21
21
21
22
22
43
44
45
46
47
48
18595
18624
18652
18681
18710
18738
98256
98250
98245
98240
98234
98229
20307
20336
20364
20393
20421
20450
97916
97910
97905
97899
97893
97887
22013
22041
22070
22098
22126
22155
97547
97541
97534
97528
97521
97515
23712
23740
23769,,
23797
23825
23853
97148
97141
97134
97127
97120
97113
25404
25432
25460
25488
25516
25545
96719
96712
96705
96697
96690
96682
17
16
15
14
13
12
2
2
2
1
1
1
23
23
24
24
25
25
49
50
51
52
53
54
18767
18795
18824
18852
18881
18910
98223
98218
98212
98207
98201
98196
20478
20507
20535
20563
20592
20620
97881
97875
97869
97863
97857
97851
22183
22212
22240
22268
22297
22325
97508
97502
97496
97489
97483
97476
23882
23910
23938
23966
23995
24023
97106
97100
97093
97086
97079
97072
25573
25601
25629
25657
25685
25713
96675
96667
96660
96653
96645
96638
11
10
9
8
7
6
1
1
1
1
1
1
26
26
27
27
28
28
55
56
57
58
59
60
18938
18967
18995
19024
19052
19081
98190
98185
98179
98174
98168
98163
20649
20677
20706
20734
20763
20791
97845
97839
97833
97827
97821
97815
22353
22382
22410
22438
22467
22495
97470
97463
97457
97450
97444
97437
N. sine.
24051
24079
24108
24136
24164
24192
97065
97058
97051
97044
97037
97030
25741
25769
25798
25826
25854
25882
96630
96623
96615
96608
96600
96593
5
4
3
2
1
0
1
0
0
0
0
0
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. cos.
N. sine.
N. cos.
N. sine.
M.
79°
78°
77°
76°
75°
TABLE 41. [Page 749
Natural Sines and Cosines.
Prop,
part*
27
16°
16°
17°
18°
19°
Prop,
parts
9
M.
N. sine.
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
N.sine. | N.coe.
N.sine.
N.coe.
0
0
1
1
2
2
3
0
1
2
3
4
5
6
25882
25910
25938
25966
25994
26022
26050
96593
96585
96578
96570
96562
96555
96547
27564
27592
27620
27648
27676
27704
27731
96126
96118
96110
96102
96094
96086
96078
29237
29265
29293
29321
29348
29376
29404
95630
95622
95613
95605
95596
95588
95579
30902
30929
30957
30985
31012
31040
31068
95106
95097
95088
95079
95070
95061
95052
32557
32584
32612
32639
32667
32694
32722
94552
94542
94533
94523
94514
94504
94495
60
59
58
57
56
55
54
9
9
9
9
8
8
8
3
I
1
7
8
9
10
11
12
26079
26107
26135
26163
26191
26219
96540
96532
96524
96517
96509
96502
27759
27787
27815
27843
27871
27899
96070
96062
96054
96046
96037
96029
29432
29460
29487
29515
29543
29571
95571
95562
95554
95545
95536
95528
31095
31123
31151
31178
31206
31233
95043
95033
95024
95015
95006
94997
32749
32777
32804
32832
32859
32887
94485
94476
94466
94457
94447
94438
53
52
51
50
49
48
8
8
8
8
7
7
I
7
7
8
8
13
14
15
16
17
18
26247 96494
26275 96486
26303 96479
26331 96471
26359 ! 96463
26387 96456
27927
27955
27983
28011
28039
28067
96021
96013
96005
95997
95989
95981
29599
2962.6
29654
29682
29710
29737
95519
95511
95502
95493
95485
95476
31261
31289
31316
31344
31372
31399
94988
94979
94970
94961
94952
94943
32914 94428
32942 • 94418
32969 ! 94409
32997 94399
33024 94390
33051 ' 94380
47
46
45
44
43
42
7
7
7
7
6
6
9
9
9
10
10
11
11
12
12
13
13
14
19
20
21
22
23
24
26415
26443
26471
26500
26528
26556
96448
96440
96433
96425
96417
96410
28095
28123
28150
28178
28206
28234
95972
95964
95956
95948
95940
95931
29765
29793
29821
29849
29876
29904
95467
95459
95450
95441
95433
95424
31427
31454
31482
31510
31537
31565
94933
94924
94915
94906
94897
94888
33079 94370
33106 i 94361
33134 i 94351
33161 1 94342
33189 94332
33216 94322
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
6
6
6
6
6
5
25
26
27
28
29
30
26584 i 96402
26612 96394
26640 ; 96386
26668 : 96379
26696 96371
26724 ! 96363
28262 95923
28290 95915
28318 95907
28346 95898
28374 95890
28402 95882
29932
29960
29987
30015
30043
30071
95415
95407
95398
95389
95380
95372
31593
31620
31648
31675
31703
31730
94878
94869
94860
94851
94842
94832
33244 j 94313
33271 94303
33298 94293
33326 ! 94284
33353 • 94274
33381 94264
5
5
5
5
5
5
14
14
15
15
16
16
31
32
33
34
35
36
26752
26780
26808
26836
26864
26892
96355
96347
96340
96332
96324
96316
28429
28457
28485
28513
28541
28569
95871
95865
95857
95849
95841
95832
30098
30126
30154
30182
30209
30237
95363
95354
95345
95337
95328
95319
31758
31786
31813
31841
31868
31896
94823
94814
94805
94795
94786
94777
33408 94254
33436 94245
33463 94235
33490 94225
33518 94215
33545 94206
4
4
4
4
4
4
17
17
18
18
18
19
37
38
39
40
41
42
43
44
45
46
47
48
26920
26948
26976
27004
27032
27060
96308
96301
96293
96285
96277
96269
28597 j 95824
28625 ; 95816
28652 j 95807
28680 ! 95799
2S708 ! 95791
28736 95782
30265
30292
30320
30348
30376
30403
95310
95301
95293
95284
95275
95266
31923
31951
31979
32006
32034
32061
94768
94758
94749
94740
94730
94721
33573 94196
33600 94186
33627 ! 94176
33655 94167
33682 94157
33710 ! 94147
23
22
21
20
19
18
3
3
3
3
3
3
19
20
20
21
21
22
27088
27116
27144
27172
27200
27228
96261
96253
96246
96238
96230
96222
28764
28792
28820
28847
28875
28903
95774
95766
95757
95749
95740
95732
30431
30459
30486
30514
30542
30570
95257
95248
95240
95231
95222
95213
32089
32116
32144
32171
32199
32227
94712
94702
94693
94684
94674
94665
33737
33764
33792
33819
33846
33874
94137
94127
94118
94108
94098
94088
17
16
15
14
13
12
3
2
2
2
2
2
22
23
23
23
24
24
49
50
51
52
53
54
27256
27284
27312
27340
27368
27396
96214
96206
96198
96190
96182
96174
28931
28959
28987
29015
29042
29070
95724
95715
95707
95698
95690
95681
30597
30625
30653
30680
30708
30736
95204
95195
95186
95177
95168
95159
32254
2 0932
32309
32337
32364
32392
94656
94646
94637
94627
94618
94609
33901
33929
33956
33983
34011
34038
94078
94068
94058
94049
94039
94029
11
10
9
8
7
6
2
2
1
1
1
1
25
25
26
26
27
27
55
56
57
58
59
60
27424
27452
27480
27508
27536
27564
96166
96158
96150
96142
96134
96126
29098
29126
29154
29182
29209
29237
95673
95664
95656
95647
95639
95630
30763
30791
30819
30846
30874
30902
95150
95142
95133
95124
95115
95106
32419
32447
32474
32502
32529
32557
94599
94590
94580
94571
94561
94552
34065
34093
34120
34147
34175
34202
94019
94009
93999
93989
93979
93969
5
4
3
2
1
0
1
1
0
0
0
0
N.cos.
N.sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N.sine.
M.
74°
73°
72°
71°
70°
Page 750] TABLE 41.
Natural Sines and Cosines.
Prop,
parts
27
20°
21°
22°
28°
24°
Prop,
parts
11
M.
N. sine.
N. cos.
N. sine.
N. coa.
N. sine.
N. coa.
N. sine.
N. cos.
N. sine.
N. cos.
0
0
1
1
2
2
3
0
1
2
3
4
5
6
34202
34229
34257
34284
34311
34339
34366
93969
93959
93949
93939
93929
93919
93909
35837
35864
35891
35918
35945
35973
36000
93358
93348
93337
93327
93316
93306
93295
37461
37488
37515
37542
37569
37595
37622
92718
92707
92697
92686
92675
92664
92653
39073
39100
39127
39153
39180
39207
39234
92050
92039
92028
92016
92005
91994
91982
40674
40700
40727
40753
40780
40806
40833
91355
91343
91331
91319
91307
91295
91283
60
59
58
57
56
55
54
11
11
11
10
10
10
10
3
4
4
5
5
5
7
8
9
10
11
12
34393
34421
34448
34475
34503
34530
93899
93889
93879
93869
93859
93849
36027
36054
36081
36108
36135
36162
93285
93274
93264
93253
93243
93232
37649
37676
37703
37730
37757
37784
92642
92631
92620
92609
92598
92587
39260
39287
39314
39341
39367
39394
91971
91959
91948
91936
91925
91914
40860
40886
40913
40939
40966
40992
91272
91260
91248
91236
91224
91212
91200
91188
91176
91164
91152
91140
53
52
51
50
49
48
47
46
45
44
43
42
10
10
9
I
9
6
6
7
7
8
8
13
14
15
16
17
18
~19~
20
21
22
23
24
"25"
26
27
28
29
30
34557
34584
34612
34639
34666
34694
93839
93829
93819
93809
93799
93789
36190
36217
36244
36271
36298
36325
93222
93211
93201
93190
93180
93169
37811
37838
37865
37892
37919
37946
92576
92565
92554
92543
92532
92521
92510"
92499
92488
92477
92466
92455
39421
39448
39474
39501
39528
39555
91902
91891
91879
91868
91856
91845
41019
41045
41072
41098
41125-
41151
9
8
8
8
8
8
9
9
9
10
10
11
34721
34748
34775
34803
34830
34857
93779
93769
93759
93748
93738
93728
36352
36379
36406
36434
36461
36488
93159
93148
93137
93127
93116
93106
37973
37999
38026
38053
38080
38107
39581
39608
39635
39661
39688
39715
91833
91822
91810
91799
91787
91775
41178
41204
41231
41257
41284
41310
91128
91116
91104
91092
91080
91068
41
40
39
38
37
36
8
7
7
7
7
7
11
12
12
13
13
14
34884
34912
34939
34966
34993
35021
93718
93708
93698
93688
93677
93667
36515
36542
36569
36596
36623
36650
93095
93084
93074
93063
93052
93042
38134
38161
38188
38215
38241
38268
92444
92432
92421
92410
92399
92388
39741
39768
39795
39822
39848
39875
91764
91752
91741
91729
91718
91706
41337
41363
41390
41416
41443
41469
91056
91044
91032
91020
91008
90996
35
34
33
32
31
30
6
6
6
6
6
6
14
14
15
15
16
16
31
32
33
34
35
36
35048
35075
35102
35130
35157
35184
93657
93647
93637
93626
93616
93606
36677
36704
36731
36758
36785
36812
93031
93020
93010
92999
92988
92978
38295
38322
38349
38376
38403
38430
92377
92366
92355
92343
92332
92321
39902
39928
39955
39982
40008
40035
91694
91683
91671
91660
91648
91636
41496
41522
41549
41575
41602
41628
90984
90972
90960
90948
90936
90924
29
28
27
26
25
24
5
5
5
5
5
4
17
17
18
18
18
19
37
38
39
40
41
42
35211
35239
35266
35293
35320
35347
93596
93585
93575
93565
93555
93544
36839
36867
36894
36921
36948
36975
92967
92956
92945
92935
92924
92913
38456
38483
38510
38537
38564
38591
92310
92299
92287
92276
92265
92254
40062
40088
40115
40141
40168
40195
91625
91613
91601
91590
91578
91566
41655
41681
41707
41734
41760
41787
90911
90899
90887
90875
90863
90851
2$
22
21
20
19
18
17
16
15
14
13
12
4
4
4
4
3
3
19
20
20
21
21
22
43
44
45
46
47
48
35375
35402
35429
35456
35484
35511
93534
93524
93514
93503
93493
93483
37002
37029
37056
37083
37110
37137
92902
92892
92881
92870
92859
92849
38617
38644
38671
38698
38725
38752
92243
92231
92220
92209
92198
92186
40221
40248
40275
40301
40328
40355
91555
91543
91531
91519
91508
91496
41813
41840
41866
41892
41919
41945
90839
90826
90814
90802
90790
90778
3
3
3
3
2
2
22
23
23
23
24
24
49
50
51
52
53
54
35538
35565
35592
35619
35647
35674
93472
93462
93452
93441
93431
93420
37164
37191
37218
37245
37272
37299
92838
92827
92816
92805
92794
92784
38778
38805
38832
38859
38886
38912
92175
92164
92152
92141
92130
92119
40381
40408
40434
40461
40488
40514
91484
91472
91461
91449
91437
91425
41972
41998
42024
42051
42077
42104
90766
90753
90741
90729
90717
90704
11
10
9
8
7
6
2
2
2
1
1
1
25
25
26
26
27
27
55
56
57
58
59
60
35701
35728
35755
35782
35810
35837
93410
93400
93389
93379
93368
93358
37326
37353
37380
37407
37434
37461
92773
92762
92751
92740
92729
92718
38939
38966
38993
39020
39046
39073
92107
92096
92085
92073
92062
92050
40541
40567
40594
40621
40647
40674
91414
91402
91390
91378
91366
91355
42130
42156
42183
42209
42235
42262
90692
90680
90668
90655
90643
90631
5
4
3
2
1
0
1
1
1
0
0
0
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
M
69°
68°
67°
66°
65°
TABLE 41. [Page 751
Natural Sines and Cosines.
Prop,
parts
i!6
25°
26°
. 27°
28°
29°
Prop.
parts
14
M.
0
1
2
3
4
5
6
N. sine.
N. cos.
N. sine. N. cos.
N. sine. N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
0
0
1
1
2
2
3
42262
42288
42315
42341
42367
42394
42420
90631
! 90618
: 90606
1 90594
90582
I 90569
| 90557
43837
43863
43889
43916
43942
43968
43994
89879
89867
89854
89841
89828
89816
89803
45399
45425
45451
45477
45503
45529
45554
89101
89087
89074
89061
89048
89035
89021
46947
46973
46999,
47024
47050
47076
47101
88295
88281
88267
88254
88240
88226
88213
48481
48506
48532
48557
48583
48608
48634
87462
87448
87434
87420
87406
87391
87377
60
59
58
57
56
55
54
14
14
14
13
13
13
13
3
3
4
4
5
5
7
8
9
10
11
12
42446
42473
42499
42525
42552
42578
90545
90532
90520
90507
90495
90483
44020
44046
44072
44098
44124
44151
89790
i 89777
89764
89752
89739
89726
45580
45606
45632
45658
45684
45710
89008
88995
88981
88968
88955
88942
47127
47153
47178
47204
47229
47255
88199
88185
88172
88158
88144
88130
48659
48684
48710
48735
48761
48786
87363
87349
87335
87321
87306
87292
53
52
51
50
49
48
12
12
12
12
11
11
6
6
7
7
7
8
13
14
15
16
17
18
42604 i 90470
42631 90458
42657 90446
42683 90433
42709 90421
42736 90408
44177
44203
44229
44255
44281
44307
89713
89700
89687
89674
89662
89649
45736 88928
45762 88915
45787 88902
45813 88888
45839 88875
45865 88862
47281
47306
47332
47358
47383
47409
88117
88103
88089
88075
88062
88048
48811
48837
48862
48888
48913
48938
87278
87264
87250
87235
87221
87207
47
46
45
44
43
42
11
11
11
10
10
10
8
9
9
10
10
10
19
20
21
22
23
24
42762
42788
42815
42841
42867
42894
90396
90383
90371
90358
90346
90334
44333
44359
44385
44411
44437
44464
89636
89623
89610
89597
89584
89571
45891 88848
45917 88835
45942 88822
45968 88808
45994 88795
46020 88782
47434
47460
47486
47511
47537
47562
88034
88020
88006
87993
87979
87965
48964
48989
49014
49040
49065
49090
87193
87178
87164
87150
87136
87121
41
40
39
38
37
36
35
34
33
32
31
30
10
9
9
9
9
8
11
11
12
12
13
13
25
26
27
28
29
30
42920 90321
42946 90309
42972 , 90296
' 42999 90284
43025 90271
43051 i 90259
44490
44516
44542
44568
44594
44620
89558
89545
89532
89519
89506
89493
46046
46072
46097
46123
46149
46175
88768
88755
88741
88728
88715
88701
47588
47614
47639
47665
47690
47716
87951
87937
87923
87909
87896
87882
49116
49141
49166
49192
49217
49242
87107
87093
87079
87064
87050
87036
8
8
8
7
7
7
13
14
14
15
15
16
31
32
33
34
35
36
43077 90246
43104 , 90233
43130 j 90221
43156 i 90208
43182 90196
43209 90183
44646
44672
44698
44724
44750
44776
89480
89467
89454
89441
89428
89415
46201
46226
46252
46278
46304
46330
88688
88674
88661
88647
88634
88620
47741
47767
47793
47818
47844
47869
87868
87854
87840
87826
87812
87798
49268
49293
49318
49344
49369
49394
87021
87007
86993
86978
86964
86949
29
28
27
26
25
24
7
7
6
6
6
6
16
16
17
17
18
18
37
38
39
40
41
42
43235 90171
43261 90158
43287 90146
43313 90133
43340 90120
43366 j 90108
44802
44828
44854
44880
44906
44932
89402
89389
89376
89363
89350
89337
46355
46381
46407
46433
46458
46484
88607
88593
88580
88566
88553
88539
47895
47920
47946
47971
47997.
48022
87784
87770
87756
87743
87729
87715
49419
49445
49470
49495
49521
49546
86935
86921
86906
86892
86878
86863
23
22
21
20
19
18
5
5
5
5
4
4
19
19
20
20
20
21
43
44
45
46
47
48
43392
43418
43471
43497
43523
90095
90082
90070
90057
90045
90032
44958
44984
45010
45036
45062
45088
89324
89311
89298
89285
89272
89259
46510
46536
46561
46587
46613
46639
88526
88512
88499
88485
88472
88458
48048
48073
48099
48124
48150
48175
87701
87687
87673
87659
87645
87631
49571
49596
49622
49647
49672
49697
86849
86834
86820
86805
86791
86777
17
16
15
14
13
12
4
4
4
3
3
3
21
22
22
23
23
23
49
50
51
52
53
54
43549
43575
43602
43628
43654
43680
90019
90007
89994
89981
. 89968
89956
45114
45140
45166
45192
45218
45243
89245
89232
89219
89206
89193
89180
46664
46690
46716
46742
46767
46793
88445
88431
88417
88404
8S390
88377
48201
48226
48252
48277
48303
48328
87617
87603
87589
87575
87561
87546
49723
49748
49773
49798
49824
49849
86762
86748
86733
86719
86704
86690
11
10
9
8
7
6
3
2
2
2
2
1
24
24
25
25
26
26
55
56
57
58
59
60
43706
43733
43759
43785
43811
43837
89943
89930
89918
89905
89892
89879
45269
45295
45321
45347
45373
45399
89167
89153
89140
89127
89114
89101
46819
46844
46870
46896
46921
46947
88363
88349
88336
88322
88308
88295
48354
48379
48405
48430
48456
48481
87532
87518
87504
87490
87476
87462
49874
49899
49924
49950
49975
50000
86675
86661
86646
86632
86617
86603
5
4
3
2
1
0
1
1
1
0
0
0
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
M.
64°
es°
62°
61°
60°
Page 752] TABLE 41.
Natural Sines and Cosines.
Prop,
parts.
25
30°
31°
82°
83°
34°
Prop,
parta.
16
M.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
0
0
1
1
2
2
3
0
1
2
3
4
5
6
50000
50025
50050
50076
50101
50126
50151
86603
86588
86573
86559
86544
86530
86515
51504
51529
51554
51579
51604
51628
51653
85717
85702
85687
85672
85657
85642
85627
52992
53017
53041
53066
53091
53115
53140
84805
84789
84774
84759
84743
84728
84712
54464
54488
54513
54537
54561
54586
54610
83867
83851
83835
83819
83804
83788
83772
55919
55943
55968
55992
56016
56040
56064
82904
82887
82871
82855
82839
82822
82806
60
59
58
57
56
55
54
16
16
15
15
15
15
14
3
3
4
4
5
5
7
8
9
10
11
12
50176
50201
50227
50252
50277
50302
86501
86486
86471
86457
86442
86427
51678
51703
51728
51753
51778
51803
85612
85597
85582
85567
85551
85536
53164
53189
53214
53238
53263
53288
84697
84681
84666
84650
84635
84619
54635
54659
54683
54708
54732
54756
83756
83740
83724
83708
83692
83676
56088
56112
56136
56160
56184
56208
82790
82773
82757
82741
82724
82708
53
52
51
50
49
48
14
14
14
13
13
13
5
6
6
7
7
8
8~
8
9
9
10
10
13
14
15
16
17
18
50327
50352
50377
50403
50428
50453
86413
86398
86384
86369
86354
86340
51828
51852
51877
51902
51927
51952
85521
85506
85491
85476
85461
85446
53312
53337
53361
53386
53411
53435
84604
84588
84573
84557
84542
84526
54781
54805
54829
54854
54878
54902
83660
83645
83629
83613
83597
83581
56232
56256
56280
56305
56329 -
56353
82692
82675
82659
82643
82626
82610
47
46
45
44
43
42
41
40
39
38
37
36
13
12
12
12
11
11
19
20
21
22
23
24
50478
50503
50528
50553
50578
50603
86325
86310
86295
86281
86266
86251
51977
52002
52026
52051
52076
52101
85431
85416
85401
85385
85370
85355
53460
53484
53509
53534
53558
53583
84511
84495
84480
84464
84448
84433
54927
54951
54975
54999
55024
55048
83565
83549
83533
83517
83501
83485
56377
56401
56425
56449
56473
56497
82593
82577
82561
82544
82528
82511
11
11
10
10
10
10
10
11
11
12
12
13
25
26
27
28
29
.30
50628
50654
50679
50704
50729
50754
86237
86222
86207
86192
86178
86163
52126
52151
52175
52200
52225
52250
85340
85325
85310
85294
85279
85264
53607
53632
53656
53681
53705
53730
84417
84402
84386
84370
84355
84339
55072
55097
55121
55145
55169
55194
83469
83453
83437
83421
83405
83389
56521
56545
56569
56593
56617
56641
82495
82478
82462
82446
82429
82413
36
34
33
32
31
30
9
9
9
9
8
8
13
13
14
14
15
15
31
32
33
34
35
36
50779
50804
50829
50854
50879
50904
86148
86133
86119
86104
86089
86074
52275
52299
52324
52349
52374
52399
85249
85234
85218
85203
85188
85173
53754
53779
53804
53828
53853
53877
84324
84308
84292
84277
84261
84245
55218
55242
55266
55291
55315
55339
83373
83356
83340
83324
83308
83292
56665
56689
56713
56736
56760
56784
82396
82380
82363
82347
82330
82314
29
28
27
26
25
24
8
7
7
7
7
6
15
16
16
17
17
18
37
38
39
40
41
42
43
44
45
46
47
48
50929
50954
50979
51004
51029
51054
86059
86045
86030
86015
86000
85985
52423
52448
52473
52498
52522
52547
85157
85142
85127
85112
85096
85081
53902
53926
53951
53975
54000
54024
84230
84214
84198
84182
84167
84151
55363
55388
55412
55436
55460
55484
83276
83260
83244-
83228
83212
83195
56808
56832
56856
56880
56904
56928
82297
82281
82264
82248
82231
82214
23
22
21
20
19
18
17
16
15
14
13
12
6
6
6
5
5
5
18
18
19
19
20
20
51079
51104
51129
51154
51179
51204
85970
85956
85941
85926
85911
85896
52572
52597
52621
52646
52671
52696
85066
85051
85035
85020
85005
84989
54049
54073
54097
54122
54146
54171
84135
84120
84104
84088
84072
84057
55509
55533
55557
55581
55605
55630
83179
83163
83147
83131
83115
83098
56952
56976
57000
57024
57047
57071
82198
82181
82165
82148
82132
82115
5
4
4
4
3
3
20
21
21
•22
22
23
49
50
51
52
53
54
51229
51254
51279
51304
51329
51354
85881
85866
85851
85836
85821
85806
52720
52745
52770
52794
52819
52844
52893
52918
52943
52967
52992
84974
84959
84943
84928
84913
84897
54195
54220
54244
54269
54293
54317
84041
84025
84009
83994
83978
83962
55654
55678
55702
55726
55750
55775
83082
83066
83050
83034
83017
83001
57095
57119
57143
57167
57191
57215
82098
82082
82065
82048
82032
82015
11
10
9
8
7
6
3
3
2
2
2
2
23
23
24
24
25
25
55
56
57
58
59
60
51379
51404
51429
51454
51479
51504
85792
85777
85762
85747
85732
85717
84882
84866
84851
84836
84820
84805
54342
54366
54391
54415
54440
54464
83946
83930
83915
83899
83883
83867
55799
55823
55847
55871
55895
55919
82985
82969
82953
82936
82920
82904
57238
57262
57286
57310
57334
57358
81999
81982
81965
81949
81932
81915
5
4
3
2
1
0
1
1
1
1
0
0
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. cos.
N.sine.
M.
59°
68°
67°
66°
65°
TABLE 41. [Page 753
Natural Sines and Cosines.
Prop,
pans
23
86°
36°
37°
38°
39°
Prop,
parts
18
M.
N. Bine.
N.cos.
N. sine.
N.cos.
N. sine.
N. cos.
N. sine.
N.cos.
N. sine.
N.cos.
0
0
1
1
2
2
2
0
1
2
3
4
5
6
57358
57381
57405
57429
57453
57477
57501
81915
81899
81882
81865
81848
81832
81815
58779
58802
58826
58849
58873
58896
58920
80902
80885
80867
80850
80833
80816
80799
60182
60205
60228
60251
60274
60298
60321
79864
79846
79829
79811
79793
79776
79758
61566
61589
61612
61635
61658
61681
61704 !
78801
78783
78765
78747
78729
78711
78694
62932 !
62955
62977
63000
63022
63045
63068
77715
77696
77678
77660
77641
77623
77605
60
59
58
57
56
55
54
18
18
17
17
17
17
16
3
3
3
4
4
5
/
8
9
10
11
12
57524
57548
57572
57596
57619
57643
81798
81782
81765
81748
81731
81714
58943
58967
58990
59014
59037
59061
80782
80765
80748
80730
80713
80696
60344
60367
60390
60414
60437
60460
79741
79723
79706
79688
79671
79653
61726
61749
61772,
61795
61818
61841
78676
78658
78640
78622
78604
78586
63090
63113
63135
63158
63180
63203
77586
77568
77550
77531
77513
77494
53
52
51
50
49
48
16
16
15
15
15
14
5
5
6
6
7
7
13
14
15
16
17
18
57667
57691
57715
57738
57762
57786
81698
81681
81664
81647
81631
81614
59084
59108
59131
59154
59178
59201
80679
80662
80644
80627
80610
80593
60483
60506
60529
60553
60576
60599
79635
79618
79600
79583
79565
79547
61864
61887
61909
61932
61955
61978
78568
78550
78532
78514
78496
78478
63225
63248
63271
63293
63316
63338
77476
77458
77439
77421
77402
77384
47
46
45
44
43
42
14
14
14
13
13
13
7
8
8
8
9
9
19
20
21
22
23
24
57810
57833
57857
57881
57904
57928
81597
81580
81563
81546
81530
81513
59225
59248
59272
59295
59318
59342
80576
80558
80541
80524
80507
80489
60622
60645
60668
60691
60714
60738
79530
79512
79494
79477
79459
79441
62001
62024
62046
62069
62092
62115
78460
78442
78424
78405
78387
78369
63361
63383
63406
63428
63451
63473
77366
77347
77329
77310
77292
77273
41
40
39
38
37
36
12
12
12
11
11
11
10
10
10
11
11
12
25
26
27
28
29
30
57952
57976
57999
58023
58047
58070
81496
81479
81462
81445
81428
81412
59365
59389
59412
59436
59459
59482
80472
80455
80438
80420
80403
80386
60761
60784
60807
60830
60853
60876
79424
79406
79388
79371
79353
79335
62138
62160
62183
62206
62229
62251
78351
78333
78315
78297
78279
78261
63496
63518
63540
63563
63585
63608
77255
77236
77218
77199
77181
77162
35
34
33
32
3f
30
11
10
10
10
9
9
12
12
13
13
13
14
31
32
33
34
35
36
58094
58118
58141
58165
58189
58212
81395
81378
81361
81344
81327
81310
59506
59529
59552
59576
59599
59622
80368
80351
80334
80316
80299
80282
60899
60922
60945.
60968
60991
61015
79318
79300
79282
79264
79247
79229
62274
62297
62320
62342
62365
62388
78243
78225
78206
78188
78170
78152
63630
63653
63675
63698
63720
63742
77144
77125
77107
77088
77070
77051
29
28
27
26
25
24
9
8
8
8
8
7
14
15
15
15
16
16
37
38
39
40
41
42
58236
58260
58283
58307
58330
58354
81293
81276
81259
81242
81225
81208
59646
59669
• 59693
59716
59739
59763
80264
80247
80230
80212
80195
80178
61038
61061
61084
61107
61130
61153
79211
79193
79176
79158
; 79140
i 79122
62411
62433
62456
62479
62502
62524
78134
78116
78098
78079
78061
78043
63765
63787
63810
63832
63854
63877
77033
77014
76996
76977
76959
76940
23
22
21
20
19
18
i
7
6
6
6
5
16
17
17
18
18
18
43
44
45
46
47
48
58378
58401
58425
58449
58472
58496
81191
81174
81157
81140
81123
81106
59786
59809
59832
59856
59879
59902
80160
80143
80125
80108
80091
80073
61176 79105
61199 ' 79087
61222 i 79069
61245 i 79051
61268 : 79033
61291 79016
62547
62570
62592
62615
6263S
62660
78025
78007
77988
77970
77952
77934
63899
63922
63944
63966
63989
64011
76921
76903
76884
76866
76847
76828
76791
76772
76754
76735
76717
17
16
15
14
13
12
5
5
5
4
4
4
19
19
20
20
20
21
49
50
51
52
53
54
58519
58543
58567
58590
58614
58637
81089
81072
81055
81038
81021
81004
59926
59949
59972
59995
60019
60042
80056
80038
' 80021
80003
79986
79968
61314 ! 78998
61337 i 78980
61360 ' 78962
613S3 78944
61406 i 78926
61429 i 78908
62683
62706
62728
62751
62774
62796
62819
62842
62864
62887
62909
62932
77916
77897
77879
77861
77843
77824
77806
77788
77769
77751
77733
77715
64033
64056
64078
64100
64123
64145
11
10
9
8
7
6
3
3
3
2
2
2
21
21
22
22
23
23
55
56
57
58
59
60
58661
58684
58708
58731
58755
58779
80987
80970
80953
80936
80919
80902
60065 79951
60089 79934
60112 79916
60135 79899
60158 79881
60182 | 79864
61451 78891
61474 78873
61497 i 78855
61520 ' 78837
61543 78819
61566 : 78801
64167
64190
64212
64234
64256
64279
76698
76679
76661
76642
76623
76604
o
4
3
o
1
o.
'2
1
1
1
0
0
N. cos.
N. sine.
N.cos. X. sine.
N. cos. N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
M.
54°
53°
52°
51°
50°
Page 754] TABLE 41.
Natural Sines and Cosines.
Prop.
parts
22
40°
41°
42°
48°
44°
Prop,
parts
19
M.
N.sine.
N. cos.
N.sine.
N. cos.
N.sine.
N. cos.
N.sine.
N.cos.
N. sine.
N. cos.
0
0
1
1
1
2
2
0
1
2
3
4
5
6
64279
64301
64323
64346
64368
64390
64412
76604
76586
76567
76548
76530
76511
76492
65606
65628
65650
65672
65694
65716
65738
75471
75452
75433
75414
75395
75375
75356
66913
66935
66956
66978
66999
67021
67043
74314
74295
74276
74256
74237
74217
74198
68200
68221
68242
68264
68285
68306
68327
73135
73116
73096
73076
73056
73036
73016
69466
69487
69508
69529
69549
69570
69591
71934
71914
71894
71873
71853
71833
71813
60
59
58
57
56
55
54
19
19
18
18
18
17
17
3
3
3
4
4
4
7
8
9
10
11
12
64435
64457
64479
64501
64524
64546
76473
76455
76436
76417
76398
76380
65759
65781
65803
65825
65847
65869
75337
75318
75299
75280
75261
75241
67064
67086
67107
67129
67151
67172
74178
74159
74139
74120
74100
74080
68349
68370
68391
68412
68434
68455
72996
72976
72957
72937
72917
72897
69612
69633
69654
69675
69696
69717
71792
71772
71752
71732
71711
71691
53
52
51
50
49
48
17
16
16
16
16
15
5
5
6
6
6
7
13
14
15
16
17
18
64568
64590
64612
64635
64657
64679
76361
76342
76323
76304
76286
76267
65891
65913
65935
65956
65978
66000
75222
75203
75184
75165
75146
75126
67194
67215
67237
67258
67280
67301
74061
74041
74022
74002
73983
73963
68476
68497
68518
68539
68561
68582
72877
72857
72837
72817
72797
72777
69737
69758
69779
69800
69821
69842
71671
71650
71630
71610
71590
71569
47
46
45
44
43
42
15
15
14
14
14
13
7
7
8
8
8
9
19
20
21
22
23
24
64701
64723
64746
64768
64790
64812
76248
76229
76210
76192
76173
76154
66022
66044
66066
66088
66109
66131
66175
66197
66218
66240
66262
75107
75088
75069
75050
75030
75011
67323
67344
67366
67387
67409
67430
73944
73924
73904
73885
73865
73846
68603
68624
68645
68666
68688
68709
72757
72737
•72717
72697
72677
72657
69862
69883
69904
69925
69946
69966
71549
71529
71508
71488
71468
71447
41
40
39
38
37
36
13
13
12
12
12
11
9
10
10
10
11
11
25
26
27
28
29
30
64834
64856
64878
64901
64923
64945
76135
76116
76097
76078
76059
76041
74992
74973
74953
74934
74915
74896
67452
67473
67495
67516
67538
67559
73826
73806
73787
73767
73747
73728
68730
68751
68772
68793
68814
68835
72637
72617
72597
72577
72557
72537
72517
72497
72477
72457
72437
72417
69987
70008
70029
70049
70070
70091
71427
71407
71386
71366
71345
71325
35
34
33
32
31
30
11
11
10
10
10
10
11
12
12
12
13
13
31
32
33
34
35
36
64967
64989
65011
65033
65055
65077
76022
76003
75984
75965
75946
75927
66284
66306
66327
66349
66371
66393
74876
74857
74838
74818
74799
74780
67580
67602
67623
67645
67666
67688
73708
73688
73669
73649
73629
73610
68857
68878
68899
68920
68941
68962
70112
70132
70153
70174
70195
70215
71305
71284
71264
71243
71223
71203
29
28
27
26
25
24
9
9
9
8
8
8
14
14
14
15
15
15
37
38
39
40
41
42
65100
65122
65144
65166
65188
65210
75908
75889
75870
75851
75832
75813
66414
66436
66458
66480
66501
66523
74760
74741
74722
74703
74683
74664
67709
67730
67752
67773
67795
67816
73590
73570
73551
73531
73511
73491
68983
69004
69025
69046
69067
69088
72397
72377
72357
72337
72317
72297
70236
70257
70277
70298
70319
70339
71182
71162
71141
71121
71100
71080
23
22
21
20
19
18
7
7
7
6
6
6
16
16
17
17
17
18
43
44
45
46
47
48
65232
65254
65276
65298
65320
65342
75794
75775
75756
75738
75719
75700
66545
66566
66588
66610
66632
66653
74644
74625
74606
74586
74567
74548
67837
67859
67880
67901
67923
67944
73472
73452
73432
73413
73393
73373
69109
69130
69151
69172
69193
69214
72277
72257
7223d
72216
72196
72176
70360
70381
70401
70422
70443
70463
71059
71039
71019
70998
70978
70957
17
16
15
14
13
12
5
5
5
4
4
4
18
18
19
19
19
20
49
50
51
52
53
54
65364
65386
65408
65430
65452
65474
75680
75661
75642
75623
75604
75585
66675
66697
66718
66740
66762
66783
74528
74509
74489
74470
74451
74431
67965
67987
68008
68029
68051
68072
73353
73333
73314
73294
73274
73254
69235
69256
69277
69298
69319
69340
72156
72136
72116
72095
72075
72055
70484
70505
70525
70546
70567
70587
70937
70916
70896
70875
70855
70834
11
10
9
8
7
6
3
3
3
3
2
2
20
21
21
21
22
22
55
56
57
58
59
60
65496
65518
65540
65562
65584
65606
75566
75547
75528
75509
75490
75471
66805
66827
66848
66870
66891
66913
74412
74392
74373
74353
74334
74314
68093
68115
68136
68157
68179
68200
73234
73215
73195
73175
73155
73135
69361
69382
69403
69424
69445
69466
72035
72015
71995
71974
71954
71934
70608
70628
70649
70670
70690
70711
70813
70793
70772
70752
70731
70711
5
4
3
2
1
0
2
1
1
1
0
0
N. cos. N. sine.
N. C08.
N. sine.
N. cos.
N. sine.
N. cos.
N.sine.
N.cos.
N. sine.
M.
49°
48°
47°
46°
46°
TABLE 4:2. [Page 755
Logarithms of Numbers.
No. 1 100. Log. 0.00000 2.00000.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
No.
tog.
1
2
3
4
5
0.00000
0. 30103
0. 47712
0.60206
0. 69897
21
22
23
24
25
. 32222
.34242
. 36173
.38021
. 39794
41
42
43
44
45
. 61278
. 62325
.63347
.64345
.65321
61
62
63
64
65
1.78533
1. 79239
1. 79934
.80618
. 81291
81
82
83
84
85
1.90849
1.91381
1. 91908
1. 92428
1.92942
6
7
8
9
10
0. 77815
a 84510
0.90309
0.95424
1.00000
26
27
28
29
30
. 41497
.43136
.44716
.46240
. 47712
46
47
48
49
50
.66276
. 67210
. 68124
.69020
. 69897
66
67
68
69
70
.81954
.82607
. 83251
. 83885
.84510
86
87
88
89
90
1.93450
1. 93952
1.94448
1.94939
1.95424
11
12
13
14
15
1. 04139
1.07918
1. 11394
. 14613
.17609
31
32
33
34
35
. 49136
.50515
.51851
. 53148
.54407
51
52
53
54
55
. 70757
.71600
.72428
. 73239
.74036
71
72
73
74
75
1. 85126
1. 85733
1. 86332
1. 86923
1. 87506
91
92
93
94
95
1.95904
1.96379
1.96848
1. 97313
1. 97772
16
17
18
19
90
.20412
.23045
.25527
. 27875
.30103
36
37
38
39
40
. 55630
. 56820
. 57978
.59106
.60206
56
57
58
59
60
. 74819
. 75587
.76343
.77085
1. 77815
76
77
78
79
80
1. 88081
1.88649
1. 89209
1. 89763
1.90309
96
97
98
99
100
1. 98227
1. 98677
1. 99123
1.99564
2.00000
Page 756] TABLE 42.
Logarithms of Numbers.
No. 100 1600. Log. 00000 20412.
No.
0
1
2
3
4
5
6
7
8
9
100
101
102
103
104
00000
00432
00860
01284
01703
00043
00475
00903
01326
01745
00087
00518
00945
01368
01787
00130
00561
00988
01410
01828
00173
00604
01030
01452
01870
00217
00647
01072
01494
01912
00260
00689
01115
01536
01953
00303
00732
01157
01578
01995
00346
00775
01199
01620
02036
00389
00817
01242
01662
02078
1
2
3
4
5
6
7
8
9
43
41
4
9
13
17
22
26
30
34
39
4
8
13
17
21
25
29
34
38
105
106
107
108
109
02119
02531
02938
03342
03743
02160
02572
02979
03383
03782
02202
02612
03019
03423
03822
02243
02653
03060
03463
03862
02284
02694
03100
03503
03902
02325
02735
03141
03543
03941
02366
02776
03181
03583
03981
02407
02816
03222
03623
04021
02449
02857
03262
03663
04060
02490
02898
03302
03703
04100
110
111
112
113
114
04139
04532
04922
05308
05690
04179
04571
04961
05346
05729
04218
04610
04999
05385
05767
04258
04650
05038
05423
05805
04297
04689
05077
05461
05843
04336
04727
05115
05500
05881
04376
04766
05154
05538
05918
04415
04805
05192
05576
05956
04454
04844
05231
05614
05994
04493
04883
05269
05652
06032
41
40
1
2
3
4
5
6
7
8
9
4
8
12
16
21
25
29
33
37
4
8
12
16
20
24
28
32
36
115
116
117
118
119
06070
06446
06819
07188
07555
06108
06483
06856
07225
07591
06145
06521
06893
07262
07628
06183
06558
06930
07298
07664
06221
06595
06967
07335
07700
06258
06633
07004
07372
07737
06296
06670
07041
07408
07773
06333
06707
07078
07445
07809
06371
06744
07115
07482
07846
06408
06781
07151
07518
07882
120
121
122
123
124
07918
08279
08636
08991
09342
07954
08314
08672
09026
09377
07990
08350
08707
09061
09412
08027
08386
08743
09096
09447
08063
08422
08778
09132
09482
08099
08458
08814
09167
09517
08135
08493
08849
09202
09552
08171
08529
08884
09237
09587
08207
08565
08920
09272
09621
08243
08600
08955
09307
09656
~F
2
3
4
5
6
7
8
9
39
38
4
8
12
16
20
23
27
31
35
4
8
11
15
19
23
27
30
34
125
126
127
128
129
09691
10037
10380
10721
11059
09726
10072
10415
10755
11093
09760
10106
10449
10789
11126
09795
10140
10483
10823
11160
09830
10175
10517
10857
11193
09864
10209
10551
10890
11227
09899
10243
10585
10924
11261
09934
10278
10619
10958
11294
09968
10312
10653
10992
11327
10003
10346
10687
11025
11361
130
131
132
133
134
11394
11727
12057
12385
12710
11428
11760
12090
12418
12743
11461
11793
12123
12450
12775
11494
11826
12156
12483
12808
11528
11860
12189
12516.
12840
11561
11893
12222
12548
12872
11594
11926
12254
12581
12905
11628
11959
12287
12613
12937
11661
11992
12320
12646
12969
11694
12024
12352
12678
13001
1
2
3
4
5
6
7
8
9
37
T
7
11
15
19
22
26
30
33
36
4
7
11
14
18
22
25
29
32
135
136
137
138
139
13033
13354
13672
13988
14301
13066
13386
13704
14019
14333
13098
13418
13735
14051
14364
13130
13450
13767
14082
14395
13162
13481
13799
14114
14426
13194
13513
13830
14145
14457
13226
13545
13862
14176
14489
13258
13577
13893
14208
14520
13290
13609
13925
14239
14551
13322
13640
13956
14270
14582
140
141
142
143
144
14613
14922
15229
15534
15836
14644
14953
15259
15564
15866
14675
14983.
15290
15594
15897
14706
15014
15320
15625
15927
14737
15045
15351
15655
15957
14768
15076
15381
15685
15987
14799
15106
15412
15715
16017
14829
15137
15442
15746
16047
14860
:5168
15473
15776
16077
14891 ,
15198
15503
15806
16107
35 34
1
2
3
4
5
6
7
8
,9
4
7
11
14
18
21
25
28
32
3
7
10
14
17
20
24
27
31
145
146
147
148
149
16137
16435
16732
17026
17319
16167
16465
16761
17056
17348
16197
16495
16791
17085
17377
16227
16524
16820
17114
17406
16256
16554
16850
17143
17435
16286
16584
16879
17173
17464
16316
16613
16909
17202
17493
16346
16643
16938
17231
17522
16376
16673
16967
17260
17551
16406
16702
16997
17289
17580
150
151
152
153
154
17609
17898
18184
18469
18752
17638
17926
18213
18498
18780
17667
17955
18241
18526
18808
17696
17984
18270
18554
18837
17725
18013
18298
18583
18865
17754
18041
18327
18611
18893
17782
18070
18355
18639
18921
17811
18099
18384
18667
18949
17840
18127
18412
18696
18977
17869
18156*
18441
18724
19005
~T
2
3
4
5
6
7
8
9
33
32
3
7
10
13
17
20
23
26
30
3
6
10
13
16
19
22
26
29
155
156
157
158
159
19033
19312
19590
19866
20140
19061
19340
19618
19893
20167
19089
19368
19645
19921
20194
19117
19396
19673
19948
20222
19145
19424
19700
19976
20249
19173
19451
19728
20003
20276
19201
19479
19756
20030
20303
19229
19507
19783
20058
20330
19257
19535
19811
20085
20358
19285
19562
19838
20112'
20385
No.
0
1
2
3
4
5
6
7
8
9
TABLE 42.
Logarithms of Numbers.
[Page 757
No. 1600 2200.
Log. 20412 34242.
No.
0
1
2
3
4
5
6
7
8
9
160
161
162
163
164
20412
20683
20952
21219
21484
20439
20710
20978
21245
21511
20466
20737
21005
21272
21537
20493
20763
21032
21299
21564
20520
20790
• 21059
21325
21590
20548
20817
21085
21352
21617
20575
20844
21112
21378
21643
20602
20871
21139
21405
21669
20629
20898
21165
21431
21696
20656
20925
21192
21458
21722
1
2
3
4
5
6
7
8
9
31
30
3
6
9
12
16
19
22
25
28
3
6
9
12
15
18
21
24
27
165
166
167
168
169
21748
22011
22272
22531
22789
21775
22037
22298
22557
22814
21801
22063
22324
22583
22840
21827
22089
22350
22608
22866
21854
22115
22376
22634
22891
21880
22141
22401
22660
22917
21906
22167
22427
22686
22943
21932
22194
22453
22712
22968
21958
22220
22479
22737
22994
21985
22246
22505
22763
23019
170
171
172
173
174
23045
23300
23553
23805
24055
23070
23325
23578
23830
24080
23096
23350
23603
23855
24105
23121
23376
23629
23880
24130
23147
23401
23654
23905
24155
23172
23426
23679
23930
24180
23198
23452
23704
23955
24204
23223
23477
23729
23980
24229
23249
23502
23754
24005
24254
23274
23528
23779
24030
24279
29
28
1
2
3
4
5
6
7
8
9
3
6
9
12
15
17
20
23
26
3
6
8
11
14
17
20
22
25
175
176
177
178
179
24304
24551
24797
25042
25285
24329
24576
24822
25066
25310
24353
24601
24846
25091
25334
24378
24625
24871
25115
25358
24403
24650
24895
25139
25382
24428
24674
24920
25164
25406
24452
24699
24944
25188
25431
24477
24724
24969
25212
25455
24502
24748
24993
25237
25479
24527
24773
25018
25261
25503
180
181
182
183
184
25527
25768
26007
26245
26482
25551
25792
26031
26269
26505
25575
25816
26055
26293
26529
25600
25840
26079
26316
26553
25624 ; 25648
25864 25888
26102 26126
26340 26364
26576 26600
25672
25912
26150
26387
26623
25696
25935
26174
26411
26647
25720
25959
26198
26435
26670
25744
25983
26221
26458
26694
T~
2
3
4
5
6
7
8
9
27
~3~
5
8
11
14
i<L
19s
22
24
26
3
5
8
10
13
16
18
21
23
185
186
187
188
189
26717
26951
27184
27416 ,
27646
26741
26975
27207
27439
27669
26764
26998
27231
27462
27692
26788
27021
27254
27485
27715
26811
27045
27277
27508
27738
26834
27068
27300
27531
27761
26858
27091
27323
27554
27784
26881
27114
27346
27577
27807
26905
27138
27370
27600
27830
26928
27161
27393
27623
27852
190
191
192
193
194
27875
28103
28330
28556
28780
27898
28126
28353
28578
28803
27921
28149
28375
28601
28825
27944
28171
28398
28623
28847
27967
28194
28421
28646
28870
27989
28217
28443
28668
28892
28012
28240
28466
28691
28914
28035
28262
28488
28713
28937
28058
28285
28511
28735
28959
28081
28307
28533
28758
28981
25
21
1
2
3
4
5
6
M
/
8
9
3
5
8
10
13
15
18
20
23
2
5
7
10
12
14
17
19
22
195
196
197
198
199
29003
29226 '
29447
29667
29885
29026
29248
29469
29688
29907
29048
29270
29491
29710
29929
29070
29292
29513
29732
29951
29092
29314
29535
29754
29973
29115
29336
29557
29776
29994
29137 i 29159 29181
29358 i 29380 29403
29579 29601 29623
29798 , 29820 29842
30016 30038 30060
29203
29425
29645
29863
30081
200
201
202
203
204
30103
30320
30535
30750
30963
30125
30341
30557
30771
30984
30146
30363
30578
30792
31006
30168
30384
30600
30814
31027
30190
30406
30621
30835
31048
30211
30428
30643
30856
31069
30233
30449
30664
30878
31091
31513
31723
31931
32139
30255
30471
30685
30899
31112
30276
30492
30707
30920
31133
30298
30514
30728
30942
31154
23
22
2
q
4
5
6
7
8
9
2
?
9
12
14
16
18
21
2
4
7
9
11
13
15
18
20
205
206
207
208
209
31175
31387
31597
31806
32015
31197
31408
31618
31827
32035
31218
31529
31639
31848
32056
31239
31450
31660
31869
32077
31260 i 31281
31471 31492
31681 j 31702
31890 j 31911
32098 1 32118
31323
31534
31744
31952
32160
31345
31555
31765
31973
32181
31366
31576
31785
31994
32201
210
211
212
213
214
32222
32428
32634
32838
33041
32243
32449
32654
32858
33062
32263
32469
32675
32879
33082
32284
32490
32695
32899
33102
32305
32510
32715
32919
33122
32325
32531
32736
32940
33143
32346
32552
32756
32960
33163
32366
32572
32777
32980
33183
32387
32593
32797
33001
33203
32408
32613
32818
21 20
33021
33224
1
2
3
4
5
6
7
8
9
2
4
6
8
11
13
15
17
19
2
4
6
8
10
12
14
16
18
215
216
217
218
219
33244
33445
33646
33846
34044
33264
33465
33666
33866
34064
33284
33486
33686
33885
34084
33304
33506
33706
33905
34104
33325
33526
33726
33925
34124
33345
33546
33746
33945
34143
33365
33566
33766
33965
34163
33385
33586
33786
33985
34183
33405
33606
33806
34005
34203
33425
33626
33826
34025
34223
No.
0
1
2 3
4 5
6 ' 7 , 8
9
Page 758] TABLE 42.
Logarithms of Numbers.
No. 2200 2800. Log. 34242 44716.
No.
0
1
2
8
4
5
6
7
8
9
220
221
222
223
224
34242
34439
34635
34830
35025
34262
34459
34655
34850
35044
34282
34479
34674
34869
35064
34301
34498
34694
34889
35083
34321
34518
34713
34908
35102
34341
34537
34733
34928
35122
34361
34557
34753
34947
35141
34380
34577
34772
34967
35160
34400
34596
34792
34986
35180
OAAf)(\
o44ZU
34616
20
34811
35005
35199
1
2
3
4
5
6
7
8
9
2
4
6
8
10
12
14
16
18
225
226
227
228
229
35218
35411
35603
35793
35984
35238
35430
35622
35813
36003
35257
35449
35641
35832
36021
35276
35468
35660
35851
36040
35295
35488
35679
35870
36059
35315
35507
35698
35889
36078
35334
35526
35717
35908
36097
35353
35545
35736
35927
36116
35372
35564
35755
35946
36135
35392
35583
35774
35965
36154
230
231
232
233
234
36173
36361
36549
36736
36922
36192
36380
36568
36754
36940
36211
36399
36586
36773
36959
36229
36418
36605
36791
36977
36248
36436
36624
36810
36996
36267
36455
36642
36829
37014
36286
36474
36661
36847
37033
36305
36493
36680
36866
37051
36324
36511
36698
36884
37070
37254
37438
37621
37803
37985
36342
36530
19
36717
36903
37088
1
2
3
4
5
6
7
8
9
2
4
6
8
10
11
13
15
17
235
236
237
238
239
37107
37291
37475
37658
37840
37125
37310
37493
37676
37858
37144
37328
37511
37694
37876
37162
37346
37530
37712
37894
37181
37365
37548
37731
37912
37199
37383
37566
37749
37931
37218
37401
37585
37767
37949
37236
37420
37603
37785
37967
37273
37457
37639
37822
38003
240
241
242
243
244
38021
38202
38382
38561
38739
38039
38220
38399
38578
38757
38057
38238
38417
38596
38775
38075
38256
38435
38614
38792
38093
38274
38453
38632
38810
38112
38292
38471
38650
38828
38130
38310
38489
38668
38846
38148-
38328
38507
38686
38863
38166
38346
38525
38703
38881
38184
38364
38543
38721
38899
18
1
2
3
4
5
6
7
8
9
2
4
5
7
9
11
13
14
16
245
246
247
248
249
38917
39094
39270
39445
39620
38934
39111
39287
39463
39637
38952
39129
39305
39480
39655
38970
39146
39322
39498
39672
38987
39164
39340
39515
39690
39005
39182
39358
39533
39707
39023
39199
39375
39550
39724
39041
39217
39393
39568
39742
39058
39235
39410
39585
39759
39076
39252
39428
39602
39777
250
251
252
253
254
39794
39967
40140
40312
40483
39811
39985
40157
40329
40500
39829
40002
40175
40346
40518
39846
40019
40192
40364
40535
39863
40037
40209
40381
40552
39881
40054
40226
40398
40569
39898
40071
40243
40415
40586
39915
40088
40261
40432
40603
39933
40106
40278
40449
40620
39950
40123
40295
40466
40637
17
1
2
3
4
5
6
7
8
9
2
3
5
7
9
10
12
14
15
255
256
257
258
259
40654
40824
40993
41162
41330
40671
40841
41010
41179
41347
40688
40858
41027
41196
41363
40705
40875
41044
41212
41380
40722
40892
41061
41229
41397
40739
40909
41078
41246
41414
40756
40926
41095
41263
41430
40773
40943
41111
41280
41447
40790
40960
41128
41296
41464
40807
40976
41145
41313
41481
260
261
262
263
264
41497
41664
41830
41996
42160
41514
41681
41847
42012
42177
41531
41697
41863
42029
42193
41547
41714
41880
42045
42210
41564
41731
41896
42062
42226
41581
41747
41913
42078
42243
41597
41764
41929
42095
42259
41614
41780
41946
42111
42275
42439
42602
42765
42927
43088
41631
41797
41963
42127
42292
41647
41814
41979
42144
42308
~T
2
3
4
5
6
7
8
9
16
2
3
5
6
8
10
11
13
14
265
266
267
268
269
42325
42488
42651
42813
42975
42341
42504
42667
42830
42991
42357
42521
42684
42846
43008
42374
42537
42700
42862
43024
42390
42553
42716
42878
43040
42406
42570
42732
42894
43056
42423
42586
42749
42911
43072
43233
43393
43553
43712
43870
42455
42619
42781
42943
43104
42472
42635
42797
42959
43120
270
271
272
273
274
43136
43297
43457
43616
43775
43152
43313
43473
43632
43791
43169
43329
43489
43648
43807
43185
43345
43505
43664
43823
43201
43361
43521
43680
43838
43217
43377
43537
43696
43854
43249
43409
43569
43727
43886
43265
43425
43584
43743
43902
44059
44217
44373
44529
44685
43281
43441
43600
43759
43917
15
1
2
3
4
5
6
7
8
9
2
3
5
6
8
9
11
12
14
275
276
277
278
279
43933
44091
44248
44404
44560
43949
44107
44264
44420
44576
43965
44122
44279
44436
44592
43981
44138
44295
44451
44607
43996
44154
44311
44467
44623
44012
44170
44326
44483
44638
44028
44185
44342
44498
44654
44044
44201
44358
44514
44669
44075
44232
44389
44545
44700
No.
0
1
2
3
4
&
6
7
8
9
TABLE 42. [Page 759
Logarithms of Numbers.
No. 2800 3400.
Log. 44716 53148.
No.
0 1 2.
3
4
5
6
7
8
9
280
281
282
283
284
44716 | 44731
44871 ! 44886
45025 i 45040
45179 i 45194
45332 ! 45347
44747
44902
45056
45209
45362
44762
44917
45071
45225
45378
44778
44932
45086
45240
45393
44793
44948
45102
45255
45408
44809
44963
45117
45271
45423
44824
44979
45133
45286
45439
44840
44994
45148
45301
45454
44855
45010
45163
45317
45469
1
2
3
4
5
6
7
8
9
16
2
3
5
6
8
10
11
13
14
285
286
287
288
289
45484
45637
45788
45939
46090
45500
45652
45803
45954
46105
45515
45667
45818
45969
46120
45530
45682
45834
45984
46135
45545
45697
45849
46000
46150
45561
45712
45864
46015
46165
45576
45728
45879
46030
46180
45591
45743
45894
46045
46195
45606
45758
45909
46060
46210
45621
45773
45924
46075
46225
290
291
292
293
294
46240
46389
46538
46687
46835
46255
46404
46553
46702
46850
46270
46419
46568
46716
46864
46285
46434
46583
46731
46879
46300
46449
46598
46746
46894
46315
46464
46613
46761
46909
46330
46479
46627
46776
46923
46345
46494
46642
46790
46938
46359 46374
46509 46523
46657 46672
46805 46820
46953 46967
15
1
2
3
4
5
6
7
8
9
2
3
5
6
8
9
11
12
14
295
296
297
298
299
46982 46997
47129 ! 47144
47276 ; 47290
47422 ! 47436
47567 I 47582
• 47012
47159
47305
47451
47596
47026
47173
47319
47465
47611
47041 47056
47188 47202
47334 47349
47480 47494
47625 i 47640
47070
47217
47363
47509
47654
47085
47232
47378
47524
47669
47100 47114
47246 47261
47392 47407
47538 47553
47683 47698
300
301
302
303
304
47712 47727
47857 47871
48001 i 48015
48144 i 48159
48287 48302
47741
47885
48029
48173
48316
47756
47900
48044
48187
48330
47770 j 47784
47914 ! 47929
48058 ' 48073
48202 ! 48216
48344 ! 48359
47799
47943
48087
48230
48373
47813
47958
48101
48244
48387
47828 47842
47972 47986
48116 48130
48259 48273
48401 48416
305
306
307
308
309
48430
48572
48714
48855
48996
48444
48586
48728
48869
49010
48458
48601
48742
48883
49024
48473
48615
48756
48897
49038
48487
48629
48770
48911
49052
48501
48643
48785
48926
49066
48515
48657
48799
48940
49080
48530
48671
48813
48954
49094
48544 48558
48686 48700
48827 48841
48968 48982
49108 49122
14
1
2
3
4
5
6
7
8
9
1
3
4
6
7
8
10
11
13
310
311
312
313
314
49136 ' 49150
49276 i 49290
49415 ! 49429
49554 i 49568
49693 I 49707
49164
49304
49443
49582
49721
49178
49318
49457
49596
49734
49192
49332
49471
49610
49748
49206
49346
49485
49624
49762
49220
49360
49499
49638
49776
49234
49374
49513
49651
49790
49248
49388
49527
49665
49803
49262
49402
49541
49679
49817
315
316
317
318
319
49831
49969
50106
50243
50379
49845
49982
50120
50256
50393
49859
49996
50133
50270
50406
49872
50010
50147
50284
50420
49886
50024
50161
50297
50433
49900 49914
50037 50051
50174 50188
50311 50325
50447 50461
49927
50065
50202
50338
50474
49941
50079
50215
50352
50488
49955
50092
50229
50365
50501
13
1
2
3
4
5
6
7
8
9
1
• 3
4
5
7
8
9
10
12
320
321
322
323
324
50515 50529
50651 50664
50786 i 50799
50920 50934
51055 51068
50542
50678
50813
50947
51081
50556
50691
50826
50961
51095
50569
50705
50840
50974
51108
50583
50718
50853
50987
51121
50596
50732
50866
51001
51135
50610
50745
50880
51014
51148
50623
50759
50893
51028
51162
50637
50772
50907
51041
51175
325
326
327
328
329
51188
51322
51455
51587
51720
51202
51335
51468
51601
51733
51215
51348
51481
51614
51746
51228
51362
51495
51627
51759
51242
51375
51508
51640
51772
51255
51388
51521
51654
51786
51268
51402
51534
51667
51799
51282
51415
51548
51680
51812
51295 1 51308
51428 1 51441
51561 ! 51574
51693 51706
51825 | 51838
330
331
332
333
334
51851
51983
52114
52244
52375
51865
51996
52127
52257-
52388
51878
52009
52140
52270
52401
51891
52022 '
52153
52284
52414
51904
52035
52166
52297
52427
51917
52048
52179
52310
52440
51930
52061
52192
52323
52453
51943
52075
52205
52336
52466
51957
52088
52218
52349
52479
51970
52101
52231
52362
52492
12
1
2
3
4
5
6
7
8
9
1
2
4
5
6
7
8
10
11
335
336
337
338
339
52504
52634
52763
52892
53020
52517
52647
52776
52905
53033
52530
52660
52789
52917
53046
52543
52673
52802
52930
53058
52556
52686
52815
52943
53071
52569
52699
52827
52956
53084
52582
52711
52840
52969
53097
52595
52724
52853
52982
53110
52608
52737
52866
52994
53122
52621
52750
52879
53007
53135
No.
0
1
2
s
4
6
6
7
8
9
Page 760] TABLE 42.
Logarithms of Numbers.
No. 3400 1000. Log. 53148 60206.
No.
0
i
2
3
4
5
6
7
8
9
340
341
342
343
344
53148
53275
53403
53529
53656
53161
53288
53415
53542
53668
53173
53301
53428
53555
53681
53186
53314
53441
53567
53694
53199
53326
53453
53580
53706
53212
53339
53466
53593
53719
53224
53352
53479
53605
53732
53237
53364
53491
53618
53744
53250
53377
53504
53631
53757
53263
53390
53517
53643
53769
13
1
2
3
4
5
6
7
8
9
1
3
4
5
7
8
9
10
12
345
346
347
348
349
53782
53908
54033
54158
54283
53794
53920
54045
54170
54295
53807
53933
54058
54183
54307
53820
53945
54070
54195
54320
53832
53958
54083
54208
54332
53845
53970
54095
54220
54345
53857
53983
54108
54233
54357
53870
53995
54120
54245
54370
53882
54008
54133
54258
54382
53895
54020
54145
54270
54394
350
351
352
353
354
54407
54531
54654
54777
54900
54419
54543
54667
54790
54913
54432
54555
54679
54802
54925
54444
54568
54691
54814
54937
54456
54580
54704
54827
54949
54469
54593
54716
54839
54962
54481
54605
54728
54851
54974
54494
54617
54741
54864
54986
54506
54630
54753
54876
54998
54518
54642
54765
54888
55011
355
356
357
358
359
55023
55145
55267
55388
55509
55035
55157
55279
55400
55522
55047
55169
55291
55413
55534
55060
55182
55303
55425
55546
55072
55194
55315
55437
55558
55084
55206
55328
55449
55570
55096
55218
55340
55461
55582
55108
55230
55352
55473
55594
. 55121
55242
55364
55485
55606
55133
55255
55376
55497
55618
12
1
2
3
4
5
6
7
8
9
1
2
4
5
6
7
8
10
11
360
361
362
363
364
55630
55751
55871
55991
56110
55642
55763
55883 .
56003
56122
55654
55775
55895
56015
56134
55666
55787
55907
56027
56146
55678
55799
55919
56038
56158
55691
55811
55931
56050
56170
55703
55823
55943
56062
56182
55715
55835
55955
56074
56194
55727
55847
5596?
56086
56205
55739
55859
55979
56098
56217
365
366
367
368
369
56229
56348
56467
56585
56703
56241
56360
56478
56597
56714
56253
56372
56490
56608
56726
56265
56384
56502
56620
56738
56277
56396
56514
56632
56750
56289
56407
56526
56644
56761
56301
56419
56538
56656
56773
56312
56431
56549
56667
56785
56324
56443
56561
56679
56797
56336
56455
56573
56691
56808
370
371
372
373
374
56820
56937
57054
57171
57287
56832
56949
57066
57183
57299
56844
56961
57078
57194
57310
56855
56972
57089
57206
57322
56867
56984
57101
57217
57334
56879
56996
57113
57229
57345
56891
57008
57124
57241
57357
56902
57019
57136
57252
57368
56914
57031
57148
57264
57380
56926
57043
57159
57276
57392
11
1
2
3
4
5
6
7
8
9
1
2
3
4
6
7
8
9
10
375
376
377
378
379
57403
57519
57634
57749
57864
57415
57530
57646
57761
57875
57426
57542
57657
57772
57887
57438
57553
57669
57784
57898
57449
57565
57680
57795
57910
57461
57576
57692
57807
57921
57473
57588
57703
57818
57933
57484
57600
57715
57830
57944
57496
57611
57726
57841
57955
57507
57852
57967
380
381
382
383
384
57978
58092
58206
58320
58433
57990
58104
58218
58331
58444
58001
58115
58229
58343
58456
58013
58127
58240
58354
58467
58024
58138
58252
58365
58478
58035
58149
58263
58377
58490
58047
58161
58274
58388
58501
58058
58172
58286
58399
58512
58070
58184
58297
58410
58524
58081
58195
58309
58422
58535
^385
386
387
388
389
58546
58659
58771
58883
58995
58557
58670
58782
58894
59006
58569
58681
58794
58906
59017
58580
58692
58805
58917
59028
58591
58704
58816
58928
59040
58602
58715
58827
58939
59051
58614
58726
58838
58950
59062
58625
58737
58850
58961
59073
58636
58749
58861
58973
59084
58647
58760
58872
58984
59095
10
390
391
392
393
394
59106
59218
59329
59439
59550
59118
59229
59340
59450
59561
59129
59240
59351
59461
59572
59140
59251
59362
59472
59583
59151
59262
59373
59483
59594
59162
59273
59384
59494
59605
59173
59284
59395
59506
59616
59184
59295
59406
59517
59627
59195
59306
59417
59528
59638
59207
59318
59428
59539
59649
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
395
396
397
398
399
59660
59770
59879
59988
60097
59671
59780
59890
59999
60108
59682
59791
59901
60010
60119
59693
59802
59912
60021
60130
59704
59813
59923
60032
60141
59715
59824
59934
60043
60152
59726
59835
59945
60054
60163
59737
59846
59956
60065
60173
59748
59857
59966
60076
60184
59759
59868
59977
60086
60195
No.
0
l
2
3
4
5
6
7
8
9
'
TABLE 42. ! Page 761
Logarithms of Numbers.
No. 4000 4600.
Log. 60206 66276.
No.
0
i
2
3
4
a
6
7
8
9
400
401
402
403
404
60206
60314
60423
60531
60638
60217
60325
60433
60541
60649
60228
60336
60444
60552
60660
60239
60347
60455
60563
60670
60249
60358
60466
60574
60681
60260
60369
60477
60584
60692
60271
60379
60487
60595
60703
60282
60390
60498
60606
60713
60293
60401
60509
60617
60724
60304
60412
60520
60627
60735
11
1
2
3
4
5
6
7
8
9
1
2
3
4
6
7
8
9
10
405
406
407
408
409
60746
60853
60959
61066
61172
60756
60863
60970
61077
61183
60767
60874
60981
61087
61194
60778
60885
60991
61098
61204
60788
60895
61002
61109
61215
60799
60906
61013
61119
61225
60810 •
60917
61023
61130
61236
60821
60927
61034
61140
61247
60831
60938
61045
61151
61257
60842
60949
61055
61162
61268
410
411
412
413
414
61278
61384
61490
61595
61700
61289
61395
61500
61606
61711
61300
61405
61511
61616
61721
61310
61416
61521
61627
61731
61321
61426
61532
61637
61742
61331
61437
61542
61648
61752
! 61342
1 61448
61553
61658
61763
61352
61458
61563
61669
61773
61363
61469
61574
61679
61784
61374
61479
61584
61690
61794
415
416
417
418
419
61805 ! 61815
61909 61920
62014 j 62024
62118 62128
62221 62232
61826
61930
62034
62138
62242
61836
61941
62045
62149
62252
61847
61951
62055
62159
62263
61857
61962
62066
62170
62273
i 61868
61972
62076
62180
62284
61878
61982
62086
62190
62294
61888
61993
62097
62201
62304
61899
62003
62107
62211
62315
420
421
422
423
424
62325 62335 62346
62428 ! 62439 62449
62531 62542 62552
62634 62644 62655
62737 ! 62747 62757
62356 62366 ! 62377
62459 62469 ! 62480
62562 62572 ; 62583
62665 62675 j 62685
62767 62778 j 62788
62387
62490
62593
62696
6279'8
62397
62500
62603
62706
62808
62408
62511
62613
62716
62818
62418
62521
62624
62726
62829
10
425
426
427
428
429
62839
62941
63043
63144
63246
62849
62951
63053
63155
63256
62859
62961
63063
63165
63266
62870 i 62880 62890
62972 ! 62982 i 62992
63073 63083 63094
63175 63185 63195
63276 63286 63296
62900 j 62910
63002 63012
63104 i 63114
63205 63215
63306 63317
62921
63022
63124
63225
63327
62931
63033
63134
63236
63337
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
430
431
432
433
434
63347 i 63357
63448 63458
63548 63558
63649 j 63659
63749 63759
63367 1 63377 i 63387 63397
63468 63478 : 63488 63498
63568 • 63579 63589 63599
63669 i 63679 63689 ! 63699
63769 ! 63779 | 63789 | 63799
63407
63508
63609
63709
63809
63417
63518
63619
63719
63819
63428
63528
63629
63729
63829
63438
63538
63639
63739
63839
435
436
437
438
439
63849 63859
63949 63959
64048 | 64058
64147 , 64157
64246 64256
63869
63969
64068
64167
64266
63879 i 63889 63899
63979 63988 ! 63998
64078 ! 64088 64098
64177 : 64187 64197
64276 ! 64286 64296
63909
64008
64108
64207
64306
63919 i 63929 63939
64018 ! 64028 64038
64118 i 64128 : 64137
64217 | 64227 64237
64316 64326 64335
440
441
442
443
444
64345
64444
64542
64640
64738
64355
64454
64552
64650
64748
64365
64464
64562
64660
64758
64375
64473
64572
64670
64768
64865
64963
65060
65157
65254
64385
64483
64582
64680
64777
64395
64493
64591
64689
64787
64404
64503
64601
64699
64797
64414
64513
64611
64709
64807
64424
64523
64621
64719
64816
64434
64532
64631
64729
64826
445
446
447
448
449
64836
64933
65031
65128
65225
64846 64856
64943 64953
65040 i 65050
65137 i 65147
65234 j 65244
64875
64972
65070
65167
65263
64885
64982
65079
65176
65273
6*895
64992
65089
65186
65283
6*904
65002
65099
65196
65292
64914
65011
65108
65205
65302
64924
65021
65118
65215
65312
9
450
451
452
453
454
65321
65418
65514
65610
65706
65331
65427
65523
65619
65715
65341
65437
65533
65629
65725
65350
65447
65543
65639
65734
65360
65456
65552
65648
65744
65369
65466
65562
65658
65753
65379
65475
65571
65667
65763
65389
65485
65581
65677
65772
65398
65495
65591
65686
65782
65408
65504
65600
65696
65792
1
2
3
4
5
6
7
8
9
1
2
3
4
5
5
6
7
8
455
456
457
458
459
65801
65896
65992
66087
66181
65811
65906
66001
66096
66191
65820
65916
66011
66106
66200
65830
65925
66020
66115
66210
65839
65935
66030
66124
66219
65849
65944
66039
66134
66229
65858
65954
66049
66143
66238
65868
65963
66058
66153
66247
65877
65973
66068
66162
66257
65887
65982
66077
66172
66266
No.
0
1
2
3
4
5
I
7
8
9
61828°—
Page 762] TABLE 42.
Logarithms of Numbers.
No. 4600 5200. Log. 66276 71600.
No.
0
i
2
3
4
5
6
7
8
9
460
461
462
463
464
66276
66370
66464
66558
66652
66285
66380
66474
66567
66661
66295
66389
66483
66577
66671
66304
66398
66492
66586
66680
66314
66408
66502
66596
66689
66323
66417
66511
66605
66699
66332
66427
66521
66614
66708
66342
66436
66530
66624
66717
66351
66445
66539
66633
66727
66361
66455
66549
66642
66736
10
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
465
466
467
468
469
66745
66839
66932
67025
67117
66755
66848
66941
67034
67127
66764
66857
66950
67043
67136
• 66773
66867
66960
67052
67145
66783
66876
66969
67062
67154
66792
66885
66978
67071
67164
66801
66894
66987
67080
67173
66811
66904
66997
67089
67182
66820
66913
67006
67099
67191
66829
66922
67015
67108
67201
470
471
472
473
474
67210
67302
67394
67486
67578
67219
67311
67403
67495
67587
67228
67321
67413
67504
67596
67237
67330
67422
67514
67605
67247
67339
67431
67523
67614
67256
67348
67440
67532
67624
67265
67357
67449
67541
67633
67274
67367
67459
6,7550
67642
67284
67376
67468
67560
67651
67293
67385
67477
67569
67660
475
476
477
478
479
67669
67761
67852
67943
68034
67679
67770
67861
67952
68043
67688
67779
67870
67961
68052
67697
67788
67879
67970
68061
67706
67797
67888
67979
68070
67715
67806
67897
67988
68079
67724
67815
67906
67997
68088
67733
67825
67916
68006
68097
67742
67834
67925
68015
68106
67752
67843
67934
68024
68115
480
481
482
483
484
68124
68215
68305
68395
68485
68133
68224
68314
68404
68494
68142
68233
68323
68413
68502
68151
68242
68332
68422
68511
68160
68251
68341
68431
68520
68169
68260
68350
68440
68529
68178
68269
68359
68449
68538
68187
'68278
68368
68458
68547
68196
68287
68377
68467
68556
68205
68296
68386
68476
68565
9
485
486
487
488
489
68574
68664
68753
68842
68931
68583
68673
68762
68851
68940
68592
68681
68771
68860
68949
68601
68690
68780
68869
68958
68610
68699
68789
68878
68966
68619
68708
68797
68886
68975
68628
68717
68806
68895
68984
68637
68726
68815
68904
68993
68646
68735
68824
68913
69002
68655
68744
68833
68922
69011
1
2
3
4
5
6
7
8
9
1
2
3
4
5
5
6
7
8
490
491
492
493
494
69020
69108
69197
69285
69373
69028
69117
69205
69294
69381
69037
69126
69214
69302
69390
69046
69135
69223
69311
69399
69055
69144
69232
69320
69408
69064
69152
69241
69329
69417
69073
69161
69249
69338
69425
69082
69170
69258
69346
69434
69090
69179
69267
69355
69443
69099
69188
69276
69364
69452
495
496
497
498
499
69461
69548
69636
69723
69810
69469
69557
69644
69732
69819
69478
69566
69653
69740
69827
69487
69574
69662
69749
69836
69496
69583
69671
69758
69845
69504
69592
69679
69767
69854
69513
69601
69688
69775
69862
69522
69609
69697
69784
69871
69531
69618
69705
69793
69880
69539
69627
69714
69801
69888
500
501
502
503
504
69897
69984
70070
70157
70243
69906
69992
70079
70165
70252
69914
70001
70088
70174
70260
69923
70010
70096
70183
70269
69932
70018
70105
70191
70278
69940
70027
70114
70200
70286
69949
70036
70122
70209
70295
69958
70044
70131
70217
70303
69966
70053
70140
70226
70312
69975
70062
70148
70234
70321
505
506
507
508
509
70329
70415
70501
70586
70672
70338
70424
70509
70595
70680
70346
70432
70518
70603
70689
70355
70441
70526
70612
70697
70364
70449
70535
70621
70706
70372
70458
70544
70629
70714
70381
70467
70552
70638
70723
70389
70475
70561
70646
70731
70398
70484
70569
70655
70740
70406
70492
70578
70663
70749
8
510
511
512
513
514
70757
70842
70927
71012
71096
70766
70851
70935
71020
71105
70774
70859
70944
71029
71113
70783
70868
70952
71037
71122
70791
70876
70961 )
71046 ]
71130
70800
70885
70969
71054
71139
70808
70893
70978
71063
71147
70817
70902
70986
71071
71155
70825
70910
70995
71079
71164
70834
70919
71003
71088
71172
1
2
3
4
5
6
7
8
9
1
2
2
3
4
5
6
6
7
515
516
517
518
519
71181
71265
71349
71433
71517
71189
71273
71357
71441
71525
71198
71282
71366
71450
71533
71206
71290
71374
71458
71542
71214
71299
71383
71466
71550
71223
71307
71391
71475
71559
71231
71315
71399
71483
71567
71240
71324
71408
71492
71575
71248
71332
71416
71500
71584
71257
71341
71425
71508
71592
No.
0
l
2
3
4
5
6
7
8
9
TABLE 42. [Page 763
*
Logarithms of Numbers.
No. 5200 5800.
Log. 71600 76343.
No.
0 1 2
3
*
5
6
1
8 9
520
521
522
523
524
71600
71684
71767
71850
71933
71609
71692
71775
71858
71941
71617
71700
71784
71867
71950
71625
71709
71792
71875
71958
71634
71717
71800
71883
71966
71642
71725
71809
71892
71975
71650
71734
71817
71900
71983
71659
71742
71825
71908
71991
71667
71750
71834
71917
71999
71675
9
71759
71842
71925
72008
1
2
3
4
5
6
7
8
9
1
2
3
4
5
5
6
7
8
525
526
527
528
529
72016
72099
72181
72263
72346
72024
72107
72189
72272
72354
72032
72115
72198
72280
72362
72041
72123
72206
72288
72370
72049
72132
72214
72296
72378
72057
72140
72222
72304
72387
72066
72148
72230
72313
72395
72074
72156
72239
72321
72403
72082
72165
72247
72329
72411
72090
72173
72255
72337
72419
530
531
532
533
534
72428
72509
72591
72673
72754
72436 i 72444
72518 72526
72599 72607
. 72681 72689
72762 72770
72452
72534
72616
72697
72779
72460
72542
72624
72705
72787
72469
72550
72632
72713
72795
72477
72558
72640
72722
72803
72485
72567
72648
72730
72811
72493
72575
72656
72738
72819
72501
72583
72665
72746
72827
535
536
537
538
539
72835
72916
72997
73078
73159
72843
72925
73006
73086
73167
72852
72933
73014
73094
73175
72860 ' 72868
72941 72949
73022 ! 73030
73102 73111
73183 i 73191
72876
72957
73038
73119
73199
72884
72965
73046
73127
73207
72892
72973
73054
73135
73215
72900 | 72908
72981 i 72989
73062 j 73070
73143 i 73151
73223 1 73231
540
541
542
543
544
73239
73320
73400
73480
73560
73247
73328
73408
73488
73568
73255
73336
73416
73496
73576
73263
73344
73424
73504
73584
73272
73352
73432
73512
73592
73280
73360
73440
73520
73600
73288
73368
73448
73528
73608
73296
73376
73456
73536
73616
73304 i 73312
73384 73392
73464 73472
73544 73552
73624 73632
8
545
546
547
548
549
73640
73719
73799
73878
73957
73648
73727
73807
73886
73965
73656
73735
73815
73894
73973
73664
73743
73823
73902
73981
73672
73751
73830
73910
73989
73679
73759
73838
73918
73997
73687
73767
73846
73926
74005
73695
73775
73854
73933
74013
73703 73711
73783 1 73791
73862 i 73870
73941 73949
74020 ! 74028
1
2
3
4
5
6
7
8
9
1
2
2
3
4
5
6
6
7
550
551
552
553
554
74036
74115
74194
74273
74351
74044 74052
74123 i 74131
74202 ! 74210
74280 i 74288
74359 i 74367
74060
74139
74218
74296
74374
74068
74147
74225
74304
74382
74076
74155
74233
74312
74390
74084
74162
74241
74320
74398
74092
74170
74249
74327
74406
74099
74178
74257
74335
74414
74107
74186
74265
74343
74421
555
556
557
558
559
74429
74507
74586
74663
74741
74437
74515
74593
74671
74749
74445
74523
74601
74679
74757
74453
74531
74609
74687
74764
74461
74539
74617
74695
74772
74468
74547
74624
74702
74780
74476
74554
74632
74710
74788
74484 i 74492
74562 74570
74640 74648
74718 74726
74796 74803
74500
74578
74656
74733
74811
560
561
562
563
564
74819
74896
74974
75051
75128
74827 74834
74904 74912
74981 74989
75059 75066
75136 75143
74842
74920
74997
75074
75151
74850
74927
75005
75082
75159
74858
74935
75012
75089
75166
74865
74943
75020
75097
75174
74873
74950
75028
75105
75182
74881
74958
75035
75113
75189
74889
74966
75043
75120
75197
565
566
567
568
569
75205
75282
75358
75435
75511
75213
75289
75366
75442
75519
75220
75297
75374
75450
75526
75228
75305
75381
75458
75534
75236
75312
75389
75465
75542
75243
75320
75397
75473
75549
75251
75328
75404
75481
75557
75259
75335
75412
75488
75565
75266
75343
75420
75496
75572
75274
75351
75427
75504
75580
7
570
571
572
573
574
75587
75664
75740
75815
75891
75595
75671
75747
75823
75899
75603
75679
75755
75831
75906
75610
75686
75762
75838
75914
75618
75694
75770
75846
75921
75626
75702
75778
75853
75929
75633
75709
75785
75861
75937
75641
75717
75793
75868
75944
75648
75724
75800
75876
75952
75656
75732
75808
75884
75959
1
2
3
4
5
6
7
8
q
1
1
2
\
4
5
6
6
575
576
577
578
579
75967
76042
76118
76193
76268
75974
76050
76125
76200
76275
75982
76057
76133
76208
76283
75989
76065
76140
76215
76290
75997
76072
76148
76223
76298
76005
76080
76155
76230
76305
76012
76087
76163
76238
76313
76020
76095
76170
76245
76320
76027
76103
76178
76253
76328
76035
76110
76185
76260
76335
No.
0
l
2
3
4
5
6
«
8
9
Page 764] TABLE 42.
Logarithms of Numbers.
No. 6800 6400. Log. 76343 80618.
No.
0
1
2
3
4
5
6
7
8
9
580
581
582
583
584
76343
76418
76492
76567
76641
76350
76425
76500
76574
76649
76358
76433
76507
76582
76656
76365
76440
76515
76589
76664
76373
76448
76522
76597
76671
76380
76455
76530
76604
76678
76388
76462
76537
76612
76686
76395
76470
76545
76619
76693
76403
76477
76552
76626
76701
76410
8
76485
76559
76634
76708
1
2
3
4
5
6
7
8
9
1
2
2
3
4
5
6
6
7
585
586
587
588
589
76716
76790
76864
76938
77012
76723
76797
76871
76945
77019
76730
76805
76879
76953
77026
76738
76812
76886
76960
77034
76745
76819
76893
76967
77041
76753
76827
76901
76975
77048
76760
76834
76908
76982
77056
76768
76842
76916
76989
77063
76775
76849
76923
76997
77070
76782
76856
76930
77004
77078
590
591
592
593
594
77085
77159
77232
77305
77379
77093
77166
77240
77313
77386
77100
77173
77247
77320
77393
77107
77181
77254
77327
77401
77115
77188
77262
77335
77408
77122
77195
77269
77342
77415
77129
77203
77276
77349
77422
77137
77210
77283
77357
77430
77144
77217
77291
77364
77437
77151
77225
77298
77371
77444
595
596
597
598
599
77452
77525
77597
77670
77743
77459
77532
77605
77677
77750
77466
77539
77612
77685
77757
77474
77546
77619
77692
77764
77481
77554
77627
77699
77772
77488
77561
77634
77706
77779
77495
77568
77641
77714
77786
77503
77576
77648
77721
77793
77510
77583
77656
77728
77801
77517
77590
77663
77735
77808
600
601
602
603
604
77815
77887
77960
78032
78104
77822
77895
77967
78039
78111
77830
77902
77974
78046
78118
77837
77909
77981
78053
78125
77844
77916
77988
78061
78132
77851
77924
77996
78068
78140
78211
78283
78355
78426
78497
77859
77931
78003
78075
78147
77866
77938
78010
78082
78154
77873
77945
78017
78089
78161
77880
77952
78025
78097
78168
7
605
606
'607
608
609
78176
78247
78319
78390
78462
78183
78254
78326
78398
78469
78190
78262
78333
78405
78476
78197
78269
78340
78412
78483
78204
78276
78347
78419
78490
78219
78290
78362
78433
78504
78226
78297
78369
78440
78512
78233
78305
78376
78447
78519
78240
78312
78383
78455
78526
1
2
3
4
5
6
7
8
9
1
1
2
3
4
4
5
6
6
610
611
612
613
614
78533
78604
78675
78746
78817
78540
78611
78682
78753
78824
78547
78618
78689
78760
78831
78554
78625
78696
78767
78838
78561
78633
78704
78774
78845
78569
78640
78711
78781
78852
78576
78647
78718
78789
78859
78583
78654
78725
78796
78866
78590
78661
78732
78803
78873
78597
78668
78739
78810
78880
78951
79021
79092
79162
79232
615
616
617
618
619
78888
78958
79029
79099
79169
78895
78965
79036
79106
79176
78902
78972
79043
79113
79183
78909
78979
79050
79120
79190
78916
78986
79057
79127
79197
78923
78993
79064
79134
79204
78930
79000
79071
79141
79211
78937
79007
79078
79148
79218
78944
79014
79085
79155
79225
*
620
621
622
623
624
79239
79309
79379
79449
79518
79246
79316
79386
79456
79525
79253
79323
79393
79463
79532
79260
79330
79400
79470
79539
79267
79337
79407
79477
79546
79274
79344
79414
79484
79553
79281
79351
79421
79491
79560
79288
79358
79428
79498
79567
79295
79365
79435
79505
79574
79302
79372
79442
79511
79581
625
626
627
628
629
79588
79657
79727
79796
79865
79595
79664
79734
79803
79872
79602
79671
79741
79810
79879
79609
79678
79748
79817
79886
79616
79685
79754
79824
79893
79623
79692
79761
79831
79900
79630
79699
79768
79837
79906
79637
79706
79775
79844
79913
79644
79713
79782
79851
79920
79650-
79720
79789
79858
79927
6
630
631
632
633
634
79934
80003
80072
80140
80209
79941
80010
80079
80147
80216
79948
80017
80085
80154
80223
79955
80024
80092
80161
80229
79962
80030
80099
80168
80236
79969
80037
80106
80175
80243
79975
80044
80113
80182
80250
79982
80051
80120
80188
80257
79989
80058
80127
80195
80264
79996
80065
80134
80202
80271
1
2
3
4
5
6
7
8
9
1
1
2
2
3
4
4
5
5
635
636
637
638
639
80277
80346
80414
80482
80550
80284
80353
80421
80489
80557
80291
80359
80428
80496
80564
80298
80366
80434
80502
80570
80305
80373
80441
80509
80577
80312
80380
80448
80516
80584
80318
80387
80455
80523
80591
80325
80393
80462
80530
80598
80332
80400
80468
80536
80604
80339
80407
80475
80543
80611
No.
0
l
2
3
4
5
6
7
8
9
TABLE 42. [Page 765
Logarithms of Numbers.
No. 6400 7000.
Log. 80618 84510.
No.
0
1
2
3
4
5
6
7
8
9
640
641
642
643
644
80618
80686
80754
80821
80889
80625
80693
80760
80828
80895
80632
80699
80767
80835
80902
80638
80706
80774
80841
80909
80645
80713
80781
80848
80916
80652
80720
80787
80855
80922
80659
80726
80794
80862
80929
80665
80733
80801
80868
80936
80672
80740
80808
80875
80943
80679
80747
80814
80882
80949
7
1 1
2 1
3 2
4 3
5 4
6 4
7 5
8 6
9 6
645
646
647
648
649
80956
81023
81090
81158
81224
80963
81030
81097
81164
81231
80969
81037
81104
81171
81238
80976
81043
81111
81178
81245
80983
81050
81117
81184
81251
80990
81057
81124
81191
81258
80996
81064
81131
81198
81265
81003
81070
81137
81204
81271
81010
81077
81144
81211
81278
81017
81084
81151
81218
81285
650
651
652
653
654
81291
81358
81425
81491
81558
81298
81365
81431
81498
81564
81305
81371
81438
81505
81571
81311
81378
81445
81511
81578
81318
81385
81451
81518
81584
81325
81391
81458
81525
81591
81331
81398
81465
81531
81598
81338
81405
81471
81538-
81604
81345
81411
81478
81544
81611
81351
81418
81485
81551
81617
655
656
657
658
659
81624
81690
81757
81823
81889
81631
81697
81763
81829
81895
81637
81704
81770
81836
81902
81644
81710
81776
81842
81908
81651
81717
81783
81849
81915
81657
81723
81790
81856
81921
81664
81730
81796
81862
81928
81671
81737
81803
81869
81935
81677
81743
81809
81875
81941
81684
81750
81816
81882
81948
660
661
662
663
664
81954
82020
82086
82151
82217
81961
82027
82092
82158
82223
81968
82033
82099
82164
82230
81974
82040
82105
82171
82236
81981
82046
82112
82178
82243
81987
82053
82119
82184
82249
81994
82060
82125
82191
82256
82000
82066
82132
82197
82263
82007
82073
82138
82204
82269
82014
82079
82145
82210
82276
665
666
667
668
669
82282
82347
82413
82478
82543
82289
82354
82419
82484
82549
82295
82360
82426
82491
82556
82302
82367
82432
82497
82562
82308
82373
82439
82504
82569
82315
82380
82445
82510
82575
82321
82387
82452
82517
82582
82328
82393
82458
82523
82588
82334
82400
82465
82530
82595
82341
82406
82471
82536
82601
670
671
672
673
674
82607
82672
82737
82802
82866
82614
82679
82743
82808
82872
82620
82685
82750
82814
82879
82627
82692
82756
82821
82885
82633
82698
82763
82827
82892
82640
82705
82769
82834
82898
82646
82711
82776
82840
82905
82653
82718
82782
82847
82911
82659
82724
82789
82853
82918
82666
82730
82795
82860
82924
675
676
677
678
679
82930
82995
83059
83123
83187
82937
83001
83065
83129
83193
82943
83008
83072
83136
83200
82950
83014
83078
83142
83206
82956
83020
83085
83149
83213
82963
83027
83091
83155
83219
82969
83033
83097
83161
83225
82975
83040
83104
83168
83232
82982
83046
83110
83174
83238
82988
83052
83117
83181
83245
680
681
682
683
684
83251
83315
83378
83442
83506
83257
83321
83385
83448
83512
83264
83327
83391
83455
83518
83270
83334
83398
83461
83525
83276
83340
83404
83467
83531
83283
83347
83410
83474
83537
83289
83353
83417
83480
83544
83296
83359
83423
83487
813550
83302
83366
83429
83493
83556
83308
83372
83436
83499
83563
685
686
687
£88
689
83569
83632
83696
83759
83822
83575
83639
83702
83765
83828
83582
83645
83708
83771
83835
83588
83651
83715
83778
83841
83594
83658
83721
83784
83847
83601
83664
83727
83790
83853
83607 ; 83613
83670 : 83677
83734 83740
83797 83803
83860 83866
83620
83683
83746
83809
83872
83626
83689
83753
83816
83879
6
690
691
692
• 693
694
83885
83948
84011
84073
84136
83891
83954
84017
84080
84142
83897
83960
84023
84086
84148
83904
83967
84029
84092
84155
83910
83973
84036
84098
84161
83916
83979
84042
84105
84167
83923
83985
84048
84111
84173
83929
83992
84055
84117
84180
83935
83998
84061
84123
84186
83942
84004
84067
84130
84192
1 1
2 1
3 2
4 2
5 3
6 4
7 4
8 5
9 5
695
696
697
698
699
84198
84261
84323
84386
84448
84205 84211
84267 i 84273
84330 84336
84392 84398
84454 84460
84217
84280
84342
84404
84466
84223
84286
84348
84410
84473
84230
84292
84354
84417
84479
84236
84298
84361
84423
84485
84242
84305
84367
84429
84491
84248
84311
84373
84435
84497
84255
84317
84379
84442
84504
No.
0
123
4 I 5
6789
Page 7661 TABLE 42.
Logarithms of Numbers.
No. 7000 7600. Log. 84510 88081.
No.
0
i
2
3
4
5
6
7
8
9
700
701
702
703
704
84510
84572
84634
84696
84757
84516
84578
84640
84702
84763
84522
84584
84646
84708
84770
84528
84590
84652
84714
84776
84535
84597
84658
84720
84782
84541
84603
84665
84726
84788
84547
84609
84671
84733
84794
84553
84615
84677
84739
84800
84559
84621
84683
84745
84807
84566
7
84628
84689
84751
84813
1
2
3
4
5
6
7
8
9
1
1
2
3
4
4
5
6
6
705
706
707
708
709
84819
84880
84942
85003
85065
84825
84887
84948
85009
85071
84831
84893
84954
85016
85077
84837
84899
84960
85022
85083
84844
84905
84967
85028
85089
84850
84911
84973
85034
85095
84856
84917
84979
85040
85101
84862
84924
84985
85046
85107
84868
84930
84991
85052
85114
84874
84936
84997
85058
85120
710
711
712
713
714
85126
85187
85248
85309
85370
85132
85193
85254
85315
85376
85138
85199
85260
85321
85382
85144
85205
85266
85327
85388
85150
85211
85272
85333
85394
85156
85217
85278
85339
85400
85163
85224
85285
85345
85406
85169
85230
85291
85352
85412
85175
85236
85297
85358
85418
85181
85242
85303
85364
85425
715
716
717
718
719
85431
85491
85552
85612
85673
85437
85497
85558
85618
85679
85443
85503
85564
85625
85685
85449
85509
85570
85631
85691
85455
85516
85576
85637
85697
85461
85522
85582
85643
85703
85467
85528
85588
85649
85709
85473
85534
85594
85655
85715
85479
85540
85600
85661
85721
85485
85546
85606
85667
85727
720
721
722
723
724
85733
85794
85854
85914
85974
85739
85800
85860
85920
85980
85745
85806
85866
85926
85986
85751
85812
85872
85932
85992
85757
85818
85878
85938
85998
85763
85824
85884
85944
86004
85769
85830
85890
85950
86010
85775
85836
85896
85956
86016
85781
85842
85902
85962
86022
85788
85848
85908
85968
86028
6
725
726
727
728
729
86034
86094
86153
86213
86273
86040
86100
86159
86219
86279
86046
86106
86165
86225
86285
86052
86112
86171
86231
86291
86058
86118
86177
86237
86297
86064
86124
86183
86243
86303
86070
86130
86189
86249
86308
86076
86136
86195
86255
86314
86082
86141
86201
86261
86320
86088
86147
86207
86267
86326
1
2
3
4
5
6
7
8
9
1
1
2
2
3
4
4
5
5
730
731
732
733
734
86332
86392
86451
86510
86570
86338
86398
86457
86516
86576
86344
86404
86463
86522
86581
86350
86410
86469
86528
86587
86356
86415
86475
86534
86593
86362
86421
86481
86540
86599
86368
86427
86487
86546
86605
86374
86433
86493
86552
86611
86380
86439
86499
86558
86617
86386
86445
86504
86564
86623
735
736
737
738
739
86629
86688
86747
86806
86864
86635
86694
86753
86812
86870
86641
86700
86759
86817
86876
86646
86705
86764
86823
86882
86652
86711
86770
86829
86888
86658
86717
86776
86835
86894
86664
86723
86782
86841
86900
86670
86729
86788
86847
86906
86676
86735
86794
86853
86911
86682
86741
86800
86859
86917
740
741
742
743
744
745
746
747
748
749
86923
86982
87040
87099
87157
86929
86988
87046
87105
87163
86935
86994
87052
87111
87169
86941
86999
87058
87116
87175
86947
87005
87064
87122
87181
86953
87011
87070
87128
87186
86958
87017
87075
87134
87192
86964
87023
87081
87140
87198
86970
87029
87087
87146
87204
86976
87035
87093
87151
87210
87216
87274
87332
87390
87448
87221
87280
87338
87396
87454
87227
87286
87344
87402
87460
87233
87291
87349
87408
87466
87239
87297
87355
87413
87471
87245
87303
87361
87419
87477
87251
87309
87367
87425
87483
87256
87315
87373
87431
87489
87262
87320
87379
87437
87495
87552
87610
87668
87726
87783
87268
87326
87384
87442
87500
5
750
751
752
753
754
87506
87564
87622
87679
87737
87512
87570
87628
87685
87743
87518
87576
87633
87691
87749
87523
87581
87639
87697
87754
87529
87587
87645
87703
87760
87535
87593
87651
87708
87766
87541
87599
87656
87714
87772
87547
87604
87662
87720
87777
87558
87616
87674
87731
87789
1
2
3
4
5
6
7
8
9
1
1
2
2
3
3
4
4
5
755
756
757
758
759
87795
87852
87910
87967
88024
87800
87858
87915
87973
88030
87806
87864
87921
87978
88036
87812
87869
87927
87984
88041
87818
87875
87933
87990
88047
i
87823
87881
87938
87996
88053
87829
87§87
87944
88001
88058
87835
87892
87950
88007
88064
87841
87898
87955
88013
88070
87846
87904
87961
88018
88076
No.
0
1
2
3
4
5
6
7
8
9
TABLE 42. [Page 767
Logarithms of Numbers.
XQ. 7600 8200. Log. 88081 91381.
No.
0 1
2
3
4
5
6
7
8 9
760
761
762
763
764
88081
88138
88195
88252
88309
88087
88144
88201
88258
88315
88093
88150
88207
88264
88321
88098
88156
88213
88270
88326
88104
88161
88218
88275
88332
88110
88167
88224
88281
88338
88116
88173
88230
88287
88343
88121
88178
88235
88292
88349
88127
88184
88241
88298
88355
88133
88190
88247
88304
88360
6
1
2
3
4
5
6
7
8
9
1
1
2
2
3
4
4
5
5
765
766
767
768
769
88366
88423
88480
88536
88593
88372
88429
88485
88542
88598
88377
88434
88491
88547
88604
88383
88440
88497
88553
88610
88389
88446
88502
88559
88615
88395
88451
88508
88564
88621
88400
88457
88513
88570
88627
88406
88463
88519
88576
88632
88412
88468
88525
88581
88638
88417
88474
88530
88587
88643
770
771
772
773
774
88649
88705
88762
88818
88874
88655
88711
88767
88824
88880
88660
88717
88773
88829
88885
88666
88722
88779
88835
88891
88672
88728
88784
88840
88897
88677
88734
88790
88846
88902
88683
88739
88795
88852
88908
88689
88745
88801
88857
88913
88694
88750
88807
88863
88919
88700
88756
88812
88868
88925
775
776
777
778
779
88930
88986
89042
89098
89154
88936
88992
89048
89104
89159
88941
88997
89053
89109
89165
88947
89003
89059
89115
89170
88953
89009
89064
89120
89176
88958
89014
89070
89126
89182
88964
89020
89076
89131
89187
88969
89025
89081
89137
89193
88975 88981
89031 89037
89087 89092
89143 89148
89198 89204
780
781
782
783
7S4
89209
89265
89321
89376
89432
89215
89271
89326
89382
89437
89221
89276
89332
89387
89443
89226
89282
89337
89393
89448
89232 89237
89287 89293
89343 89348
89398 89404
89454 i 89459
89243
89298
89354
89409
89465
89248
89304
89360
89415
89470
89254
89310
89365
89421
89476
89260
89315
89371
89426
89481
785
786
787
788
789
89487
89542
89597
89653
89708
89492
89548
89603
89658
89713
89498
89553
89609
89664
89719
89504
89559
89614
89669
89724
89509
89564
89620
89675
89730
89515
89570
89625
89680
89735
89520
89575
89631
89686
89741
89526
89581
89636
89691
89746
89531
89586
89642
89697
89752
89862
89916
89971
90026
89537
89592
89647
89702
89757
790
791
792
793
794
89763
89818
89873
89927
89982
89768
89823
89878
• 89933
89988
89774
89829
89883
89938
89993
89779 89785
89834 89840
89889 89894
89944 89949
89998 90004
89790
89845
89900
89955
90009
89796
89851
89905
89960
90015
89801
89856
89911
89966
90020
89812
89867
89922
89977
90031
795
796
797
798
799
90037
90091
90146
90200
90255
90042
90097
90151
90206
90260
90048
90102
90157
90211
90266
90053
90108
90162
90217
90271
90059
90113
90168
90222
90276
90064
90119
90173
90227
90282
90069
90124
90179
90233
90287
90075
90129
90184
90238
90293
90080
90135
90189
90244
90298
90086
90140
90195
90249
90304
800
801
802
803
804
90309
90363
90417
90472
90526
90314
90369
90423
90477
90531
90320
90374
90428
90482
90536
90325
90380
90434
90488
90542
90331
90385
90439
90493
90547
90336
90390
90445
90499
90553
90342
90396
90450
90504
90558
90347
90401
90455
90509
90563
90352
90407
90461
90515
90569
90358
90412
90466
90520
90574
805
806
807
808
809
90580
90634
90687
90741
90795
90585
90639
90693
90747
90800
90590
90644
90698
90752
90806
90596
90650
90703
90757
90811
90601
90655
90709
90763
90816
90607
90660
90714
90768
90822
90612
90666
90720
90773
90827
90617
90671
90725
90779
90832
90623
90677
90730
90784
90838
90628
90682
90736
90789
90843
5
810
811
812
813
814
90849
90902
90956
91009
91062
90854
90907
90961
91014
91068
90859
90913
90966
91020
91073
90865
90918
90972
91025
91078
90870
90924
90977
91030
91084
90875
90929
90982
91036
91089
90881
90934
90988
91041
91094
90886
90940
90993
91046
91100
90891
90945
90998
91052
91105
90897
90950
91004
91057
91110
1
2
3
4
5
6
7
8
9
1
1
2
2
3
3
4
4
5
815
816
817
818
819
91116
91169
91222
91275
91328
91121
91174
91228
91281
91334
91126
91180
91233
91286
91339
91132
91185
91238
91291
91344
91137
91190
91243
91297
91350
91142
91196
91249
91302
91355
91148
91201
91254
91307
91360
91153
91206
91259
91312
91365
91158
91212
91265
91318
91371
91164
91217
91270
91323
91376
Ho.
0
1
2
3 4
5
6
7
8
9
Page 768] TABLE 42.
Logarithms of Numbers.
No. 8200 8800. Log. 91381 94448
No.
0
1
o
3
4
5
6
7
8
9
820
821
822
823
824
91381
91434
91487
91540
91593
91387
91440
91492
91545
91598
91392
91445
91498
91551
91603
91397
91450
91503
91556
91609
91403
91455
91508
91561
91614
91408
91461
91514
91566
91619
91413
91466
91519
91572
91624
91418
91471
91524
91577
91630
91424
91477
91529
91582
91635
91429
91482
91535
91587
91640
6
1
2
3
4
5
6
7
8
9
1
1
2
2
3
4
4
5
5
825
826
827
828
829
91645
91698
91751
91803
91855
91651
91703
91756
91808
91861
91656
91709
91761
91814
91866
91661
91714
91766
91819
91871
91666
91719
91772
91824
91876
91672
91724
91777
91829
91882
91677
91730
91782
91834
91887
91682
91735
91787
91840
91892
91687
91740
91793
91845
91897
91693
91745
91798
91850
91903
830
831
832
833
834
91908
91960
92012
92065
92117
91913
91965
92018
92070
92122
91918
91971
92023
92075
92127
91924
91976
92028
92080
92132
91929
91981
92033
92085
92137
91934
91986
92038
92091
92143
91939
91991
92044
92096
92148
91944
91997
92049
92101
92153
91950
92002
92054
92106
92158
91955
92007
92059
92111
92163
835
836
837
838
839
92169
92221
92273
92324
92376
92174
92226
92278
92330
92381
92179
92231
92283
92335
92387
92184
92236
92288
92340
92392
92189
92241
92293
92345
92397
92195
92247
92298
92350
92402
92200
92252
92304
92355
92407
92205
92257
92309
92361
92412
92210
92262
92314
92366
92418
92215
92267
92319
92371
92423
840
841
842
843
844
92428
92480
92531
92583
92634
92433
92485
92536
92588
92639
92438
92490
92542
92593
92645
92443
92495
92547
92598
92650
92449
92500
92552
92603
92655
92454
92505
92557
92609
92660
92459
92511
92562
92614
92665
92464
92516
92567
92619
92670
92469
92521
92572
92624
92675
92474
92526
92578
92629
92681
5
845
846
847
848
849
92686
92737
92788
92840
92891
92691
92742
92793
92845
92896
92696
92747
92799
92850
92901
92701
92752
92804
92855
92906
92706
92758
92809
92860
92911
92711
92763
92814
92865
92916
92716
92768
92819
92870
92921
92722
92773
92824
92875
92927
92727
92778
92829
92881
92932
92732
92783
92834
92886
92937
1
2
3
4
5
6
7
8
9
1
1
2
2
3
3
4
4
5
850
851
852
853
854
92942
92993
'93044
93095
93146
92947
92998
93049
93100
93151
92952
93003
93054
93105
93156
92957
93008
93059
93110
93161
92962
93013
93064
93115
93166
92967
93018
93069
93120
93171
92973
93024
93075
93125
93176
92978
93029
93080
93131
93181
92983
93034
93085
93136
93186
92988
93039
93090
^93141
93192
855
856
857
858
859
93197
93247
93298
93349
93399
93202
93252
93303
93354
93404
93207
93258
93308
93359
93409
93212
93263
93313
93364
9-3414
93217
93268
93318
93369
93420
93222
93273
93323
93374
93425
93227
93278
93328
93379
93430
93232
93283
93334
93384
93435
93237
93288
93339
93389
93440
93242
93293
93344
93394
93445
860
861
862
863
864
93450
93500
93551
93601
93651
93455
93505
93556
93606
93656
93460
93510
93561
93611
93661
93465
93515
93566
93616
93666
93470
93520
93571
93621
93671
93475
93526
93576
93626
93676
93480
93531
93581
93631
93682
93485
93536
93586
93636
93687
93490
93541
93591
93641
93692
93495
93546
93596
93646
93697
865
866
867
868
869
93702
93752
93802
93852
93902
93707
93757
93807
93857
93907
93712
93762
93812
93862
93912
93717
93767
93817
93867
93917
93722
93772
93822
93872
93922
93727
93777
93827
93877
93927
93732
93782
93832
93882
93932
93737
93787
93837
93887
93937
93742
93792
93842
93892
93942
93747
93797
93847
93897
93947
4
870
871
872
873
874
93952
94002
94052
94101
94151
93957
94007
94057
94106
94156
93962
94012
94062
94111
94161
93967
94017
94067
94116
94166
93972
94022
94072
94121
94171
93977
94027
94077
94126
94176
93982
94032
94082
94131
94181
93987
94037
94086
94136
94186
93992
94042
94091'
94141
94191
93997
94047
94096
94146
94196
1
2
3
4
5
6
7
8
9
0
1
1
2
2
2
3
3
4
875
876
877
878
879
94201
94250
94300
94349
94399
94206
94255
94305
94354
94404
94211
94260
94310
94359
94409
94216
94265
94315
94364
94414
94221
94270
94320
94369
94419
94226
94275
94325
94374
94424
94231
94280
94330
94379
94429
94236
94285
94335
94384
94433
94240
94290
94340
94389
94438
94245
94295
94345
94394
94443
No.
0
1
2
3
4
6
6
7
8
9
TABLE 42.
Logarithms of Numbers.
[Page 769
No. 8SOO 9400.
Log. 94448 97313.
No.
0
1
•
3
4
5
6
7
8
9
880
881
882
883
884
94448
94498
94547
94596
94645
94453
94503
94552
94601
94650
94458
94507
94557
94606
94655
94463
94512
94562
94611
94660
94468
94517
94567
94616
94665
94473
94522
94571
94621
94670
94478
94527
94576
94626
94675
94483
94532
94581
94630
94680
94488
94537
94586
94635
94685
94493
94542
94591
94640
94689
5
1
2
3
4
5
6
7
8
9
1
1
2
2
3
3
4
4
5
885
886
887
888
889
94694
94743
94792
94841
94890
94699
94748
94797
94846
94895
94704
94753
94802
94851
94900
94709
94758
94807
94856
94905
94714
94763
94812
94861
94910
94719
94768
94817
94866
94915
94724
94773
94822
94871
94919
94729
94778
94827
94876
94924
94734
94783
94832
94880
94929
94738
94787
94836
94885
94934
890
891
892
893
894
94939
94988
95036
95085
95134
94944
94993
95041
95090
95139
94949
94998
95046
95095
95143
94954
95002
95051
95100
95148
94959 94963
95007 95012
95056 95061
95105 95109 .
95153 95158
94968
95017
95066
95114
95163
94973
95022
95071
95119
95168
94978
95027
95075
95124
95173
94983
95032
95080
95129
95177
95226
95274
95323
95371
95419
•
895
896
897
898
899
95182
95231
95279
95328
95376
95187
95236
95284
95332
95381
95192
95240
95289
95337
95386
95197
95245
95294
95342
95390
95202
95250
95299
95347
95395
95207
95255
95303
95352
95400
95211
95260
95308
95357
95405
95216
95265
95313
95361
95410
95221
95270
95318
95366
95415
900
901
902
903
904
95424 * 95429
95472 i 95477
95521 i 95525
95569 ! 95574
95617 95622
95434
95482
95530
95578
95626
95439
95487
95535
95583
95631
95444
95492
95540
95588
95636
95448
95497
95545
95593
95641
95453
95501
95550
95598
95646
95458 95463
95506 ! 95511
95554 !' 95559
95602 ! 95607
95650 95655
! 95468
! 95516
i 95564
i 95612
95660
905
906
907
908
909
95665
95713
95761
95809
95856
95670 95674
95718 95722
95766 95770
95813 95818
95861 95866
95679
95727
95775
95823
95871
95684
95732
95780
95828
95875
95689
95737
95785
95832
95880
95694
95742
95789
95837
95885
95698 95703
95746 95751
95794 95799
95842 ! 95847
95890 95895
95708
95756
95804
95852
95899
910
911
912
913
914
95904 j 95909 ; 95914
95952 | 95957 ' 95961
95999 ! 96004 i 96009
96047 j 96052 96057
96095 ! 96099 96104
95918
95966
96014
96061
96109
95923
95971
96019
96066
96114
95928
95976
96023
96071
96118
95933
95980
96028
96076
96123
95938 ; 95942
95985 i 95990
96033 96038
96080 96085
96128 96133
95947
95995
96042
96090
96137
915
916
917
918
919
96142 ! 96147 i 96152
96190 96194 ! 96199
96237 96242 i 96246
96284 96289 ! 96294
96332 i 96336 96341
96156
96204
96251
96298
96346
96161
96209
96256
96303
96350
96166
96213
96261
96308
96355
96171
96218
96265
96313
96360
96175 96180
96223 96227
96270 96275
96317 96322
96365 96369
96185
96232
96280
96327
96374
920
921
922
923
924
96379
. 96426
96473
96520
96567
96384
96431
96478
96525
96572
96388
96435
96483
96530
96577
96393
96440
96487
96534
96581
96398
96445
96492
96539
96586
96402
96450
96497
96544
96591
96407
96454
96501
96548
96595
96412 96417
96459 96464
96506 96511
96553 96558
96600 -i 96605
96421
96468
96515
96562
96609
925
926
927
928
929
96614 96619
96661 96666
96708 96713
96755 96759
96802 i 96806
96624
96670
96717
96764
96811
96628
96675
96722
96769
96816
96633
96680
96727
96774
96820
96638
96685
96731
96778
96825
96642
96689
96736
96783
96830
96647
96694
96741
96788
96834
96652
96699
96745
96792
96839
96656
96703
96750
96797
96844
1
2
3
4
5
6
7
8
9
4
930
931
932
933
934
935
936
937
938
939
96848
96895
96942
96988
97035
96853
96900
96946
96993
97039
96858
96904
96951
96997
97044
96862
96909
96956
97002
97049
96867
96914
96960
97007
97053
96872
96918
96965
97011
97058
96876
96923
96970
97016
97063
96881
96928
96974
97021
97067
96886
96932
96979
97025
97072
96890
96937
96984
97030
97077
0
1
1
2
2
2
3
3
4
97081
97128
97174
97220
97267
97086
97132
97179
97225
97271
97090
97137
97183
97230
97276
97095
97142
97188
97234
97280
97100
97146
97192
97239
97285
97104
97151
97197
97243
97290
97109
97155
97202
97248
97294
97114
97160
97206
97253
97299
97118
97165
97211
97257
97304
97123
97169
97216
97262
97308
No.
0 12345
6
7 8
9
Page 770] TABLE 42.
Logarithms of Numbers.
No. 9400- 10000. Log. 97313 99996.
No.
0
i
2
3
4
5
6
7
8
9
940
941
942
943
944
97313
97359
97405
97451
97497
97543
97589
97635
97681
97727
97317
97364
97410
97456
97502
97322
97368
97414
97460
97506
97327
97373
97419
97465
97511
97331
97377
97424
97470
97516
97336
97382
97428
97474
97520
97340
97387
97433
97479
97525
97345
97391
97437
97483
97529
97350
97396
97442
97488
97534
97354
97400
97447
97493
97539
5
1 1
2 1
3 2
4 2
5 3
6 3
7 4
8 4
9 5
945
946
947
948
949
97548
97594
97640
97685
97731
97552
97598
97644
97690
97736
97557
97603
97649
97695
97740
97786
97832
97877
97923
97968
97562
97607
97653
97699
97745
97566
97612
97658
97704
97749
97571
97617
97663
97708
97754
97575
97621
97667
97713
97759
97580
97626
97672
97717
97763
97585
97630
97676
97722
97768
950
951
952
953
954
97772
97818
97864
97909
97955
97777
97823
97868
97914
97959
97782
97827
97873
97918
97964
97791
97836
97882
97928
97973
97795
97841
97886
97932
97978
97800
97845
97891
97937
97982
97804
97850
97896
97941
97987
97809
97855
97900
97946
97991
97813
97859
97905
97950
97996
955
956
957
958
959
98000
98046
98091
98137
98182
98005
98050
98096
98141
98186
98009
98055
98100
98146
98191
98014
98059
98105
98150
98195
98019
98064
98109
98155
98200
98023
98068
98114
98159
98204
98028
98073
98118
98164
98209
98032
98078
98123
98168
98214
98037
98082
98127
98173
98218
98041
98087
98132
98177
98223
960
961
962
963
964
98227
98272
98318
98363
98408
98232
98277
98322
98367
98412
98236
98281
98327
98372
98417
98241
98286
98331
98376
98421
98245
98290
98336
98381
98426
98250
98295
98340
98385
98430
98254
98299
98345
98390
98435
98259
98304
98349
98394
98439
98263
98308
98354
98399
98444
98268
98313
98358
98403
98448
965
966
967
968
969
98453
98498
98543
98588
98632
98457
98502
98547
98592
98637
98462
98507
98552
98597
98641
98466
98511
98556
98601
98646
98471
98516
98561
98605
98650
98475
98520
98565
98610
98655
98480
98525
98570
98614
98659
98484
98529
98574
98619
98664
98489
98534
98579
98623
98668
98493
98538
98583
98628
98673
970
971
972
973
974
98677
98722
98767
98811
98856
98682
98726
98771
98816
98860
98686
98731
98776
98820
98865
98691
98735
98780
98825
98869
98695
98740
98784
98829
98874
98700
98744
98789
98834
98878
98704
98749
98793
98838
98883
98709
98753
98798
98843
98887
98713
98758
98802
98847
98892
98717
98762
98807
98851
98896
975
976
977
978
979
98900
98945
98989
99034
99078
98905
98949
98994
99038
99083
98909
98954
98998
99043
99087
98914
98958
99003
99047
99092
98918
98963
99007
99052
99096
98923
98967
99012
99056
99100
98927
98972
99016
99061
99105
98932
98976
99021
99065
99109
98936
98981
99025
99069
99114
98941
98985
99029
99074
99118
980
981
982
983
984
99123
99167
99211
99255
99300
99127
99171
99216
99260
99304
99131
99176
99220
99264
99308
99136
99180
99224
99269
99313
99140
99185
99229
99273
99317
99145
99189
99233
9^277
99322
99149
99193
99238
99282
99326
99154
99198
99242
99286
99330
99158
99202
99247
99291
99335
99162
99207
99251
99295
99339
985
986
987
988
989
99344
99388
99432
99476
99520
99348
99392
99436
99480
99524
99352
99396
99441
99484
99528
99357
99401
99445
99489
99533
99361
99405
99449
99493
99537
99366
99410
99454
99498
99542
99370
99414
99458
99502
99546
99374
99419
99463
99506
99550
99379
99423
99467
99511
99555
99383
99427
99471
99515
99559
4
990
991
992
993
994
995
996
997
998
999
99564
99607
99651
99695
99739
99568
99612
99656
99699
99743
99572
99616
99660
99704
99747
99577
99621
99664
99708
99752
99581
99625
99669
99712
99756
99585
99629
99673
99717
99760
99590
99634
99677
99721
99765
99594
99638
99682
99726
99769
99599
99642
99686
99730
99774
99603
99647
99691
99734
99778
1 0
2 1
3 1
4 2
5 2
6 2
7 3
8 3
9 4
99782
99826
99870
99913
99957
99787
99830
99874
99917
99961
99791
99835
99878
99922
99965
99795
99839
99883
99926
99970
99800
99843
99887
99930
99974
99804
99848
99891
99935
99978
99808
99852
99896
99939
99983
99813
99856
99900
99944
99987
99817
99861
99904
99948
99991
99822
99865
99909
99952
99996
No.
o
1
2
3
4
5
6
7
8
9
TABLE 43. [Page 771
Logarithmic Sines, Tangents, and Secants to every Point and Quarter Point of the Compass.
Points.
Sine.
Cosine.
Tangent.
Cotangent.
Secant.
Cosecant.
|
Inf. neg.
8. 69080
8. 99130
9. 16652
10.00000
9. 99948
9. 99790
9. 99527
Inf. neg.
8. 69132
8.99340
9. 17125
Infinite.
11. 30868
11. 00660
10. 82875
10.00000
10.00052
10. 00210
10. 00473
Infinite.
11. 30920
11. 00870
10. 83348
8
7*
7*
1
If
9.29024
9. 38557
9. 46282
9. 52749
9. 99157
9. 98679
9. 98088
9. 97384
9. 29866
9. 39879
9.48194
9. 55365
10. 70134
10. 60121
10. 51806
10. 44635
10. 00843
10. 01321
10. 01912
10. 02616
10. 70976
10. 61443
10. 53718
10.47251
7
6*
2
2*
2|
9. 58284
9. 63099
9. 67339
9. 71105
9. 96562
9. 95616
9. 94543
9. 93335
9. 61722
9. 67483
9. 72796
9. 77770
10. 38278
10. 32517
10. 27204
10. 22230
10. 03438
10. 04384
10. 05457
10. 06665
10. 41716
10. 36901
10. 32661
10. 28895
6
5|
5*
i
3
3*
3*
3f
9. 74474
9. 77503
9. 80236
9. 82708
9. 91985
9. 90483
9. 88819
9. 86979
9. 82489
9. 87020
9. 91417
9. 95729
10. 17511
10. 12980
10. 08583
10. 04271
10. 08015
10. 09517
10. 11181
10. 13021
10. 25526
10. 22497
10. 19764
10. 17292
5
4*
4
9.84949
9.84949
10.00000
10.00000
10. 15051
10. 15051
4
Coaine.
Sine.
Cotangent.
Tangent.
Cosecant.
Secant
Pointo.
Page 772] TABLE 44.
Log. Sines, Tangents, and Secants.
0° ^ 179°
M.
Hour A. M.
Hour P. M.
Sine.
Diff. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
12 0 0
11 59 52
59 44
59 36
59 28
000
0 8
0 16
0 24
0 32
Inf. neg.
6. 46373
76476
94085
7. 06579
30103
17609
12494
9691
Infinite.
13. 53627
23524
05915
12. 93421
Inf. neg.
6. 46373
76476
94085
7. 06579
30103
17609
12494
9691
Infinite.
13. 53627
23524
05915
12. 93421
10. 00000
00000
00000
00000
00000
10. 00000
00000
00000
00000
00000
5
6
7
8
9
10
11
12
13
14
11 59 20
59 12
59 4
58 56
58 48
0 0 40
0 48
0 56
1 4
1 12
7. 16270
24188
30882
36682
41797
7918
6694
5800
5115
4576
12. 83730
75812
69118
63318
58203
7. 16270
24188
30882
36682
41797
7918
6694
5800
5115
4576
12. 83730
75812
69118
63318
58203
10. 00000
00000
00000
00000
00000
10. 00000
00000
00000
00000
00000
55
54
53
52
51
50
49
48
47
46
11 58 40
58 32
58 24
58 16
58 8
0 1 20
1 28
1 36
1 44
1 52
7. 46373
50512
54291
57767
60985
4139
3779
3476
3218
2997
12. 53627
49488
45709
42233
39015
7. 46373
50512
54291
57767
60986
4139
3779
3476
3219
2996
12. 53627
49488
45709
42233
39014
10. 00000
00000
00000
00000
00000
10. 00000
00000
00000
00000
00000
15
16
17
13
19
11 58 0
57 52
57 44
57 36
57 28
02'0
2 8
2 16
2 24
2 32
7. 63982
66784
69417
71900
74248
2802
2633
2483
2348
2227
12. 36018
33216
30583
28100
25752
7. 63982
66785
69418
71900
74248
2803
2633
2482
2348
2228
12. 36018
33215
30582
28100
25752
10. 00000
00000
00001
00001
00001
10. 00000
00000
9. 99999
99999
99999
45
44
43
42
41
20
21
22
23
24
11 57 20
57 12
57 4
56 56
56 48
0 2 40
2 48
2 56
3 4
3 12
7. 76475
78594
80615
82545
84393
2119
2021
1930
1848
1773
12. 23525
21406
19385
17455
15607
7. 76476
78595
80615
82546
84394
2119
2020
1931
1848
1773
12. 23524
21405
19385
17454
15606
10. 00001
00001
00001
00001
00001
9. 99999
99999
99999
99999
99999
40
39
38
37
36
25
26
27
28
29
11 56 40
56 32
56 24
56 16
56 8
0 3 20
3 28
3 36
3 44
3 52
7. 86166
87870
89509
91088
92612
1704
1639
1579
1524
1472
12. 13834
12130
10491
08912
07388
7. 86167
87871
89510
91089
92613
1704
1639
1579
1524
1473
12. 13833
12129
10490
08911
07387
10. 00001
00001
00001
00001
00002
9. 99999
99999
99999
99999
99998
35
34
33
32
31
30
31
32
33
34
11 56 0
55 52
55 44
55 36
55 28
040
4 8
4 16
4 24
4 32
7. 94084
95508'
96887
98223
99520
1424
1379
1336
1297
1259
12. 05916
04492
03113
01777
00480
7. 94086
95510
96889
98225
99522
1424
1379
1336
1297
1259
12. 05914
04490
03111
01775
00478
10. 00002
00002
00002
00002
00002
9. 99998
99998
99998
99998
99998
30
29
28
27
26
35
36
37
38
39
11 55 20
55 12
55 4
54 56
54 48
0 4 40
4 48
4 56
5 4
5 12
8. 00779
02002
03192
04350
05478
1223
1190
1158
1128
1100
11. 99221
97998
96808
95650
94522.
8. 00781
02004
03194
04353
05481
1223
1190
1159
1128
1100
11. 99219
97996
96806
95647
94519
10. 00002
00002
00003
00003
00003
9. 99998
99998,
99997
"^9997
99997
25
24
23
22
21
40
41
42
43
44
11 54 40
54 32
54 24
54 16
54 8
0 5 20
5 28
5 36
5 44
5 52
8. 06578
07650
08696
09718
10717
1072
1046
1022
999
976
11. 93422
92350
91304
90282
89283
8. 06581
07653
08700
09722
10720
1072
1047
1022
998
976
11. 93419*
92347
91300
90278
89280
10. 00003
00003
00003
00003
00004
9. 99997
99997
99997
99997
99996
20
19
18
17
16
45
46
47
48
49
~50~
51
52
53
54
11 54 0
53 52
53 44
• 53 36
53 28
060
6 8
6 16
6 24
6 32
8. 11693
12647
13581
14495
15391
954
934
914
896
877
11.88307
87353
86419
85505
84609
8. 11696
12651
13585
14500
15395
955
934
915
895
878
11. 88304
87349
86415
85500
84605
10. 00004
00004
00004
00004
00004
9. 99996
99996
99996
99996
99996
15
14
13
12
11
10
9
8
7
6
11 53 20
53 12
53 4
52 56
52 48
0 6 40
6 48
6 56
7 4
. 7 12
8. 16268
17128
17971
18798
19610
8BO
843
827
812
797
11. 83732
82872
82029
81202
80390
8. 16273
17133
17976
18804
19616
860
843
828
812
797
11. 83727
82867
82024
81196
80384
10. 00005
00005
00005
00005
00005
9. 99995
99995
99995
99995
99995
55
56
57
58
59
60
11 52 40
52 32
52 24
52 16
52 8
52 0
0 7 20
7 28
7 36
7-44
7 52
8 0
8. 20407
21189
21958
22713
23456
24186
782
769
755
743
730
717
11. 79593
78811
78042
77287
76544
75814
8. 20413
21195
21964
22720
23462
24192
782
769
756
742
730
718
11. 79587
78805
78036
77280
76538
75808
10. 00006
00006
00006
00006
00006
00007
9. 99994
99994
99994
99994
99994
99993
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.i'.
Secant.
Cotangent. | Diff.i'.
Tangent.
Cosecant.
Sine.
M.
W° 89°
TABLE 44. [Page 773
Log. Sines, Tangents, and Secants.
10 . 178°
M.
Hour A. M.
Hour P. M.
Sine.
Diff. 1'.
Cosecant.
Tangent. Diff. 1'. Cotangent.
Secant. Cosine.
M.
60
59
58
57
56
0
1
2
3
4
11 52 0
51 52
51 44
51 36
51 28
080
8 8
8 16
8 24
8 32
8. 24186
24903
25609
26304
26988
717
706
695
684
673
11. 75814
75097
74391
73696
73012
8. 24192
24910
25616
26312
26996
718
706
696
684
673
11. 75808
75090
74384
73688
73004
10.00007
00007
00007
00007
00008
9.99993
99993
99993
99993
99992
5
6
7
8
9
11 51 20
51 12
51 4
50 56
50 48
0 8 40
8 48
8 56
9 4
9 12
8. 27661
28324
28977
29621
30255
663
653
644
634
624
11. 72339
71676
71023
70379
69745
8. 27669
28332
28986
29629
30263
663
654
643
634
625
11. 72331
71668
71014
70371
69737
10.00008
00008
00008
00008
00009
9. 99992
99992
99992
99992
99991
55
54
53
52
51
10
11
12
13
14
11 50 40
50 32
50 24
50 16
50 8
0 9 20
9 28
9 36
9 44
9 52
8. 3C879
31495
32103
32702
33292
616
608
599
590
583
11. 69121
68505
67897
67298
66708
8. 30888
31505
32112
32711
33302
617
607
599
591
584
11. 69112
68495
67888
67289
66698
10. 00009
00009
00010
00010
00010
9.99991
99991
99990
99990
99990
50
49
48
47
46
15
16
17
18
19
11 50 0
49 52
49 44
49 36
49 28
0 10 0
10 8
10 16
10 24
10 32
8. 33875
34450
35018
35578
36131
575
568
560
553
547
11. 66125
65550
64982
64422
63869
8. 33886
34461
35029
35590
36143
575
568
561
553
546
11. 66114
65539
64971
64410
63857
10. 00010
00011
00011
00011
00011
9.99990
99989
99989
99989
99989
45
44
43
42
41
20
21
22
23
24
11 49 20
49 12
49 4
48 56
48 48
0 10 40
10 48
10 56
11 4
11 12
8. 36678
37217
37750
38276
38796
539
533
526
520
514
11. 63322
62783
62250
61724
61204
8. 36689
37229
37762
38289
38809
540
533
527
520
514
11. 63311
62771
62238
61711
61191
10. 00012
00012
00012
00013
00013
9. 99988
99988
99988
99987
99987
40
39
38
37
36
25
26
27
28
29
11 48 40
48 32
48 24
48 16
48 8
0 11 20
11 28
11 36
11 44
11 52
8. 39310
39818
40320
40816
41307
508
502
496
491
485
11. 60690
60182
59680
59184
58693
8. 39323
39832
40334
40830
41321
509
502
496
491
486
11. 60677
60168
59666
59170
58679
10. 00013
00014
00014
00014
00015
9. 99987
99986
99986
99986
99985
35
34
33
32
31
30
31
32
33
34
11 48 0
47 52
47 44
47 36
47 28
0 12 0
12 8
12 16
12 24
12 32
8.41792
42272
42746
43216
43680
480
474
470
464
459
11. 58208
57728
57254
56784
56320
8. 41807
42287
42762
43232
43696
480
475
470
464
460
11. 58193
57713
57238
56768
56304
10. 00015
00015
00016
00016
00016
9. 99985
99985
99984
99984
99984
30
29
28
27
26
35
36
37
38
39
11 47 20
47 12
47 4
46 56
_ 46 48
0 12 40
12 48
12 56
13 4
' 13 12
8. 44139
44594
45044
45489
45930
455
450
445
441
436
11. 55861
55406
54956
54511
54070
8. 44156
44611
45061
45507
45948
455
450
446
441
437
11. 55844
55389
54939
54493
54052
10. 00017
00017
00017
00018
00018
9. 99983
99983
99983
99982
99982
25
24
23
22
21
40
41
42
43
44
45
46
47
48
49
11 46 40
46 32
46 24
46 16
46 8
0 13 20
• 13 28
13 36
13 44
13 52
8. 46366
46799
47226
47650
48069
433
427
424
419
416
11. 53634
53201
52774
52350
51931
8. 46385
46817
47245
47669
48089
432
428
424
420
416
11. 53615
53183
52755
52331
51911
10. 00018
00019
00019
00019
00020
9. 99982
99981
99981
99981
99980
20
19
18
17
16
11 46 0
45 52
45 44
45-36
45 28
0 14 0
14 8
14 16
14 24
14 32
8. 48485
48896
49304
49708
50108
411
408
404
400
396
11. 51515
51104
50696
50292
49892
8. 48505
48917
49325
49729
50130
412
408
404
401
397
11. 51495
51083
50675
50271
49870
10. 00020
00021
00021
00021
00022
9. 99980
99979
99979
99979
99978
15
14
13
12
11
50
51
52
53
54
11 45 20
45 12
45 4
44 56
44 48
0 14 40
14 48
14 56
15 4
15 12
8. 50504
50897
51287
51673
52055
393
390
386
382
379
11. 49496
49103
48713
48327
47945
8. 50527
50920
51310
51696
52079
393
390
386
383
380
376
373
370
367
363
361
11. 49473
49080
48690
48304
47921
10. 00022
00023
00023
00023
00024
9. 99978
99977
99977
99977
99976
10
9
8
7
6
55
56
57
58
59
60
11 44 40
44 32
44 24
44 16
44 8
44 0
0 15 20
15 28
15 36
15 44
15 52
16 0
8. 52434
52810
53183
53552
53919
54282
376
373
369
367
363
360
11. 47566
47190
46817
46448
46081
45718
8. 52459
52835
53208
53578
53945
54308
11. 47541
47165
46792
46422
46055
45692
10. 00024
00025
00025
00026
00026
00026
9. 99976
99975
99975
99974
99974
99974
5
4
3
2
1
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff. 1'.
Secant.
Cotangent . Diff. 1'. Tangent.
Cosecant, j Sine.
M.
91° 88°
Page 774] TABLE 44.
Log. Sines, Tangents, and Secants.
2° 1 177°
M.
Hour A. M.
Hour P. M.
Sine.
DiflE. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
0
1
2
3
4
5
6
7
8
9
11 44 0
43 52
43 44
43 36
43 28
0 16 0
16 8
16 16
16 24
16 32
8. 54282
54642
54999
55354
55705
360
357
355
351
349
11. 45718
45358
45001
44646
44295
8.54308
54669
55027
55382
55734
361
358
355
352
349
11.45692
45331
44973
44618
44266
10. 00026
00027
00027
00028
00028
9. 99974
99973
99973
99972
99972
60
59
58
57
56
11 43 20
43 12
43 4
42 56
42 48
0 16 40
16 48
16 56
17 4
17 12
8. 56054
56400
56743
57084
57421
346
343
341
337
336
11. 43946
43600
43257
42916
42579
8. 56083
56429
56773
57114
57452
346
344
341
338
336
333
330
328
326
323
11.43917
43571
43227
42886
42548
10. 00029
00029
00030
00030
00031
9. 99971
99971
99970
99970
99969
55
54
53
52
51
10
11
12
13
14
11 42 40
42 32
42 24
42 16
42 8
0 17 20
17 28
17 36
17 44
17 52
8. 57757
58089
58419
58747
59072
332
330
328
325
323
11. 42243
41911
41581
41253
40928
8.57788
58121
58451
58779
59105
11. 42212
41879
41549
41221
40895
10. 00031
00032
00032
00033
00033
9. 99969
99968
99968
99967
99967
50
49
48
47
46
15
16
17
18
19
11 42 0
41 52
41 44
41 36
41 28
0 18 0
18 8
18 16
18 24
18 32
8. 59395
59715
60033
60349
60662
320
318
316
313
311
11. 40605
40285
39967
39651
39338
8. 59428
59749
60068
60384
60698
321
319
316
314
311
11. 40572
40251
39932
39816
39302
10. 00033
00034
00034
00035
00036
9. 99967
99966
99966
99965
99964
45
44
43
42
41
20
21
22
23
24
11 41 20
41 12
41 4
40 56
40 48
0 18 40
18 48
18 56
19 4
19 12
8. 60973
61282
61589
61894
62196
309
307
305
302
301
11. 39027
38718
38411
38106
37804
8. 61009
61319
61626
61931
62234
310
307
305
303
301
11. 38991
38681
38374
38069
37766
10. 00036
00037
00037
00038
00038
9. 99964
99963
99963
99962
99962
40
39
38
37
36
25
26
27
28
29
11 40 40
40 32
40 24
40 16
40 8
0 19 20
19 28
19 36
19 44
19 52
8. 62497
62795
63091
63385
63678
298
296
294
293
290
11.37503
37205
36909
36615
36322
8. 62535
62834
63131
63426
6371£
299
297
295
292
291
11. 37465
37166
36869
36574
36282
10. 00039
00039
00040
00040
00041
9. 99961
99961
99960
99960
99959
35
34
33
32
31
30
31
32
33
34
11 40 0
39 52
39 44
39 36
39 28
0 20 0
20 8
20 16
20 24
20 32
8. 63968
64256
64543
64827
65110
288
287
284
283
281
11. 36032
35744
35457
35173
34890
8. 64009
64298
64585
64870
65154
289
287
285
284
281
11. 35991
35702
35415
35130
34846
10. 0004U
00042
00042
00043
00044
9. 99959
99958
99958
99957
99956
30
29
28
27
26
35
36
37
38
39
11 39 20
39 12
39 4
38 56
38 48
0 20 40
20 48
20 56
21 4
21 12
8. 65391
65670
65947
66223
66497
279
277
276
274
272
11. 34609
34330
34053
33777
33503
8. 65435
65715
65993
66269
66543
280
278
276
274
273
11. 34565
34285
34007
33731
33457
10. 00044
00045
00045
00046
00046
9. 99956
99955
99955
99954
99954
25
24
23
22
21
40
41
42
43
44
11 38 40
38 32
38 24
38 16
38 8
0 21 20
21 28
21 36
21 44
21 52
8. 66769
67030
67308
67575
67841
270
269
267
266
263
11. 33231
32961
32692
32425
32159
8. 66816
67087
67356
67624
67890
271
269
268
266
264
11. 33184
32913
32644
32376
32110
10. 00047
00048
00048
00049
00049
9. 99953
99952
99952
99951
99951
20
19
18
17-
16
45
46
47
48
49
11 38 0
37 52
37 44
37 36
37 28
0 22 0
22 8
22 16
22 24
22 32
8. 68104
68367
68627
68886
69144
263
260
259
258
256
11. 31896
31633
3J373
31114
30856
8. 68154
68417
68678
68938
69196
263
261
260
258
257
11. 31846
31583
31322
31062
30804
10. 00050
00051
00051
00052
00052
9. 99950
99949
99949
99948
99948
15
14
13
12
11
50
51
52
53
54
11 37 20
37 12
37 4
36 56
36 48
0 22 40
22 48
22 56
23 4
23 12
8. 69400
69654
69907
70159
70409
254
253
252
250
249
11. 30600
30346
30093
29841
29591
8. 69453
69708
69962
70214
70465
255
254
252
251
249
11. 30547
30292
30038
29786
29535
10. 00053
00054
00054
00055
00056
9. 99947
99946
99946
99945
99944
10
9
8
7
6
55
56
57
58
59
60
11 36 40
36 32
36 24
36 16
36 8
36 0
0 23 20
'23 28
23 36
23 44
23 52
24 0
8. 70658
70905
71151
71395
71638
71880
247
246
244
243
242
240
11. 29342
29095
28849
28605
28362
28120
8. 70714
70962
71208
71453
71697
71940
248
246
245
244
243
241
11. 29286
29038
28792
28547
28303
28060
10. 00056
00057
00058
00058
00059
00060
9.99944
99943
99942
99942
99941
99940
5
4
3
2
1
0
M.
Hour P.M.
Hour A. M.
Cosine.
Diff. 1'.
Secant.
Cotangent
Diff. 1'.
Tangent.
Cosecant.
Sine.
M.
930 870
TABLE 4A. [Page 775
Log. Sines, Tangents, and Secants.
8° 176°
M.
Hour A. M.
Hour P. M.
Sine.
Diff. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
0
1
2
3
4
11 36 0
35 52
35 44
35 36
35 28
0 24 0
24 8
24 16
24 24
24 32
8. 71880
72120
72359
72597
72834
240
239
238
237
235
11. 28120
27880
27641
27403
27166
8. 71940
72181
72420
72659
72896
241
239
239
237
236
11. 28060
27819
27580
27341
27104
10.00060
00060
00061
00062
00062
9.99940
99940
99939
99938
99938
60
59
58
57
56
5
6
7
8
9
11 35 20
35 12
35 4
34 56
34 48
0 24 40
24 48
24 56
25 4
25 12
8. 73069
73303
73535
73757
73997
234
232
232
230
229
11. 26931
26697
26465
26233
26003
8. 73132
73366
73600
73832
74063
234
234
232
231
229
11.26868
26634
26400
26168
25937
10. 00063
00064
00064
00065
00066
9. 99937
99936
99936
99935
99934
55
54
53
52
51
10
11
12
13
14
11 34 40
34 32
34 24
34 16
34 8
0 25 20
25 28
25 36
25 44
25 52
8. 74226
74454
74680
74906
75130
228
226
226
224
223
11. 25774
25546
25320
25094
24870
8. 74292
74521
74748
74974
75199
229
227
226
225
224
11. 25708
25479
25252
25026
24801
10. 00066
00067
00068
00068
00069
9. 99934
99933
99932
99932
99931
50
49
48
47
46
15
16
17
1 18
19
11 34 0
33 52
33 44
33 36
33 28
0 26 0
26 8
26 16
26 24
26 32
8. 75353
75575
75795
76015
76234
222
220
220
219
217
11. 24647
24425
24205
23985
23766
8. 75423
75645
75867
76087
76306
222
222
220
219
219
11. 24577
24355
24133
23913
23694
10. 00070
00071
00071
00072
00073
9. 99930
99929
99929
99928
99927
45
44
43
42
41
20
21
22
23
24
11 33 20
33 12
33 4
32 56
32 48
0 26 40
26 48
26 56
27 4
27 12
8. 76451
76667
76883
77097
77310
216
-216
214
213
212
11. 23549
23333
23117
22903
22690
8. 76525
76742
76958
77173
77387
217
216
215
214
213
11. 23475
23258
23042
22827
22613
10. 00074
00074
00075
00076
00077
9. 99926
99926
99925
99924
99923
40
39
38
37
36
25
26
27
28
29
11 32 40
32 32
32 24
32 16
32 8
0 27 20
27 28
27 36
27 44
27 52
8. 77522
77733
77943
78152
78360
211
210
209
208
208
11. 22478
22267
22057
218*48
21640
8. 77600 211
77811 211
78022 210
78232 i 209
78441 208
11. 22400
22189
21978
21768
21559
10. 00077
00078
00079
00080
00080
9. 99923
99922
99921
99920
99920
35
34
33
32
31
30
31
32
33
34
11 32 0
31 52
31 44
31 36
31 28
0 28 0
28 8
28 16
28 24
28 32
8. 78568
78774
78979
79183
79386
206
205
204
203
202
11. 21432
21226
21021
20817
20614
8. 78649 206
78855 206
79061 205
79266 204
79470 203
11.21351
21145
20939
20734
20530
10. 00081
00082
00083
00083
00084
9. 99919
99918
99917
99917
99916
30
29
28
27
26
35
36
37
38
39
11 31 20
31 12
31 4
30 56
30 48
0 28 40
28 48
28 56
29 4
29 12
8. 79588
79789
79990
80189
80388
201
201
199
199
197
11. 20412
20211
20010
19811
19612
8.79673 202 11.20327
79875 201 20125
80076 201 19924
80277 199 19723
80476 198 19524
10.00085
00086
00087
00087
00088
9. 99915
99914
99913
99913
99912
25
24
23
22
21
40
41
42
43
44
11 30 40
30 32
30 24
30 16
30 8
0 29 20
29 28
29 36
29 44
29 52
8. 80585
80782
80978
81173
81367
197
196
195
194
193
11. 19415
19218
19022
18827
18633
8. 80674 j 198
80872 ; 196
81068 i 196
81264 195
81459 194
11. 19326
19128
18932
18736
18541
10. 00089
00090
00091
00091
00092
9. 99911
99910
99909
99909
99908
20
19
18
17
16
45
46
47
48
49
11 30 0
29 52
29 44
29 36
29 28
0 30 0
30 8
30 16
30 24
30 32
8.81560 ! 192
81752 i 192
81944 ! 190
82134 j 190
82324 189
11. 18440
18248
18056
17866
17676
8.81653 193
81846 i 192
82038 i 192
82230 190
82420 I 190
11. 18347
18154
17962
17770
17580
10. 00093
00094
00095
00096
00096
9. 99907
99906
99905
99904
99904
15
14
13
12
11
50
51
52
53
54
11 29 20
29 12
29 4
28 56
28 48
0 30 40
30 48
30 56
31 4
31 12
8. 82513 188
82701 i 187
82888 187
83075 186
83261 ! 185
11. 17487
17299
17112
16925
16739
8. 82610 189
82799 188
82987 188
83175 186
83361 186
11. 17390
17201
17013
16825
16639
10. 00097
00098
00099
00100
00101
9. 99903
99902
99901
99900
99899
10
9
8
7
6
55
56
57
58
59
60
11 28 40
28 32
28 24
28 16
28 8
28 0
0 31 20
31 28
31 36
31 44
31 52
32 0
8.83446
83630
83813
83996
84177
84358
184
183
183
181
181
181
11. 16554
16370
16187
16004
15823
15642
8. 83547
83732
83916
84100
84282
84464
185
184
184
182
182
182
11. 16453
16268
16084
15900
15718
15536
10. 00102
00102
00103
00104
00105
00106
9. 99898
99898
99897
99896
99895
99894
5
4
3
2
1
0
M.
Hour p. M.
Hour A. M.
Cosine. | Diff. 1'.
Secant,
Cotangent. | Diff. 1'. Tangent. Cosecant.
Sine
M.
93° 8«°
Page 776] TABLE 44.
Log. Sines, Tangents, and Secants.
4° 176°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.l'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
0
1
2
3
4
11 28 0
27 52
27 44
27 36
27 28
0 32 0
32 8
32 16
32 24
32 32
8. 84358
84539
84718
84897
85075
181
179
179
178
177
11. 15642
15461
15282
15103
14925
8.84464
84646
84826
85006
85185
182
180
180
179
178
11. 15536
15354
15174
14994
14815
10. 00106
00107
00108
00109
00109
9. 99894
99893
99892
99891
99891
60
59
58
57
56
5
6
7
8
9
11 27 20
27 12
27 4
26 56
26 48
0 32 40
32 48
32 56
33 4
33 12
8. 85252
85429
85605
85780
85955
177
176
175
175
173
11. 14748
14571
14395
14220
14045
8. 85363
85540
85717
85893
86069
177
177
176
176
174
11. 14637
14460
14283
14107
13931
10. 00110
00111
00112
00113
00114
9. 99890
99889
99888
99887
99886
55
54
53
52
51
10
11
12
13
14
11 26 40
26 32
26 24
26 16
26 8
0 33 20
33 28
33 36
33 44
33 52
8. 86128
86301
86474
86645
86816
173
173
171
171
171
11. 13872
13699
13526
13355
13184
8. 86243
86417
86591
86763
86935
174
174
172
172
171
11. 13757
13583
13409
13237
13065
10. 00115
00116
00117
00118
00119
9. 99885
99884
99883
99882
99881
50
49
48
47
46
15
16
17
18
19
11 26 0
25 52
25 44
25 36
25 28
0 34 0
34 8
34 16
34 24
. 34 32
8. 86987
87156
87325
87494
87661
169
169
169
167
168
11. 13013
12844
12675
12506
12339
8. 87106
87277
87447
87616
87785
171
170
169
169
168
11. 12894
12723
12553
12384
12215
10. 00120
00121
00121
00122
00123
9. 99880
99879
99879
99878
99877
45
44
43
42
41
20
21
22
23
24
11 25 20
25 12
25 4
24 56
24 48
0 34 40
34 48
34 56
35 4
35 12
8. 87829
87995
88161
88326
88490
166
166
165
164
164
11. 12171
12005
11839
11674
11510
8. 87953
88120
88287
88453
88618
167
167^
166
165
165
11. 12047
11880
11713
11547
11382
10. 00124
00125
00126
00127
00128
9. 99876
99875
99874
99873
99872
40
39
38
37
36
25
26
27
28
29
11 24 40
24 32
24 24
24 16
24 8
0 35 20
35 28
35 36
35 44
35 52
8. 88654
88817
88980
89142
89304
163
163
162
162
160
11. 11346
11183
11020
10858
10696
8. 887bd
88948
89111
89274
89437
165
163
163
163
161
11. 11217
11052
10889
10726
10563
10. 00129
00130
00131
00132
00133
9. 99871
99870
99869
99868
99867
35
34
33
32
31
30
31
32
33
34
11 24 0
23 52
23 44
23 36
23 28
0 36 0
36 8
36 16
36 24
36 32
8. 89464
89625
89784
89943
90102
161
159
159
159
158
11. 10536
10375
10216
10057
09898
8. 89598
89760
89920
90080
90240
162
160
160
160
159
11. 10402
10240
10080
09920
09760
10. 00134
00135
00136
00137
00138
9. 99866
99865
99864
99863
99862
30
29
28
27
26
35
36
37
38
39
11 23 20
23 12
23 4
22 56
22 48
0 36 40
36 48
36 56
37 4
37 12
8. 90260
90417
90574
90730
90885
157
157
156
155
155
11. 09740
09583
09426
09270
09115
8. 90399
90557
90715
90872
91029
158
158
157
157
156
11. 09601
09443
09285
09128
08971
10. 00139
00140
00141
00142
00143
9. 99861
99860
99859
99858
99857
25
24
23
22
21
40
41
42
43
44
11 22 40
22 32
22 24
22 16
22 8
0 37 20
37 28
37 36
37 44
37 52
8. 91040
91195
91349
91502
91655
155
154
153
153
152
11. 08960
08805
08651
08498
08345
8. 91185
91340
91495
91650
91803
155
155
155
153
154
11. 08815
08660
08505
08350
08197
10. 00144
00145
00146
00147
00148
9. 99856
99855
99854
99853
99852
20
19
18
17
16
45
46
47
48
49
11 22 0
21 52
21 44
21 36
21 28
0 38 0
38 8
38 16
38 24
38 32
8. 91807
91959
92110
92261
92411
152
151
151
150
150
11. 08193
08041
07890
07739
07589
8. 91957
92110
92262
92414
92565
153
152
152
151
151
11. 08043
07890
07738
07586
07435
10. 00149
00150
00152
00153
00154
9. 99851
99850
99848
99847
99846
15
14
13
12
11
50
51
52
53
54
11 21 20
21 12
21 4
20 56
20 48
0 38 40
38 48
38 56
39 4
39 12
8. 92561
92710
92859
93007
93154
149
149
148
147
147
11. 07439
07290
07141
06993
06846
8. 92716
92866
93016
93165
93313
150
150
149
148
149
11. 07284
07134
06984
06835
06687
10. 00155
00156
00157
00158
00159
9. 99845
99844
99843
99842
99841
10
9
8
7
6
55
56
57
58
59
60
11 20 40
20 32
20 24
20 16
20 8
20 0
0 39 20
39 28
39 36
39 44
39 52
40 0
8. 93301
93448
93594
93740
93885
94030
147
146
146
145
145
144
11. 06699
06552
06406
06260
06115
05970
8. 93462
93609
93756
93903
94049
94195
147
147
147
146
146
145
11. 06538
06391
06244
06097
05951
05805
10. 00160
00161
00162
00163
00164
00166
9. 99840
99839
99838
99837
99836
99834
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff. 1'.
Secant.
Cotangent.
Diff.l'.
Tangent.
Cosecant
Sine.
M.
94° 86°
TABLE U. [Page 777
Log. Sines, Tangents, and Secants.
6« A A B B C C 174°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
0
2
4
7
9
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
11 20 00
19 52
19 44
19 36
19 28
0 40 00
40 08
40 16
40 24
40 32
8. 94030
94174
94317
94461
94603
11. 05970
05826
05683
05539
05397
8. 94195
94340
94485
94630
94773
0
o
4
7
9
11. 05805
05660
05515
05370
05227
10. 00166
00167
00168
00169
00170
0
0
0
°0
9. 99834
99833
99832
99831
99830
60
59
58
57
56
5
6
7
8
9
11 19 20
19 12
19 04
18 56
18 48
0 40 40
40 48
40 56
41 04
41 12
8. 94746
94887
95029
95170
95310
11
13
15
18
20
11. 05254
05113
• 04971
04830
04690
8. 94917
95060
95202
95344
95486
11
13
15
18
20
11. 05083
04940
04798
04656
04514
10. 00171
00172
00173
00175
00176
0
0
0
0
0
9. 99829
99828
99827
99825
99824
55
54
53
52
51
10
11
12
13
14
IT
16
17
18
19
11 18 40
18 32
18 24
18 16
18 08
0 41 20
41 28
41 36
41 44
41 52
8. 95450
95589
95728
95867
96005
22
24
26
29
31
11.04550
04411
04272
04133
03995
8. 95627
95767
95908
96047
96187
22
24
27
29
31
11. 04373
04233
04092
03953
03813
10. 00177
00178
00179
00180
00181
0
0
0
0
0
9. 99823
99822
99821
99820
99819
50
49
48
47
46
11 18 00
17 52
17 44
17 36
17 28
0 42 00
42 08
42 16
42 24
42 32
8. 96143
96280
96417
96553
96689
33
35
37
39
42
11. 03857
03720
03583
03447
03311
8. 96325
96464
96602
96739
96877
33
35
38
40
42
11. 03675
03536
03398
03261
03123
10. 00183
00184
00185
00186
00187
0
0
0
0
0
0
0
0
0
0
9. 99817
99816
99815
99814
99813
45
44
43
42
41
20
21
22
23
24
11 17 20
17 12
17 04
16 56
16 48
0 42 40
42 48
42 56
43 04
43 12
8. 96825
96960
97095
97229
97363
44
46
48
50
53
11.03175
03040
02905
02771
02637
8. 97013
97150
97285
97421
97556
44
46
49
51
53
11. 02987
02850
02715
02579
02444
10. 00188
00190
00191
00192
00193
9. 99812
99810
99809
99808
99807
40
39
38
37
36
25
26
27
28
29
11 16 40
16 32
16 24
16 16
16 08
0 43 20
43 28
43 36
43 44
43 52
8. 97496
97629
97762
97894
98026
55
57
59
61
64
11. 02504
02371
02238
02106
01974
8. 97691
97825
97959
98092
98225
55
58
60
62
64
11. 02309
02175
02041
01908
01775
10. 00194
00196
00197
00198
00199
1
1
1
1
1
9. 99806
99804
99803
99802
99801
35
34
33
32
31
30
31
32
33
34
11 16 00
15 52
15 44
15 36
15 28
0 44 00
44 08
44 16
44 24
44 32
8. 98157
98288
98419
98549
98679
66
68
70
72
75
11. 01843
01712
01581
01451
01321
8. 98358
98490
98622
98753
988S4>
66
69
71
73
75
11.01642
01510
01378
01247
01116
10. 00200
00202
00203
00204
OQ205
1
1
1
1
e 1
9.99800
99798
99797
99796
99795
30
29
28
27
26
35
36
37
38
39
11 15 20
15 12
15 04
14 56
14 48
0 44 40
44 48
44 56
45 04
45 12
8. 98808
98937
99066
99194
99322
77
79
81
83
86
11. 01192
01063
00934
00806
00678
8. 99015
99145
99275
99405
99534
77
80
82
84
86
11.00985
00855
00725
00595
00466
10. 00207
00208
00209
00210
00212
1
1
1
1
1
9. 99793
99792
99791
99790
99788
25
24
23
22
21
40
41
42
43
44
11 14 40
14 32
14 24
14 16
14 08
0 45 20
45 28
45 36
45 44
45 52
8. 99450
99577
99704
99830
99956
88
90
92
94
96
11. 00550
00423
00296
00170
00044
8. 99662
99791
99919
9.00046
00174
89
91
93
95
97
11. 00338
00209
00081
10. 99954
99826
10. 00213
00214
00215
00217
00218
1
1
I
1
1
9. 99787
99786
99785
99783
99782
20
19
18
17
16
45
46
47
48
49
11 14 00
13 52
13 44
13 36
13 28
0 46 00
46 08
46 16
46 24
46 32
9.00082
00207
00332
00456
00581
99
101
103
105
107
10. 99918
99793
99668
99544
99419
9. 00301
00427
00553
00679
00805
100
102
104
106
108
111
113
115
117
120
10. 99699
99573
99447
99321
99195
10. 00219
00220
00222
00223
00224
1
1
1
1
1
9. 99781
99780
99778
99777
99776
15
14
13
12
11
50
51
52
53
54
11 13 20
13 12
13 04
12 56
12 48
0 46 40
46 48
46 56
47 04
47 12
9.00704
00828
00951
01074
01196
110
112
114
116
118
10. 99296
99172
99049
98926
98804
9. 00930
01055
01179
01303
01427
10. 99070
98945
98821
98697
98573
10. 00225
00227
00228
00229
00231
1
1
1
1
1
9.99775
99773
99772
p ;:i
99769
10
9
8
7
6
55
56
57
58
59
60
11 12 40
12 32
12 24
12 16
12 08
12 00
0 47 20
47 28
47 36
47 44
47 52
48 00
9. 01318
01440
01561
01682
01803
01923
121
123
125
127
129
132
Diff.
10. 98682
98560
98439
98318
98197
98077
9. 01550
01673
01796
01918
02040
02162
122
124
126
128
131
133
10. 98450
98327
98204
98082
97960
97838
10. 00232
00233
00235
00236
00237
00239
1
1
1
1
1
1
99768
99767
99765
99761
99763
99761
5
4
3
2
1
0
M.
M.
Hour P. M.
Sour A. M.
Cosine.
Secant.
Cotangent,
Diff.
Tangent.
Cosecant.
Diff. Sine.
9o° A A B B C C 84°
Seconds of timfi
!•
.»,
•?"
41
•»
7* \
("A
Prop, parts of cols. < B
lc
ie
17
0
33
33
0
49
50
0
66
66
1
82
83
1
99
100
1
115 j
11
Page 778] TABLE 44.
Log. Sines, Tangents, and Secants.
6° A A B B C C 173°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
0
2
4
6
8
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
11 12 00
11 52
11 44
11 36
11 28
0 48 00
48 08
48 16
48 24
48 32
9. 01923
02043
02163
02283
02402
0
2
4
6
7
9
11
13
15
17
10. 98077
97957
97837
97717
97598
9. 02162
02283
02404
02525
02645
10. 97838
97717
97596
97475
97355
10.97234
97115
96995
96876
96758
10. 00239
00240
00241
00243
00244
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9. 99761
99760
99759
99757
99756
60
59
58
57
56
5
6
7
8
9
11 11 20
11 12
11 04
10 56
10 48
0 48 40
48 48
48 56
49 04
49 12
9. 02520
02639
02757
02874
02992
10. 97480
97361
97243
97126
97008
9. 02766
02885
03005
03124
03242
9
11
13
15
17
10. 00245
00247
00248
00249
00251
9. 99755
99753
99752
99751
99749
55
54
53
52
51
10
11
12
13
14
11 10 40
10 32
10 24
10 16
10 08
0 49 20
49 28
49 36
49 44
49 52
9. 03109
03226
03342
03458
03574
19
20
22
24
26
10. 96891
96774
96658
96542
96426
9. 03361
03479
03597
03714
03832
19
21
23
24
26
10. 96639
96521
96403
96286
96168
10. 00252
00253
00255
00256
00258
9. 99748
99747
99745
99744
99742
50
49
48
47
46
45
44
43
42
41
15
16
17
18
19
11 10 00
9 52
9 44
9 36
9 28
0 50 00
50 08
50 16
50 24
50 32
9. 03690
03805
03920
04034
04149
28
30
31
33
35
10. 96310
96195
96080
95966
95851
9. 03948
04065
04181
04297
04413
28
30
32
34
36
10. 96052
95935
95819
95703
95587
10. 00259
00260
00262
00263
00264
9. 99741
99740
99738
99737
99736
20
21
22
23
24
11 9 20
9 12
9 04
8 56
8 48
0 50 40
50 48
50 56
51 04
51 12
9. 04262
04376
04490
04603
04715
37
39
41
43
44
10. 95738
95624
95510
95397
95285
9. 04528
04643
04758
04873
04987
38
39
41
43
45
10. 95472
95357
95242
95127
95013
10. 00266
00267
00269
00270
00272
0
1
1
1
1
9. 99734
99733
99731
99730
99728
40
39
38
37
36
25
26
27
28
29
30
31
32
33
34
11 8 40
8 32
8 24
8 16
8 08
0 51 20
51 28
51 36
51 44
51 52
9. 04828
04940
05052
05164
05275
46
48
50
52
54
10. 95172
95060
94948
94836
94725
9. 05101
05214
05328
05441
05553
47
49
51
53
54
10. 94899
94786
94672
94559
94447
10. 00273
00274
00276
00277
00279
1
1
1
1
1
9. 99727
99726
99724
99723
99721
35
34
33
32
31
11 8 00
7 52
7 44
7 36
7 28
0 52 00
52 08
52 16
52 24
52 32
9. 05386
05497
05607
05717
05827
56
57
59
61
63
10. 94614
94503
94393
94283
94173
9. 05666
05778
05890
06002
06113
56
58
60
62
64
10. 94334
94222
94110
93998
93887
10. 00280
00282
00283
00284
00286
1
1
1
1
1
9. 99720
99718
99717
99716
99714
30
29
28
27
26
35
36
37
38
39
11 7 20
7 12
7 04
6 56
6 48
0 52 40
52 48
52 56
53 04
53 12
9. 05937
06046
06155
06264
06372
65
67
69
70
72
10. 94063
93954
93845
93736
93628
9. 06224
06335
06445
06556
06666
66
68
69
71
73
10. 93776
93665
93555
93444
93334
10. 00287
00289
00290
00292
00293
10. 00295
00296
00298
00299
00301
1
1
1
1
1
9. 99713
99711
99710
99708
99707
25
24
23
22
21
40
41
42
43
44
11 6 40
6 32
6 24
6 16
6 08
0 53 20
53 28
53 36
53 44
53 52
9. 06481
06589
06696
06804
06911
74
76
78
80
81
10. 93519
93411
93304
93196
93089
9. 06775
06885
06994
07103
07211
75
77
79
81
83
10. 93225
93115
93006
92897
92789
1
1
1
1
1
9. 99705
99704
99702
99701
99699
20
19
18
17
16
45
46
47
48
49
11 6 00
5 52
5 44
5 36
5 28
0 54 00
54 08
54 16
54 24
54 32
9. 07018
07124
07231
07337
07442
83
85
87
89
91
10. 92982
92876
92769
92663
92558
9. 07320
07428
07536
07643
07751
84
86
88
90
92
10. 92680
92572
92464
92357
92249
10. 00302
00304
00305
00307
00308
1
1
1
1
1
9. 99698
99696
99695
99693
99692
15
14
13
12
11
50
51
52
53
54
11 5 20
5 12
5 04
4 56
4 48
0 54 40
54 48
54 56
55 04
55 12
9. 07548
07653
07758
07863
07968
93
94
96
98
100
102
104
106
107
109
111
10. 92452
92347
92242
92137
92032
9. 07858
07964
08071
08177
08283
94
96
98
99
101
10. 92142
92036
91929
91823
91717
10. 00310
00311
00313
00314
00316
1
1
1
1
1
9. 99690
99689
99687
99686
99684
10
9
8
7
6
155
56
57
58
59
60
11 4 40
4 32
4 24
4 16
4 08
4 00
0 55 20
55 28
55 36
55 44
55 52
56 00
9. 08072
08176
08280
08383
08486
08589
10. 91928
91824
91720
91617
91514
91411
9. 08389
08495
08600
08705
08810
08914
103
105
107
109
111
113
10. 91611
91505
91400
91295
91190
91086
10. 00317
00319
00320
00322
00323
00325
1
1
1
1
1
1
9. 99683
99681
99680
99678
99677
99675
5
4
3
2
1
0
M.
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
96° A A B B C C 83°
Seconds of tLxie ...
1s
2"
3s
4s
5*
6"
7»
(A
Prop, parts of CQj s. < B
lc
14
14
0
28
28
0
42
42
1
56
56
1
69
70
1
83
84
1
97
98
1
7° A
TABLE 4A.
Log. Sines, Tangents, and Secants.
A B B C
[Page 779
C 172°
M.
Hour A. M. Hour p. M.
Sine.
,Diff.
T
2
3
< 5
6
10
11
13
M
Cosecant.
Tangent.
Diff.
Coumgent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
11 4 0 0 56 0
3 52 56 8
3 44 56 16
3 36 56 24
3 28 i 56 32
9. 08589
08692
08795
08897
08999
10. 91411
91308
91205
91103
91001
9. 08914
09019
09123
09227
09330
0
2
3
5
7
10. 91086
90981
90877
90773
90670
10. 00325
00326
00328
00330
00331
0
0
0
0
0
9. 99675
99674
99672
99670
99669
60
59
58
57
56
5
6
7
8
9
11 3 20
3 12
3 4
2 56
2 48
0 56 40
56 48
56 56
57 4
57 12
9. 09101
09202
09304
09405
09506
10. 90899
90798
90696
90595
90494
9.09434
09537
09640
09742
09845
! 8
i 10
11
13
15
10. 90566
90463
90360
90258
90155
10. 00333
00334
00336
00337
00339
0
0
0
0
1 °
0
0
0
0
0
9.99667
99666
99664
99663
99661
55
54
53
52
51
10
11
12
13
14
11 2 40
2 32
2 24
2 16
2 8
0 57 20
57 28
57 36
57 44
57 52
9. 09606
09707
09807
09907
10006
16
IS
19
21
22
10. 90394
90293
90193
90093
89994
9. 09947
10049
10150
10252
10353
16
18
; 20
21
23
10. 90053
89951
89850
89748
89647
10. 00341
00342
00344
00345
00347
9. 99659
99658
99656
99655
99653
50
49
48
47
46
15
16
17
18
19
11 2 0 0 58 0
1 52 58 8
1 44 58 16
1 36 ; 58 24
1 28 58 32
9. 10106
10205
10304
10402
10501
24
26
27
29
30
10. 89894
89795
89696
89598
89499
9. 10454
10555
10656
10756
10856
24
26
28
29
31
10. 89546
89445
89344
89244
89144
10. 00349
00350
00352
00353
00355
[
! 0
1
1
9. 99651
99650
99648
99647
99645
45
44
43
42
41
20
21
22
23
24
11 1 20 ; 0 58 40
1 12 1 58 48
14 58 56
0 56 59 4
0 48 59 12
9. 10599
10697
10795
10893
10990
32
34
35
37
38
40
42
43
| 45
46
10. 89401
89303
89205
89107
89010
9. 10956
11056
11155
11254
11353
33
34
36
37
39
10. 89044
88944
88845
88746
88647
10. 00357
00358
00360
00362
00363
1
1
1
1
1
1
1
1
9.99643
99642
99640
99638
99637
40
39
38
37
36
25
26
27
28
29
11 0 40 0 59 20
0 32 59 28
0 24 59 36
0 16 59 44
08: 59 52
9. 11087
11184
11281
11377
11474
10. 88913
88816
88719
88623
88526
9. 11452
11551
11649
11747
11845
41
42
44
46
47
10. 88548
88449
88351
88253
88155
10. 00365
00367
00368
00370
00371
9. 99635
99633
99632
99630
99629
35
34
33
32
31
30
31
32
33
34
11 0 0 '• 1 0 0
10 59 52 08
59 44 0 16
59 36 0 24
59 28 0 32
9. 11570
11666
11761
11857
11952
. 48
50
51
53
54
56
58
59
61
62
10. 88430
88334
88239
88143
88048
9. 11943
12040
12138
12235
12332
49
51
52
54
55
10. 88057
87960
87862
87765
87668
10. 00373
00375
00376
00378
00380
1
1
1
1
1
1
1
9. 99627
99625
99624
99622
99620
30
29
28
27
26
35
36
37
38
39
10 59 20 1 0 40
59 12 0 48
59 4 0 56
58 56 i 14
58 48 1 12
9. 12047
12142
12236
12331
12425
10. 87953
87858
87764
87669
87575
9. 12428
12525
12621
12717
12813
57
59
60
62
64
10. 87572
87475
87379
87283
87187
10. 00382
00383
00385
00387
00388
9. 99618
99617
99615
99613
99612
25
24
23
22
21
40
41
42
43
44
10 58 40
58 32
58 24
58 16
58 8
1 1 20
1 28
1 36
1 44
1 52
9. 12519
12612
12706
12799
12892
64
66
67
69
70
10. 87481
87388
87294
87201
87108
9. 12909
13004
13099
13194
13289
65
67
68
70
72
10. 87091
86996
86901
86806
86711
10. 00390
00392
00393
00395
00397
1
1
1
1
1
9. 99610
99608
99607
99605
99603
20
19
18
17
16
45
46
47
48
49
tlO 58 0
57 52
57 44
57 36
57 28
120
2 8
2 16
2 24
2 32
9.12985
13078
13171
13263
13355
72
74
75
77
78
10. 87015
86922
86829
86737
86645
9. 13384
13478
13573
13667
13761
73
75
77
78
80
10. 86616
86522
86427
86333
86239
10. 00399
00400
00402
00404
00405
1
1
1
I
9. 99601
99600
99598
99596
99595
15
14
13
12
11
50
51
52
53
54
10 57 20
57 12
57 4
56 56
56 48
1 2 40
2 48
2 56
3 4
3 12
9.13447
13539
13630
13722
13813
80
82
83
85
87
10. 86553
86461
86370
86278
86187
9. 13854
13948
14041
14134
14227
81
83
85
86
88
10. 86146
86052
85959
85866
85773
10. 00407
00409
00411
00412
00414
1
1
1
1
2
9. 99593
99591
99589
99588
99586
10
9
8
7
6
55
56
57
58
59
60
10 56 40
56 32
56 24
56 16
56 8
56 0
1 3 20
3 28
3 36
3 44
3 52
4 0
9.13904
13994
14085
14175
14266
14356
88
90 1
91
93
95
96
10. 86096
86006
85915
85825
85734
85644
9. 14320
14412
14504
14597
14688
14780
90
91
93
95
96
98
10. 85680
85588
85496
85403
85312
85220
10. 00416
00418
00419
00421
00423
00425
2
2
2
2
2
Diff.
9. 99584
99582
99581
99579
99577
99575
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Sine.
M.
97J A
A B
B C
C 82°
Seconds of time
l!
•2'
3'
4s
5*
6s 7«
(A
Prop, parts of cols. •< B
12
12
24
24
36
37
48
49
60
61
72 | 84
73 86
(C
0
0
1
1
1
1 1
Page 780] TABLE 44.
Log. Sines, Tangents, and Secants.
8° A A B B C C 171°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
10 56 0
55 52
55 44
55 36
55 28
140
4 8
4 16
4 24
4 32
9. 14356
14445
14535
14624
14714
0
1
3
4
6
tj
(
8
10
11
13
10. 85644
85555
85465
85376T
85286
9. 14780
14872
14963
15054
15145
0
1
3
4
6
10. 85220
85128
85037
84946
84855
10. 00425
00426
00428
00430
00432
0
0
0
0
0
9. 99575
99574
99572
99570
99568
10 55 20
55 12
55 4
54 56
54 48
1 4 40
4 48
4 56
5 4
5 12
9. 14803
14891
14980
15069
15157
10. 85197
85109
85020
84931
84843
9. 15236
15327
15417
15508
15598
7
9
10
12
13
10. 84764
84673
84583
84492
84402
10. 00434
00435
00437
00439
00441
0
0
0
0
0
9. 99566
99565
99563
99561
99559
55
54
53
52
51
10 54 40
54 32
54 24
54 16
54 8
1 5 20
5 28
5 36
5 44
5 52
9. 15245
15333
15421
15508
15596
14
16
17
18
20
10. 84755
84667
84579
84492
84404
9. 15688
15777
15867
15956
16046
14
16
17
19
20
10. 84312
84223
84133
84044
83954
10. 00443
00444
00446
00448
00450
0
0
0
0
0
9. 99557
99556
99554
99552
99550
50
49
48
47
46
15
16
17
18
19
10 54 0
53 52
53 44
53 36
53 28
160
6 8
6 16
6 24
6 32
9. 15683
15770
15857
15944
16030
21
23
24
25
27
10. 84317
84230
84143
84056
83970
9. 16135
16224
16312
16401
16489
22
23
25
26
27
10. 83865
83776
83688
83599
83511
10. 00452
00454
00455
00457
00459
0
1
1
1
1
1
1
1
1
1
9. 99548
99546
99545
99543
99541
45
44
43
42
41
20
21
22
23
24
10 53 20
53 12
53 4
52 56
52 48
1 6 40
6 48
6 56
7 4
7 12
9. 16116
16203
16289
16374
16460
28
30
31
32
34
10. 83884
83797.
83711
83626
83540
9. 16577
16665
16753
16841
16928
29
30
32
33
35
10. 83423
83335
83247
83159
83072
10. 00461
00463
00465
00467
00468
9. 99539
99537
99535
99533
99532
40
39
38
37
36
25
26
27
28
29
10 52 40
52 32
52 24
52 16
52 8
1 7 20
7 28
7 36
7 44
7 52
9. 16545
16631
16716
16801
16886
35
37
38
39
41
10. 83455
83369
83284
83199
83114
9. 17016
17103
17190
17277
17363
36
37
39
40
42
10. 82984
82897
82810
82723
82637
10. 00470
1 00472
00474
00476
00478
1
1
1
1
1
9. 99530
99528
99526
99524
99522
35
34
33
32
31
30
31
32
33
34
10 52 0
51 52
51 44
51 36
51 28
180
8 8
8 16
8 24
8 32
9. 16970
17055
17139
17223
17307
42
44
45
47
48
10. 83030
82945
82861
82777
82693
9. 17450
17536
17622
17708
17794
43
45
46
48
49
10. 82550
82464
82378
82292
82206
10. 00480
00482
00483
00485
00487
1
1
1
1
1
9. 99520
99518
99517
99515
99513
30
29
28
27
26
35
36
37
38
39
10 51 20
51 12
51 4
50 56
50 48
1 8 40
8 48
8 56
9 4
9 12
9. 17391
17474
17558
17641
17724
49
51
52
54
55
10. 82609
82526
82442
82359
82276
9. 17880
17965
18051
18136
18221
50
52
53
55
56
10. 82120
82035
81949
81864
81779
10. 00489
00491
00493
00495
00497
1
1
1
1
1
9. 99511
99509
99507
99505
99503
25
24
23
22
21
40
41
42
43
44
10 50 40
50 32
50 24
50 16
50 8
1 9 20
9 28
9 36
9 44
9 52
9. 17807
17890
17973
18055
18137
56
58
59
61
62
10. 82193
82110
82027
81945
81863
9. 18306
18391
18475
18560
18644
58
59
61
62
63
10. 81694
81609
81525
81440
81356
10. 00499
00501
00503
00505
00506
1
1
1
1
1
9. 99501
99499
99497
99495
99494
20
19
18
17
16
45
46
47
48
49
10 50 0
49 52
49 44
49 36
49 28
1 10 0
10 8
10 16
10 24
10 32
9. 18220
18302
18383
18465
18547
(33
65
66
68
69
10. 81780
81698
81617
81535
81453
9. 18728
18812
18896
18979
19063
65
66
68
69
71
10. 81272
81188
81104
81021
80937
10. 00508
00510
00512
00514
00516
1
1
1
2
2
9. 99492
99490
99488
99486
99484
15
14
13
12
11
50
51
52
53
54
10 49 20
49 12
49 4
48 56
48 48
1 10 40
10 48
10 56
11 4
11 12
9. 18628
18709
18790
18871
18952
71
72
73
75
76
10. 81372
81291
81210
81129
81048
9. 19146
19229
19312
19395
19478
72
74
75
76
78
10. 80854
80771
80688
80605
80522
10. 00518
00520
00522
00524
00526
2
2
2
2
2
9. 99482
99480
99478
99476
99474
10
9
8
7
6
55
56
57
58
59
60
10 48 40
48 32
48 24
48 16
48 8
48 0
1 11 20
11 28
11 36
11 44
11 52
12 0
9. 19033
19113
19193
19273
19353
19433
78
79
80
82
83
85
10. 80967
80887
80807
80727
80647
80567
9. 19561
. 19643
19725
19807
19889
19971
79
81
82
84
85
87
10. 80439
80357
80275
80193
80111
80029
10. 00528
00530
00532
00534
- 00536
00538
2
2
2
2
2
2
9. 99472
99470
99468
99466
99464
99462
5
4
3
2
1
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
98° A A B B C C 81°
Seconds of time
IB
I
8s
4s
5"
6*
1*
(A
11
21
32
42
53
63
74
Prop, parts of cols. <B
11
22
32
43
64
65
76
[c
0
0
1
1
1
1
2
TABLE 44. [Page 781
Log. Sines, Tangents, and Secants.
9° A A B B C C 170°
M.
Hour A. M.
1 Hour P. M.
Sine.
Diff. Cosecant.
Tangent.
Diff.l Cotangent
Secant.
Diff.
Cosine.
ML
0
1
2
3
4
10 48 0
47 52
47 44
47 36
47 28
1 12 0
12 8
12 16
12 24
12 32
9. 19433
19513
19592
19672
19751
0
1
3
4
5
10. 80567
80487
80408
80328
80249
9. 19971
20053
20134
20216
20297
0
1
3
4
5
10. 80029
79947
79865
79784
79703
10. 00538
00540
00542
00544
00546
0
0
0
0
0
9. 99462
99460
99458
99456
99454
60
59
58
57
56
5
6
7
8
9
lr
11
12
*13
14
10 47 20
47 12
47 4
46 56
46 48
1 12 40
12 48
12 56
13 4
13 12
9. 19830
19909
19988
20067,
20145
6
8
9
10.
il
10.80170
80091
80012
79933
79855
9. 20378
20459
20540
20621
20701
6
8
9
10
12
10. 79622
79541
79460
79379
79299
10. 00548
00550
00552
00554
00556
0
0
0
0
0
9. 99452
99450
99448
99446
99444
55
54
53
52
51
10 46 40
46 32
46 24
46 16
46 8
1 13 20
13 28
13 36
13 44
13 52
9. 20223
20302
20380
20458
20535
ia
14
15
16
18
10. 79777
79698
79620
79542
79465
9. 20782-
20862
20942
21022
21102
13
14
16
17
18
10. 79218
79138
79058
78978
78898
10. 00558
00560
00562
00564
00566
0
0
0
0
0
9.99442
99440
99438
99436
99434
50
49
48
47
46
15
16
17
18
19
10 46 0
45 52
45 44
45 36
45 28
1 14 0
14 8
14 16
14 24
14 32
9. 20613
20691
20768
20845
20922
19
20
21
23
24
10. 79387
79309
79232
79155
79078
9. 21182
21261
21341
21420
21499
19
21
22
23
25
10. 78818
78739
78659
78580
78501
10. 00568
00571
00573
00575
00577
1
1
1
1
1
9. 99432
99429
99427
99425
. 99423
45
44
43
42
41
20
21
22
23
24
10 45 20 1 14 40
45 12 14 48
45 4 14 56
44 56 15 4
44 48 15 12
9. 20999
21076
21153
21229
21306
9. 21382
21458
21534
21610
21685
25
26
28
29
30
31
33
34
35
37
10. 79001
78924
78847
78771
78694
9. 21578
21657
21736
21814
21893
26
27
28
30
31
10. 78422
78343
78264
78186
78107
10. 00579
00581
00583
00585
00587
1
1
1
1
1
9. 99421
99419
99417
99415
99413
40
39
38
37
36
35
34
33
32
31
25
26
27
28
29
10 44 40
44 32
44 24
44 16
44 8
1 15 20
15 28
15 36
15 44
15 52
10. 78618
78542
78466
78390
78315
9. 21971
22049
22127
22205
22283
32
34
35
36
38
10. 78029
77951
77873
77795
77717
10. 00589
00591
00593
00596
00598
1
1
1
1
1
9. 99411
99409
99407
99404
99402
30
31
32
33
34
10 44 0
43 52
43 44
43 36
43 28
1 16 0
16 8
16 16
16 24
16 32
9. 21761
21836
21912
21987
22062
38
39
40
42
43
10. 78239
78164
78088
78013
77938
9. 22361
22438
22516
22593
22670
39
40
41
43
44
10. 77639
77562
77484
77407
77330
10. 00600
00602
00604
00606
00608
1
1
1
1
1
9.99400
99398
99396
99394
99392
30
29
28
27
26
35
36
37
38
39
10 43 20
43 12
43 4
42 56
42 48
1 16 40
16 48
16 56
17 4
17 12
9. 22137
22211
22286
22361
22435
44
45
47
48
49
10. 77863
77789
77714
77639
77565
9. 22747
22824
22901
22977
23054
45
47
48
49
50
10. 77253
77176
77099
77023
76946
10. 00610
00612
00615
00617
00619
1
1
9. 99390
99388
99385
99383
99381
25
24
23
22
21
40
41
42
43
44.
10 42 40
42 32
42 24
42 16
42 8
1 17 20
17 28
17 36
17 44
17 52
9. 22509
22583
22657
22731
22805
50
52
53
54
55
10. 77491
77417
77343
77269
77195
9. 23130
23206
23283
23359
23435
52
53
54
56
57
10. 76870
76794
76717
76641
76565
10. 00621
00623
00625
00628
00630
2
2
9. 99379
99377
99375
99372
99370
20
19
18
17
16
45
46
47
48
49
10 42 0
41 52
41 44
41 36
41 28
1 18 0
18 8
18 16
18 24
18 32
9. 22878
22952
23025
23098
23171
o/
58
59
60
62
10. 77122
77048
76975
76902
76829
9. 23510
23586
23661
23737
23812
58
60
61
62
63
10. 76490
76414
76339
76263
76188
10. 00632
00634
00636
00638
00641
2
2
2
2
2
9. 99368 .
99366
99364
99362
99359
15
14
13
12
11
50
51
52
53
54
10 41 20
41 12
41 4
40 56
40 48
1 18 40
18 48
18 56
19 4
19 12
9. 23244
23317
23390
23462
23535
63
64
65
67
68'
69
71
72
73
74
76
10. 76756
76683
76610
76538
76465
9. 23887
23962
24037
24112
24186
65
66
67
69
70
10. 76113
76038
75963
75888
75814
10. 00643
00645
00647
00649
00652
2
2
2
2
2
9. 99357
99355
99353
99351
99348
10
9
8
7
6
55
56
57
58
59
60
10 40 40
40 32
40 24
40 16
•40 8
40 0
1 19 20
19 28
19 36
19 44
19 52
20 0
9. 23607
23679
23752
23823
23895
- 23967
10. 76393
76321
76248
76177
76105
76033
9. 24261
24335
24410
24484
24558
24632
71
73
74
75
76
78
10. 75739
75665
75590
75516
75442
75368
10. 00654
00656
00658
00660
00663
00665
2
2
2
2
2
2
9. 99346
99344
99342
99340
99337
99335
5
4
3
2
1
0
k.
Hour P. M.
Hour A. M.
CosiM.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.j Sirte. '
M.
09° Iff A B B C C 80°
Seconds of time
l«
8»
3'
4*
5s
6*
<• 1
1
(A
Prop, parts of cols. <B
1C
9
10
0
19
19
1
28
1
38
39
1
47
49
1
57
58
•2
66
II
Page 782] TABLE 44.
Log. Sines, Tangents, and Secants.
10° A A B B C C 169°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secamt.
Diff.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
10 40 0
39 52
39 44
39 36
39 28
1 20 0
20 8
20 16
20 24
20 32
9. 23967
24039
24110
24181
24253
0
1
2
3
5
10. 76033
75961
75890
75819
75747
9. 24632
24706
24779
24853
24926
0
1
2
4
5
10. 75368
75294
75221
75147
75074
10. 00665
00667
00669
00672
00674
0
0
0
0
0
9. 99335
99333
99331
99328
99326
5
6
7
8
9
10 39 20
39 12
39 4
38 56
38 48
1 20 40
20 48
20 56
21 4
21 12
9. 24324
24395
24466
24536
24607
6
Q
9
10
11
13
14
15
16
10. 75676
75605
75534
75464
75393
9. 25000
25073
25146
25219
25292
6
7
8
9
11
10. 75000
74927
74854
74781
74708
10. 00676
00678
00681
00683
00685
0
0
0
0
0
9. 99324
99322
99319
99317
99315
55
54
53
52
51
10
11
12
13
14
10 38 40
38 32
38 24
38 16
38 8
1 21 20
21 28
21 36
21 44
21 52
9. 24677
24748
24818
24888
24958
10. 75323
75252
75182
75112
75042
9. 25365
25437
25510
25582
25655
12
13
14
15
16
18
19
20
21
22
10. 74635
74563
74490
74418
74345
10. 00687
00690
00692
00694
00696
0
0
0
1
1
9. 99313
99310
99308
99306
99304
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
15
16
17
18
19
10 38 0
37 52
37 44
37 36
37 28
1 22 0
22 8
22 16
22 24
22 32
9. 25028
25098
25168
25237
25307
17
18
19
20
22
~W
24
25
26
27
10. 74972
74902
74832
74763
74693
9. 25727
25799
25871
25943
26015
10. 74273
74201
74129
74057
73985
10. 00699
00701
00703
00706
00708
1
1
1
1
1
9. 99301
99299
99297
99294
99292
20
21
22
23
24
10 37 20
37 12
37 4
36 56
36 48
1 22 40
22 48
22 56
23 4
23 12
9. 25376
25445
25514
25583
25652
10. 74624
74555
74486
74417
74348
9. 26086
26158
26229
26301
26372
24
25
26
27
28
10. 73914
73842
73771
73699
73628
10. 00710
00712
00715
00717
00719
1
1
1
1
1
9. 99290
99288
99285
99283
99281
9. 99278
99276
99274
99271
99269
25
26
27
28
29
10 36 40
36 32
36 24
36 16
36 8
1 23 20
23 28
23 36
23 44
23 52
9. 25721
25790
25858
25927
25995
28
30
31
32
33
10. 74279
74210
74142
74073
74005
9. 26443
26514
26585
26655
26726
29
31
32
33
34
10. 73557
73486
73415
73345
73274
101 00722
00724
00726
00729
00731
1
1
1
1
1
30
31
32
33
34
•sr
36
37
38
39
40
41
42
43
44
10 36 0
35 52
35 44
35 36
35 28
1 24 0
24 8
24 16
24 24
24 32
9. 26063
26131
26199
26267
26335
34
35
36
38
39
10. 73937
73869
73801
73733
73665
9. 26797
26867
26937
27008
27078
35
36
38
39
40
10. 73203
73133
73063
72992
72922
10. 00733
00736
00738
00740
00743
1
1
]
1
1
9. 99267
99264
99262
99260
99257
10 35 20
35 12
35 4
34 56
34 48
1 24 40
24 48
24 56
25 4
25 12
9. 26403
26470
26538
26605
26672
40
41
42
43
44
10. 73597
73530
73462
73395
73328
9. 27148
27218
27288
27357
27427
41
42
44
45
46
10. 72852
72782
72712
72643
72573
10. 00745
00748
00750
00752
00755
1
1
1
1
2
9. 99255
99252
99250
99248
99245
25
24
23
22
21
10 34 40
34 32
34 24
34 16
34 8
1 25 20
25 28
25 36
25 44
25 52
9. 26739
26806
26873
26940
27007
45
47
48
49
50
10. 73261
73194
73127
73060
72993
9. 27496
27566
27635
27704
27773
47
48
49
51
52
10. 72504
72434
72365
72296
72227
10. 00757
00759
00762
00764
00767
2
2
2
2
2
9. 99243
99241
99238
99236
99233
20
19
18
17
16
45
46
47
48
49
10 34 0
33 52
33 44
33 36
33 28
1 26 0
26 8
26 16
26 24
26 32
9.. 27073
27140
27206
27273
27339
51
52
53
55
56
10. 72927
72860
72794
72727
72661
9. 27842
27911
27980
28049
28117
53
54
55
56
58
10. 72158
72089
72020
71951
71883
10. 00769
00771
00774
00776
00779
2
2
2
2
2
9. 99231
99229
99226
99224
99221
15
14
13
12
11
50
51
52
53
54
10 33 20
33 12
33 4
32 56'
32 48
1 26 40
26 48
26 56
27 4
27 12
9. 27405
27471
J2Z537
27602
27668
57
58
59
60
61
10. 72595
72529
72463
72398
72332
9. 28186
28254
28323
28391
28459
59
60
61
62
63
10. 71814
71746
71677
71609
71541
10. 00781
00783
00786
00788
00791
2
2
2
2
2
9. 99219
99217
99214
99212
99209
10
9
8
7
6
55
56
57
58
59
60
10 32 40
32 32
32 24
32 16
32 8
32 0
1 27 20
27 28
27 36
27 44
27 52
28 0
9. 27734
27799
27864
27930
27995
28060
63
64
65
66
67
68
10. 72266
72201
72136
72070
72005
71940
9. 28527
28595
28662
28730
28798
28865
65
66
67
68
69
71
10. 71473
71405
71338
71270
71202
71135
10. 00793
00796,
00798
00800
00803
00805
2
2
2
2
2
2
9. 99207
99204
99202
99200
99197
99195
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine. ! Diff.
Secant.
Cotangent. Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.-
100° A A B B C C 79°
Seconds of time
1"
2»
33
4"
5s
6"
7s
(A
9
17
26
34
43
51
60
Prop, parts of cols. <B
9
0
18
1
26
1
35
1
44
1
53
2
62
2
11°
Log.
A
TABLE 44. Page 783
Sines, Tangents, and Secants.
A B B C C 168°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent. 1 Diff.
Cotangent
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
10 32 0
31 52
31 44
31 36
31 28
1 28 0
28 8
28 16
28 24
28 32
9.28060
28125
28190
28254
28319
0
1
2
3
4
10. 71940
71875
71810
71746
71681
9. 28865
28933
29000
29067
29134
) o
1
2
3
4
10. 71135
71067
71000
70933
70866
10. 00805
00808
00810
00813
00815
0
0
0
0
0
9. 99195
99192
99190
99187
99185
60
59
58
57
56
5
6
8
9
10 31 20
31 12
31 4
30 56
30 48
1 28 40
28 48
28 56
29 4
29 12
9. 28384
28448
28512
28577
28641
5
6
7
8
9
10. 71616
71552
71488
71423
71359
9. 29201
29268
29335
29402
29468
5
6
8
9
10
10. 70799
70732
70665
70598
70532
10. 00818
00820
00823
00825
00828
0
0
0
0
0
9. 99182
99180
99177
99175
99172
55
54
53
52
51
10
11
12
13
14
10 30 40
30 32
30 24
30 16
30 8
1 29 20
29 28
29 36
29 44
29 52
9. 28705
28769
28833
28896
28960
10
11
12
13
14
10. 71295
71231
71167
71104
71040
9.29535
29601
29668
29734
29800
11
12
13
14
15
10. 70465
70399
70332
70266
70200
10. 00830
00833
00835
00838
00840
0
0
1
1
1
9. 99170
99167
99165
99162
99160
50
49
48
47
46
15
16
17
18
19
10 30 0
29 52
29 44
29 36
29 28
1 30 0
30 8
30 16
30 24
30 32
9. 29024
29087
29150
29214
29277
16
17
38
19
20
"2T
22
23
24
25
10. 70976
70913
70850
70786
70723
9.29866
29932
29998
30064
30130
16
17
18
19
20
10. 70134
70068
70002
69936
69870
10. 00843
00845
00848
00850
00853
1
1
1
1
1
9. 99157
99155
99152
99150
99147
45
44
43
42
41
40
39
38
37
36
20
21
22
23
24
10 29 20
29 12
29 4
28 56
28 48
1 30 40
30 48
30 56
31 4
31 12
9. 29340
29403
29466
29529
29591
10. 70660
70597
70534
70471
70409
9. 30195
30261
30326
30391
30457
22
23
24
25
26
10. 69805
69739
69674
69609
69543
10.00855
00858
00860
00863
00865
1
1
1
1
1
9. 99145
99142
99140
99137
99135
25
26
27
28
29
10 28 40
28 32
28 24
28 16
28 8
1 31 20
31 28
31 36
31 44
31 52
9.29654
29716
29779
29841
29903
26
27
28
29
30
10. 70346
70284
70221
70159
70097
9. 30522
30587
30652
30717
30782
27
28
29
30
31
10. 69478
69413
69348
69283
69218
10. 00868
00870
00873
00876
00878
1
1
1
1
1
9. 99132
99130
99127
99124
99122
35
34
33
32
31
30
31
32
33
34
10 28 0
27 52
27 44
27 36
27 28
1 32 0
32 8
32 16
32 24
32 32
9. 29966
30028
30090
30151
30213
31
32
33
34
35
10. 70034
69972
69910
69849
69787
9. 30846
30911
30975
31040
31104
32
33
35
36
37
-38-
39
40
41
42
10. 69154
69089
69025
68960
68896
10. 00881
00883
00886
00888
00891
1
1
1
9. 99119
99117
99114
99112
99109
30
29
28
27
26
35
36
37
38
39
40
41
42
43
44
10 27 20
27 12
27 4
26 56
26 48
1 32 40
32 48
32 56
33 4
33 12
9. 30275
30336
30398
30459
30521
36
37
38
39
40
10. 69725
69664
69602
69541
69479
9. 31168
31233
31297
31361
31425
10. 68832
68767
68703
68639
68575
10. 00894
00896
00899
00901
00904
2
2
2
2
2
9. 99106
99104
99101
99099
99096
25
24
23
22
21
10 26 40
26 32
26 24
26 16
26 8
-1 33 20
33 28
33 36
33 44
33 52
9. 30582
30643
30704
30765
30826
41
42
43
45
46
10. 69418
69357
69296
69235
69174
9.31489 43 10.68511
31552 44 68448
31616 45 68384
31679 46 68321
31743 47 68257
10.00907
00909
00912
00914
00917
2
2
2
2
2
9. 99093
99091'
99088
99086
99083
20
19
18
17
16
45
46
47
48
49
10 26 0
25 52
25 44
25 36
25 28
1 34 0
34 8
34 16
34 24
34 32
9. 30887-
30947
31008
31068
31129
47
48
49
50
51
~52~
53
54
55
56
10. 69.113
69053
68992
68932
68871
9. 31806 49
31870 50
31933 51
31996 52
32059 53
10. 68194
68130
68067
68004
67941
10. 00920
00922
00925
00928
00930
2
2
2
2
2
9. 99080
99078
99075
99072
99070
15
14
13
12
11
50
51
52
53
54
10 25 20
25 12
25 4
24 56
24 48
1 34 40
34 48
34 56
35 4
35 12
9. 31189
31250
31310
31370
31430
10. 68811
68750
68690
68630
68570
9. 32122
32185
32248
32311
32373
54
55
56
57
58
59
60
61
63
64
65
Diff.
10. 67878
67815
67752
67689
67627
10. 00933
00936
00938
00941
00944
2
9
*2
2
2
2
2
2
2
3
3
9. 99067
99064
99062
99059
99056
10
9
8
i
6
55
56
57
58
59
60
10 24 40
24 32
24 24
24 16
24 8
24 0
1 35 20
35 28
35 36
35 44
35 52
36 0
9. 31490
31549
31609
31669
31728
31788
57
5&
59
60
61
62
10. 68510
68451
68391
68331
68272
68212
9. 32436
32498
32561
32623
32685
32747
10. 67564
67502
67439
67377
67315
67253
10. 00946
00949
00952
00954
00957
00960
9. 99054
99051
99048
99046
99043
99040
5
4
3
2
1
0
M.
Hour p. M. | Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Tangent.
Cose
Diff.
Sine.
1C.
101°
A
A B EC C 78°
Seconds of time
1*
.>;
&
4*
a* &>
fA
8
16
23
31
39 : 47
Prop, parts of cols. {B
8
16
24
32
40 i 49
1C
0
1
1
1
2 i 2
Page 784] TABLE M.
Log. Sines, Tangents, and Secants.
12° A A B B C C 167°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
0
1
2
3
4
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
10 24 0
23 52
23 44
23 36
23 28
1 36 0
36 8
36 16
36 24
36 32
9. 31788
31847
31907
31966
32025
10. 68212
68153
68093
68034
67975
9. 32747
32810
32872
32933
32995
0
1
2
3
4
10. 67253
67190
67128
67067
67005
10. 00960
00962
00965
00968
00970
0
0
0
0
0
9. 99040
99038
99035
99032
99030
60
59
58
57
56
5
6
7
8
9
10 23 20
23 12
23 4
22 56
22 48
1 36 40
36 48
36 56
37 4
37 12
9. 32084
32143
32202
32261
32319
5
6
7
8
9
10. 67916
67857
67798
67739
67681
9. 33057
33119
33180
33242
33303
5
6 '
7
8
9
10
11
12
13
14
10. 66943
• 66881
66820
66758
66697
10. 00973
00976
00978
00981
00984
0
0
0
0
0
9. 99027
99024
99022
99019
99016
55
54
53
52
51
10
11
12
13
14
10 22 40
22 32
22 24
22 16
22 8
1 37 20
37 28
37 36
37 44
37 52
9. 32378
32437
32495
32553
32612
10
10
11
12
13
10. 67622
67563
67505
67447
67388
9. 33365
33426
33487
33548
33609
10. 66635
66574
66513
66452
66391
10. 00987
00989
00992
00995
00998
0
1
1
1
1
9. 99013
99011
99008
99005
99002
50
49
48
47
46
45
44
43
42
41
15
*6
17
18
19
10 22 0
21 52
21 44
21 36
21 28
1 38 0
38 8
38 16
38 24
38 32
9. 32670
32728
32786
32844
32902
14
15
16
17
18
10. 67330
67272
67214
67156
67098
9. 33670
33731
33792
33853
33913
15
16
17
18
19
20
21
22
23
24
10. 66330
66269
66208
66147
66087
10. 01000
01003
01006 -
01009
01011
1
1
1
1
1
9. 99000
98997
98994
98991
98989
20
21
22
23
24
10 21 20
21 12
21 4
20 56
20 48
1 38 40
38 48
38 56
39 4
39 12
9. 32960
33018
33075
33133
33190
19
20
21
22
23
10. 67040
66982
66925
66867
66810
9. 33974
34034
34095
34155
34215
10. 66026
65966
65905
65845
65785
10. 01014
01017
01020
01022
01025
1
1
1
1
9. 98986
98983
98980
98978
98975
40
39
38
37
36
25
26
27
28
29
10 20 40
20 32
20 24
20 16
20 8
1 39 20
39 28
39 36
39 44
39 52
9. 33248
33305
33362
33420
33477
24
25
26
27
28
10. 66752
66695
66638
66580
66523
9. 34276
34336
34396
34456
34516
25
26
27
28
29
10. 65724
65664
65604
65544
65484
10. 01028
01031
01033
01036
01039
J_
JL
i
i
9. 98972
98969
98967
98964
98961
35
34
33
32
31
30
31
32
33
34
10 20 0
19 52
19 44
19 36
19 28
1 40 0
40 8
40 16
40 24
40 32
9. 33534
33591
33647
33704
33761
29
29
30
31
32
10. 66466
66409
66353
66296
66239
9. 34576
34635
34695
34755
34814
30
31
32
33
34
10. 65424
65365
65305
65245
65186
10. 01042
01045
01047
01050
01053
i
i
i
2
2
9. 98958
98955
98953
98950
98947
30
29
28
27
26
35
36
37
38
39
10 19 20
19 12
19 4
18 56
18 48
1 40 40
40 48
40 56
41 4
41 12
9. 33818
33874
33931
33987
34043
33
34
35
36
37
10. 66182
66126
66069
66013
65957
9. 34874
34933
34992
35051
35111
35
36
37
38
39
40
41
42
43
44
10. 65126
65067
65008
64949
64889
10. 01056
01059
01062
01064
01067
2
2
2
2
2
9. 98944
98941
98938
98936
98933
25
24
23
22
21
40
41
42
43
44
10 18 40
18 32
18 24
18 16
18 8
1 41 20
41 28
41 36
41 44
41 52
9. 34100
34156
34212
34268
34324
38
39
40
41
42
10. 65900
65844
65788
65732
65676
9. 35170
35229
35288
35347
35405
10. 64830
64771
64712
64653
64595
10. 01070
01073
01076
01079
01081
2
2
2
2
2
9. 98930
98927
98924
98921
98919
20
19
18
17
16
45
46
47
48
49
10 18 0
17 52
17 44
17 36
17 28
1 42 0
42 8
42 16
42 24
42 32
9. 34380
34436
34491
34547
34602
43
44
45
46
47
10. 65620
65564
65509
65453
65398
9. 35464
35523
35581
35640
35698
45
46
47
48
49
10. 64536
64477
64419
. 64360
64302
10. 01084
01087
01090
01093
01096
2
2
2
2
2
9. 98916
98913
98910
98907
98904
15
14
13
12
11
50
51
52
53
54
10 17 20
17 12
17 4
16 56
16 48
1 42 40
42 48
42 56
43 4
43 12
S. 84658
34713
34769
34824
34879
48
48
49
50
51
10. 65342
65287
65231
65176
65121
9. 35757
35815
35873
35931
35989
50
51
52
53
54
10. 64243
64185
64127
64069
64011
10. 01099
01102
01104
01107
OHIO
2
2
2
2
3
9. 98901
98898
98896
98893
98890
10
9
8
7
6
55
56
57
58
59
60
10 16 40
16 32
16 24
16 16
16 8
16 0
1 43 20
43 28
43 36
43 44
43 52
44 0
9. 34934
' 34989
35044
35099
35154
35209
52
53
54
55
56
57
10. 65066
65011
64956
64901
64846
64791
9. 36047
36105
36163
36221
36279
36336
55
56
57
58
59
60
10. 63953
63895
63837
63779
63721
63664
10. 01113
01116
01119
01122
01125
01128
3
3
3
3
3
3
9. 98887
98884
98881
98878
98875
98872
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
102° A A B B C C 77°
Seconds of time
1s
Os
3"
4*
o»
6>
fA
7
14
21
29
36
43
50
Prop, parts of cols.<B
[c
7
0
15
1
22
1
30
1
37
2
45
2
52
2
TABLE 44. [Page 785
Log. Sines, Tangents, and Secants.
13° A A B B C C 166°
M.
Hour A. M. Hour p. M.
Sine. Diff.
Cosecant.
Tangent.
Diff.
Cotangent
Secant.
Diff.
Cosine.
M.
60
59
58
57
56
55
54
53
52
51
0
1
2
3
4
10 16 0
15 52
15 44
15 36
15 28
1 44 0
44 8
44 16
44 24
44 32
9. 35209
35263
35318
35373
35427
0
1
2
3
4
10. 64791
64737
64682
64627
64573
9. 36336
36394
36452
36509
36566
0
1
2
3
4
10. 63664
63606
63548
63491
63434
10. 01128
01131
01133
01136
01139
0
0
0
0
0
9. 98872
98869
98867
98864
98861
o
6
7
8
9
10 15 20
15 12
15 4
14 56
14 48
1 44 40
44 48
44 56
45 4
45 12
9. 35481
35536
35590
35644
35698
4
5
6
7
8
10. 64519
64464
64410
64356
64302
9. 36624
36681
36738
36795
36852
5
6
6
7
8
10. 63376
63319
63262
63205
63148
10. 01142
01145
01148
01151
01154
0
0
0
0
0
9. 98858
98855
98852
98849
98846
10
11
12
13
14
10 14 40
14 32
14 24
14 16
14 8
1 45 20
45 28
45 36
45 44
45 52
9. 35752
35806
35860
35914
35968
9
10
11
11
12
13
14
15
16
17
10. 64248
64194
64140
64086
64032
9.36909
36966
37023
37080
37137
9
10
11
12
13
10. 63091
63034
62977
62920
62863
10. 01157
01160
01163
01166
01169
1
1
1
1
1
9.98843^
98840
98837
98834
98831
50
49
48
47
46
15
16
17
18
19
10 14 0
13 52
13 44
13 36
13 28
1 46 0
46 8
46 16
46 24
46 32
9. 36022
36075
36129
36182
36236-
10. 63978
63925
63871
63818
63764
9. 37193
37250
37306
37363
37419
14
15
16
17
18
10. 62807
62750
62694
62637
62581
10. 01172
01175
01178
01181
01184
1
1
1
1
1
9. 98828
98825
98822
98819
98816
45
44
43
42
41
20
21
22
23
24
10 13 20
13 12
13 4
12 56
12 48
1 46 40
46 48
46 56
47 4
47 12
9. 36289
36342
36395
36449
36502
18
18
19
20
21
10. 63711
63658
63605
63551
63498
9. 37476
37532
375S8
37644
37700
19
19
20
21
22
23
24
25
26
27
10. 62524
62468
62412
62356
62300
10. 01187
01190
01193
01196
01199
1
1
1
1
1
9.98813
98810
98807
98804
98801
40
39
38
37
36
25
26
27
28
29
10 12 40
12 32
12 24
12 16
12 8
1 47 20
47 28
47 36
47 44
47 52
9. 36555
36608
36660
36713
36766
22
23
24
25
25
10. 63445
63392
63340
63287
63234
9. 37756
37812
37868
37924
37980
10. 62244
62188
62132
62076
62020
10. 01202
01205
01208
01211
01214
1
1
1
1
1
9. 98798
98795
98792
98789
98786
35
34
33
32
31
30
31
32
33
34
0 12 0
11 52
11 44
11 36
11 28
1 48 0
48 8
48 16
48 24
48 32
9. 36819
36871
36924
36976
37028
26
27
28
29
30
10. 63181
63129
63076
63024
62972
9. 38035
38091
38147
38202
38257
28 10.61965
29 61909
30 61853
31 61798
32 61743
10.01217
01220
01223
01226
01229
2
2
2
2
2
9. 98783
98780
98777
98774
98771
30
29
28
27
26
35
36
37
38
39
0 11 20
11 12
11 4
10 56
10 48
1 48 40
48 48
48 56
49 4
49 12
9. 37081
37133
37185
37237
37289
31
32
32
33
34
10. 62919
62867
62815
62763
62711
9. 38313
38368
38423
38479
38534
32
33
34
35
36
10. 61687
61632
61577
61521
61466
10. 01232
01235
01238
01241
01244
2
2
2
2
2
9. 98768
98765
98762
98759
98756
25
24
23
22
21
40
41
42
43
44
45
46
47
48
49
0 10 40
10 32
10 24
10 16
10 8
1 49 20
49 28
49 36
49 44
49 52
9. 37341
37393
37445
37497
37549
35
36
37
38
39
10. 62659
62607
62555
62503
62451
9. 38589
38644
38699
38754
38808
37
38
39
40
41
10. 61411
61356
61301
61246
61192
10. 01247
01250
01254
01257
01260
2
2
2
2
2
9. 98753
98750
98746
98743
98740
20
19
18
17
16
0 10 0
9 52
9 44
9 36
9 28
1 50 0
50 8
50 16
50 24
50 32
9. 3760J
37652
37703
37755
37806
39 I
40
41
42
43
10. 62400
62348
62297
62245
62194
9. 38863
38918
38972
39027
39082
42
43
44
45
45
10. 61137
61082
61028
60973
60918
10. 01263
01266
01269
01272
01275
2
2
2
2
2
9. 98737
98734
98731
98728
98725
15
14
13
12
11
50
51
52
53
54
0 9 20
9 12
9 4
8 56
8 48
1 50 40
50 48
50 56
51 4
51 12
9. 37858
37909
37960
38011
38062
44
45
46
47
47
10. 62142
62091
62040
61989
61938
9. 39136
39190
39245
39299
39353
46
47
48
49
50
51
52
53
54
55
56
10. 60864
60810
60755
60701
60647
10. 8l278
01281
01285
01288
01291
3
3
3
3
3
9. 98722
98719
98715
98712
98709
10
9
8
7
6
5o
36
57
58
59
60
0 8 40
8 32
8 24
8 16
8 8
8 0
1 51 20
, 51 28
51 36
51 44
51 52
52 0
9. 38113
38164
38215
38266
38317
38368
48
49
50
51
52
53
10. 61887
61836
61785
61734
61683
61632
9. 39407
39461
39515
39569
' 39623
39677
10. 60593
60539
60485
60431
60377
60323
10. 01294
01297
01300
01303
01306
01310
3
3
3
3
3
3
9. 98706
98703
98700
98697
98694
98690
5
4
3
2
1
0
M.
Hour P.M. Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.) Diff.
Tangent
Cosecant.
Diff.
Sine.
M.
103° A A B B C C 76°
Seconds of time .
1s
93
35
At
b*
6*
7»
(A
Prop, parts of colsJB
1C
I
13
!?
20
21
26
28
2
33
35
2
39
42
2
46
49
3
Page 786] TABLE 44. j
Log. Sines, Tangents, and Secants. i
14° A A B B C C 165° 1
M.
Hcmr A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
0
1
2
3
3
Cotangent.
Secant.
Diff.
Cosine.
M.
60
59
58
57
W\
55
541
53
52
51
0
1
2
3
4
10 8 0
7 52
7 44
7 36
7 28
1 52 0
52 8
52 16
52 24
52 32
9. 38368
38418
38469
38519
38570
0
1
2
2
3
10. 61632
61582
61531
61481
61430
9. 39677
39731
39785
39838
39892
10. 60323
60269
60215
60162
60108
10. 01310
01313
01316
01319
01322
0
0
0
0
0
9. 98690
98687
98684
98681
98678
5
6
7
8
9
10 7 20
7 12
7 4
6 56
6 48
1 52 40
52 48
52 56
53 4
53 12
9. 38620
38670
38721
38771
38821
4
5
6
7
7
10. 61380
61330
61279
61229
61179
9. 39945
39999
40052
40106
40159
4
5
6
7
8
10. 60055
60001
599-*8
59894
59841
10. 01325
01329
01332
01335
01338
0
0
0
0
0
9. 98675
98671
98668
98665
98662
10
11
12
13
14
15
16
17
18
19
10 6 40
6 32
6 24
6 16
6 8
1 53 20
53 28
53 36
53 44
53 52
9. 38871
38921
38971
39021
39071
8
9
10
11
11
10. 61129
61079
61029
60979
60929
9.40212
40266
40319
40372
40425
9
10
10
11
12
~ir
14
15
16
17
17
18
19
20
21
10. 59788
59734
59681
59628
59575
10. 01341
01344
01348
01351
01354
1
1
1
1
1
9. 98659
98656
98652
98649
98646
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
10 6 0
5 52
5 44
5 36
5 28
1 54 0
54 8
54 16
54 24
54 32
9. 39121
39170
39220
39270
39319
12
13
14
15
15
10. 60879
60830
60780
60730
60681
9. 40478
40531
40584
40636
40689
10. 59522
59469
59416
59364
59311
10. 01357
01360
01364
01367
01370
1
1
1
1
1
9. 98643
98640
98636
98633
98630
20
21
22
23
24
10 5 20
5 12
5 4
4 56
4 48
1 54 40
54 48
54 56
55 4
55 12
9. 39369
39418
39467
39517
39566
16
17
18
19
20
10. 60631
60582
60533
60483
60434
9. 40742
40795
40847
40900
40952
10. 59258
59205
59153
59100
59048
10. 01373
01377
01380
01383
01386
1
1
1
1
1
9. 98627
98623
98620
98617
98614
25
26
27
28
29
10 4 40
4 32
4 24
4 16
4 8
1 55 20
55 28
55 36
55 44
55 52
9. 39615
39664
39713
39762
39811
20
21
22
23
24
10. 60385
60336
60287
60238
60189
9. 41005
41057
41109
41161
41214
22
23
23
24
25
10. 58995
58943
58891
58839
58786
10. 01390
01393
01396
01399
01403
1
1
1
2
2
9. 98610
98607
98604
98601
98597
35
34
33
32
31
30
31
32
33
34
10 4 0
3 52
3 44
3 36
3 28
1 56 0
56 8
56 16
56 24
56 32
9. 39860
39909
39958
40006
40055
24
25
26
27
28
10. 60140
60091
60042
59994
59945
9. 41266
41318
41370
41422
41474
26
27
28
29
30
10. 58734
58682
58630
58578
58526
10. 01406
01409
01412
01416
01419
2
2
2
2
2
9. 98594
98591
98588
98584
98581
30
29
28
27
26
35
36
37
38
39
10 3 20
3 12
3 4
2 56
2 48
1 56 40
56 48
56 56
57 4
57 12
9. 40103
40152
40200
40249
40297
29
29
30
31
32
10. 59897
59848
59800
59751
59703
9. 41526
41578
41629
41681
41733
30
31
32
33
34
10. 58474
58422
58371
58319
58267
01422
01426
01429
01432
OH35
2
2
2
2
2
9. 98578
98574
98571
98568
98565
25
24
23
22
21
40
41
42
43
44
10 2 40
2 32
2 24
2 16
2 8
1 57 20
57 28
57 36
57 44
57 52
9. 40346
40394
40442
40490
40538
33
33
34
35
36
10. 59654
59606
59558
59510
59462
9. 41784
41836
41887
41939
41990
35
36
36
37
38
10. 58216
58164
58113
58061
58010
10. 01439
01442
01445
01449
01452
2
2
2
2
2
9. 98561
98558
98555
98551
985*8
20
19
18
17
16
45
46
47
48
49
10 2 0
1 52
1 44
1 36
1 28
1 58 0
58 8
58 16
58 24
58 32
9. 40586
40634
40682
40730
40778
37
37
38
39
40
10. 59414
59366
59318
59270
59222
9. 42041
42093
42144
42195
42246
39
40
41
42
43
10. 57959
57907
57856
57805
57754
10. 01455
01459
01462
01465
01469
2
3
3
3
3
9. 98545
98541
98538
98535
98531
15
14
13
12
11
50
51
52
53
54
10 1 20
1 12
1 4
0 56
0 48
1 58 40
58 48
58 56
59 4
59 12
9. 40825
40873
40921
40968
41016
41
42
42
43
44
10. 59175
59127
59079
59032
58984
9. 42297
42348
42399
42450
42501
43
44
45
46
47
10. 57703
57652
57601
57550
57499
10. 01472
01475
01479
01482
01485
3
3
3
3
3
~T
3
3
3
3
3
9. 98528
98525
98521
98518
98515
10
1
y
55
56
57
58
59
60
10 0 40
0 32
0 24
0 16
0 8
0 0
1 59 20
59 28
59 36
59 44
59 52
200
9. 41063
41111
41158
41205
41252
41300
45
46
46
47
48
.49
10. 58937
58889
58842
58795
58748
58700
9. 42552
42603
42653
42704
42755
42805
48
49
50
50
51
52
10. 57448
57397
57347
57296
57245
57195
10. 01489
01492
01495
01499
01502
01506
9. 98511
98508
98505
98501
98498
98494
5
4
3
2
l\
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
104° A A B B C C 75° |
Seconds of time
1s
2*
3"
43
5s
69
fA
Prop, parts of cols. < B
(c
6
7
0
12
13
1
18
20
1
24
26
2
31
35
2
37
39
2
43
46
3
TABLE M. [Page 787
Log. Sines, Tangents, and Secants.
15° A A B B C C 164°
M.
Hour A.M.
Hour P.M.
Sine. ! Diff. Cosecant.
Tangent. Diff. Cotangent.
Secant. Diff.
Cosine.
M.
0
1
9
3
4
10 0 0
9 59 52
59 44
59 36
59 28
200
0 8
0 16
0 24
0 32
9. 41300
41347
41394
41441
41488
o
f\
3
^T
5
5
6
7
8
8
9
10
11
10. 58700
58653
58606
58559
58512
9. 42805
42856
42906
42957
43007
0
1
2
2
3
10. 57195
57144
57094
57043
56993
iO. 01506
01509
01512
01516
01519
0
0
0
0
0
9. 98494
98491
98488
98484
98481
60
59
52
Ol
56
5
6
7
8
9
10
11
12
13
14
9 59 20
59 12
59 4
58 56
58 48
2 0 40
0 48
0 56
1 4
1 12
9.41535
41582
41628
41675
41722
10. 58465
58418
58372
58325
58278
9. 43057
43108
^43158
" 43208
43258
4
5
6
7
7
10. 56943
56892
56842
. 56792
56742
10. 01523
01526
01529
01533
01536
0
0
0
0
1
9. 98477 55
98474 54
98471 58
98467 52
98464 51
9 58 40
58 32
58 24
58 16
58 8
2 20
28'
36
44
52
9. 41768
41815
41861
41908
41954
10. 58232
58185
58139
58092
58046
9. 43308
43358
43408
43458
43508
8
9
10
11
11
10. 56692
56642
56592
56542
56492
10. 01540
01543
01547
01550
01553
1
1
1
1
1
9. 98460
98457
98453
98450
98447
50
49
48
47
46
15
16
17
18
19
9 58 0
57 52
57 44
57 36
57 28
220
2 8
2 16
2 24
2 32
9. 42001
42047
42093
42140
42186
11
12
13
14
14
10. 57999
57953
57907
57860
57814
9.43558
43607
43657
43707
43756
12
13
14
15
16
10. 56442
56393
56343
56293
56244
10. 01557
01560
01564
01567
01571
1
1
1
1
1
9. 98443
98440
98436
98433
98429
45
44
43
42
41
20
21
22
23
24
9 57 20
57 12
57 4
56 56
56 48
2 2 40
2 48
2 56
3 4
3 12
9. 42232
42278
42324
42370
42416
15
18
10. 57768
57722
57676
57630
57584
9. 43806
43855
43905
43954
44004
16 10.56194
17 56145
18 i 56095
19 56046
20 55996
10. 01574
01578
01581
01585
01588
9. 98426
98422
98419
98415
98412
40
39
38
37
36
25
26
27
28
29
9 56 40
56 32
56 24
56 16
56 8
2 3 20
3 28
3 36
3 44
3 52
9. 42461
42507
42553
42599
42644
19
20
21
21
22
10. 57539
57493
57447
57401
57356
9. 44053
44102
44151
44201
44250
20
21
22
23
24
25
25
26
27
28
10. 55947
55898
55849
55799
55750
10. 01591
01595
01598
01602
01605
1
2
2
2
2
9. 98409
98405
98402
98398
98395
35
34
33
32
31
30
31
32
33
34
9 56 0
55 52
55 44
55 36
55 28
240
4 8
4 16
4 24
4 32
9. 42690
42735
42781
42826
42872
23
24
24
25
26
10. 57310
57265
57219
57174
57128
9. 44299
44348
44397
44446
44495
10. 55701
55652
55603
55554
55505
10. 01609
01612
01616
01619
01623
2
2
2
2
2
9. 98391
98388
98384
98381
98377
30
29
28
27
26
25
24
23
22
21
35
36
37
38
39
9 55 20
55 12
55 4
54 56
54 48
2 4 40
4 48
4 56
5 4
5 12
9. 42917
42962
43008
43053
43098
27
27
28
29
30
30
31
32
33
33
"34"
35
3fc
36
37
10. 57083
57038
56992
56947
56902
9. 44544
44592
44641
44690
44738
29
29
30
.31
32
10. 55456
55408
55359,
55310
55262
10. 01627
01630
01634
01637
01641
2
2
2
2
2
9. 98373
98370
98366
98363
98359
40
41
42
43
44
9 54 40
54 32
54 24
54 16
54 8
2 5 20
5 28
5 36
5 44
5 52
9. 43143
43188
43233
43278
43323
10. 56857
56812
56767
56722
56677
9. 44787
44836
44884
44933
44981
33
34
34
35
36
10. 55213
55164
55116
55067
55019
10. 01644
01648
01651
01655
01658
2
2
2
3
3
9. 98356
98352
98349
98345
98342
20
19
18
17
16
45
46
47
48
49
9 54 0
53 52
53 44
53 36
53 28
260
6 8
6 16
6 24
6 32
9. 43367
43412
43457
43502
43546
10. 56633
56588
56543
56498
56454
9. 45029
45078
45126
45174
45222
37
38
38
39
40
10. 54971
54922
54874
54826
54778
10. 01662
01666
01669
01673
01676
3
3
3
3
3
9. 98338
98334
98331
98327
98324
15
14
13
12
11
50
51
52
53
54
9 53 20
53 12
53 4
52 56
52 48
2 6 40
6 48
6 56
7 4
7 12
9. 43591
43635
43680
43724
43769
38
39
39
40
41
10. 56409
56365
56320
56276
56231
9. 45271
45319
45367
45415
45463
41
42
43
43
44
10. 54729
54681
54633
54585
54537
10. 01680
01683
01687
01691
01694
3
3
3
3
3
9. 98320
98317
98313
98309
98306
10
9
8
7
6
55
56
57
58
59
60
9 52 40
52 32
52 24
52 16
52 8
52 0
2 7 20
7 28
7 36
7 44
7 52
8 0
9. 43813
43857
43901
43946
43990
44034
42
43
43
44
45
46
10. 56187
56143
56099
56054
56010
55966
9. 45511
45559
45606
45654
45702
45750
45
46
47
47
48
49
10. 54489
54441
54394
54346
54298
§4250
10. 01698
01701
01705
01709
01712
01716
3
3
3
3
3
4
9. 98302
98299
98295
98291
98288
98284
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
105°^ A A B B C C 74°
Seconds of time
1«
2s
3"
4s
5s
6s
7s
fA
Prop, parts of cols. < B
lc
6
6
0
11
12
1
17
18
1
23
25
2
28
31
2
34
37
3
40
43
3
Page 788] TABLE 4A.
Log. Sines, Tangents, and Secants.
16° A A B B C C 163°
M.
Hour A. M,
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
5
6
7
8
9
"IT
11
12
13
14
9 52 0
51 52
51 44
51 36
51 28
280
8 8
8 16
8 24
8 32
9. 44034
44078
44122
44166
44210
0
1
1
2
3
10. 55966
55922
55878
55834
55790
9. 45750
45797
45845
45892
45940
0
1
2
2
3
4
5
5
6
7
10. 54250
54203
54155
54108
54060
10. 01716
01719
01723
01727
01730
0
0
0
0
0
0
0
0
0
1
T
i
i
i
i
9. 98284
98281
98277
98273
98270
60
59
58
57
56
9 51 20
51 12
51 4
50 56
50 48
2 8 40
8 48
8 56
9 4
9 12
9. 44253
44297
44341
44385
44428
4
4
5
6
6
10. 55747
55703
55659
55615
55572
9. 45987
46035
46082
46130
46177
10. 54013
53965
53918
53870
53823
10. 01734
01738
01741
01745
01749
9. 98266
98262
98259
98255
98251
55
54
53
52
51
9 50 40
50 32
50 24
50 16
50 8
2 9 20
9 28
9 36
9 44
9 52
9. 44472
44516
44559
44602
44646
7
8
9
9
10
10. 55528
55484
55441
55398
55354
9. 46224
46271
46319
46366
46413
8
9
9
10
11
10. 53776
53729
53681
53634
53587
10. 01752
01756
01760
01763
01767
9. 98248
98244
98240
98237
98233
50
49
48
47
46
15
16
17
18
19
9 50 0
49 52
49 44
49 36
49 28
2 10 0
10 8
10 16
10 24
10 32
9. 44689
44733
44776
44819
44862
11
11
12
13
14
10. 55311
55267
55224
55181
55138
9. 46460
46507
46554
46601
46648
12
12
13
14
15
10. 53540
53493
53446
53399
53352
10. 01771
01774
01778
01782
01/85
i
i
i
i
i
9. 98229
98226
98222
98218
98215
45
44
43
42
41
20
21
22
23
24
9 49 20
49 12
49 4
48 56
48 48
2 10 40
10.48
10 56
11 4
11 12
9. 44905
44948
44992
45035
45077
14
15
16
16
17
10. 55095
55052
55008
54965
54923
9. 46694
46741
46788
46835
46881
15
16
17
18
19
10. 53306
53259
53212
53165
53119
10. 01789
01793
01796
01800
01804
i
i
i
i
i
9. 98211
98207
98204
98200
98196
40
39
38
37
36
25
26
27
28
29
9 48 40
48 32
48 24
48 16
48 8
2 11 20
11 28
11 36
11 44
11 52
9. 45120
45163
45206
45249
45292
18
18
19
20
21
10. 54880
54837
54794
54751
54708
9. 46928
46975
47021
47068
47114
19
20
21
22
22
10. 53072
53025
52979
52932
52886
10. 01808
01811
01815
01819
01823
2
2
2
2
2
9. 98192
98189
98185
98181
98177.
35
34
33
32
31
30
31
32
33
34
9 48 0
47 52
47 44
47 36
47 28
2 12 0
12 8
12 16
12 24
12 32
9. 45334
45377
45419
45462
45504
21
22
23
23
24
25
26
26
27
28
10. 54666
54623
54581
54538
54496
9. 47160
47207
47253
47299
47346
23
24
25
26
26
10. 52840
52793
52747
52701
52654
10. 01826
01830
01834
01838
01841
2
2
2
2
2
9. 98174
98170
98166
98162
98159
9. 98155
98151
98147
98144
98140
30
29
28
27
26
25
24
23
22
21
35
36
37
38
39
9 47 20
47 12
47 4
46 56
46 48
2 12 40
12 48
12 56
13 4
13 12
9. 45547
45589
45632
45674
45716
10. 54453
54411
54368
54326
54284
9. 47392
47438
47484
47530
47576
27
28
29
29
30
10. 52608
52562
52516
52470
52424
10. 01845
01849
01853
01856
01860
2
2
2
2
2
40
41
42
43
44
9 46 40
46 32
46 24
46 16
46 8
2 13 20
13 28
13 36
13 44
13 52
9. 45758
45801
45843
45885
45927
28
29
30
31
31
10. 54242
54199
54157
54115
54073
9. 47622
47668
47714
47760
47806
31
32
32
33
34
10. 52378
52332
52286
52240
52194
10. 01864
01868
01871
01875
01879
.-2-
3
3
3
3
k9. 98136
"»
98125
98121
20
-19
18
17
16
45
46
47
48
49
9 46 0
45 52
45 44
45 36
45 28
2 14 0
14 8
14 16
14 24
14 32
9. 45969
46011
46053
46095
46136
32
33
33
34
35
10. 54031
53989
53947
53905
53864
9. 47852
47897
47943
47989
48035
35
36
36
37
38
10. 52148
52103
52057
52011
51965
10. 01883
01887
01890
01894
01898
3
3
3
3
3
~3~
3
3
3
3
9. 98117
98113
98110
98106
98102
15
14
13
12
11
50
51
52
53
54
9 45 20
45 12
45 4
44 56
44 48
2 14 40
14 48
14 56
15 4
15 12
9. 46178
46220
46262
46303
46345
36
36
37
38
38
10. 53822
53780
53738
53697
53655
9. 48080
48126
48171
48217
48262
39
39
40
41
42
10. 51920
51874
51829
51783
51738
10. 01902
01906
01910
01913
01917
9. 98098
98094
98090
98087
98083
10
9
8
7
6
55
56
57
58
59
60
9 44 40
44 32
44 24
44 16
44 8
44 0
2 15 20
15 28
15 36
15 44
15 52
16 0
9. 46386
46428
46469
46511
46552
46594
39
40
41
41
42
43
10. 53614
53572
53531
53489
53448
53406
9. 48307
48353
48398*
48443
48489
48534
43
43
44
45
46
46
10. 51693
51647
51602
51557
51511
51466
10. 01921
01925
01929
01933
01937
01940
3
3
4
4
4
4
9. 98079
98075-
98071
98067
98063
98060
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent
Diff.
Tangent.
Cosecant.
Diff,
Sine.
M.
106° A A B B C C 73°
Seconds of time
!•
2s
3'
4s
5a
6"
7s
(A
6
11
16
21
27
82
37
Prop, parts of cols.1 B
(c
6
0
12
1
17
1
23
2
29
2
85
3
41
3
TABLE 44. [Page 789
Log. Sines, Tangents, and Secants.
17° A A B B C C 162°
If.
Hour A. M.
Hour P. M.
Sine.
Di3.
Cosecant.
Tangent.
Diff.
Cotangent
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
9 44 0
43 52
43 44
43 36
43 28
2 16 0
16 8
16 16
16 24
16 32
9. 46594
46635
i6676
46717
46758
0
1
1
2
3
10. 53406
53365
53324
53283
53242
9.48534
48579
48624
48669
48714
0
1
1
2
3
10. 51466
51421
51376
51331
51286
10. 01940
01944
01948
01952
01956
0
0
0
0
0
0
0
0
1
1
9.98060
98056
98052
98048
98044
60
59
58
57
56
5
6
\
8
9
9 43 20
43 12
43 4
42 56
42 48
2 16 40
16 48
16 56
17 4
17 12
9.46800
46841
468S2
46923
46964
3
4
5
5
6
10. 53200
53159
53118
53077
. 53036
9.48759
48804
48849
48894
48939
4
4
5
6
7
10. 51241
51196
51151
51106
51061
10. 01960
01964
01968
01971
01975
9. 98040
98036
98032
98029
98025
55
54
53
52
51
10
11
12
13
14
15
16
17
18
19
9 42 40
42 32
42 24
42 16
42 8
2 17 20
17 28
17 36
17 44
17 52
9. 47005
47045
47086
47127
47168
7
7
8
9
9
10. 52995
52955
52914
52873
52832
9. 48984
49029
49073
49118
49163
7
8
9
10
10
10. 51016
50971
50927
50882
50837
10. 01979
01983
01987
01991
01995
1
1
1
1
1
9. 98021
98017
98013
98009
98005
50
49
48
47
46
9 42 0
41 52
41 44
41 36
41 28
2 18 0
18 8
18 16
18 24
18 32
9. 47209
47249
47290
47330
47371
10
11
11
12
13
10. 52791
52751
52710
52670
52629
9. 49207
49252
49296
49341
49385
11
12
12
13
14
10. 50793
50748
50704
50659
50615
10. 01999
02003
02007
02011
02014
1
1
1
1
1
9. 98001
97997
97993
97989
97986
45
44
43
42
41
40
39
38
37
36
20
21
22
23
24
9 41 20
41 12
41 4
40 56
40 48
2 18 40
18 48
18 56
19 4
19 12
9.47411
47452*.
47492
47533
47573
^4
15
15
16
10. 52589
52548
52508
52467
52427
9. 49430
49474
49519
49563
49607
15
15
16
17
18
10. 50570
50526
50481
50437
50393
10. 02018
02022
02026
02030
02034
1
1
1
2
2
9. 97982
97978
97974
97970
97966
25
26
27
28
29
9 40 40
40 32
40 24
40 16
40 8
2 19 20
19 28
19 36
19 44
19 52
9. 47613
47654
47694
47734
47774
17
17
18
19
19
10. 52387
52346
52306
52266
52226
9. 49652
49696
49740
49784
49828
18
19
20
21
21
10. 50348
50304
50260
50216
50172
10. 02038
02042
02046
02050
02054
2
2
2
2
2
2
2
2
2
2
9. 97962
97958
97954
97950
97946
35
34
33
32
31
30
31
32
33
34
9 40 0
39 52
39 44
39 36
39 28
2 20 0
20 8
20 16
20 24
20 32
9.47814
47854
47894
47934
47974
20
21
21
22
23
10. 52186
52146
52106
52066
52026
9. 49872
49916
49960
50004
50048
22
23
24
24
25
10. 50128
50084
50040
49996
49952
10. 02058
02062
02066
02070
02074
9. 97942
97938
97934
97930
97926
30
29
28
27
26
35
36
37
38
39
9 39 20
39 12
39 4
38 56
38 48
2 20 40
20 48
20 56
21 4
21 12
9. 48014
48054
48094
48133
48173
23
24
25
25
26
10. 51986
51946
51906
51867
51827
9. 50092
50136
50180
50223
50267
26
26
27
28
29
10. 49908
49864
49820
49777
49733
10. 02078
02082
02086
02090
02094
2
2
2
3
3
9. 97922
97918
97914
97910
97906
25
24
23
22
21
40
41
42
43
44
9 38 40
38 32
38 24
38 16
38 8
2 21 20
21 28
21 36
21 44
21 52
9. 48213
48252
48292
48332
48371
27
27
28
29
29
10. 51787
51748
51708
51668
51629
9. 50311
50355
50398
50442
50485
29
30
31
32
32
10. 49689
49645
49602
49558
49515
10. 02098
02102
02106
02110
02114
3
3
3
3
3
9. 97902
97898
97894
97890
97886
20
19
18
17
16
45
46
47
48
49
9 38 0
37 52
37 44
37 36
37 28
2 22 0
22 8
22 16
22 24
22 32
9.48411
48450
48490
48529
48568
30
31
31
32
33
10. 51589
51550
51510
51471
51432
9. 50529
50572
50616
50659
50703
33
34
35
35
36
10. 40471
49428
49384
49341
49297
10. 02118
02122
02126
02130
02134
3
3
3
3
3
9. 97882
97878
97874
97870
97866
15
14
13
12
11
50
51
52
53
54
9 37 20
37 12
37 4
36 56
36 48
2 22 40
22 48
22 56
- 23 4
23 12
9.48607
48647
48686
48725
48764
33
34
35
35
36
10. 51393
51353
51314
51275
51236
9. 50746
50789
50833
50876
50919
37
37
38
39
40
10. 49254
49211
49167
49124
49081
10. 02139
02143
02147
02151
02155
3
3
3
4
4
9. 97861
97857
97853
97849
97845
10
9
8
7
6
55
56
57
58
59
60
9 36 40
36 32
1 36 24
36 16
36 8
36 0
2 23 20
23 28
23 36
23 44
23 52
24 0
9. 48803
48842
48881
48920
48959
48998
37
37
38
39
39
40
10. 51197
51158
51119
51080
51041
51002
9. 50962
51005
51048
51092
51135
51178
40
41
42
43
43
44
10. 49038
48995
48952
48908
48865
48822
10. 02159
02163
02167
02171
02175
02179
4
4
4
4
4
4
9. 97841
97837
97833
97829
97825
97821
5
4
3
2
1
0
M.
M.
Hour P.M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
107° A A B B C C 72°
Seconds of time
1«
»
3'
*•
5»
6>
7«
(A
5
10
15
20
25
30
35
Prop, parts of cols. <B
6
0
11
1
17
1
22
2
28
2
33
,3
39
3
Page 790] TABLE 44.
Log. Sines, Tangents, and Secants.
18° A A B B C C 161°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
9 36 0
35 52
35 44
35 36
35 28
2 24 0
24 8
24 16
24 24
24 32
9. 48998
49037
49076
49115
49153
0
1
1
2
3
10. 51002
50963
50924
50885
50847
9. 51178
51221
51264
51306
51349
0
1
1
2
3
10.48822
48779
48736
48694
48651
10. 02179
02183
02188
02192
02196
0
0
0
0
0
9. 97821
97817
97812
97808
97804
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
5
6
7
8
9
9 35 20
35 12
35 4
34 56
34 48
2 24 40
24 48
24 56
25 4
25 12
9. 49192
49231
49269-
49308
49347
3
4
4
5
6
10. 50808
50769
50731
50692
50653
9. 51392
51435
51478
51520
51563
3
4
5
6
6
10. 48608
48565
48522
48480
48437
10. 02200
02204
02208
02212
02216
0
0
0
1
1
9. 97800
97796
97792
97788
97784
10
11
12
13
14
9 34 40
34 32
34 24
34 16
34 8
2 25 20
25 28
25 36
25 44
25 52
9. 49385
49424
49462
49500
49539
6
7
8
8
9
10. 50615
50576
50538
50500
50461
9. 51606
51648
51691
51734
51776
7
8
8
9
10
10. 48394
48352
48309
48266
48224
10. 02221
02225
02229
02233
02237
1
1
1
1
1
9. 97779
97775
97771
97767
97763
15
16
17
18
19
20
21
22
23
24
9 34 0
33 52
33 44
33 36
33 28
2 26 0
26 8
26 16
26 24
26 32
9. 49577
49615
49654
49692
49730
9
10
11
11
12
10. 50423
50385
50346
50308
50270
9. 51819
51861
51903
51946
51988
10
11
12
13
13
10. 48181
48139
48097
48054
48012
10. 02241
02246
02250
02254
02258
1
1
1
1
1
9. 97759
97754
97750
97746
97742
45
44
43
42
41
9 33 20
33 12
33 4
32 56
32 48
2 26 40
26 48
26 56
27 4
27 12
9. 49768
49806
49844
49882
49920
13
13
14
14
15
10. 50232
50194
50156
50118
50080
9. 52031
52073
52115
52157
52200
14
15
15
16
17
10. 47969
47927
47885
47843
47800
10. 02262
02266
02271
02275
02279
1
1
2
2
2
9. 97738
97734
97729
97725
97721
40
39
38
37
36
25
26
27
28
29
9 32 40
32 32
32 24
32 16
32 8
2 27 20
27 28
27 36
27 44
27 52
9. 49958
49996
50034
50072
50110
16
16
17
18
18
10. 50042
50004
49966
49928
49890
9. 52242
52284
52326
52368
52410
17
18
19
20
20
10. 47758
47716
47674
47632
47590
10. 02283
02287
02292
02296
02300
2
2
2
2
2
9. 97717
.97713
97708
97704
97700
35
34
33
32
31
30
31
32
33
34
9 32 0
31 52
31 44
31 36
31 28
2 28 0
28 8
28 16
28 24
28 32
9. 50148
50185
50223
50261
50298
19
20
20
21
21
10. 49852
49815
49777
49739
49702
9. 52452
52494
52536
52578
52620
21
22
22
23
24
10. 47548
47506
47464
47422
47380
10. 02304
02309
02313
02317
02321
2
2
2
2
2
9. 97696
97691
97687
97683
97679
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
35
36
37
38
39
9 31 20
31 12
31 4
30 56
30 48
2 28 40
28 48
28 56
29 4
29 12
9. 50336
50374
50411
50449
50486
22
23
23
24
25
10. 49664
49626
49589
49551
49514
9. 52661
52703
52745
52787
52829
24
25
26
27
27
10. 47339
47297
47255
47213
47171
10. 02326
02330
02334
02338
02343
2
3
3
3
3
9. 97674
97670
97666
97662
97657
40
41
42
43
44
9 30 40
30 32
30 24
30 16
30 8
2 29 20
29 28
29 36
29 44
29 52
9. 50523
50561
50598
50635
50673
25
26
26
27
28
10. 49477
49439
49402
49365
49327
9. 52870
52912
52953
52995
53037
28
29
29
30
31
10. 47130
47088
47047
47005
46963
10. 02347
02351
02355
02360
02364
3
3
3
3
3
9. 97653
97649
97645
97640
97636
45
46
47
48
49
50
51
52
53
54
9 30 0
29 52
29 44
29 36
29 28
9 29 20
29 12
29 4
28 56
28 48
2 30 0
30 8
30 16
30 24
30-32
9. 50710
50747
50784
50821
50858
28
29
30
30
31
10. 49290
49253
49216
49179
49142
9. 53078
53120
53161
53202
53244
31
32
33
34
34
10.46922-
46880
46839
46798
46756
10. 02368
02372
02377
02381
02385
3
3
3
3
3
9. 97632
97628
97623
97619
97615
15
14
13
12
11
2 30 40
30 48
30 56
31 4
31 12
9. 50896
50933
50970
f!007
51043
31
32
33
33
34
10. 49104
49067
49030
48993
48957
9. 53285
53327
53368
53409
53450
35
36
36
37
38
10. 46715
46673
46632
46591
46550
10. 02390
02394
02398
02403
02407
4
4
4
4
4
9. 97610
97606
97602
97597
97593
10
9
8
7
6
-T
4
3
2
1
0
55
56
57
58
59
60
9 28 40
28 32
28 24
28 16
28 8
28 0
2 31 20
31 28
31 36
31 44
31 52
32 0
9. 51080
51117
51154
51191
51227
51264
35
35
36
37
37
38
10. 48920
48883
48846
48809
48773
48736
9. 53492
53533
53574
53615
53656
53697
38
39
40
41
41
42
Diff.
10. 46508
46467
46426
46385
46344
46303
10. 02411
02416
02420
02424
02429
02433
4
4
4
4
4
4
9. 97589
97584
97580
97576
97571
97567
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Tangent.
Cosecant.
Diff.
Sine.
M.
108° A A B B C C 71°
Seconds of time . ...
1s
2"
3s
4s
5"
6*
fA
5
9
14
19
24
28
33
Prop, parts of cols. < B
(c
5
1
10
1
16
2
21
26
3
31
3
37
4
TABLE 44. [Page 791
Log. Sines, Tangents, and Secanta.
19° A A B B C C 160°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
9 28 0
27 52
27 44
27 36
27 28
2 32 0
32 8
32 16
32 24
32 32
9. 51264
51301
51338
51374
51411
0
1
1
2
2
10. 48736
48699
48662
48626
48589
9. 53697
53738
53779
53820
53861
0
1
1
2
3
10. 46303
46262
46221
46180
46139
10. 02433
02437
02442
02446
02450
0
0
0
0
0
9. 97567
97563
97558
97554
97550
60
59
58
57
56
5
6
/
8
9
10
11
12
13
14
9 27 20
27 12
27 4
26 56
26 48
2 32 40
32 48
32 56
33 4
33 12
9. 51447
51484
51520
51557
51593
3
4
4
5
5
10. 48553
48516
48480
48443
48407
9. 53902
53943
53984
54025
54065
3
4
5
5
6
10.46098
46057
46016
45975
45935
10. 02455
02459
02464
02468
02472
0
0
1
1
1
9. 97545
97541
97536
97532
97528
55
54
53
52
51
9 26 40
26 32
26 24
26 16
26 8
2 33 20
33 28
33 36
33 44
33 52
9. 51629
51666
51702
51738
51774
6
7
7
8
8
10. 48371
48334
48298
48262
48226
9. 54106
54147
54187
54228
54269
7
7
8
9
9
10. 45894
45853
45813
45772
45731
10. 02477
02481
02485
02490
02494
1
1
_
9. 97523
97519
97515
97510
97506
50
49
48
47
46
15
16
17
18
19
9 26 0
25 52
25 44
25 36
25 28
2 34 0
34 8
34 16
34 24
34 32
9.51811
51847
51883
51919
51955
9
10
10
11
11
12
12
13
14
14
10. 48189
48153
48117
48081
48045
9. 54309
54350
54390
54431
54471
10
11
11
12
13
10. 45691
45650
45610
45569
45529
10. 02499
02503
02508
02512
0251,6.
9. 97501
97497
97492
97488
97484
45
44
43
42
41
20
21
22
23
24
25
26
27
28
29
9 25 20
25 12
25 4
24 56
24 48
2 34 40
34 48
34 56
35 4
35 12
9. 51991
52027
52063
52099
52135
10. 48009
47973
47937
47901
47865
9. 54512
54552
54593
54633
54673
13 10.45488
14 45448
15 45407
15 ! 45367
k- 16 45327
10. 02521
02525,
02530
02534
02539
2
2
2
2
9. 97479
97475
97470
97466
97461
40
39
38
37
36
9 24 40
24 32
24 24
24 16
24 8
2 35 20
35 28
35 36
35 44
35 52
9.52171
52207
52242
52278
52314
15
15
16
17
17
10. 47829
47793
47758
47722
47686
9. 54714
54754
54794
54835
54875
17
17
18
19
19
10. 45286
45246
45206
45165
45125
10. 02543
02547
02552
02556
02561
2
2
2
2
2
9. 97457
97453
97448
97444
97439
35
34
33
32
31
30
31
32
33
34
9 24 0
23 52
23 44
23 36
23 28
2 36 0
36 8
36 16
36 24
36 32
9. 52350
52385
52421
52456
52492
18
18
19
20
20
10. 47650
47615
47579
47544
47508
9. 54915
54955
54995
55035
55075
20
21
21
22
23
10. 45085
45045
45005
44965
44925
10. 02565
02570
02574
02579
02583
2
2
2
2
3
3
3
3
3
3
9. 97435
97430
97426
97421
97417
30
29
28
27
26
35
36
37
38
39
9 23 20
23 12
23 4
22 56
22 48
2 36 40
36 48
36 56
37 4
37 12
9. 52527
52563
52598
52634
52669
21
21
22
23
23
10. 47473
47437
47402
47366
47331
9.55115
55155
55195
55235
55275
23
24
25
25
26
10. 44885
44845
44805
44765
44725
10. 02588
02592
02597
02601
02606
9. 97412
97408
97403
97399
97394-
25
24
23
'~>2
21
40
41
42
43
44
9 22 40
22 32
22 24
22 16
22 8
2 37 20
37 28
37 36
37 44
37 52
9. 52705
52740
52775
52811
52846
24
24
25
26
26
10. 47295
47260
47225
47189
47154
9. 55315
55355
55395
55434
55474
2V
27
28
29
29
10. 44685
44645
44605
44566
44526
10. 02610
02615
02619
02624
02628
3
3
3
3
3
9. 97390
97385
97381
97376
97372
20
19
18
17
16
45
46
47
48
9 22 0
21 52
21 44
21 36
21 28
2 38 0
38 8
38 16
38 24
38 32
9. 52881
52916
52951
52986
53021
27
27
28
29
29
10.47119
47084
47049
47014
46979
9. 55514
55554
55593
55633
55673
30
31
31
32
33
10. 44486
44446
44407
44367
44327
10. 02633
02637
02642
02647
02651
3
3
3
4
4
~T
4
4
4
4
9. 97367
97363
97358
97353
97349
15
14
13
12
11
49
50
51
52
53
54
9 21 20
21 12
21 4
20 56
•20 48
2 38 40
38 48
38 56
39 4
39 12
9. 53056
53092
53126
53161
53196
30
30
31
32
32
10. 46944
46908
46874
46839
46804
9.55712
55752
55791
55831
55870
33
34
35
35
36
10. 44288
44248
44209
44169
44130
10. 02656
02660
02665
02669
02674
9. 97344
97340
97335
97331
97326
' 97317
97312
97308
97303
97299
10
9
8
7
6
5
4
3
9
1
0
55
56
57
58
59
60
M.
9 20 40
20 32
20 24
20 16
20 8
20 0
2 39 20
39 28
39 36
39 44
39 52
40 0
9. 53231
53266
53301
53336
53370
53405
33
33
34
34
35
36
10. 46769
46734
46699
46664
46630
46595
9. 55910
55949
55989
56028
56067
56107
37
37
38
39
39
40
10.44090
44051
44011
43972
43933
43893
10. 02678
02683
02688
02692
02697
02701
4
4
4
4
4
4
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
109° A A B B C C 70°
Seconds of time
1»
23
S'
4*
5< 1 6-
;s
fA
4
9
13
IS
22 I 27
31
Prop, parts of cols.-(B
1C
5
1
10
1
15
2
20
0
2-5 30
3 3
35
4
Page 792J TABLE 44.
Log. Sines, Tangents, and Secants.
20° A A B B C C 159° 1
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
9 20 0
19 52
19 44
19 36
19 28
2 40 0
40 8
40 16
40 24
40 32
9. 53405
53440
53475
53509
53544
0
1
1
2
2
3
3
4
5
5
10. 46595
46560
46525
46491
46456
9. 56107
56146
56185
56224
56264
0
1
1
2
3
10. 43893
43854
'43815
43776
43736
10. 02701
02706
02711
02715
02720
0
0
0
0
0
9. 97299
97294
97289
97285
97280
60
59
58
57
56
55
54
53
52
51
5
6
7
8
9
9 19 20
19 12
19 4
18 56
18 48
2 40 40
40 48
40 56
41 4
41 12
9. 53578
53613
53647
53682
53716
10. 46422
46387
46353
46318
46284
9. 56303
56342
56381
56420
56459
3
4
4
5
6
10. 43697
43658
43619
43580
43541
10. 02724
02729
02734
02738
02743
0
0
1
1
1
9. 97276
97271
97266
97262
97257
10
11
12
13
14
9 18 40
18 32
18 24
18 16
18 8
2 41 20
41 28
41 36
41 44
41 52
9. 53751
53785
53819
53854
53888
6
6
7
7
8
10. 46249
46215
46181
46146
46112
9. 56498
56537
56576
56615
56654
6
7
8
8
9
10. 43502
43463
43424
43385
43346
10. 02748
02752
02757
02762
02766
1
1
1
1
1
9. 97252
97248
97243
97238
97234
50 1
49
48
47
46
15
16
17
18
19
9 18 0
17 52
17 44
17 36
. 17 28
2 42 0
42 8
42 16
42 24
42 32
9. 53922
53957
53991
54025
54059
8
9
10
10
11
10. 46078
46043
46009
45975
45941
9. 56693
56732
56771
56810
56849
10
10
11
12
12
10. 43307
43268
43229
43190
43151
10. 02771
02776
02780
02785
02790
1
1
1
1
1
9. 97229
97224
97220
97215
97210
45
44
43
42
41
20
21
22
23
24
9 17 20
17 12
17 4
16 56
16 48
2 42 40
42 48
42 56
43 4
43 12
9. 54093
54127
54161
54195
54229
11
12
12
13
14
10. 45907
45873
45839
45805
45771
9. 56887
56926
56965
57004
57042
13
13
14
15
15
10. 43113
43074
43035
42996
42958
10. 02794
02799
02804
02808
02813
2
2
2
2
2
9. 97206
97201
97196
97192
97187
40
39
38
37
36
25
26
27
28
29
9 16 40
16 32
16 24
16 16
16 8
2 43 20
43 28
43 36
43 44
43 52
9.54263
54297
54331
54365
54399
14
15
15
16
16
10. 45737
45703
45669
45635
45601
9. 57081
57120
57158
57197
57235
16
17
17
18
19
10. 42919
42880
42842
42803
42765
10. 02818
02822
02827
02832
02837
2
2
2
2
2
9. 97182
97178
97173
97168
97163
35
34
33
32
31
30
31
32
33
34
9 16 0
15 52
15 44
15 36
15 28
2 44 0
44 8
44 16
44 24
44 32
9. 54433
54466
54500
54534
54567
17
17
18
19
19
10. 45567
45534
45500
45466
45433
9. 57274
57312
57351
57389
57428
19
20
21
21
22
10. 42726
42688
42649
42611
42572
10. 02841
02846
02851
02855
02860
2
2
3
3
3
9. 97159
97154
97149
97145
97140
30
29
28
27
26
35
36
37
38
39
9 15 20
15 12
15 4
14 56
14 48
2 44 40
44 48
44 56
45 4
45 12
9. 54601
54635
54668
54702
54735
20
20
21
21
22
10. 45399
45365
45332
45298
45265
9. 57466
57504
57543
57581
57619
22
23
24
24
25
10. 42534
42496
42457
42419
42381
10. 02865
02870
02874
02879
02884
3
3
3
3
3
9. 97135
97130
97126
97121
97116
25
24
23
22
21 |
40
41
42
43
44
9 14 40
14 32
14 24
14 16
14 8
2 45 20
45 28
45 36
45 44
45 52
9. 54769
54802
54836
54869
54903
23
23
24
24
25
10. 45231
45198
45164
45131
45097
9. 57658
57696
57734*
57772N
57810
26
26
-27
28
28
10. 42342
42304
42266
42228
42190
10. 02889
02893
02898
02903
02908
3
3
3
3
3
9. 97111
97107
97102
97097
97092
20 j
19
18
17
16
~I5~
14
13
12
11
45
46
47
48
49
9 14 0
13 52
13 44
13 36
13 28
2 46 0
46 8
46 16
46 24
46 32
9. 54930
54969
55003
55036
55069
25
26
26
27
28
10. 45064
45031
44997
44964
44931
9. 57849
57887
57925
57963
58001
29,
30
30
31
31
10. 42151
42113
42075
42037
41999
10. 02913
02917
02922
02927
02932
4
4
4
4
4
9. 97087
97083
97078
97073
97068
50
51
52
53
54
9 13 20
13 12
13 4
12 56
12 48
2 46 40
46 48
46 56
47 4
47 12
9. 55102
55136
55169
55202
55235
28
29
29
30
30
10. 44898
44864
44831
44798
44765
9. 58039
58077
58115
58153
58191
32
33
33
34
35
10. 41961
41923
41885
41847
41809
10. 02937
02941
02946
02951
02956
4
4
4
4
4
9. 97063
97059
97054
97049
97044
10
!
y
~H
3
n
-
M. 1
55
56
57
58
59
60
9 12 40
12 32
12 24
12 16
12 8
12 0
2 '7 20
47 28
47 36
47 44
47 52
48 0
9. 55268
55301 .
55334
55367
55400
55433
31
32
32
33
33
34
10. 44732
44699
44666
44633
44600
44567
9. 58229
58267
58304
58342
58380
58418
35
36
37
37
38
39
10. 41771
41733
41696
41658
41620
41582
10. 02961
02965
02970
02975
02980
02985
4
4
4
5
5
5
9. 97039
97035
97030
97025
97020
97015
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
110° A A . B B C C 69° I
li»»i ii •• III»A . ^ — •• • • ^^n. • i^— . »••• • m^^ ^ ^^••J
Seconds of time
li
2»
3*
4*
5'
6*
V
{A
4
8 *
13
17
21
25
30
B
5
1
10
1
14
2
19
2
24
3
29
4
34
4
21o
TABLE 44. [Page 793
Log. Sines, Tangents, and Secants.
A A B B C C 158°
M.
Hour A. M.
Hour P.M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Dill.
Cosine.
^L
60
59
58
57
56
0
1
2
3
4
9 12 0
11 52
11 44
11 36
11 28
2 48 0
48 8
48 16
48 24
48 32
9. 55433
55466
55499
55532
55564
0
1
1
2
O
10.44567
445:34
44501
44468
44436
9. 58418
58455
58493
58531
58569
0
1
1
2
2
10. 41582
41545
41507
41469
41431
10. 02985
02990
02995
02999
03004
0
0
0
0
0
9. 97015
97010
97005
97001
96996
5
6
7
8
9
10
11
12 •
13
14
9 11 20
11 12
11 4
10 56
10 48
2 48 40
48 48
48 56
49 4
49 12
9. 55597
55630
55663
55695
55728
3
3
4
4
5
10.44403
44370
44337
44305
44272
9.58606
58644
58681
58719
58757
3
4
4
5
6
10. 41394
41356
41319
41281
41243
10. 03009
03014
03019
03024
03029
0
0
1
1
1
9. 96991
96986
96981
96976
96971
55
54
53
52
51
50
49
48
47
46
9 10 40
10 32
10 24
10 16
10 8
2 49 20
49 28
49 36
49 44
49 52
9. 55761
55793
55826
55858
55891
5
6
6
7
7
10. 44239
44207
44174
44142
44109
9. 58794
58832
58869
58907
58944
6
7
7
8
9
~9"
10
10
11
12
10. 41206
41168
41131
41093
41056
10. 03034
03038
03043
03048
03053
1
i
9.96966
96962
96957
96952
96947
15
16
17
18
19
9 10 0
9 52
9 44
9 36
9 28
2 50 0
50 8
50 16
50 24
50 32
9. 55923
55956
55988
56021
56053
8
9
9
10
10
10. 44077
44044
44012
43979
43947
9. 58981
59019
59056
59094
59131
10. 41019
40981
40944
40906
40869
10. 03058
03063
03068
03073
03078
i
1
2
2
2
2
i
T
1
2
9. 96942
96937
96932
96927
96922
45
44
43
42
41
20
21
22
23
24
9 9 20
9 12
9 4
8 56
8 48
2 50 40
50 48
50 56
51 4
51 12
9.56085
56118
56150
56182
56215
11 10.43915
11 43882
12 43850
12 43818
13 43785
9. 59168
59205
59243
59280
59317
12
13
14
14
15
10. 40832
40795
40757
40720
40683
10. 03083
03088
03093
03097
03102
9. 96917
96912
96907
96903
96898
40
39
38
37
36
25
26
27
28
29
9 8 40
8 32
8 24
8 16
8 8
2 51 20
51 28
51 36
51 44
51 52
9. 56247
56279
56311
56343
56375
13
14
14
15
16
10. 43753
43721
• 43689
43657
43625
9.59354
59391
59429
59466
59503
15
16
17
17
18
10. 40646
40609
40571
40534
40497
10. 03107
03112
03117
03122
03127
9. 96893
96888
96883
96878
96873
35
34
33
32
31
30
29
28
27
26
30
31
32
33
34
980
7 52
7 44
7 36
7 28
2 52 0
52 8
52 16
52 24
52 32
9. 56408
56440
56472
56504
56536
16 10.43592
17 43560
17 43528
18 43496
18 434G4
9. 59540
59577
59614
59651
596S8
19
19
20
20
21
22
22
23
23
24
10.40460
40423
40386
40349
40312
10. 03132
03137
03142
03147
03152
2
3
3
3
3
9. 96868
96863
96858
96853
96848
35
36
37
38
39
9 7 20
7 12
7 4
6 56
6 48
2 52 40
52 48
52 56
53 4
53 12
9. 56568
56599
56631
56663
56695
19 10.43432
19 43401
20 43369
20 43337
21 43305
9. 59725
59762
59799
59835
59872
10. 40275
40238
40201
40165
40128
10. 03157
03162
03167
03172
03177
3
3
o
Q
o
9. 96843
9683S
96833
96828
96823
25
24
23
22
21
40
41
42
43
44
9 6 40
6 32
6 24
6 16
6 8
2 53 20
53 28
53 36
53 44
53 52
9. 56727
56759
56790
56822
56854
21
22
22
23
24
10. 43273
43241
43210
43178
43146
9.59909
59946
59983
60019
. 60056
25
25
26
27
27
10. 40091
40054
40017
39981
39944
10. 03182
03187
03192
03197
03202
3
3
3
4
4
9. 96818
96813
96808
96803
96798
20
19
18-
17
16
45
46
47
48
49
960
5 52
5 44
5 36
5 28
2 54 0
54 8
54 16
54 24
54 32
9. 5' -
56917
56949
56980
57012
24
25
25
26
26
10.43114
43083
43051
43020
42988
9.60093
60130
60166
60203
60240
28
28
29
30
30
10. 39907
39870
39834
39797
39760
10. 03207
03212
03217
03222
03228
4
4
4
4
4
9. 96793
96788
96783
96778
96772
15
14
13
12
11
50
51
52
53
54
9 5 20
5 12
5 4
4 56
4 48
2 54 40
54 48
54 56
55 4
55 12
9. 57044 27
57075 27
57107 28
57138 i 28
57169 29
10. 42956
42925
42893
42862
42831
9. 60276
60313
60349
60386
60422
31
31
32
33
33
10. 39724
39687
39651
39614
39578
10. 03233
03238
03243
0324S
03253
4
4
4
4
4
9. 96767
96762
96757
96752
96747
10
9
8
I
55
56
57
58
59
60
KL
9 4 40
4 32
4 24
4 16
4 8
4 0
2 55 20
55 28
55 36
55 44
55 52
56 0
9. 57201
57232
57264
57295
57326
57358
29
30
30
31
32
32
10. 42799
42768
42736
42705
42674
42642
9. 60459
60495
60532
60568
60605
60641
34
35
35
36
36
10. 39541
39505
39468
39432
39395
39359
10. 03258
03263
03268
03273
03278
03283
5
5
5
5
5
5
Diff.
9. 96742
96737
96732
96727
96722
96717
I
3
I
0
Hour P.M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent. Diff.
Tangent.
Cosecant
Sine. 1 M.
111°
A A B
B C C 68°
Second of TITTIP
Is
.).
33
4*
o3
6s
_,
(A
Prop, parts of cols.<B
1C
4
5
1
8
9
1
12
1-i
2
16
19
2
20
23
3
24
28
4
28
32
4
61828°— 16 i3
Page 794] TABLE 44.
Log. Sines, Tangents, and Secants.
22° A A B B C C 157°
M.
Hour A.. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
940
3 52
3 44
3 36
3 28
2 56 0
56 8
56 16
56 24
56 32
9. 57358
57389
57420
57451
57482
0
1
1
2
2
10. 42642
42611
42580
42549
42518
9. 60641
60677
60714
60750
60786
0
1
1
2
2
10. 39359
39323
39286
39250
39214
10. 03283
03289
03294
03299
03304
0
0
0
0
0
~0"
1
1
1
1
9. 96717
96711
96706
96701
96696
60
59
58
57
56
'55
54
53
52
51
5
6
7
8
9
9 3 20
3 12
3 4
2 56
2 48
2 56 40
56 48
56 56
57 4
57 12
9. 57514
57545
57576
57607-
57638
3
3
4
4
5
10. 42486
42455
42424
42393
42362
9. 60823
60859
60895
60931
60967
3
4
4
5
5
10. 39177
39141
39105
39069
39033
10. 03309
03314
03319
03324
03330
9. 96691
96686
96681
96676
96670
10
11
12
13
14
9 2 40
2 32
2 24
2 16
2 8
2 57 20
57 28
57 36
57 44
57 52
9. 57669
57700
57731
57762
57793
5
6
6
7
7
10. 42331
42300
42269
42238
42207
9. 61004
61040
61076
61112
61148
6
7
7
8
8
10. 38996
38960
38924
38888
38852
10. 03335
03340
03345
03350
03355
1
1
1
1
1
9. 96665
96660
96655
96650
96645
50
49
48
47
46
15
16
17
18
19
920
1 52
1 44
1 36
1 28
2 58 0
58 8
58 16
58 24
58 32
9. 57824
57855
57885
57916
57947
8
8
9
9
10
10. 42176
42145
42115
42084
42053
9. 61184
61220
61256
61292
61328
9
10
10
11
11
10. 38816
38780
38744
38708
38672-
10. 03360
03366
03371
03376
03381
1
1
1
2
2
9. 96640
96634
96629
96624
96619
45
44
43
42
41
40
39
38
37
36
20
21
22
23
24
9 1 20
1 12
1 4
0 56
0 48
2 58 40
58 48
58 56
59 4
59 12
9. 57978
58008
58039
58070
58101
10
11
11
12
12
10. 42022
41992
41961
41930
41899
9. 61364
61400
61436
61472
61508
12
13
13
14
14
10. 38636
38600
38564
38528
38492
10. 03386
03392
03397
03402
03407
2
2
2
2
2
9. 96614
96608
96603
96598
96593
25
26
27
28
29
30
31
32
33
34
9 0 40
0 32
0 24
0 16
0 8
2 59 20
59 28
59 36
59 44
59 52
9. 58131
58162
58192
58223
58253
13
13
14
14
15
10. 41869
41838
41808
'41777
41747
9. 61544
61579
61615
61651
61687
15
15
16
17
17
10. 38456
38421
38385
38349
38313
10. 03412
03418
03423
03428
03433
2
2
2
2
3
9. 96588
96582
96577
96572
96567
35
34
33
32
31
30~
29
28
27
26
900
8 59 52
59 44
59 36
59 28
300
0 8
0 16
0 24
0 32
9. 58284
58314
58345
58375
58406
15
16
16
17
17
10. 41716
41686
41655
41625
41594
9. 61722
61758
61794
61830
61865
18
18
19
20
20
10. 38278
38242
38206
38170
38135
10. 03438
03444
03449
03454
03459
3
3
3
3
3
9. 96562
96556
96551
96546
96541
35
36
37
38
39
8 59 20
59 12
59 4
58 56
58 48
3 0 40
0 48
0 56
1 4
1 12
9. 58*436
58467
58497
58527
58557
18
18
19
19
20
10. 41564
41533
41503
41473
41443
9. 61901
61936
61972
62008
62043
21
21
22
23
23
10. 38099
38064
38028
37992
37957
10. 03465
03470
03475
03480
03486
3
3
3
3
3
9. 96535
96530
96525
96520
96514
25
24
23
22
21
40
41
42
43
44
8 58 40
58 32
58 24
58 16
58 8
3 1 20
1 28
1 36
1 44
1 52
9. 58588
58618
58648
58678
58709
20
21
21
22
22
10. 41412
41382
41352
41322
41291
9. 62079
62114
62150
62185
62221
24
24
25
26
26
10. 37921
37886
37850
37815
37779
10. 03491
03496
03502
03507
03512
3
4
4
4
4
9. 96509
96504
96498
96493
96488
20
19
18
17
16
45
46
i
49
So"
51
52
53
54
8 58 0
57 52
57 44
57 36
57 28
320
2 8
2 16
2 24
2 32
9. 58739
/JJ?7C',>
,68799*
23
23
. 24
! 24.
25
10. 41261
41231
41201
41171
41141
9. 62256
62292
62327
62362
62398
27
27
28
29
29
10. 37744
37708
37673
37638
37602
10. 03517
03523
03528
03533
03539
4
4
4
4
4
9. 96483
96477
96472
96467
96461
15
14
13
12
11
8 57 20
57 12
57 4
56 56
56 48
3 2 40
2 48
2 56
3 4
3 12
9. 58889
58919
58949
58979
59009
25
26
26
27
27
10.41111
41081
41051
41021
40991
9. 62433
62468
62504
62539
62574
30
30
31
32
32
10. 37567
37532
37496
37461
37426
10. 03544
03549
03555
03560
03565
4
4
5
5
5
9. 96456
96451
96445
96440
96435
10
9
8
7
6
55
56
57
58
59
60
8 56 40
56 32
56 24
56 16
56 8
56 0
3 3 20
3 28
3 36
3 44
3 52
4 0
9. 59039
59069
59098
59128
59158
59188
28
28
29
29
30
31
10. 40961
40931
40902
40872
40842
40812
9. 62609
62645
62680
62715
62750
62785
33
33
34
35
35
36
10. 37391
37355
37320
37285
37250
37215
10. 03571
03576
03581
03587
03592
03597
5
5
5
5
5
5
9. 96429
96424
96419
96413
96408
96403
5
4
3
2
1
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
112° A A B B C C 67°
Seconds of time
1s
2s
3s
4s
5s
G9
fA
Prop, parts of cols. < B
lc
4
4
1
8
9
1
11
13
2
15
18
3
19
22
3
23
27
4
27
31
5
TABLE 44. [Page 795
Log. Sines, Tangents, and Secants.
23° A A B B C C 156°
M.
Hour A. M. Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff. 1 Cotangent.
Secant.
Diff.
Cosine.
Iff.
0
1
9
m
3
4
8 56 0
55 52
55 44
55 36
55 28
:-} 4 o
4 8
4 16
4 24
4 32
9. 59188
59218
59247
59277
59307
0
0
1
1
2
~2~
3
3
4
4
10. 40812
40782
40753
40723
40693
9. 62785
62820
62855
62890
62926
0
1
1
2
2
10. 37215
37180
37145
37110
37074
10. 03597
03603
03608
03613
03619
0
0
0
0
0
9.96403
96397
96392
96387
96381
60
59
58
57
56
55
54
53
52
51
5
6
7
8
9
8 55 20
55 12
55 4
54 56
54 48
3 4 40
4 48
4 56
5 4
5 12
9. 59336
59366
59396
59425
59455
10.40664
40634
40604
40575
40545
9. 62961
62996
63031
63066
63101
3
3
4
5
5
10. 37039
37004
36969
36934
36899
10. 03624
03630
03635
03640
03646
0
1
1
1
1
9. 96376
96370
96365
96360
96354
10
11
12
13
14
15
16
17
18
19
8 54 40 : 3 5 20
54 32 5 28
54 24 5 36
54 16 5 44
54 5 52
9. 59484
59514
59543
59573
59602
b
5
6
6
7
10. 40516
40486
40457
40427
40398
9. 63135
63170
63205
63240
63275
6
7
7
8
10. 36865
36830
36795
36760
36725
10. 03651
03657
03662
03667
03673
1
1
1
1
1
9.96349
96343
96338
96333
96327
50
49
48
47
46
8 54 0
53 52
53 44
53 36
53 28
360
6 8
6 16
6 24
6 32
9. 59632
59661
59690
59720
59749
7
8
8
9
9
10. 40368
40339
40310
40280
40251
9. 63310
63345
63379
63414
63449
9 10.36690
9 i 36655
10 36621
10 36586
11 36551
10. 03678
03684
036$
03695
03700
1
1
2
2
2
9. 96322
96316
96311
96305
96300
45
44
43
42
41
20
21
22
2C
24
8 53 20 3 6 40
53 12 6 48
53 4 6 56
52 56 74
52 48 7 12
9. 59778
59808
59837
59866
59895
10
10
11
11
L2
10. 40222
40192
40163
40134
40105
9.63484 12 10.36516
63519 12 36481
63553 13 i 36447
63588 13 36412
63623 14 36377
10. 03706
03711
03716
03722
03727
2
2
2
2
2
9. 96294
96289
96284
96278
96273
40
39
38
37
36
25
26
27
28
29
8 52 40
52 32
52 24
52 16
52 8
3 7 20
7 28
7 36
7 44
7 52
9. 59924
59954
59983
60012
60041
12
13
13
14
14
10. 40076
40046
40017
39988
39959
9. 63657
63692
63726
63761
63796
14
15
16
16
17
10. 36343
36308
36274
36239
36204
10. 03733
03738
03744
03749
03755
2
2
2
3
3
9. 96267
96262
96256
96251
96245
35
34
33
32
31
30
31
32
33
34
8 52 0
51 52
51 44
51 36
51 28
380
8 8
8 16
8 24
8 32
9. 60070 15
60099 15
60128 15
60157 16
60186 i 16
10. 39930
39901
39872
39843
39814
9. 63830 17
63865 18
63899 18
63934 19
63968 20
10. 36170
36135
36101
36066
36032
10. 03760
03766
03771
03777
03782
3
3
3
3
3
9. 96240
96234
96229
96223
96218
30
29
28
27
26
35
36
37
38
39
8 51 20 3 8 40
51 12 i 8 48
51 4 8 56
50 56 94
50 48 ! 9 12
9. 60215
60244
60273
60302
60331
17
17
18
18
19
19
20
20
21
21
10. 39785
39756
39727
39698
39669
9.64003
64037
64072
64106
64140
20
21
21
22
22
10. 35997
35963
35928
35894
35860
10. 03788
03793
03799
03804
03810
3
3
3
3
4
9. 96212
96207
96201
96196
96190
25
24
23
22
21
40
41
42
43
44
8 50 40
50 32
50 24
50 16
50 8
3 9 20
9 28
9 36
9 44
9 52
9. 60359
60388
60417
60446
60474
10. 39641
39612
39583
39554
39526
9. 64175
64209
64243
64278
64312
23
24
24
25
25
10. 35825
35791
35757
35722
35688
10. 03815
03821
03826
03832
03838
4
4
4
4
4
9. 96185
96179
96174
96168
96162
20
19
18
17
16
45
46
47
48
49
8 50 0 | 3 10 0
49 52 10 8
49 44 10 16
49 36 10 24
49 28 10 32
9. 60503
60532
60561
60589
60618
22
22
23
23
24
10. 39497
39468
39439
39411
39382
9.64346
64381
64415
64449
64483
26
26
27
28
28
10. 35654
35619
355S5
35551
35517
10. 03843
03849
03854
03860
03865
4
4
4
4
4
9. 96157
96151
96146
96140
96135
15
14
13
12
11
50
51
52
53
54
8 49 20
49 12
49 4
48 56
48 48
3 10 40
10 48
10 56
11 4
11 12
9. 60646
60675
60704
60732
60761
24
25
25
26
26
10. 39354
39325
39296
39268
39239
9. 64517
64552
64586
64620
64654
29
29
30
31
31
"32"
32
33
33
34
35
10. 35483
35448
35414
35380
35346
10. 03871
03877
03882
03888
03893
5
5
5
5
5
9. 96129
96123
96118
96112
96107
10
9
8
7
6
oo
56
57
58
59
60
8 48 40
48 32
48 24
48 16
48 8
48 0
3 11 20
11 28
11 36
11 44
11 52
12 0
9. 60789
60818
60846
60875
60903
60931
27
27
28
28
29
29
10. 39211
39182
39154
39125
39097
39069
9. 64688
64722
64756
64790
64824
64858
10. 35312
35278
35244
35210
35176
35142
10. 03899
03905
03910
03916
03921
03927
5
5
5
5
5
6
9. 96101
96095
96090
96084
96079
96073
5
4
3
2
1
0
M.
Hour P.M. Hour A.M.
Cosine.
Diff. Secant.
Cotangent.
Diff.
Tangent,
f Cosecant, i Diff.
Sine.
M.
113° A A B • B C C 66°
Seconds of time
1s
•is
3s
4s
o3
63
75
(A
4
7
11
15
18
22
25
Prop, parts of cols. < B
LC
4
1
9
1
13
2
17
3
22
3
5
31
5
Page 796] TABLE 44.
Log. Sines, Tangents, and Secants.
24° A A B B C C 155°
M.
Hour A.M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
8 48 0
47 52
47 44
47 36
47 28
3 12 0
12 8
12 16
12 24
12 32
9. 60931
60960
60988
61016
61045
0
0
1
1
2
10. 39069
39040
39012
38984
38955
9. 64858
64892
64926
64960
64994
0
1
1
2
2
10. 35142
35108
35074
35040
35006
10.03927
03933
03938
03944
03950
0
0
0
0
0
9. 96073
96067
96062
96056
96050
60
59
58
57
56
5
6
7
8
9
8 47 20
47 12
47 4
46 56
46 48
3 12 40
12 48
12 56
13 4
13 12
9. 61073
61101
61129
61158
61186
2
3
3
4
4
10. 38927
38899
38871
38842
38814
9. 65028
65062
65096
65130
65164
3
3
4
4
5
10. 34972
34938
34904
34870
34836
10. 03955
03961
03966
03972
03978
0
1
1
1
1
9. 96045
96039
96034
96028
96022
55
54
53
52
51
10
11
12
13
14
8 46 40
46 32
46 24
46 16
46 8
3 13 20
13 28
13 36
13 44
13 52
9. 61214
61242
61270
61298
61326
5
5
6
6
6
10. 38786
38758
38730
38702
38674
9. 65197
65231
65265
65299
65333
6
6
7
7
8
10. 34803
34769
34735
34701
34667
10. 03983
03989
03995
04000
04006
1
1
1
1
1
9. 96017
96011
96005
96000
95994
50
49
48
47
46
15
16
17
18
19
8 46 0
45 52
45 44
45 36
45 28
3 14 0
14 8
14 16
14 24
14 32
9. 61354
61382
61411
61438
61466
7
8
8
9
10. 38646
38618
38589
38562
38534
9. 65366
65400
65434
65467
65501
8
9
9
10
11
10. 34634
34600
34566
34533
34499
10. 04012
04018
04023
04029
04035
1
2
2
2
2
9. 95988
95982
95977
95971
95965
45
44
43
42
41
20
21
22
23
24
8 45 20.
45 12
45 4
44 56
44 48
3 14 40
14 48
14 56
15 4
15 12
9. 61494
61522
61550
61578
61606
9
10
10
11
11
10. 38506
38478
38450
38422
38394
9. 65535
65568
65602
65636
65669
11
12
12
13
13
10. 34465
34432
34398
34364
34331
10. 04040
04046
04052
04058
04063
2
2
2
2
2
9. 95960
95954
95948
95942
95937
40
39
as
37
36
25
26
27
28
29
8 44 40
44 32
44 24
44 16
44 8
3 15 20
15 28
15 36
15 44
15 52
9. 61634
61662
61689
61717
61745
12
12
12
13
13
10. 38366
38338
38311
38283
38255
9. 65703
65736
65770
65803
65837
14
15
15
16
16
10. 34297
34264
34230
34197
34163
10. 04069
04075
04080
04086
04092
2
2
3
3
3
9. 95931
95925
95920
95914
95908
35
34
33
32
31
30
31
32
33
34
8 44 0
43 52
43 44
43 36
43 28
3 16 0
16 8
16 16
16 24
16 32
9. 61773
61800
61828
61856
61883
14
14
15
15
16
10. 38227
38200
38172
38144
38117
9. 65870
65904
65937
65971
66004
17
17
18
18
19
20
20
21
21
22
10. 34130
34096
34063
34029
33996
10. 04098
04103
04109
04115
04121
3
3
3
3
3
9. 95902
95897
95891
95885
95879
30
29
28
27
26
35
36
37
38
39
8 43 20
43 12
43 4
42 56
42 48
3 16 40
16 48
16 56
17 4
17 12
9. 61911
61939
61966
61994
62021
16
17
17
18
18
18
19
19
20
20
10. 38089
38061
38034
38006
37979
9. 66038
66071
66104
66138
66171
10. 33962
33929
33896
33862
33829
10. 04127
04132
04138
04144
04150
3
3
4
4
4
9. 95873
95868
95862
95856
95850
25
24
23
22
21
40
41
42
43
44
8 42 40
42 32
42 24
42 16
42 8
3 17 20
17 28
17 36
17 44
17 52
9. 62049
6207«
62104
62131
62159
10. 37951
37924
37896
37869
37841
9. 66204
66238
66271
66304
66337
22
23
23
24
25
10. 33796
33762
33729
33696
33663
10. 04156
04161
04167
04173
04179
4
4
4
4
4
9. 95844
95839
95833
95827
95821
20
19
18
17
16
45
46
47
48
49
8 42 0
41 52
41 44
41 36
41 28
3 18 0
18 8
18 16
18 24
18 32
9. 62186
62214
62241
62268
62296
21
21
22
22
23
10. 37814
37786
37759
37732
37704
9. 66371
66404
66437
66470
66503
25
26
26
27
27
28
28
29
30
30
10. 33629
33596
33563
33530
33497
10. 04185
04190
04196
04202
04208
4
4
5
5
5
9. 95815
95810
95804
95798
95792
15
14
13
12
11
50
51
52
53
54
8 41 20
41 12
41 4
40 56
40 48
3 18 40
18 48
18 56
19 4
.19 12
9. 62323
62350
62377
62405
62432
23
24
24
24
25
25
26
26
27
27
28
10. 37677
37650
37623
37595
37568
9. 66537
66570
66603
66636
66669
10. 33463
33430
33397
33364
33331
10. 04214
04220
04225
04231
04237
5
5
5
5
5
9. 95786
95780
95775
95769
95763
10
9
8
7
6
55
56
57
58
59
60
8 40 40
40 32
40 24
40 16
40 8
40 0
3 19 20
19 28
19 36
19 44
19 52
20 0
9. 62459
62486
62513
62541
62568
62595
10. 37541
37514
37487
37459
37432
37405
9. 66702
66735
66768
66801
66834
66867
31
31
32
32
33
33
10. 33298
33265
33232
33199
33166
33133
10. 04243
04249
04255
04261
04267
04272
5
5
'5
6
6
6
9. 95757
95751
95745
95739
95733
95728
5
4
3
2
1
0~
M.
Hour P. M.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
114° A A B B C C 65°
Seconds of time
I3
2»
3*
4»
5'
6"
7s
(A
3
7
10
14
17
21
24
Prop, parts of cols.'JB
lc
4
1
8
1
13
2
17
3
21
4
25
4
29
5
TABLE 44. [Page 797 j
Log. Sines, Tangents, and Secants.
25° A A B B C C 154° |
M.
Hour A. M.
Hour P. M.
Sine.
! Diff.
Cosecant.
Tangent.
Diff.
Cotangent
Secant.
Diff.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
8 40 0
39 52
39 44
39 36
39 28
3 20 0
20 8
20 16
20 24
20 32
9. 62595
62622
62649
62676
62703
0
0
1
1
2
10. 37405
37378
37351
37324
37297
9.66867
66900
66933
66966
66999
0
1
1
2
2
3
3
4
4
5
10. 33133
33100
33067
33034
33001
10. 04272
04278
04284
04290
04296
0
0
0
0
0
9. 95728
95722
95716
95710
95704
o
6
7
8
9
10
11
12
13
14
8 39 20
39 12
39 4
38 56
38 48
3 20 40
20 48
20 56
21 4
21 12
9. 62730
62757
62784
62811
62838
2
i
4
4
10. 37270
37243
37216
37189
37162
9. 67032i
67065
67098
67131
67163
10. 32968
32935
32902
32869
32837
10. 04302
04308
04314
04320
04326
9. 95698
95692
95686
95680
95674
55
54
53
52
51
8 38 40
38 32
38 24
38 16
38 8
3 21 20
21 28
21 36
21 44
21 52
9. 62865
62892
62918
62945
62972
4
5
5
6
6
10. 37135
37108
37082
37055
37028
9. 67196
67229
67262
67295
67327
5 ilO. 32804
6 32771
7 32738
7 32705
8 i 32673
10.04332
04337
04343
04349
04355
1
1
1
2
2
2
2
2
9.95668
95663
95657
95651
95645
50
49
48
47
46
15
16
17
18
19
8 38 0
37 52
37 44
37 36
37 28
3 22 0
22 8
22 16
22 24
22 32
9. 62999
63026
63052-
63079 -
63106
7 10.37001
7 36974
8 36948
8 36921
8 36894
9. 67360
67393
67426
67458
67491
8
9
9
10
10
11
11
12
12
13
10. 32640
32607
32574
32542
32509
10. 04361
04367
04373
04379
04385
9. 95639
95633
95627
95621
35615
45
44
43
42
41
40
39
38
37
36
20
21
22
23
24
8 37 20
37 12
37 4
36 56
36 48
3 22 40
22 48
22 56
23 4
23 12
9. 63133
63159
63186
63213
63239
9 10.36867
ft 36841
10 ; 36814
10 36787
11 36761
9. 67524
67556
67589
67622
67654
10. 32476
32444
32411
32378
32346
10. 04391
04397
04403
04409
04415
2
2.
2
2
2
"T
3
3
3
3
9.95609
95603
95597
95591
95585
25
26
27
28
29
8 36 40 3 23 20
36 32 i 23 28
36 24 ,j 23 36
36 16 I 23 44
36 8 ! 23 52
9.63266
63292
63319
63345
63372
11
11
12
12
13
10. 36734
36708
'
36655
36628
9. 67687
67719
67752
67785
67817
14
14
15
15
16
10. 32313
32281
32248
32215
32183
10. 04421
04427
04433
04439
04445
9. 95579
95573
95567
95561
95555
35
34
33
32
31
30
31
32
33
34
8 36 03 24 0
35 52 24 8
35 44 24 16
35 36 24 24
35 28 24 32
9. 63398
63425*
63451
63478
63504
13 10.36602
14 36575
14 36549
15 36522
15 • 36496
9. 67850 16
67882 17
67915 17
67947 18
67980 IS
10. 32150
32118
32085
32053
32020
10. 04451 .
04457
04463
04469
04475
3
3
3
o
3
9. 95549
95543
95537
95531
95525
30
29
28=
27
•26
35
36
37
38
39
8 35 20 3 24 40
35 12 24 48
35 4 24 56
34 56 i 25 4
34 48 25 12
9. 63531
63557
63583
63610
63636
15
16
16
17
17
10. 36469
36443
36417
36390
36364
9. 68012 19
68044 20
68077 i 20
68109 j 21
68142 21
10. 31988
31956
31923
31891
31858
10. 04481
04487
04493
04500
04506
4
4
4
4
4
9. 95519
95513
95507
95500
95494
25
24
23
22
21
^0"
19
18
17
16
40
41
42
43
44
8 34 40
34 32
34 24
34 16
34 8
3 25 20
25 28
25 36
25 44
25 52
9. 63662
63689
63715
63741
63767
18
18
19
19
19
10. 36338
36311
36285
36259
36233
9.68174
68206
68239
68271
68303
22
22
23
23
24
10. 31826
31794
31761
31729
31697
10. 04512
04518
04524
04530
04536
4
4
4
4
4
9.95488
95482
95476
95470
95464
45
46
47
48
49
8 34 0
33 52
33 44
33 36
33 28
3 26 0
26 8
26 16
26 24
26 32
9. 63794
63820
63846
63872
63898
20
20
21
21
22
10. 36206
36180
36154
36128
36102
9. 68336
68368
68400
68432
68465
24
25
25
26
27
10. 31664
31632
31600
31568
31535
10.04542
04548
04554
04560
04566
5
5
5
5
5
9.95458
95452
95446
95440
95434
15
14
13
12
11
^0~
•
M
M
'I
50
51
52
53
54
8 33 20
33 12
33 4
32 56
32 48
3 26 40
26 48
26 56
27 4
27 12
9. 63924
63950
63976
64002
64028
22
23
23
23
24
10. 36076
36050
36024
35998
35972
9. 68497
68529
68561
68593
68626
27
28
28
29
29
10. 31503
31471
31439
31407
31374
10. 04573
04579
04585
04591
04597
5
5
5
5
5
9. 95427
95421
95415
95409
95403
55
56
57
58
59
60
8 32 40
32 32
32 24
32 16
32 8
32 0
3 27 20
27 28
27 36
27 44
27 52
28 0
9. 64054
64080
64106
64132
64158
64184
24
25
25
26
26
26
10. 35946
35920
35894
35868
35S42
35816
9.68658
68690
6S722
68754
68786
68818
30
30
31
31
32
33
10. 31342
31310
31278
31246
31214
31182
10. 04603
04609
04616
04622
04628
04634
6
6
6
6
6
6
9. 95397
95391
95384
95378
95372
95366
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent, j Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
115° A A B B C C 64°
Seconds of time < 1*
2s
3s
4s
.s
6'
;•
(A | 3
Prop, parts of cols. < B I 4
(C 1
I
2
10
12
0
13
16
3
17
20
4
20
24
23
tt
5
Page 798] TABLE M.
Log. Sines, Tangents, and Secants.
26° A A B B C C 15^°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangfent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
8 32 0
31 52
31 44
31 36
31 28
3 28 0
28 8
28 16
28 24
28 32
9. 64184
64210
64236
64262
64288
0
0
1
1
2
10. 35816
35790
35764
35738
35712
10735687"
35661
35635
35609
35583
9. 68818
68850
68882
68914
68946
0
1
1
2
2
10. 31182
31150
31118
31086
31054
10. 04634
04640
04646
04652
04659
0
0
0
0
0
9. 95366
95360
95354
95348
95341
60
59
58
57
56
5
6
7
8
9
8 31 20
31 12
31 4
30 56
30 48
3 28 40
28 48
28 56
29 4
29 12
9. 64313
64339
64365
64391
64417
2
3
3
3
4
9. 68978
69010
69042
69074
69106
3
3
4
4
5
10. 31022
30990
30958
30926
30894
10. 04665
04671
04677
04683
04690
1
1
1
1
1
9. 95335
95329
95323
95317
95310
55
54
53
52
51
10
11
12
13
14
8 30 40
30 32
30 24
30 16
30 8
3 29 20
29 28
29 36
29 44
29 52
9. 64442
64468
64494
64519
64545
4
5
5
5
6
10. 35558
35532
35506
35481
35455
9. 69138
69170
69202
69234
69266
5
6
6
7
7
10. 30862
30830
30798
30766
30734
10. 04696
04702
04708
04714
04721
1
1
1
1
1
9. 95304
95298
95292
95286
95279
50
49
48
47
46
15
16
17
18
19
8 30 0
29 52
29 44
29 36
29 28
3 30 0
30 8
30 16
30 24
30 32
9. 64571
64596
64622
64647
64673
9~. 64698
64724
64749
64775
64800
6
7
7
8
8
10. 35429
35404
35378
•35353
35327
9. 69298
69329
69361
69393*-
69425
8
8
9
9
10
10. 30702
30671
30639
30607
30575
10. 04727
04733
04739
04746
04752
2
2
2
2
2
9. 95273
95267
95261
95254
95248
45
44
43
42
41
20
21
22
23
24
8 29 20
29 12
29 4
28 56
28 48
3 30 40
30 48
30 56
31 4
31 12
8
9
9
10
10
10. 35302
35276
35251
35225
35200
9. 69457
69488
69520
69552
69584
11
11
12
12
13
10. 30543
30512
30480
30448
30416
10. 04758
04764
04771
04777
04783
2
2
2
2
3
9. 95242
95236
95229
95223
95217
40
39
38
37
36
25
26
27
28
29
8 28 40
28 32
28 24
28 16
28 8
3 31 20
31 28
31 36
31 44
31 52
9. 64826
64851
64877
64902
64927
11
11
11
12
12
10. 35174
35149
35123
35098
35073
9. 69615
69647
69679
69710
69742
13
14
14
15
15
10. 30385
30353
30321
30290
30258
10. 04789
04796
04802
04808
04815
3
3
3
3
3
9.95211
95204
95198
95192
95185
35
34
33
32
31
30
31
32
33
34
8 28 0
27 52
27 44
27 36
27 28
3 32 0
32 8
32 16
32 24
32 32
9. 64953
64978
65003
65029
65054
13
13
14
14
14
10. 35047
35022
34997
34971
34946
9. 69774
69805
69837
69868
69900
16
16
17
17
18
10. 30226
30195
30163
30132
30100
10. 04821
• 04827
04833
04840
04846
3
3
3
3
4
9. 95179
95173
95167
95160
95154
30
29
28
27
26
35
36
37
38
39
8 27 20
27 12
27 4
26 56
26 48
3 32 40
32 48
32 56
33 4
33 12
9. 65079
65104
65130
65155
65180
15
15
16
16
16
10. 34921
34896
34870
34845
34820
9. 69932
69963
69995
70026
70058
18
19
20
20
21
10. 30068
30037
30005
29974
29942
10. 04852
04859
04865
04871
04878
4
4
4
4
4
9. 95148
95141
95135
95129
95122
25
24
23
22
21
40
41
42
43
44
8 26 40
26 32
26 24
26 16
26 8
3 33 20
33 28
33 36
33 44
33 52
9. 65205
65230
65255
65281
65306
17
17
18
18
ia
10. 34795
34770
34745
34719
34694
9. 70089
70121
70152
70184
70215
21
22
22
23
23
10. 29911
29879
29848
29816
29785
10. 04884
04890
04897
04903
04910
4
4
4
5
5
9.95116
95110
95103
95097
95090
20
19
18
17
16
45
46
47
48
49
8 26 0
25 52
25 44
25 36
25 28
3 34 0
34 8
34 16
34 24
34 32
9. 65331
65356
65381
65406
65431
19
19
20
20
21
10. 34669
34644
34619
34594
34569
9. 70247
70278 \
70309
70341
70372
24
24
25
25
26
10. 29753
29722
29691
29659
29628
10. 04916
04922
04929
04935
04941
5
5
5
5
5
9. 95084
95078
95071
95065
95059
15
14
13
12
11
50
51
52
53
54
8 25 20
25 12
25 4
24 56
24 48
3 34 40
34 48
34 56
35 4
35 12
9. 65456
65481
65506
65531
65556
21
22
22
22
23
10. 34544
34519
34494
34469
34444
9. 70404
70435
70466
70498
70529
26
27
27
28
28
10. 29596
29565
29534
29502
29471
10. 04948
04954
04961
04967
04973
5
5
5
6
6
9. 95052
95046
95039
95033
95027
10
9
8
7
6
55
56
57
58
59
60
8 24 40
24 32
24 24
24 16
24 8
24 0
3 35 20
35 2C
35 36
35 44
35 52
36 0
9. 65580
65605
65630
65655
65680
65705
23
24
24
25
25
25
10. 34420
34395
34370
34345
34320
34295
9. 70560
70592
70623
70654
70685
70717
29
30
30
31
31
32
10. 29440
29408
29377
29346
29315
29283
10. 04980
04986
04993
04999
05005
05012
6
6
6
6
6
6
9. 95020
95014
95007
95001'
94995
94988
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant. •
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
116° A A B B C C 63°
Seconds of time
1»
29
3'
4"
5"
6*
7»
(A
3
6
10
13
16
19
22
Prop, parts of cols. < B
LC
4
1
8
2
12
2
16
3
20
24
5
28
6
TABLE 44. [Page 799
Log. Sines, Tangents, and Secants.
27° A A B B C C 152°
If.
Hour A.M.
Hour P. M.
Sine. Dili.
Cosecant.
Tangent.
Diff.
0
1
1
2
2
3
3
4
4
5
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
8 24 0
23 52
23 44
23 36
23 28
3 36 0
36 8
36 16
36 24
36 32
9. 65705
65729
65754
65779
65804
0
0
1
1
2
10. 34295
34271
34246
34221
34196
9. 70717
70748
70779
70810
70841
10. 29283
29252
29221
29190
29159
10. 05012
05018
05025
05031
05038
0
0
0
0
0
9. 94988
94982
94975
94969
94962
60
59
58
57
56
5
6
7
8
9
8 23 20
23 12
23 4
22 56
22 48
3 36 40
36 48
36 56
37 4
37 12
9. 65828
65853
65878
65902
65927
2
2
3
3
4
10. 34172
34147
34122
34098
34073
9. 70873
70904
70935
70966
70997
10. 29127
29096
29065
29034
29003
10. 05044
05051
05057
05064
05070
1
1
1
1
1
9. 94956
94949
94943
94936
94930
55
54
53
52
51
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
8 22 40
22 32
22 24
22 16
22 8
3 37 20
37 28
37 36
37 44
37 52
9. 65952
65976
66001
66025
-66050
4
4
5
5
6
10. 34048
34024
33999
33975
33950
9. 71028
71059
71090
71121
71153
5
6
6
7
7
10. 28972
28941
28910
28879
28847
10. 05077
05083
05089
05096
05102
1
1
1
1
2
9. 94923
94917
94911
94904
94898
50
49
48
47
46
8 22 0
21 52
21 44
21 36
21 28
3 38 0
38 8
38 16
38 24
38 32
(& 66075
66099
ti^l24
^661433
(joT73
6
6
7
7
8
10. 33925
33901
33876
33852
33827
9. 71184
71215
71246
71277
71308
8
8
9
9
10
10. 28816
28785
28754
28723
28692
10. 05109
05115
05122
05129
05135
2
2
2
2
2
9. 94891
94885
94878
94871
94865
45
44
43
42
41
8 21 20
21 12
21 4
20 56
20 48
3 38 40
38 48
38 56
39 4
39 12
9. 66197
66221
66246
66270
66295
8
8
9
9
10
10
11
11
11
12
10. 33803
33779
33754
33730
33705
9. 71339
71370
71401
71431
71462
10
11
11
12
12
10. 28661
28630
28599
28569
28538
10. 05142
05148
05155
05161
05168
2
2
2
3
3
9.94858
94852
94845
94839
94832
40
39
38
37
36
25
26
27
28
29
8 20 40
20 32
20 24
20 16
20 8
3 39 20
39 28
39 36
39 44
39 52
9. 66319
66343
66368
66392
66416
10. 33681
33657
33632
33608
33584
9. 71493
71524
71555
71586
71617
13
13
14
14
15
10. 28507
28476
28445
28414
28383
10. 05174
05181
05187
05194
05201
3
3
3
3
3
9. 94826
94819
94813
94806
94799
35
34
33
32
31
30
31
32
33
34
35
36
37
38
39
8 20 0
19 52
19 44
19 36
19 28
3 40 0
40 8
40 16
40 24
40 32
9.66441
66465
66489
66513
66537
12
13
13
13
14
10. 33559
33535
33511
33487
33463
9. 71648
71679
71709
71740
71771
15
16
16
17
17
10. 28352
28321
28291
28260
28229
10. 05207
05214
05220
05227
05233
3
3
4
4
4
9. 94793
94786
94780
94773
94767
30
29
28
27
26
8 19 20
19 12
19 4
18 56
18 48
3 40 40
40 48
40 56
41 4
41 12
9. 66562
66586
66610
66634
66658
14
15
15
15
16
10. 33438
33414
33390
33366
33342
9. 71802
71833
71863
71894
71925
18
19
19
20
20
10. 28198
28167
28137
28106
28075
10. 05240
05247
05253
05260
05266
4
4
4
4
4
9. 94760
94753
94747
94740
94734
25
24
23
22
21
40
41
42
43
44
8 18 40
18 32
18 24
18 16
18 8
3 41 20
41 28
41 36
41 44
41 52
9. 66682
66706
66731
66755
66779
16
17
17
17
18
10. 33318
33294
33269
33245
33221
9. 71955
71986
72017
72048
72078
21
21
22
22
23
10. 28045
28014
27983
27952
27922
LO. 05273
05280
05286
05293
05300
4
4
5
5
5
9. 94727
94720
94714
94707
94700
20
19
18
17
16
45
46
47
48
49
$ 18 0
17 52
17 44
17 36
17 28
3 42 0
42 8
42 16
42 24
42 32
9. 66803
66827
66851
66875
66899
18
19
19
19
20
10. 33197
33173
33149
33125
33101
9. 72109
72140
72170
72201
72231
23
24
24
25
25
10. 27891
27860
27830
27799
27769
10. 05306
05313
05320
05326
05333
5
5
5
5
5
9. 94694
94687
94680
94674
94667
15
14
13
12
11
50
51
52
53
54
8 17 20
17 12
17 4
16 56
16 48
3 42 40
42 48
42 56
43 4
43 12
9. 66922
66946
66970
66994
67018
20
21
21
21
22
10. 33078
33054
33030
33006
32982
9. 72262
72293
72323
72354
72384
26
26
27
27
28
28
29
29
30
30
31
10. 27738
27707
27677
27646
27616
10. 05340
05346
05353
05360
05366
5
6
6
6
6
9. 94660
94654
94647
94640
94634
10
9
8
7
6
55
56
57
58
59
60
M.
8 16 40
16 32
16 24
16 16
16 8
16 0
3 43 20
43 28
43 36
43 44
43 52
44 0
9. 67042
67066
67090
67113
67137
67161
22
23
23
23
24
24
10. 32958
32934
32910
32887
32863
32839
9. 72415
72445
72476
72506
72537
72567
10. 27585
27555
27524
27494
27463
27433
10. 05373
05380
05386
05393
05400
05407
6
6
6
6
6
7
9. 94627
94620
94614
94607
94600
94593
5
4
3
2
1
0
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
117° A A B B C C 62°
Seconds of time
I3
•>> 3' 4'
5*
G3
7s I
fA
Prop, parts of cols. {B
C
!
6 9 12
8 i 12 1 15
21 21 3
15
19
4
18
23
5
21
27
6
Page 800] TABLE 44.
Log. Sines, Tangents, and Secants.
28° A A B B C C 161°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
8 16 0
15 52
15 44
15 36
15 28
3 44 0
44 8
44 16
44 24
44 32
9. 67161
67185
67208
67232
67256
0
0
1
1
2
10. 32839
32815
32792
32768
32744
9. 72567
72598
72628
72659
72689
0
1
1
2
2
10. 27433
27402
27372
27341
27311
10. 05407
05413
05420
05427
05433
0
0
0
0
0
9.94593
94587
94580
94573
94567
60
59
58
57
56
5
6
7
8
9
8 15 20
15 12
15 4
14 56
14 48
3 44 40
44 48
44 56
45 4
45 12
9. 67280
67303
67327
67350
67374
2
2
3
3
3
10. 32720
32697
32673
32650
32626
9. 72720
72750
72780
72811
72841
3
3
4
4
5
10. 27280
27250
27220
27189
27159
10. 05440
05447
05454
05460
05467
1
1
1
1
1
9. 94560
94553
94546
94540
94533
55
54
53
52
51
10
11
12
13
14
8 14 40
14 32
14 24
14 16
14 8
3 45 20
45 28
45 36
45 44
45 52
9. 67398
67421
67445
67468
67492
4
4
5
5
5
10. 32602
32579
32555
32532
32508
9. 72872
72902
72932
72963
72993
5
6
6
7
7
10. 27128
27098
27068
27037
27007
10. 05474
05481
05487
05494
05501
1
1
1
1
2
9. 94526
94519
94513
94506
94499
50
49
48
47
46
15
16
17
18
19
8 14 0
13 52
13 44
13 36
13 28
3 46 0
46 8
46 16
46 24
46 32
9. 67515
67539
67562
67586
67609
6
6
7
7
7
10. 32485
32461
32438
32414
32391
9. 73023
73054
73084
73114
73144
8
8
9
9
10
10. 26977
26946
26916
26886
26856
10. 05508
05515
05521
05528
05535
2
2
2
2
2
9. 94492
94485
94479
94472
94465
45
44
43
42
41
20
21
22
2T
24
8 13 20
13 12
13 4
12 56
12 48
3 46 40
46 48
46 56
47 4
47 12
9. 67633
67656
67680
67703
67726
8
8
9
9
9
10. 32367
32344
32320
32297
32274
9. 73175
73205
73235
73265
73295
10
11
11
12
12
10. 26825
26795
26765
26735
26705
10. 05542
05549
05555
05562
05569
2
2
3
3
3
9. 94458
94451
94445
94438
94431
40
39
38
37
36
25
26
27
28
29
~30~
31
32
33
34
8 12 40
12 32
12 24
12 16
12 8
3 47 20
47 28
47 36
47 44
47 52
9. 67750
67773
67796
67820
67843
10
10
10
11
11
10. 32250
32227
32204
32180
32157
9.73326
73356
73386
73416
73446
13
13
14
14
15
10. 26674
26644
26614
26584
26554
10. 05576
05583
05590
05596
05603
3
3
3
3
3
9. 94424
94417
94410
94404
94397
35
34
33
32
31
8 12 0
11 52
11 44
11 36
11 28
3 48 0
48 8
48 16
48 24
48 32
'9. 67866
67890
67913
67936
67959
12
12
12
13
13
10. 32134
32110
32087
32064
32041
9. 73476
73507
73£37
73567
73597
15
16
16
17
17
10. 26524
26493
26463
26433
26403
10. 05610
05617
Q5S24
1)5631
05638
3
4
4
4
4
9. 94390
94383
94376
94369
94362
30
29
28
27
26
35
36
37
38
39
8 11 20
11 12
11 4
10 56
10 48
3 48 40
48 48
48 56
49 4
49 12
9. 67982
68006
68029
68052
68075
14
14
14
15
15
10. 32018
31994
31971
31948
31925
9. 73627
73657
73687
73717
73747
18
18
19
19
20
10. 26373
26343
26313
26283
26253
10. 05645
05651
05658
05665
05672
4
4
4
4
4
9. 94355
94349
94342
94335
94328
25
24
23
22
21
40
41
42
43
44
45
46
47
48
49
8 10 40
10 32
10 24
10 16
10 8
3 49 20
49 28
49 36
49 44
49 52
9. 68098
68121
68144
68167
68190
16
16
16
17
17
10. 31902
31879
31856
31833
31810
9. 73777
73807
73837
73867
73897
20
21
21
22
22
10. 26223
26193
26163
26133
26103
10. 05679
05686
05693
05700
05707
5
5
5
5
5
9. 94321
94314
94307
94300
94293
20
19
18
17
16
8 10 0
9 52
9 44
9 36
9 28
3 50 0
50 8
50 16
50 24
50 32
9. 68213
68237
68260
68283
68305
17
18
18
19
19
10. 31787
31763
31740
31717
31695
9. 73927
73957
73987
74017
74047
23
23
24
24
25
25
26
26
27
27
10. 26073
26043
26013
25983
25953
10. 05714
. 05721
05727
05734
05741
5
5
5
5
6
9. 94286
94279
94273
94266
94259
15
14
13
12
11
50
51
52
53
54
8 9 20
9 12
9 4
8 56
8 48
3 50 40
50 48
50 56
51 4
51 12
9. 68328
68351
68374
68397
68420
19
20
20
21
21
10.31672
31649
31626
31603
31580
9. 74077
74107
74137
74166
74196
10. 25923
25893
25863
25834
25804
10. 05748
05755
05762
05769
05776
10. 05783
05790
05797
05804
05811
05818
6
6
6
6
6
9. 94252
94245
94238
94231
94224
10
9
8
7
6-
55
56
57
58
59
60
8 8 40
8 32
8 24-
8 16
8 8
8 0
3 51 20
51 28
51 36
51 44
51 52
52 0
9. 68443
68466
68489
68512
68534
68557
21
22
22
22
23
23
10. 31557
31534
31511
31488
31466
31443
9. 74226
74256
74286
74316
74345
74375
28
28
29
29
30
30
10. 25774
25744
25714
25684
25655
25625
6
6
7
7
7
7
9. 94217
94210
94203
94196
94189
94182
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M
118° A A B B C C 61°
Seconds of time
1"
P
3*
4*
5"
6»
7»
fA
3
6
9
12
15
17
20
Prop, parts of cols. •( B
4
8
11
15
19
23
26
1C
1
2
8
3
4
5
6
TABLE 44. [Page 801
Log. Sines, Tangents, and Secants.
29° A A B B C C 150°
M.
Hour A. M. i Hour p. M.
i
Sine. I Diff.
1
Cosecant.
Tangent.
Diff.
0
0
1
1
2
Cotangent
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
880
7 52
7 44
7 36
7 28
3 52 0
52 8
52 16
52 24
52 32
9. 6S557
68580
68603
68625
68648
0
0
1
1
10. 31443
31420
31397
31375
31352
9. 74375
74405
74435
74465
74494
10. 25625
25595
25565
25535
25506
10. 05818
05825
05832
05839
05846
0
0
0
0
0
9. 94182
94175
94168
94161
94154
60
59
58
57
56
5
6
7
8
9
8 7 20
7 12
7 4
6 56
6 48
3 52 40
52 48
52 56
53 4
53 12
9. 68671
68694
68716
68739
68762
2
2
3
3
3
10. 31329
31306
31284
31261
31238
9. 74524
74554
74583
74613
74643
2
3
3
4
4
10. 25476
25446
25417
25387
25357
10. 05853
05860
05867
05874
05881
1
1
1
1
1
9. 94147
94140
94133
94126
94119
55
54
53
52
51
10
11
12
13
14
15
16
17
18
19
8 6 40
6 32
6 24
6 16
6 8
3 53 20
53 28
53 36
53 44
53 52
9. 68784
68807
68829
68852
68875
4
4
4
5
5
10. 31216
31193
31171
31148
31125
9. 74673
74702
74732
74762
74791
5
5
6
6
7
7
8
8
9
9
10. 25327
25298
25268
25238
25209
10. 05888
05895
05902
05910
05917
1
1
1
2
2
2
2
2
2
2
9. 94112
94105
94098
94090
94083
9. 94076
94069
94062
94055
94048
50
49
48
47
46
45
44
43
42
41
860
5 52
5 44
5 36
5 28
3 54 0
54 8
54 16
54 24
54 32
9. 68897
68920
68942
68965
68987
1 6
6
6
7
7
10. 31103
31080
31058
31035
31013
9. 74821
74851
74880
74910
74939
10. 25179
25149
25120
25090
25061
10. 05924
05931
05938
05945
05952
20
21
22
23
24
8 5 20
5 12
5 4
4 56
4 48
3 54 40
54 48
54 56
55 4
55 12
9. 69010
69032
69055
69077
69100
7
8
8
9
9
10. 30990
30968
30945
30923
30900
9. 74969
74998
7502S
75058
75087
10
10
11
11
12
10.25031
25002
24972
24942
24913
10. 05959
05966
05973
05980
05988
2
3
3
3
3
9. 94041
94034
94027
94020
94012
-40
39
38
37
36
25
26
27
28
29
8 4 40
4 32
4 24
4 16
4 8
3 55 20
55 28
55 36
55 44
55 52
9. 69122
69144
69167
69189
69212
9
10
10
10
11
10. 30878
30856
30833
30811
30788
9. 75117
75146
75176
75205
75235
12
13
13
14
14
15
15
16
16
17
10. 24883
24854
24824
24795
24765
10. 05995
06002
06009
06016
06023
3
3
3
3
3
9. 94005
93998
93991
93984
93977
35
34
33
32
31
30
29
28
27
26
30
31
32
33
34
840
3 52
3 44
3 36
3 28
3 56 0
56 8
56 16
56 24
56 32
9. 69234
69256
69279
69301
69323
11
12
12
12
13
10. 30766
30744
30721
30699
30677
9. 75264
75294
75323
75353
75382
10. 24736
24706
24677
24647
24618
10. 06030
06037
06045
06052
06059
,4
4
4
4
4
4
4
4
5
5
9. 93970
93963
93955
93948
93941
35
36
37
38
39
40
41
42
~rr
44
8 3 20
3 12
3 4
2 56
2 48
3 56 40
56 48
56 56
57 4
57 12
9. 69345
69368
69390
69412
69434
13
13
14
14
15
15
15
16
16
16
10. 30655
30632
30610
30588
30566
9. 75411
75441
75470
75500
75529
17
18
18
19
19
10. 24589
24559
24530
24500
24471
10. 06066
06073
06080
06088
06095
9. 93934
93927
93920
93912
93905
25
24
23
22
21
20
19
18
17
16
8 2 40
2 32
2 24
2 16
2 8
3 57 20
57 28
57 36
57 44
57 52
9. 69456
69479
69501
69523
69545
10. 30544
30521
' 30499
30477
30455
9. 75558
75588
75617
75647
75676
20
20
21
21
22
10. 24442
24412
24383
24353
24324
10. 06102
06109
961 lfi_
06124
06131
5
5
5
5
5
9. 93898
93891
93884
93876
93869
45
46
47
48
49
820
1 52
1 44
1 36
1 28
3 58 0
58 8
58 16
58 24
58 32
9. 69567
69589
69611
69633
69655
17
17
17
18
18
10. 30433
30411
30389
30367
30345
9. 75705
75735
75764
75793
75822
22
23
23
24
24
10. 24295
24265
24236
24207
24178
10. 06138
06145
06153
06160
06167
5
5
6
6
6
9. 93862
93855
93847
93840
93833
15
14
13
12
11
50
51
52
53
54
8 1 20
1 12
1 4
0 56
0 48
3 58 40
58 48
58 56
59 4
59 12
9. 69677
69699
69721
69743
69765
19
19
19
20
20
10. 30323
30301
30279
30257
30235
9. 75852
75881
75910
75939
75969
25
25
26
26
27
10. 24148
24119
24090
24061
24031
10.06174
06181
06189
06196
06203
6
6
6
6
6
9. 93826
93819
93811
93804
93797
10
9
8
7
6
55
56
57
58
59
60
8 0 40
0 32
0 24
0 16
0 8
0 0
3 59 20
59 28
59 36
59 44
59 52
400
9. 69787
69809
69831
69853
69875
69897
20
21
21
22
22
22
10. 30213
30191
30169.
30147
30125
30103
9. 75998
76027
76056
76086
76115
76144
27
28
28
29
29
29
10. 24002
23973
23944
23914
23885
23856
10. 06211
06218
06225
06232
06240
06247
7
7
7
7
7
7
9. 93789
93782"
93775
93768
93760
93753
5
4,
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
119° A A B B C C 00°
"^ t' \
Seconds of time
tf
•>s
8*
43
o» i 6*
7'
{A
B
c
3
4
1
6
7
8
11
o
11
15
4
14 17
18 ! 22
4 | 5
20
26
6
Page 802] TABLE 4A.
Log. Sines, Tangents, and Secants.
80° A A B B C C 149°
M.
0
1
2
3
4
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
800
7 59 52
59 44
59 36
59 28
400
0 8
0 16
0 24
0 32
9. 69897
69919
69941
69963
69984
0
0
1
1
1
10. 30103
30081
30059
30037
30016
9. 76144
76173
76202
76231
76261
0
0
1
1
2
10. 23856
23827
23798
23769
23739
1Q. 06247
06254
06262
06269
06276
0
0
0
0
0
9. 93753
93746
93738
93731
93724
60
59
58
57
56
5
6
7
8
9
7 59 20
59 12
59 4
58 56
58 48
4 0 40
0 48
0 56
1 4
1 12
9. 70006
70028
70050
70072
70093
2
2
3
3
3
10. 29994
29972
29950
29928
29907
9. 76290
76319
76348
76377
76406
2
3
3
4
4
10. 23710
23681
23652
23623
23594
10. 06283
06291
06298
06305
06313
1
1
1
1
1
9. 93717
93709
93702
93695
93687
55
54
53
52
51
10
11
12
13
14
7 58 40
58 32
58 24
58 16
58 8
4 1 20
1 28
1 36
1 44
1 52
9. 70115
70137
70159
70180
70202
4
4
4
5
5
10. 29885
29863
29841
29820
29798
9. 76435
76464
76493
76522
76551
5
5
6
6
7
10. 23565
23536
23507
23478
23449
10. 06320
06327
06335
06342
06350
1
1
1
2
2
9. 93680
93673
93665
93658
93650
50
49
48
47
46
15
16
17
18.
19
7 58 0
57 52
57 44
57 36
57 28
420
2 8
2 16
2 24
2 32
9. 70224
70245
70267
70288
70310
5
6
6
6
7
7
8
8
8
9
10. 29776
29755
29733
29712
29690
9. 76580
76609
76639
76668
76697
7
8
8
9
9
10. 23420
23391
23361
23332
23303
10. 06357
06364
06372
06379,.
06386
2
2
2
2
~2~
3
3
3
3
9. 93643
93636
93628
93821
93614
45
44
43
42
41
20
21
22
23
24
7 57 20
57 12
57 4
56 56
56 48
4 2 40
2 48
2 56
3 4
3 12
9. 70332
70353
70375
70396
70418
10. 29668
29647
29625
29604
29582
9. 76725
76754
76783
76812
76841
10
10
11
11
12
10. 23275
23246
23217
23188
23159
10. 06394
06401
06409
06416
06423
9. 93606
93599
93591
93584
93577
40
39
38
37
36
25
26
27
28
29
7 56 40
56 32
56 24
56 16
56 8
4 3 20
3 28
3 36
3 44
3 52
9. 70439
70461
70482
70504
70525
9
9
10
10
10
10. 29561
29539
29518
29496
29475
9. 76870
76899
76928
76957
76986
12
13
13
13
14
10. 23130
23101
23072
23043
23014
10. 06431
06438"
06446
06453
06461
3
3
3
3
4
4
4
4
4
4
9. 93569
93562
93554
93547
93539
35
34
33
32
31
30
31
32
33
34
7 56 0
55 52
55 44
55 36
55 28
440
4 8
4 16
4 24
4 32
9. 70547
70568
70590
70611
70633
11
11
11
12
12
10. 29453
29432
29410
29389
29367
9. 77015
77044
77073
77101
77130
14
15
15
16
16
10. 22985
22956
22927
22899
22870
10. 06468
06475
06483
06490
06498
9. 93532
93525
93517
93510
93502
30
29
28
27
26
35
36
37
38
39
7 55 20
55 12
55 4
54 56
54 48
4 4 40
4 48
4 56
5 4
5 12
9. 70654
70675
70697
70718
70739
13
13
13
14
14
10. 29346
29325
29303
29282
29261
10. 29239
29218
29197
29176
29154
9.77159
77188
77217
77246
77274
17
17
18
18
19
10. 22841
22812
22783
22754
22726
10. 06505
06513
06520
06528
06535
4
4
5
5
5
~5"
5
5
5
5
9. 93495
93487
93480
93472
93465
25
24
23
22
21
40
41
42
43
44
7 54 40
54 32
54 24
54 16
54 8
4 5 20
5 28
5 36
5 44
5 52
9. 70761
70782
70803
70824
70846
14
15
15
15
16
9. 77303
77332
77361
77390
77418
19.
20
20
21
21 H
10. 22697
22668
22639
22610
22582
10. 06543
06550
06558
06565
06573
9. 93457
93450
93442
93435
93427
20
19
18
17
16
45
46
47
48
49
7 54 0
53 52
53 44
53 36
53 28
460
6 8
6 16
6 24
6 32
9. 70867
70888
70909
70931
70952
16
16
17
17
18
10. 29133
29112
29091
29069
29048
9. 77447
77476
77505
77533
77562
22
22
23
23
24
10. 22553
22524
22495
22467
22438
10. 06580
06588
06595
06603
06610
6
6
6
6
6
9. 93420
93412
93405
93397
93390
15
14
13
12
11
10
9
8
7
6
50
51
52
53
54
7 53 20
53 12
53 4
52 56
52 48
4 6 40
6 48
6 56
7 4
7 12
9. 70973
70994
71015
71036
71058
18
18
19
19
19
10. 29027
29006
28985
28964
28942
9. 77591
77619
77648
77677
77706
24
25
25
26
26
10. 22409
22381
22352
22323
22294
10. 06618
06625
06633
06640
06648
6
6
6
7
7
9. 93382
95375
93367
93360
93352
55
56
57
58
59
60
7 52 40
52 32
52 24
52 16
52 8
52 0
4 7 20
7 28
7 36
7 44
7 52
8 0
9. 71079
71100
71121
71142
71163
71184
20
20
20
21
21
21
10. 28921
28900
28879
28858
28837
28816
9. 77734
77763
77791
77820
77849
77877
26
27
27
28
28
29
10. 22266
22237
22209
22180
22151
22123
10. 06656
06663
06671
06678
06686
06693
7
7
7
7
7
7
9. 93344
93337
93329
93322
93314
93307
5
4
3
2
1
0
M.
Hour P. M,
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
120° A A B B C C 69°
Seconds of time
I8
2s
3s
4s
5'
6*
7"
(A
3
5
8
11
13
16
19
Prop, parts of cols.-{B
1C
4
1
7
2
11
3
14
4
18
5
22
6
25
7
TABLE 44. [Page 803
Log. Sines, Tangents, and Secants.
81« A A B B C C 148°
M.
Hour A.M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
I Diff.
0
0
1
1
2
Cotangent
Secant.
Din.
Cosine.
M.
0
1
2
3
4
7 52 0
51 52
51 44
51 36
51 28
480
8 8
8 16
8 24
8 32
9. 71184
71205
71226
71247
71268
0
0
1
1
1
10. 28816
28795
28774
28753
28732
9. 77877
77906
77935
77963
77992
10. 22123
22094
22065
22037
22008
10. 06693
06701
06709
06716
06724
0
0
0
0
1
9. 93307
93299
93291
93284
93276
60
59
58
57
56
5
6
7
8
9
7 51 20
51 12
51 4
50 56
50 48
4 8 40
8 48
8 56
9 4
9 12
9. 71289
71310
71331
71352
71373
2
2
2
3
3
10. 28711
28690
28669
28648
28627
9. 78020
78049
78077
78106
78135
2
3
3
4
4
10. 21980
21951
21923
21894
21865
10. 06731
06739
06747
06754
06762
1
1
1
1
1
9. 93269
93261
93253
93246
93238
55
54
53
52
61
10
11
12
13
14
7 50 40
50 32
50 24
50 16
50 8
4 9 20
9 28
9 36
9 44
9 52
9. 71393
71414
71435
71456
71477
3
4
4
4
5
10. 28607
28586
28565
28544
28523
9. 78163
78192
78220
78249
78277
5
5
6
6
7
10. 21837
21808
21780
21751
21723
10. 06770
06777
06785
06793
06800
1
1
2
9
2
9. 93230
93223
93215
93207
93200
50
49
48
47
46
15
16
17
18
19
7 50 0
49 52
49 44
49 36
49 28
4 10 0
10 8
10 16
10 24
10 32
9. 71498
71519
71539
71560
71581
5
5
6
6
7
10. 28502
28481
28461
28440
28419
9. 78306
78334
78363
78391
78419
7
8
8
9
9
10. 21694,
21666
21637
21609
21581
10. 06808
06816
06823
06831
06839
2
2
9
2
2
9. 93192
93184
93177
93169
93161
45
44
43
42
41
20
21
22
23
24
7 49 20
49 12
49 4
48 56
48 48
4 10 40
10 48
10 56
11 4
11 12
9. 71602
71622
71643
71664
71685
rj
j
8
8
8
10. 28398
28378
28357
28336
28315
9.78448
78476
78505
78533
78562
Q
10
10
11
11
10. 21552
21524
21495
21467
21438
10. 06846
06854
06862
06869
06877
3
3
3
3
3
9. 93154
93146
93138
93131
93123
40
39
38
37
36
25
26
27
28
29
7 48 40
48 32
48 24
48 16
48 8
4 11 20
11 28
11 36
11 44
11 52
9. 71705
71726
71747
71767
71788
9
9
9
10
10
10. 28295
28274
28253
28233
28212
9. 78590
78618
78647
78675
78704
12
12
13
13
14
10. 21410
21382
21353
21325
21296
10. 06885
06892
06900
06908
06916
3
3
3
4
4
9.93115
93108
93100
93092
93084
35
34
33
32
31
30
31
32
33
34
7 48 0
47 52
47 44
47 36
47 28
4 12 0
12 8
12 16
12 24
12 32
9. 71809
71829
71850
71870
71891
10
11
11
11
12
10. 28191
28171
28150
28130
28109
9. 78732
78760
78789
78817
78845
14
15
15
16
16
10. 21268
21240
21211
21183
21155
10. 06923
06931
06939
06947
06954
4
4
4
4
4
9. 93077
93069
93001
93053
93046
30
29
28
27
26
25
24
23
22
21
35
36
37
38
39
7 47 20
47 12
47 4
46 56
46 48
4 12 40
12 48
12 56
13 4
13 12
9. 71911
71932
71952
71973
71994
12
12
13
13
13
10. 28089
28068
28048
28027
28006
9. 78874
78902
78930
78959
78987
17
1*7
17
18
18
10. 21126
21098
21070
21041
21013
10. 06962
06970
06978
06986
06993
5
5
5
5
5
9. 93038
93030
93022
93014
93007
40
41
42
43
44
7 46 40
46 32
46 24
46 16
46 8
4 13 20
13 28
13 36
13 44
13 52
9. 72014
72034
72055
72075
72096
14
14
14
15
15
10. 27986
27966
27945
27925
27904
9. 79015
79043
79072
79100
79128
19 10.20985
19 20957
20 20928
20 20900
21 20872
10. 07001
07009
07017
07024
' 07032
5
5
5
6
6
9. 92999
92991
92983
92976
92968
20
19
18
17
16
45
46
47
48
49
7 46 0
45 52
45 44
45 36
45 28
4 14 0
14 8
14 16
14 24
14 32
9. 72116
72137
72157
72177
72198
15
16
16
16
17
10. 27884
27863
27843
27823
27802
9. 79156
79185
79213
79241
79269
21
22
22
23
23
24
24
25
25
26
10. 20844
20815
20787
20759
20731
10. 07040
07048
07056
07064
07071
6
6
6
6
6
9. 92960
92952
92944
92936
92929
15
14
13
12
11
50
51
52
53
54
7 45 20
45 12
45 4
44 56
44 48
4 14 40
14 48
14 56
15 4
15 12
9. 72218
72238
72259
72279
72299
17
18
18
18
19
10. 27782
27762
27741
27721
27701
9. 79297
79326
79354
79382
79410
10. 20703
20674
20646
20618
20590
10. 07079
07087
07095
07103
07111
6
7
7
7
7
9. 92921
92913
92905
92897
92889
10
9
8
i
6
55
56
57
58
59
60
7 44 40
44 32
44 24
44 16
44 8
44 0
4 15 20
15 28
15 36
15 44
15 52
16 0
9. 72320
72340
72360
72381
72401
72421
19
19
20
20
20
21
10. 27680
27660
27640
27619
27599
27579
9. 79438
79466
79495
79523
79551
79579
26
26
27
27
28
28
10. 20562
20477
20449
20421
10. 07119
07126
07134
07142
07150
07158
7
7
7
7
8
8
9. 92881
92874
92866
92858
92850
92842
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
121° A A B B C C 6$P
fA
3
5
8
10
13
15
18
Prop, parts of cols. ! B
1C
4
1
7
2
11
3
14
4
18
5
21
6
25
Page 804]
32°
TABLE 44.
Log. Sines, Tangents, and Secants.
A A B B C C 147°
M.
Hour A. M.
Hour P. M.
Sine.
Difif.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
7 44 0
43 52
43 44
43 36
43 28
4-lffO
16 8
16 16
16 24
16 32
9. 72421
72441
72461
72482
72502
0
0
1
1
1
10. 27579
27559
27539
27518
27498
9. 79579
79607
79635
79663
79691
0
0
1
1
2
10. 20421
20393
20365
20337
20309
10. 07158
07166
07174
07182
07190
0
0
0
0
1
9. 92842
92834
92826
92818
92810
60
59
58
57
56
55
54
53
52
51
5
6
7
8
9
10
11
12
13
14
7 43 20
43 12
43 4
42 56
42 48
4 16 40
16 48
16 56
17 4
17 12
9. 72522
72542
72562
72582
72602
2
2
2
3
3
10. 27478
27458
27438
27418
27398
9. 79719
79747
79776
79804
79832
2
3
3
4
4
10. 20281
20253
20224
20196
20168
10. 07197
07205
07213
07221
07229
1
1
1
1
1
9. 92803
92795
92787
92779
92771
7 42 40
42 32
42 24
42 16
42 8
4 17 20
17 28
17 36
17 44
17 52
9. 72622
72643
72663
72683
72703
3
4
4
4
5
10. 27378
27357
27337
27317
27297
9. 79860
79888
79916
79944
79972
5
5
6
6
7
10. 20140
20112
20084
20056
20028
10. 07237
07245
07253
07261
07269
1
1
2
2,
2
2
2
2
2
3
9. 92763
92755
92747
92739
92731
50
49
48
47
46
45
44
43
42
41
15
16
17
18
19
20
21
22
23
24
7 42 0
41 52
41 44
41 36
41 28
4 18 0
18 8
18 16
18 24
18 32
9. 72723
72743
72763
72783
72803
5
5
6
6
6
10. 27277
27257
27237
27217
27197
9. 80000
80028
80056
80084
80112
7
7
8
8
9
10. 20000
19972
19944
19916
19888
10. 07277
07285
07293
07301
07309
9. 92723
92715
92707
92699
92691
7 41 20
41 12
41 4
40 56
40 48
4 18 40
18 48
18 56
19 4
19 12
9. 72823
72843
72863
72883
72902
7
7
7
8
8
10. 27177
27157
27137
27117
27098
9. 80140
80168
80195
80223
80251
9
10
10
11
11
10. 19860
19832
19805
19777
19749
10. 07317
07325
07333
07341
07349
3
3
3
3
3
9. 92683
92675
92667
92659
92651
40
39
38
37
36
25
26
'27
28
29
7 40 40
40 32
40 24
40 16
40 8
4 19 20
19 28
19 36
19 44
19 52
9. 72922
72942
72962
72982
73002
8
9
9
9
10
10. 27078
27058
27038
27018
26998
9. 80279
80307
80335
80363
80391
12
12
13
13
13
10. 19721
19693
19665
19637
19609
10. 07357
07365
07373
07381
07389
3
3
4
4
4
9. 92643
92635
92627
92619
92611
35
34
33
32
31
30
31
32
33
34'
7 40 0
39 52
39 44
39 36
39 28
4 20 0
20 8
20 16
20 24
20 32
9. 73022
73041
73061
73081
73101
10
10
11
11
11
10. 26978
26959
26939
26919
26899
9. 80419
80447
80474
80502
80530
14
14
15
15
16
10. 19581
19553
19526
19498
19470
10. 07397
07405
07413
07421
07429
4
4
4
4
5
9. 92603
92595
92587
92579
92571
30
29
28
27
26
35
36
37
38
39
7 39 20
39 12
39 4
38 56
38 48
4 20 40
20 48
20 56
21 4
21 12
9. 73121
73140
73160
73180
73200
12
12
12
13
13
10. 26879
26860
26840
26820
26800
9. 80558
80586
80614
80642
80669
16
17
17
18
18
10. 19442
19414
19386
19358
19331
10. 07437
07445
07454
07462
07470
5
5
5
5
5
9. 92563
92555
92546
92538
92530
25
24
23
22
21
40
41
42
43
44
7 38 40
38 32
38 24
38 16
38 8
4 21 20
21 28
21 36
21 44
21 52
9. 73219
73239
73259
73278
73298
13
14
14
14
15
10. 26781
26761
26741
26722
26702
9. 80697
80725
80753
80781
80808
19
19
20
20
20
10. 19303
19275
19247
19219
19192
10. 07478
07486
07494
07502
07510
5
6
6
6
6
9. 92522
92514
92506
92498
92490
20
19
18
17
16
45
46
47
48
49
7 38 0
37 52
37 44
37 36
37 28
4 22 0
22 8
22 16
22 24
22 32
9. 73318
73337
73357
73377
73396
15
15
16
16
16
10. 26682
26663
26643
26623
26604
9. 80836
80864
80892
80919
80947
21
21
22
22
23
23
24
24
25
25
10. 19164
19136
19108
19081
19053
10. 07518
07527
07535
07543
07551
6
6
6
6
7-
9. 92482
9"2473
92465
92457
92449
15
14
13
12
11
50
51
52
53
54
7 37 20
37 12
37 4
36 56
36 48
4 22 40
22 48
22 56
23 4
23 12
9. 73416
73435
73455
73474
73494
17
17
17
18
18
10. 26584
26565
26545
26526
26506
9. 80975
81003
81030
81058
81086
10. 19025
18997
18970
18942
18914
10. 07559
07567
07575
07584
07592
7
7
7
7
7
9. 92441
92433
92425
92416
92408
10
9
8
7
6
55
56
57
58
59
60
7 36 40
36 32
36 24
36 16
36 8
36 0
4 23 20
23 28
23 36
23 44
23 52
24 0
9. 73513
73533
73552
73572
73591
73611
18
19
19
19
20
20
10. 26487
26467
26448
26428
26409
26389
9. 81113
81141
81169
81196
81224
81252
26
-26
26
27
27
28
10. 18887
18859
18831
18804
18776
18748
10. 07600
07608
07616
07624
07633
07641
7
8
8
8
8
8
9. 92400
92392
92384
92376
92367
92359
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
122° A A B B C C 57°
Seconds of time
is
29
3"
4"
5"
6'
7s
{A
2
5
7
10
12
15
17
B
3
1
7
2
10
3
14
4
17
5
21
6
24
7
TABLE 44. [Page 805
Log. Sines, Tangents, and Secanta.
83° A A B B C C 146°
1C.
Hour A.M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
7 36 0
35 52
35 44
35 36
35 28
4 24 0
24 8
24 16
24 24
24 32
9. 73611
73630
73650
73669
73689
0
0
1
1
1
10. 26389
26370
26350
26331
26311
9. 81252
81279
81307
81335
81362
0
0
1
1
2
10. 18748
18721
18693
18665
18638
10. 07641
07649
07657
07665
07674
0
0
0
0
1
9. 92359
92351
92343
92335
92326
60
59
58
57
56
55
54
53
52
51
0
6
7
8
9
7 35 20
35 12
35 4
34 56
34 48
4 24 40
24 48
24 56
25 4
25 12
9. 73708
73727
73747
73766-
737S5
2
2
2
3
3
10. 26292
26273
26253
26234
26215
9. 81390
81418
81445
81473
81500
2
3
3
4
4
10. 18610
18582
18555
18527
18500
10. 07682
07690
07698 •
07707
07715
1
1
1
1
1
9. 92318
92310
92302
92293
92285
10
11
12
13
14
7 34 40
34 32
34 24
34 16
34 8
4 25 20
25 28
25 36
25 44
25 52
9. 73805
73824
73843
73863
73882
a
3
4
4
4
10. 26195
26176
26157
26137
26118
9. 81528
81556
81583
81611
81638
5
5
5
6
6
10. 18472
18444
18417
18389
18362
10. 07723
07731
07740
07748
07756
1
2
2
2
2
9. 92277
92269
92260
92252
92244
50
49
48
47
46
15
16
17
18
19
7 34 0
33 52
33 44
33 36
33 28
4 26 0
26 8
26 16
26 24
26 32
9. 73901
73921
73940
73959
73978
5
5
5
6
6
10. 26099
26079
26060
26041
26022
9. 81666
81693
81721
81748
81776
7
7
8
8
9
10. 18334
18307
18279
18252
18224
10. 07765
07773
07781
07789
07798
2
2
2
3
3
9.92235
92227
92219
92211
92202
45
44
43
42
41
20
21
22
23
24
7 33 20
33 12
33 4
32 56
32 48
4 26 40
26 48
26 56
27 4
27 12
9. 73997
74017
74036
74055
74074
6
7
7
7
8
10. 26003
25983
25964
25945
25926
9. 81803
81831
81858
81886
81913
9
10
10
11
11
10. 18197
18169
18142
18114
18087
10. 07806
07814
07823
07831
07839
3
3
3
3
3
9. 92194
92186
92177
92169
92161
40
39
38
37
36
25
26
27
28
29
7 32 40
32 32
32 24
32 16
32 8
4 27 20
27 28
27 36
27 44
27 52
9. 74093
74113
74132
74151
74170
8
8
9
9
9
10. 25907
25887
25868
25849
25830
9. 81941
81968
81996
82023
82051
11
12
12
13
13
14
14
15
15
16
10. 18059
18032
18004
17977
17949
10. 07848
07856
07864
07873
07881
3
4
4
4
4
9. 92152
92144
92136
92127
92119
35
34
33
32
31
30
31
32
33
34
7 32 0
31 52
31 44
31 36
31 28
4 28 0
28 8
28 16
28 24
28 32
9. 74189
74208
74227
74246
74265
10
10
10
10
11
10. 25811
. 25792
25773
25754
25735
9. 82078
82106
82133
82161
82188
10. 17922
17894
17867
17839
17812
10. 07889
07898
07906
07914
07923
4
4
4
5
5
9.92111
92102
92094
92086
92077
30
29
28
27
26
35
36
37
38
39
7 31 20
31 12
31 4
30 56
30 48
4 28 40
28 48
28 56
29 4
29 12
9.74284
74303
74322
74341
74360
11
11
12
12
12
10. 25716
25697
25678
25659
25640
9. 82215
82243
82270
82298
82325
16
16
17
17
18
10. 17785
17757
17730
17702
17675
10. 07931
07940
07948
07956
07965
5
5
5
5
5
9. 92069
92060
92052
92044
92035
25
24
23
22
21
40
41
42
43
44
7 30 40
30 32
30 24
30 16
30 8
4 29 20
29 28
29 36
29 44
29 52
9. 74379
74398
74417
74436
74455
13
13
13
14
14
10. 25621
25602
25583
25564
25545
9. 82352
82380
82407
82435
82462
18
19
19
20
20
10. 17648
17620
17593
17565
17538
10. 07973
07982
07990
079S8
08007
6
6
6
6
6
9. 92027
92018
92010
92002
91993
20
19
18
17
16
4o
46
47
48
49
7 30 0
29 52
29 44
29 36
29 28
4 30 0
30 8
30 16
30 24
30 32
9. 74474
74493
74512
74531
74549.
14
15
15
15
16
10. 25526
25507
25488
25469
25451
9. 82489
,v2517
82544
82571
82599
21
21
22
22
22
10. 17511
17483
17456
17429
17401
10. 08015
OS024
08032
08041
08049
6
6
7
7
7
9. 91985
91976
91968
91959
91951
15
14
13
12
11
50
51
52
53
54
7 29 20
29 12
29 4
28 56
28 48
4 30 40
30 48
30 56
31 4
31 12
9. 74568
745S7
74606
74625
74644
16
16
17
17
17
10. 25432
25413
25394
25375
25356
9. 82626
82653
82681
82708
82735
23
23
24
24
25
10. 17374
17347
17319
17292
17265
10. 08058
08066
08075
08083
08092
7
7
7
7
8
9. 91942
91934
91925
91917
91908
10
9
8
7
6
55
56
57
58
59
60
7 28 40
28 32
28 24
28 16
28 8
28 0
4 31 20
31 28
31 36
31 44
31 52
32 0
9. 74662
74881
74700
74719
74737
74756
17
18
18
18
19
19
10. 25338
25319
25300
25281
25263
25244
9. 82702
82790
82817
82844
82871
82899
25
26
26
27
27
27
10.17238
17210
17183
17156
17129
17101
10. 08100
08109
08117
08126
08134
08143
8
8
8
8
8
8
9. 91900
91891
91883
91874
91866
91857
5
4
3
2
1
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant,
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
123° A A B B C C 56°
Seconds of time
I3
£
33
6»
fc
fA
Prop, parts of cols. -JB
2
3
5
7
7
10
10
14
12
17
14
21
17
24
1C
1
2
3
4
£
6
7
Page 806] TABLE 44.
Log. Sines, Tangents, and Secants.
34° A A B B C C 145®
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
7 28 0
27 52
27 44
27 36
27 28
4 32 0
32 8
32 16
32 24
32 32
9. 74756
74775
74794
74812
74831
0
0
1
1
1
10. 25244
25225
25206
25188
25169
9. 82899
82926
82953
82980
83008
0
0
1
1
2
10. 17101
17074
17047
17020
16992
10. 08143
08151
08160
08168
08177
0
0
0
0
1
9. 91857
91849
91840
91832
91823
5
6
7
8
9
7 27 20
27 12
27 4
26 56
26 48
4 32 40
32 48
32 56
33 4
33 12
9. 74850
74868
74887
74906
74924
2
2
2
2
3
10. 25150
25132
25113
25094
25076
9. 83035
83062
83089
83117
83144
2
3
3
4
4
10. 16965
16938
16911
16883
16856
10. 08185
08194
08202
08211
08219
1
1
1
1
1
9. 91815
91806
91798
91789
91781
55
54
53
52
51
50
49
48
47
46
10
11
12
13
14
7 26 40
26 32
26 24
26 16
26 8
4 33 20
33 28
33 36
33 44
33 52
9. 74943
74961
74980
74999
75017
3
3
4
4
4
10. 25057
25039
25020
25001
24983
9. 83171
83198
83225
83252
83280
5
5
5
6
6
10. 16829
16802
16775
16748
16720
10. 08228
08237
08245
08254
08262
1
2
2
2
2
9. 91772
91763
91755
91746
91738
15
16
17
18
19
7 26 0
25 52
25 44
25 36
25 28
4 34 0
34 8
34 16
34 24
34 32
9. 75036
75054
75073
75091
75110
5
5
5
6
6
10. 24964
24946
24927
24909
24890
9. 83307
83334
83361
83388
83415
7
• 7
8
8-
9
10. 16693
16666
16639
16612
16585
10. 08271
08280
08288
08297
08305
10. 08314 ~
08323
08331
08340
08349
2
2
2
3
3
9. 91729
91720
91712
91703
91695
45
44
43
42
41
20
21
22
23
24
7 25 20
25 12
25 4
24 56
24 48
4 34 40
34 48
34 56
35 4
35 12
9. 75128
75147
75165
75184
75202
6
6
7
7
7
10. 24872
24853
24835
24816
24798
9. 83442
83470
83497
83524
83551
9
9
10
10
11
10. 16558
16530
16503
16476
16449
3
3
3
3
3
9. 91686
91677
91669
91660
91651
40
59
38
37
36
^5"
34
33
32
31
"30"
29
28
27
26
25
26
27
28
29
7 24 40
24 32
24 24
24 16
24 8
4 35 20
35 28
35 36
35 44
35 52
9. 75221
75239
75258
75276
75294
8
8
8
9
9
10. 24779
24761
24742
24724
24706
9. 83578
83605
83632
83659
83686
11
12
12
13
13
10. 16422
16395
16368
16341
16314
10. 08357
08366
08375
08383
08392
4
4
4
4
4
9. 91643
91634
91625
91617
91608
30
31
32
33
34
7 24 0
23 52
23 44
23 36
23 28
4 36 0
36 8
36 16
36 24
36 32
9. 75313
75331
75350
75368
75386
9
9
10
10
10
10. 24687
24669
24650
24632
24614
9. 83713
83740
83768
83795
83822
14
14
14
15
15
16
16
17
17
18
10. 16287
16260
16232
16205
16178
10. 08401
08409
08418
08427
08435
4
4
5
5
5
9. 91599
91591
91582
91573
91565
35
36
37
38
39
7 23 20
23 12
23 4
22 56
22 48
4 36 40
36 48
36 56
37 4
37 12
9. 75405
75423
75441
75459
75478-
11
11
11
12
12
10. 24595
24577
24559
24541
24522
9. 83849
83876
83903
83930
83957
10. 16151
16124
16097
16070
16043
10. 08444
08453
08462
08470
08479
5
5
5
5
6
9. 91556
91547
91538
91530
91521
25
24
23
22
21
40
41
42
43
44
7 22 40
22 32
22 24
22 16
22 8
4 37 20
37 28
37 36
37 44
37 52
9. 75496
75514
75533
75551
75569
12
13
13
13
13
10. 24504
24486
24467
24449
24431
9. 83984
84011
84038
84065
84092
18
18
19
19
20
10. 16016
15989
15962
15935
15908
10. 08488
08496
08505
08514
08523
6
6
6
6
6
9.91512
91504
91495
91486
91477
9. 91469
91460
91451
91442
91433
20
19
18
17
16
45
46
47
48
49
7 22 0
21 52
21 44
21 36
21 28
4 38 0
38 8
38 16
38 24
38 32
9. 75587
75605
75624
75642
75660
14
14
14
15
15
"15
16
16
16
17
10. 24413
24395
24376
24358
24340
9. 84119
84146
84173
84200
84227
20
21
21
22
22
10. 15881
15854
15827
15800
15773
10. 08531
08540
08549
08558
08567
7
7
7
7
7
15
14
13
12
11
50
51
52
53
54
7 21 20
2i 12
21 4
20 56
20 48
4 38 40
38 48
38 56
39 4
39 12
9. 75678
75696
75714
75733
75751
10. 24322
24304
24286
24267
24249
9. 84254
84280
84307
84334
84361
23
23
23
24
24
10. 15746
15720
15693
15666
15639
10. 08575
08584
08593
08602
08611
7
7
8
8
8
9. 91425
91416
91407
91398
91389
10
9
8
7
6
55
56
57
58
.59
60
7 20 40
20 32
20 24
20 16
20 8
20 0
4 39 20
39 28
39 36
39 44
39 52
40 0
9. 75769
75787
75805
75823
75841
75859
17
17
17
18
18
18
10. 24231
24213
24195
24177
24159
24141
9. 84388
84415
84442
84469
84496
84523
25
25
26
26
27
27
10. 15612
15585
15558
15531
15504
15477
10. 08619
08628
08637
08646
08655
08664
8
8
8
8
9
9
9. 91381
91372
91363
91354
91345
91336
5
4
3
2
1
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
I
^M-
124° A A B B C C 6£
Seconds of time .
1s
2"
3s
4*
5"
6'
7»
fA
2
5
7
9
11
14
16
Prop, parts of cols. -IB
1C
3
1
7
2
10
3
14
4
17
6
20
7
24
8
TABLE 44. [Page 807
Log. Sines, Tangents, and Secants.
86° A A B B C C 144°
M.
Hour A. M. Hour p. M.
Sine. Diff.
Cosecant.
Tangent.
Diff. i Cotangent.
Secant.
Diff. | Cosine.
M.
0
1
2
3
4
7 20 0
19 52
19 44
19 36
19 28
4 40 0
40 8
40 16
40 24
40 32
9. 75859
75877
75895
75913
75931
0
0
1
1
1
1
2
2
2
3
10. 24141
24123
24105
24087
24069
9.84523
84550
84576
84603
84630
0
0
1
1
2
10. 15477
15450
15424
15397
15370
10. 08664
08672
08681
08690
08699
0
0
0
0
1
9. 91336
91328
91319
91310
91301
60
59
58
57
56
5
6
7
8
9
7 19 20
]9 12
19 4
18 56
18 48
4 40 40
40 48
40 56
41 4
41 12
9. 75949
75967
75985
76003
76021
10. 24051
24033
24015
23997
23979
9. 84657
84684
84711
84738
84764
2
3
3
4
4
10. 15343
15316
15289
15262
15236
10. 08708
08717
08726
08734
08743
1
1
1
1
1
9. 91292
91283
91274
91266
91257
55
54
53
52
51
10
11
12
13
14
7 18 40
18 32
18 24
18 16
18 8
4 41 20
41 28
41 36
41 44
41 52
9. 76039
76057
76075
76093
76111
3
3
4
4
4
10. 23961
23943
23925
23907
23889
9. 84791
84818
84845
84872
84899
4
5
5
6
6
10. 15209
15182
15155
15128
15101
10. 08752
08761
08770
08779
08788
2
2
2
2
2
9. 91248
91239
91230
91221
91212
50
49
48
47
46
45
44
43
42
41
15
16
17
18
19
7 18 0
17 52
17 44
17 36
17 28
4 42 0
42 8
42 16
42 24
42 32
9. 76129
76146
76164
76182
76200
4
5
5
5
6
10. 23871
23854
23836
23818
23800
9. 84925
84952
84979
85006
85033
7
/
8
8
8
10. 15075
15048
15021
14994
14967
10. 08797
08806
08815
08824
08833
2
2
3
3
3
3
3
3
3
4
9. 91203
91194
91185
91176
91167
20
21
22
23
24
7 17 20
17 12
17 4
16 56
16 48
4 42 40
42 48
42 56
43 4
43 12
9. 76218
76236
76253
76271
76289
6
6
6
7
7
10. 23782
23764
23747
23729
23711
9. 85059
85086
85113
85140
85166
9
9
10
10
11
10. 14941
14914
14887
14860
14834
10. 08842
08851
08859
08868
08877
9. 91158
91149
91141
91132
91123
40
39
38
37
36
25
26
27
28
29
7 16 40
16 32
16 24
16 16
16 8
4 43 20
43 28
43 36
43 44
43 52
9. 76307
76324
76342
76360
76378
i
8
8
8
9
10. 23693
23676
23658
23640
23622
9. 85193
8-5220
85247
85273
85300
11
12
12
12
13
10. 14807
14780
14753
14727
14700
10. 08886
08895
08904
08913
08922
4
4
4
4
4
9.91114
91105
91096
91087
91078
35
34
33
32
31
30
31
32
33
34
7 16 0
15 52
15 44
15 36
15 28
4 44 0
44 8
44 16
44 24
44 32
9. 76395
76413
76431
76448
76466
9
9
9
10
10
10. 23605
23587
23569
23552
23534
9. 85327
85354
85380
85407
85434
13
14
14
15
15
10. 14673
14646
14620
14593
14566
10. 08931
08940
08949
08958
08967
5
5
5
5
5
9. 91069
91060
91051
91042
91033
30
29
28
27
26
35
36
37
38
39
40
41
42
43
44
"45"
46
47
48
49
7 15 20
15 12
15 4
14 56
14 48
4 44 40
44 48
44 56
45 4
45 12
9.76484
76501
76519
76537
76554
10
11
11
11
12
10. 23516
23499
23481
23463
23446
9. 85460
85487
85514
85540
85567
16
16
.16
17
17
10. 14540
14513
14486
14460
14433
10. 08977
08986
08995
09004
09013
5
5
6
6
6
9. 91023
91014
91005
90996
90987
25
24
23
22
21
7 14 40
14 32
14 24
14 16
14 8
4 45 20
45 28
45 36
45 44
45 52
9. 76572
76590
76607
76625
76642
12
12
12
13
13
10. 23428
23410
23393
23375
23358
9. 85594
85620
85647
85674
85700
18
18
19
19
20
10. 14406
14380
14353
14326
14300
10. 09022
09031
09040
09049
09058
6
6
6
6
7
9. 90978
90969
90960
90951
90942
20
19
18
17
16
7 14 0
13 52
13 44
13 36
13 28
4 46 0
46 8
46 16
46 24
46 32
9. 76660
76677
76695
76712
76730
13
14
14
14
14
10. 23340
23323
23305
23288
23270
9. 85727
85754
85780
85807
85834
20
20
21
21
22
10. 14273
14246
14220
14193
14166
10. 09067
09076
09085
09094
09104
7
7
7
7
7
9. 90933
90924
90915
90906
90896
15
14
13
12
11
50
51
52
53
54
7 13 20
13 12
13 4
12 56
12 48
4 46 40
46 48
46 56
47 4
47 12
9. 76747
76765
76782
76800
76817
15
15
15
16
16
10. 23253
23235
23218
23200
23183
9.85860
8oSS7
85913
85940
85967
22
23
23
24
24
10. 14140
14113
14087
14060
14033
10.09113
09122
09131
09140
09149
8
8
8
8
8
9.90887
90878
90869
90860
90851
10
9
8
7
6
oo
56
57
58
59
60
7 12 40
12 32
12 24
12 16
12 8
12 0
4 47 20
47 28
47 36
47 44
47 52
48 0
9. 76835
76852
76870
76887
76904
76922
16
17
17
17
17
18
10. 23165
23148
23130
23113
230P6
23078
9.85993
86020
86046
86073
86100
86126
24
25
25
26
26
27
10. 14007
13980
13954
13927
13900
13874
10. 09158
09168
09177
09186
09195
09204
8
8
9
9
9
9
9. 90842
90832
90828
90796
o
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent, j Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
125° A A B B C C 54°
Seconds of time
I3
°' &
i>
5*
6*
{A
2
4 7
9
11
13
16
B
c
3
1
7 ! 10
3
13
5
17
6
20
23
8
Page 808] TABLE 44.
Log. Sines, Tangents, and Secants.
86° V A B B C C 143°
M.
Hour A. M.
Hour p. M.'
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
.Cosine.
M.
0
1
2
3
4
7 12 0
11 52
11 44
11 36
11 28
4 48 0
48 8
48 16
48 24
48 32
9. 76922
76939
76957
76974
76991
0
0
1
1
1
10. 23078
23061
23043
23026
23009
9. 86126
86153
86179
86206
86232
0
0
1
1
2
10. 13874
13847
13821
13794
13768
10. 09204
09213
09223
09232
09241
0
0
0
0
1
9. 90796
90787
90777
90768
90759
60
59
58
57
56
5
6
7
8
9
7 11 20
11 12
11 4
10 56
10 48
4 48 40
48 48
48 56
49 4
49 12
9. 77009
77026
77043
77061
77078
1
2
2
2
3
10. 22991
22974
22957
22939
22922
10.22905
22888
22870
22853
22836
9. 86259
86285
86312
86338
86365
2
3
3
4
4
10. 13741
13715
13688
13662
13635
10. 09250
09259
09269
09278
09287
1
1
1
1
1
9. 90750
90741
90731
90722
90713
55
54
53
52
51
10
11
12
13
14
7 10 40
10 32
10 24
10 16
10 8
4 49 20
49 28
49 36
49 44
49 52
9. 77095
77112
77130
77147
77164
3
3
3
4
4
9. 86392
86418
86445
86471
86498
5
5
6
6
10. 13608
13582
13555
13529
13502
10. 09296
09306
09315
09324
09333
2
2
2
2
2
9. 90704
90694
90685
90676
90667
50
49
48
47
46
15
16
17
18
19
7 10 0
9 52
9 44
9 36
9 28
4 50 0
50 8
50 16
50 24
50 32
9. 77181
77199
77216
77233
77250
4
5
5
5
5
10. 22819
22801
22784
22767
22750
9. 86524
86551
86577
86603
86630
7
7
7
8
8
10. 13476
13449
13423
13397
13370
10. 09343
09352
09361
09370
09380
2
2
3
3
3
9. 90657
90648
90639
90630
90620
45
44
43
42
41
20
21
22
23
24
7 9 20
9 12
9 4
8 56
8 48
4 50 40
50 48
50 56
51 4
51 12
9. 77268
77285
77302
77319
77336
6
6
6
7
7
10. 22732
22715
22698
22681
22664
9. 86656
86683
86709
86736
86762
9
9
10
10
11
10. 13344
13317
13291
13264
13238
10. 09389
09398
09408
09417
09426
3
3
3
4
4
9. 90611
90602
90592
90583
90574
40
39
38
37
36
25
26
27
28
29
7 8 40
8 32
8 24
8 16
8 8
4 51 20
51 28
51 36
51 44
51 52
9. 77353
77370
77387
77405
77422
7
7
8
8
8
10. 22647
22630
22613
22595
22578
9. 86789
86815
86842
86868
86894
11
11
12
12
13
10. 13211
13185
13158
13132
13106
10. 09435
09445
09454
09463
09473
4
4
4
4
5
9. 90565
90555
90546
90537
90527
35
34
33
32
31
30
31
32
33
34
780
7 52
7 44
7 36
7 28
4 52 0
52 8
52 16
52 24
52 32
9. 77439
77456
77473
77490
77507
9
9
9
9
10
10. 22561
22544
22527
22510
22493
9. 86921
86947
86974
87000
87027
13
14
14
15
15
10. 13079
13053
13026
13000
12973
10. 09482
09491
09501
09510
09520
5
5
5
5
5
9. 90518
90509
90499
90490
90480
30
29
28
27
26
35
36
37
38
39
7 7 20
7 12
7 4
6 56
6 48
4 52 40
52 48
52 56
53 4
53 12
9. 77524
77541
77558
77575
77592
10
10
11
11
11
10. 22476
22459
22442
22425
22408
9. 87053
87079
87106
87132
87158
15
16
16
17
17
10. 12947
12921
12894
12868
12842
10. 09529
09538
09548
09557
09566
5
6
6
6
6
9. 90471
90462
90452
90443
90434
25
24
23
22
21
40
41
42
43
44
7 6 40
6 32
6 24
6 16
6 8
4 53 20
53 28
53 36
53 44
53 52
9. 77609
77626
77643
77660
77677
11
12
12
12
13
10. 22391
22374
22357
22340
22323
9. 87185
87211
87238
87264
87290
18
18
18
19
19
10. 12815
12789
12762
12736
12710
10. 09576
09585
09595
09604
09614
6
6
7
7
7
9. 90424
90415
90405
90396
90386
20
19
18
17
16
45
46
47
48
49
760
5 52
5 44
5 36
5 28
4 54 0
54 8
54 16
54 24
54 32
9. 77694
77711
77728
77744
77761
13
13
13
14
14
10. 22306
2^289
22272
22256
22239
9. 87317
87343
87369
87396-
87422
20
20
21
21
22
10. 12683
12657
12631
12604
12578
10. 09623
09632
09642
09651
09661
7
7
7
7
8
9. 90377
90368
90358
90349
90339
15
14
13
12
11
50
51
52
53
54
55
56
5r
58
59
60
M.
7 5 20
5 12
5 4
4 56
4 48
4 54 40
54 48
54 56
55 4
55 12
9. 77778
77795
77812
77829
77846
14
15
15
15
15
10. 22222
22205
22188
22171
22154
10. 22138
22121
22104
22087
22070
22054
9. 87448
87475
87501
87527
87554
22
22
23
23
24
10. 12552
12525
12499
12473
12446
10. 09670
09680
09689
09699
09708
8
8
8
8
8
9. 90330
90320
90311
90301
90292
9. 90282
90273
90263
90254
90244
90235
10
9
8
7
6
7 4 40
jm 32
- **424
4 16
4 8
4 0
4 55 20
55 28
55 36
55 44
55 52
56 0
9. 77862
77879
77896
. 77913
77930
77946
16
16
16
16
17
17
9. 87580
87606
87633
87659
87685
87711
24
25
25
26
26
26
10. 12420
12394
12367
12341
12315
12289
10.09718
09727
09737
09746
09756
09765
9
9
9
9
9
9
5
4
3
2
1
0
Hour p. M.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
126° A A B B C C 53°
Seconds of time .
1*
2s
33
4s
5»
6'
* I3
fA
2
4
6
9
11
13
15
jProp. parts of cols. •! B
3
J
7
2
10
4
13
5
17
6
20
7
23
8
TABLE 44. [Page 809
Log. Sines, Tangents, and Secants.
37° A A B B C C 142°
M.
Hour A.M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
740
3 52
3 44
3 36
3 28
4 56 0
56 8
56 16
56 24
56 32
9. 77946
77963
77980
77997
78013
0
0
1
1
1
10. 22054
22037
22020
22003
21987
9. 87711
87738
87764
87790
87817
0
0
1
1
2
2
3
3
3
4
10. 12289
12262
12236
12210
12183
10. 09765
09775
09784
09794
09803
0
0
0
0
1
9. 90235
90225
' 90216
90206
90197
60
59
58
57
56
5
6
7
8
9
7 3 20
3 12
3 4
2 56
2 48
4 56 40
56 48
56 56
57 4
57 12
9. 78030
78047
78063
78080
78097
1
2
o
2
2
10. 21970
21953
21937
21920
21903
9. 87843
87869
87895
87922
87948
10. 12157
12131
12105
12078
12052
10. 09813
09822
09832
09841
09851
1
1
1
1
1
9. 90187
90178
90168
90159
90149
55
54
53
52
51
50
49
48
47
46
10
11
12
13
14
7 2 40
2 32
2 24
2 16
2 8
4 57 20
57 28
57 36
57 44
57 52
9. 78113
78130
78147
78163
781SO
3
3
3
4
4
10. 21887
21870
21853
21837
21820
9. 87974
88000
88027
88053
88079
4
5
5
6
6
10. 12026
12000
11973
11947
11921
10. 09861
09870
09880
09889
09899
2
2
2
2
2
9. 90139
90130
90120
90111
90101
15
16
17
18
19
720
1 52
1 44
1 36
1 28
4 58 0
58 8
58 16
58 24
58 32
9. 78197
76213
78230
78246
78263
4
4
5
5
5
10. 21803
21787
21770
21754
21737
9. 88105
88131
88158
88184
88210
7
7
7
8
8
10. 11895
11869
11842
11816
11790
10. 09909
09918
09928
09937
09947
2
3
3
3
3
9. 90091
90082
90072
90063
90053
45
44
43
42
41
20
21
22
23
24
7 1 20
1 12
1 4
0 56
0 48
4 58 40
58 48
58 56
59 4
59 12
9. 78280
78296
78313
78329
78346
5
6
6
6
7
10.21,20
21704
21687
21671
21654
9. 88236
88262
88289
88315
88341
9
9
10
10
10
10. 11764
11738
11711
11685
11659
10. 09957
09966
09976
09986
09995
3
3
4
4
4
9.90043
90034
90024
90014
90005
40
39
38
37
36
25
26
27
28
29
7 0 40
0 32
0 24
0 16
0 8
4 59 20
59 28
59 36
59 44
59 52
9. 78362
78379
78395
78412
78428
7
7
7
8
8
10. 21038
21621
21605
21588
21572
9. 88367
88393
88420
8S446
88472
11
11
12
12
13
10. 11633
11607
11580
11554
11528
10. 10005
10015
10024
10034
10044
4
4
4
5
5
9. 89995
89985
89976
89966
89956
35
34
33
32
31
30
31
32
33
34
700
6 59 52
59 44
59 36
59 28
500
0 8
0 16
0 24
0 32
9. 78445
78461
78478
78494
-78510
8
9
9
9
9
10. 21555
21539
21522
21506
21490
9. 88498
88524
88550
88577
88603
13
14
14
14
15
10. 11502
11476
11450
11423
11397
10. 10053
10063
10073
10082
10092
5
5
5
5
5
9. 89947
89937
89927
89918
89908
30
29
28
27
26
35
36
37
38
39
6 59 20
59 12
59 4
58 56
58 48
5 0 40
0 48
0 56
1 4
1 12
9. 78527
78543
78560
78576
78592
10
10
10
10
11
10. 21473
21457
21440
21424
21408
9. 88629
88655
88681
88707
88733
15
16
16
17
17
10. 11371
11345
11319
11293
11267
10. 10102
10112
10121
10131
10141
6
6
6
6
6
9. 89898
89888
89879
89869
89859
25
24
23
22
21
40
&
43
44
6 58 40
58 32
58 24
58 16
58 8
5 1 20
1 28
1 36
1 44
1 52
9. 78609
78625
78642
78658
" 78674
11
11
12
12
12
10. 21391
21375
21358
21342
21326
9. 88759
88786
88812
88838
88864
17
18
18
19
19
10. 11241
11214
11188
11162
11136
10. 10151
10160
10170
10180
10190
6
7
7
7
7
9. 89849
89840
89830
89820
89810
20
19
18
17
16
45
46
47
48
49
6 58 0
57 52
57 44
57 36
57 28
520
2 8
2 16
2 24
2 32
9. 78691
78707
78723
78739
78756
12
13
13
13
13
10. 21309
21293
21277
21261
21244
9. 88890
88916
88942
88968
88994
20
20
20
21
21
10. 11110
11084
11058
11032
11006
10. 101b9
10209
10219
10229
10239
7
7
8
8
8
8
8
8
9
9
9. 89801
89791
89781
89771
89761
15
14
13
12
11
50
51
52.
53
54
6 57 20
57 12
57 4
56 56
56 48
5 2 40
2 48
2 56
3 4
3 12
9. 78772
78788
78805
78821
78837
14
14
14
15
15
10. 21228
21212
21195
21179
21163
9. 89020
89046
89073
89099
89125
22
22
23
23
24
10. 10980
10954
10927
10901
10875
10. 10248
10258
10268.,
102'7S
10288
9. 89752
89742
89132-
89722
89712
10
9
- 8
7
6
55
56
57
58
59
60
6 56 40
56 32
56 24
56 16
56 8
56 0
5 3 20
3 28
3 36
3 44
3 52
4 0
9. 78853
78869
78886
78902
78918
78934
15
15
16
16
16
16
10. 21147
21131
21114
21098
21082
21066
9. 89151
89177
89203
89229
89255
89281
24
24
25
25
26
26
10. 10849
10823
10797
10771
10745
10719
10. 10298
10307
10317
10327
10337
10347
9
9
9
9
10
10
9. 89702
89693
89683
89673
89663
89653
5
4
3
2
1
0
If.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
1-27° A A B B C C o'2°
Seconds of time
1»
»3
33
4*
53
6s
-s
(A
2
4
fi
8
10
12
U
Prop, parts of cols.-{B
1C
3
1
7
2
10
4
13
5
16
6
20
7
23
8
61828°— 16-
Page 810] TABLE 44.
Log. Sines, Tangents, and Secants.
88° A A B B C C 141°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
0
0
1
1
2
Cotangent.
Secant.
Diff.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
6 56 0
55 52
55 44
55 36
55 28
540
4 8
4 16
4 24
4 32
9. 78934
78950
78967
78983
78999
0
0
1
1
1
10. 21066
21050
21033
21017
21001
9. 89281
89307
89333
89359
89385
10. 10719
10693
10667
10641
10615
10. 10347
10357
10367
10376
10386
0
0
0
1
1
1
1
1
1
2
9. 89653
8964$
89633
89624
89614
5
6
7
8
9
6 55 20
55 12
55 4
54 56
54 48
5 4 40
4 48
4 56
5 4
5 12
9. 79015
79031
79047
79063
79079
1
2
2
2
2
10. 20985
20969
20953
20937
20921
9. 89411
89437
89463
89489
89515
2
3
3
3
4
10. 10589
10563
10537
10511
10485
10. 10396
"T0406
10416
10426
10436
9. 89604
89594
89584
89574
89564
55
54
53
52
51
10
11
12
13
14
6 54 40
54 32
54 24
54 16
54 8
5 5 20
5 28
5 36
5 44
5 52
9. 79095
79111
79128
79144
79160
3
3
3
3
4
10. 20905
20889
20872
20856
20840
9. 89541
89567
89593
89619
89645
4
5
5
6
6
10. 10459
10433
10407
10381
10355
10. 10446
10456
10466
10476
10486
2
2
2
2
2
9. 89554
89544
89534
89524
89514
50
49
48
47
46
15
16
17
18
19
6 54 0
53 52
53 44
53 36
53 28
560
6 8
6 16
6 24
6 32
9. 79176
79192
79208
79224
79240
4
4
5
5
5
10. 20824
20808
20792
20776
20760
9. 89671
89697
89723
89749
89775
6
7
7
8
8
10. 10329
10303
10277
10251
10225
10. 10496
10505
10515
10525
10535
3
3
3
3
3
9. 89504
89495
89485
89475
89465
45
44
43
42
41
20
21
22
23
24
6 53 20
53 12
53 4
52 56
52 48
5 6 40
6 48
6 56
7 4
7 12
9. 79256
79272
79319
5
6
6
6
6
10. 20744
20728
20712
20696
20681
9. 89801
89827
89853
89879
89905
9
9
10
10
10
10. 10199
10173
10147
10121
10095
10. 10545
10555
10565
10575
10585
3
4
4
4
4
9. 89455
89445
89435
89425
89415
40
39
38
37
36
25
26
27
28
29
6 52 40
52 32
52 24
52 16
52 8
5 7 20
7 28
7 36
7 44
7 52
9. 79335
79351 •
79367
79383
79399
7
- 7
7
7
8
10. 20665
20649
20633
20617
20601
9. 8993}
89957
89983
90009
90035
11
11
12
12
13
10. 10069
10043
10017
09991
09965
10. 10595
10605
10615
10625
10636
4
4
5
5
5
9. 89405
89395
89385
89375
89364
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
30
31
32
33
34
6 52 0
51 52
51 44
51 36
51 28
580
8 8
8 16
8 24
8 32
9. 79415
79431
79447
79463
79478
8
8
8
9
9
10. 20585
20569
20553
20537
20522
9. 90061
90086
90112
90138
90164
13
13
14
14
15
15
16
16
16
17
10. 09939
09914
09888
09862
09836
10. 09810
09784
09758
09732
09706
10. 10646
10656
10666
10676
10686
5
5
5
6
6
6
6
6
6
7
9. 89354
89344
89334
89324
89314
35
36
37
38
39
6 51 20
51 12
51 4
50 56
50 48
5 8 40
8 48
8 56
9 4
9 12
9. 79494
79510
79526
79542
79558
9
10
10
10
10
10. 20506
20490
20474
20458
20442
9. 90190
90216
90242
90268
90294
10. 10696
10706
10716
10726
10736
9. 89304
89294
89284
89274
89264
40
41
42
43
44
45
46
47
48
49
6 50 40
50 32
50 24
50 16
50 8
5 9 20
9 28
9 36
9 44
9 52
9. 79573
79589
79605
79621
79636
11
11
11
11
12
12
12
12
13
13
10. 20427
20411
20395
20379
20364
9. 90320
90346
90371
90397
90423
17
18
18
19
19
19
20
20
21
21
10. 09680
09654
09629
09603
09577
10. 10746
10756
10767
10777
10787
7
7
7
7
7
9. 89254
89244
89233
89223
89213
20
19
18
"ir
16
6 50 0
49 52
49 44
49 36
49 28
5 10 0
10 8
10 16
10 24
10 32
9. 79652
79668
79684
79699
79715
10. 20348
20332
20316
20301
20285
9. 90449
90475
90501
90527
90553
10. 09551
09525
09499
09473
09447
10. 10797
10807
10817
10827
10838
8
8
8
8
8
9. 89203
89193
89183
89173
89162
15
14
13
12
11
50
51
52
53
54
6 49 20
49 12
49 4
48 56
48 48
5 10 40
10.48
10 56
11 4
11 12
9. 79731
79746
79762
79778
79793
13
14
14
14
14
10. 20269
20254
20238
20222
20207
9. 90578
90604
90630
90656
90682
22
22
22
23
23
10. 09422
09396
09370
09344
09318
10. 10848
10858
10868
10878
10888
10. 10899
10909
10919
10929
10940
10950
8
9
9
g
9
9. 89152
89142
89132
89122
89112
10
9
8
7
6
55
56
57
58
59
60
6 48 40
48 32
48 24
48 16
48 8
48 0
5 11 20
11 28
11 36
11 44
11 52
12 0
9. 79809
79825
79840
79856
79872
79887
15
15
15
15
16
16
10. 20191
20175
20160
20144
20128
20113
9. 90708
90734
90759
90785
90811
90837
24
24
-25
25
26
26
10. 09292
09266
09241
09215
09189
09163
9
9
10
10
10
10
9. 89101
89091
89081
89071
89060
89050
5
4
3
2
1
0
M.
M.
Hour P. M.
Hour A. M.
Cosi,ne.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff. Sine.
128° A A -B B C C 51°
Seconds of time
Is
,,s
3'
43
5*
6»
7s
(A
2
4
6
8
10
12
14
Prop, parts of cols.JB
[C
3
1
6
3
10
4
13
5
16
6
19
8
23
9
TABLE 44. [Page 811
Log. Sines, Tangents, and Secants.
39° A A B B C C 140°
M.
Hour A. M.
Hour P. M.
Sine. i Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
o
6
7
8
9
6 48 0
47 52
47 44
47 36
47 28
5 12 0
12 8
12 16
12 24
12 32
9. 79887
79903
79918
79934
79950
0
0
1
1
1
10. 20113
20097
20082
20066
20050
9. 90837
90863
90889
90914
90940
0
0
1
1
2
10.09163
09137
09111
09086
09060
10. 10950
10960
10970
10980
10991
0
0
0
1
1
1
1
1
1
2
~2~
2
2
2
2
3
3
3
3
3
3
4
4
4
4
9. 89050
89040
89030
89020
89009
60
59
58
57
56
6 47 20
47 12
47 4
46 56
46 48
5 12 40
12 48
12 56
13 4
13 12
9. 79965
79981
79996
80012
80027
1
2
2
2
2
10. 20035
20019
20004
19988
19973
9. 90966
90992
91018
91043
91069
2
3
3
3
4
10. 09034
09008
08982
08957
08931
10. 11001
11011
11022
11032
11042
9. 88999
88989
88978
88968
88958
55
54
53
52
51
10
11
12
13
14
6 46 40
46 32
46 24
46 16
46 8
5 13 20
13 28
13 36
13 44
13 52
9.80043
80058
80074
80089
* 80105
3
3
3
3
4
10. 19957
19942
19926
19911
19895
9. 91095
91121
91147
91172
91198
4
5
5
6
6
10. 08905
08879
08853
08828
08802
10. 11052
11063
11073
11083
11094
9.88948
88937
88927
88917
88906
50
49
48
47
46
15
16
17
18
19
6 46 0
45 52
45 44
45 36
45 28
5 14 0
14 8
14 16
14 24
14 32
9. 80120
80136
80151
80166
80182
4
4
4
5
5
10. 19880
19864
19849
19834
19818
9. 91224
91250
91276
91301
91327
6
7
7
8
8
10. 08776
08750
08724
08699
08673
10. 11104
11114
11125
11135
11145
9. 88896
88886
88875
88865
88855
45
44
43
42
41
20
21
22
23
24
6 45 20
45 12
45 4
44 56
44 48
5 14 40
14 48
14 56
15 4
15 12
9. 80197
80213
80228
80244
80259
5
5
6
6
6
10. 19803
19787
19772
19756
19741
9. 91353
91379
91404
91430
91456
9
9
9
10
10
10. 08647
08621
08596
08570
08544
10. 11156
11166
11176
11187
11197
9.88844
&S834
88824
88813
88803
40
39
38
37
36
25
26
27
28
29
6 44 40
44 32
44 24
44 16
44 8
5 15 20
15 28
15 36
15 44
15 52
9. 80274
80290
80305
80320
80336
6
7
7
7
7
10. 19726
19710
19695
19686
19664
9. 91482
91507
91533
91559
91585
11
11
12
12
12
10. 08518
08493
08467
08441
08415
10. 11207
11218
11228
11239
11249
4
5
5
5
5
9. 88793
88782
88772
. 88761
88751
35
34
33
32
31
30
31
32
33
34
6 44 0
43 52
43 44
43 36
43 28
5 16 0
16 8
16 16
16 24
16 32
9. 80351
80366
80382
80397
80412
8
8
8
8
9
10. 19649
19634
19618
19603
19588
9. 91610
91636
91662
91688
91713
13
13
14
14
15
10. 08390
08364
08338
08312
08287
10. 11259
11270
11280
11291
11301
5
5
6
6
6
6
6
6
7
7
9. 88741
88730
88720
88709
88699
30
29
28
27
26
35
36
37
38
39
6 43 20
43 12
43 4
42 56
42 48
5 16 40
16 48
16 56
17 4
17 12
9. 80428
80443
80458
80473
80489
9
9
9
10
10
10. 19572
19557
19542
19527
19511
9. 91739
91765
91791
91816
91842
15
15
16
16
17
10. 08261
08235
08209
08184
08158
10. 11312
11322
11332
11343
- 11353
9. 88688
88678
88668
88657
88647
25
24
23
22
21
40
41
42
43
44
45
46
47
48
49
6 42 40
42 32
42 24
42 16
42 8
5 17 20
17 28
17 36
17 44
17 52
9. 80504
80519
80534
80550
80565
10
10
11
11
11
10. 19496
19481
19466
19450
19435
9. 91868
91893
91919
91945
91971
17
18
18
18
19
10. 08132
08107
08081
08055
08029
10. 11364
11374
11385
11395
11406
7
7
7
7
8
9. 88636
88626
88615
88605
88594
20
19
18
17
16
6 42 0
41 52
41 44
41 36
41 28
5 18 0
18 8
18 16
18 24
18 32
9. 80580
80595
80610
80625
80641
12
12
12
12
13
10. 19420
19405
19390
19375
19359
9. 91996
92022
92048
92073
92099
19
20
20
21
21
10. 08004
07978
07952
07927
07901
10. 11416
11427
11437
11448
11458
8
8
8
8
9
9.88584
88573
88563
88552
88542
15
14
13
12
11
50
51
52
53
54
6 41 20
41 12
41 4
40 56
40 48
5 18 40
18 48
18 56
19 4
19 12
9.80656
80671
80686
80701
80716
13
13
13
14
14
10. 19344
19329
19314
19299
19284
9. 92125
92150
92176
92202
92227
21
22
22
23
23
10. 07875
07850
07824
07798
07773
10. 11469
11479
11490
11501
11511
9
9
9
9
9
9. 88531
88521
88510
88499
88489
10
9
8
7
6
5
4
3
2
1
0
oo
56
57
58
59
60
6 40 40
40 32
40 24
40 16
40 8
40 0
5 19 20
19 28
19 36
19 44
19 52
20 0
9. 80731
80746
80762
80777
80792
80807
14
14
15
15
15
15
10. 19269
19254
19238
19223
19208
19193
9. 92253
92279
92304
92330
92356
9£381
24
24
24
25
25
26
10. 07747
07721
07696
07670
07644
07619
10. 11522
11532
11543
11553
11564
11575
10
10
10
10
10
10
9. 88478
88468
88457
88447
88436
88425
If.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
1293 A A B B C C 60°
1§
2»
3 *
41
5*
6'
1*
{A
B
c
i
1
6
10
4
8
13
5
10
16
. 7
12
19
8
13
23
9
Page 812] TABLE 44.
Log. Sines, Tangents, and Secants.
40° A A B B C C 139°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
6 40 0
39 52
39 44
39 36
39 28
5 20 0
20 8
20 16
20 24
20 32
9. 80807
80822
80837
80852
80867
0
0
0
1
1
10. 19193
19178
19163
19148
19133
9. 92381
92407
92433
92458
92484
0
0
1
1
2
10. 07619
07593
07567
07542
07516
10. 11575
11585
11596
11606
11617
10. 11628
11638
11649
11660
11670
0
0
0
1
1
9. 88425
88415
88404
88394
88383
60
59
58
57
56
5
6
7
8
9
6 39 20
39 12
39 4
38 56
38 48
5 20 40
20 48
20 56
21 4
21 12
9. 80882
80897
80912
80927
80942
1
1
2
2
2
10. 19118
19103
19088
19073
19058
9. 92510
92535
92561
92587
92612
2
3
3
3
4
10. 07490
07465
07439
07413
07388
1
1
1
1
2
9. 88372
88362
88351
88340
88330
55
54
53
52
51
50
49
48
47
46
10
11
12
13
14
6 38 40
38 32
38 24
38 16
38 8
5 21 20
21 28
21 36
21 44
21 52
9. 80957
80972
80987
81002
81017
2
3
3
3
3
10. 19043
19028
19013
18998
18983
9. 92638
92663
92689
92715
92740
4
5
5
6
6
10. 07362
07337
07311
07285
07260
10. 11681
11692
11702
11713
11724
2
2
2
2
3
9. 88319
88308
88298
88287
88276
15
16
17
18
19
6 38 0
37 52
37 44
37 36
37 28
5 22 0
22 8
22 16
22 24
22 32
9. 81032
81047
81061
81076
81091
4
4
4
4
5
10. 18968
18953
18939
18924
18909
9. 92766
92792
92817
92843
92868
6
7
7
8
8
10. 07234
07208
07183
07157
07132
10. 11734
11745
11756
11766
11777
3
3
3
3
3
9. 88266
88255
88244
88234
88223
45
44
43
42
41
20
21
22
23
24
6 37 20
37 12
' 37 4
36 56
36 48
5 22 40
22 48
22 56
23 4
23 12
9. 81106
81121
81136
81151
81166
b
5
5
6
6
10. 18894
18879
18864
18849
18834
9. 92894.
92920
92945
92971
92996
9
9
9
10
10
10. 07106
07080
07055
07029
07004
10. 11788
11799
11809
11820
11831
4
4
4
4
4
9. 88212
88201
88191
88180
88169
40
39
38
37
36
25
26
27
28
29
6 36 40
36 32
36 24
36 16
36 8
5 23 20
23 28
23 36
23 44
23 52
9.81180
81195
81210
81225
81240
6
6
7
7
7
10. 18820
18805
18790
18775
18760
9. 93022
93048
93073
93099
93124
11
11
12
12
12
10. 06978
06952
06927
06901
06876
10. 11842
11852
11863
11874
11885
4
5
5
5
5
9. 88158
88148
88137
88126
88115
35
34
33
32
31
30
29
28
27
26
30
31
32
33
34
6 36 0
35 52
35 44
35 36
35 28
5 24 0
24 8
24 16
24 24
24 32
9. 81254
81269
81284
81299
81314
7
8
8
8
8
10. 18746
18731
18716
18701
18686
9. 93150
93175
93201
93227
93252
13
13
14
14
14
10. 06850
06825
06799
06773
06748
10. 11895
11906
11917
11928
11939
5
6
6
6
6
6
6
7
7
7
9. 88105
88094
88083
88072
88061
35
36
37
38
39
6 35 20
35 12
35 4
34 56
34 48
5 24 40
24 48
24 56
25 4
25 12
9. 81328
81343
81358
81372'
81387
9
9
9
9
10
10. 18672
18657
18642
18628
18613
9. 93278
93303
93329
93354
93380
15
15
16
16
17
10. 06722
06697
06671
06646
06620
10. 11949
11960
11971
11982
11993
9. 88051
88040
88029
88018
88007
25
24
23
22
21
40
41
42
43
44
6 34 40
34 32
34 24
34 16
34 8
5 25 20
25 28
25 36
25 44
25 52
9. 81402
81417
81431
81446
81461
10
10
10
11
11
10. 18598
18583
18569
18554
18539
9. 93406
93431
93457
93482
93508
17
17
18
18
19
10. 06594
06569
06543
06518
06492
10. 12004
12015
12025
12036
12047
7
7
8
8
8
9. 87996
87985
87975
87964
87953
20
19
18
17
16
45
46
47
.48
49
6 34 0
33 52
33 44
33 36
33 28
5 26 0
26 8
26 16
26 24
26 32
9. 81475
81490
81505
81519
81534
11
11
12
12
12
10. 18525
18510
18495
18481
18466
9. 93533
93559
93584
93610
93636
19
20
20
20
21
10. 06467
06441
06416
06390
06364
10. 12058
12069
12080
12091
12102
8
8
8
9
9
9. 87942
87931
87920
87909
87898
15
14
13
12
11
10
9
8
7
6
50
51
52
53
54
6 33 20
33 12
33 4
32 56
32 48
5 26 40
26 48
26 56
27 4
27 12
9. 81549
81563
81578
81592
81607
12
13
13
13
13
10. 18451
18437
18422
18408
18393
9. 93661
93687
93712
93738
93763
21
22
22
23
23
10. 06339
06313
06288
06262
06237
10. 12113
12123
12134
12145
12156
9
9
9
10
10
9. 87887
87877
87866
87855-
87844
55
56
57
58
59
60
6 32 40
32 32
32 24
32 16
32 8
32 0
5 27 20
27 28
27 36
27 44
27 52
28 0
9. 81622
81636
81651
81665
81680
81694
14
14
14
14
15
15
10. 18378
18364
18349
18335
18320
18306
9. 93789
93814
93840
93865
93891
93916
23
24
24
25
25
26
10. 06211
06186
06160
06135
06109
06084
10. 12167
12178
12189
12200
12211
12222
10
10
10
10
11
11
9. 87833
87822
87811
87800
87789
87778
5
4
3
2
1
0
M.
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
130° A A B B C C 49°
I8
2«
3"
4»
5*
6»
7 9
{A
2
4
6
7
9
11
13
B
c
3
1
6
3
10
4
13
5
16
7
19
8
22
9
41°
TABLE 44. [Page 813
Log. Sines, Tangents, and Secants.
A A B B C C 138°
If.
Hour A. M.
Hour P. M.
Sine. I Diff.
Cosecant.
Tangent.
Diff.
Cotangent
Secant.
Diff
Cosine.
M.
0
1
2
3
4
6 32 0
31 52
31 44
31 36
31 28
5 28 0
28 8
28 16
28 24
28 32
9. 81694
81709
81723
81738
81752
0
0
0
I
1
10. 18306
18291
18277
18262
18248
9. 93916
93942
93967
93993
94018
0
0
1
1
2
10. 06084
06058
06033
06007
05982
10. 12222
12233
12244
12255
12266
0
0
0
1
1
9. 87778
87767
87756
87745
87734
60
59
58
57
56
5
6
7
8
9
6 31 20
31 12
31 4
30 56
30 48
5 28 40
28 48
28 56
29 4
29 12
9. 81767
81781
81796
81810
81825
1
1
2
2
2
, 2
3
3
3
3
10. 18233
18219
18204
18190
18176
9.94044
94069
94095
94120
94146
2
3
3
3
4
10. 05956
05931
05905
05880
05854
10. 12277
12288
12299
12310
12321
1
1
1
1
2
9. 87723"
87712
87701
87690
87679
55
54
53
52
51
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
6 30 40
30 32
30 24
30 16
30 8
5 29 20
29 28
29 36
29 44
29 52
9. 81839
81854
81868
81882
81897
10. 18161
18146-
18132
18118
18103
9.94171
94197
94222
94248
94273
4
5
5
6
6
10. 05829
05803
05778
05752
05727
10. 12332
12343-
12354
12365
12376
2
2
2
2
3
9.87668
87657
87646
87635
87624
50
49
48
47
46
6 30 0
29 52
29 44
29 36
29 28
5 30 0
30 8
30 16
30 24
30 32
9. 81911
81926
81940
81955
81969
4
4
4
4
5
10. 18089
18074
18060
18045
18031
9. 94299
94324
94350
94375
94401
6
7
7
8
8
10. 05701
05676
05650
05625
05599
10. 12387
12399
12410
12421
12432
3
3
3
3
4
9. 87613^
87601
87590
87579
87568
45
44
43
42
41
6 29 20
29 12
29 4
28 56
28 48
5 30 40
30 48
30 56
31 4
31 12
9. 81983
81998
82012
82026
82041
5
5
5
5
6
10. 18017
18002
17988
17974
17959
9. 94426
. 94452
94477
94503
94528
8
9
9
10
10
10. 05574
05548
05523
05497
05472
10. 12443
12454
12465
12476
12487
4
4
4
4
4
9. 87557
87546
87535
87524
87513
40
39
38
37
36
25
26
27
28
29
6 28 40
28 32
28 24
28 16
28 8
5 31 20
31 28
31 36
31 44
31 52
9. 82055
82069
82084
82098
82112
6
6
6
7
7
10. 17945
17931
17916
17902
17888
9. 94554
94579
94604
94630
94655
11
11
11
12
12
10. 05446
05421
05396
05370
05345
10. 12499
12510
12521
12532
12543
5
5
5
5
5
9. 87501
87490
87479
87468
87457
35
34
33
32
31
30
31
32
33
34
6 28 0
27 52
27 44
27 36
27 28
5 32 0
32 8
32 16
32 24
32 32
9. 82126
82141
82155
82169
82184
7
7
8
8
8
10. 17874
17859
17845
17831
17816
9. 94681
94706
94732
94757
94783
13
13
14
14
14
10. 05319
05294
05268
05243
05217
10. 12554
12566
12577
12588
12599
6
6
6
6
6
9. 87446
87434
87423
87412
87401
30
29
28
27
26
35
36
37
38
39
6 27 20
27 12
27 4
26 56
26 48
5 32 40
32 48
32 56
33 4
33 12
9. 82198
82212
82226
82240
82255
8
9
9
9
9
10. 17802
17788
17774
17760
17745
9. 94808
94834
94859
94884
94910
15
15
16
16
17
10. 05192
05166
05141
05116
05090
10. 12610
12622
12633
12644
12655
7
7
7
7
7
9. 87390
87378
87367
87356
87345
25
24
23
22
21
40
41
42
43
44
6 26 40
26 32
26 24
26 16
26 8
5 33 20
33 28
33 36
33 44
33 52
9. 82269
82283
82297
82312
82326
10
10
10
10
10
10. 17731
17717
17703
17689
17674
9. 94935
94961
94986
95012
95037
17
17
18
18
19
10. 05065
05039
05014
04988
04963
10. 12666
12678
12689
12700
12712
7
8
8
8
8
9. 87334
87322
87311
87300
87288
20
19
18
17
16
45
46
47
48
49
6 26 0
25 52
25 44
25 36
25 28
5 34 0
34 8
34 16
34 24
34 32
9. 82340
82354
82368
82382
8239Q
11
11
11
11
12
10. 17660
17646
17632
17618
17604
9. 95062
95088
95113
95139
95164
19
20
20
20
21
10. 04938
04912
04887
04861
04836
10. 12723
12734
12745
12757
12768
8
9
9
9
9
9. 87277
87266
87255
87243
87232
15
14
13
12
11
50
51
52
53
54
6 25 20
25 12
25 4
24 56
24 48
5 34 40
34 48
• 34 56
35 4
35 12
9. 82410
82424
82439
82453
82467
12
12
12
13
13
10. 17590
17576
17561
17547
17533
9. 95190
95215
95240
95266
95291
21
22
22
22
23
10. 04810
04785
04760
04734
04709
0. 12779
12791
12802
12813
12825
9
10
10
10
10
9. 87221
87209
87198
87187
87175
10
9
8
7
6
55
56
57
58
59
60
6 24 40
24 32
24 24
24 16
24 8
24 0
5 35 20
35 28
35 36
35 44
35 52
36 0
9. 82481
82495
82509
82523
82537
82551
13
13
14
14
14
14
10. 17519
17505
17491
17477
17463
17449
9. 95317
95342
95368
95393
95418
95444
23
24
24
25
25
25
10. 04683
04658
04632
04607
04582
04556
0. 12836
12847
12859
12870
12881
12893
10
10
11
11
11
11
9. 87164
87153
87141
87130
87119
87107
5
4
3
2
1
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
131° A A B B C C 48°
Seconds of time
I8
•2*
3s
^S
5s
6*
7» •
(A
2
4
5
7
9
11
12
Prop, parts of cols.-JB
1C
3
2
6
3
10
4
13
6
16
19
8
22
10
Page 814] TABLE M.
Log. Sines, Tangents, and Secants.
42° A A B B C C 187°
M.
Hour A. M
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
0
0
1
1
2
Cotangent
Secant.
Diff.
0
0
0
1
1
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
6 24 0
23 52
23 44
23 36
23 28
5 36 0
36 8
36 16
36 24
36 32
9. 82551
82565
82579
82593
82607
0
0
0
1
1
10. 17449
17435
17421
17407
17393
9. 95444
95469
95495
95520
95545
10. 04556
04531
04505
04480
04455
10. 12893
12904
12915
12927
12938
9. 87107
87096
87085
87073
87062
5
6
7
8
9
6 23 20
23 12
23 4
22 56
22 48
5 36 40
36 48
36 56
37 4
37 12
9. 82621
82635
82649
82663
82677
1
1
2
2
2
10. 17379
17365
17351
17337
17323
9. 95571
95596
95622
95647
95672
2
3
3
3
4
10. 04429
04404
04378
04353
04328
10. 12950
12961
12972
12984
12995
1
i
i
2
2
9. 87050
87039
87028
87016
87005
55
54
53
52
51
10
11
12
13
14
6 22 40
22 32
22 24
22 16
22 8
5 37 20
37 28
37 36
37 44
37 52
9. 82691
82705
82719
82733
82747
2
3
3
3
3
10. 17309
17295
17281
-17267
17253
9. 95698
95723
95748
95774
95799
4
5
5
5
6
10. 04302
04277
04252
04226
04201
10. 13007
13018
13030
13041
13053
2
2
o
JB
3
3
9. 86993
86982
86970
86959
86947
50
49
48
47
46
15
16
17
18
19
6 22 0
21 52
21 44
21 36
21 28
5 38 0
38 8
38 16
38 24
38 32
9. 82761
82775
82788
82802
82816
3
4
4
4
4
10. 17239
17225
17212
17198
17184
9. 95825
95850
95875
95901
95926
6
7
7
8
8
10. 04175
04150
04125
04099
04074
10. 13064
13076
13087
13098
13110
3
3
3
3
4
9. 86936
86924
86913
86902
86890
45
44
43
42
41
20
21
22
23
24
6 21 20
21 12
21 4
20 56
20 48
5 38 40
38 48
38 56
39 4
39 12
9. 82830
82844
82858
82872
82885
5
5
5
5
6
6
6
6
6
7
10. 17170
17156
17142
17128
17115
9. 95952
95977
' 96002
96028
96053
8
9
9
10
10
10. 04048
04023
03998
03972
03947
10. 13121
13133
13145
13156
13168
10. 13179
13191
13202
13214
13225
4
4
4
4
5
9. 86879
86867
86855
86844
86832
40
39
38
37
36
25
26
27
28
29
6 20 40
20 32
20 24
20 16
20 8
5 39 20
39 28
39 36
39 44
39 52
9. 82899
82913
82927
82941
82955
10. 17101
17087
17073
17059
17045
9. 96078
96104
96129
96155
96180
11
11
11
12
12
10. 03922
03896
03871
03845
03820
5
5
5
5
6
9. 86821
86809
86798
86786
86775
35
34
33
32
31
30
31
32
33
34
6 20 0
19 52
19 44
19 36
19 28
5 40 0
40 8
40 16
40 24
40 32
9. 82968
82982
82996
83010
83023
7
7
7
8
8
10. 17032
17018
17004
16990
16977
9. 96205
96231
96256
96281
96307
13
13
14
14
14
10. 03795
• 03769
03744
03719
03693
10. 13237
13248
13260
13272
13283
6
6
6
6
7
9. 86763
86752
86740
86728
86717
30
29
28
27
26
35
36
37
38
39
6 19 20
19 12
19 4
18 56
18 48
5 40 40
40 48
40 56
41 4
41 12
9. 83037
83051
83065
83078
83092
8
8
8
9
9
10. 16963
16949
16935
16922
16908
9. 96332
96357
96383
96408
96433
15
15
16
16
16
10. 03668
03643
03617
03592
03567
10. 13295
13306
13318
13330
13341
7
7
7
7
8
9. 86705
86694
86682
86670
86659
25
24
23
22
21
40
41
42
43
44
6 18 40
18 32
18 24
18 16
18 8
6 18 0
17 52
17 44
17 36
17 28
5 41 20
41 28
41 36
41 44
41 52
9. 83106
83120
83133
83147
83161
9
9
10
10
10
10. 16894
16880
16867
16853
16839
9. 96459
96484
96510
96535
96560
17
17
18
18
19
10. 03541
03516
03490
03465
03440
10. 13353
13365
13376
13388
13400
8
8
8
8
8
9
9
9
9
9
9. 86647
86635
86624
86612
86600
20
19
18
17
16
45
46
47
48
49
5 42 0
42 8
42 16
42 24
42 32
9. 83174
83188
83202
83215
83229
10
11
11
11
11
10. 16826
16812
16798
16785
16771
9. 96586
96611
96636
96662
96687
19
19
20
20
21
21
22
22
22
23
10. 03414
03389
03364
03338
03313
10. 13411
13423
13435
13446
13458
9. 86589
86577
86565
86554
86542
15
14
13
12
11
50
51
52
53
54
6 17 20
17 12
17 4
16 56
16 48
5 42 40
42 48
42 56
43 4
43 12
9. 83242
83256
83270
83283
83297
11
12
12
12
12
10. 16758
16744
16730
16717
16703
9. 96712
96738
96763
96788
96814
10. 03288
03262
03237
03212
03186
10. 13470
13482
13493
13505
13517
10
10
10
10
10
9. 86530
86518
86507
86495
86483
10
9
8
7
6
55
56
57
58
59
60
6 16 40
16 32
16 24
16 16
16 8
16 0
5 43 20
43 28
43 36
43 44
43 52
44 0
9. 83310
83324
83338
83351
83365
83378
13
13
13
13
14
14
10. 16690
16676
16662
16649
16635
16622
9. 96839
96864
96890
96915
96940
96966
23
24
24
25
25
25
Diff.
10. 03161
03136
03110
03085
03060
03034
10. 13528
13540
13552
13564
13575
13587
11
11
11
11
11
12
9. 86472
86460
86448
86436
86425
86413
5
4
3
2
1
0
M.
M.
Hour P.M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Tangent.
Cosecant.
Diff.
Sine.
132° A A B B C C 47°
Seconds of time
1s
2s
3"
41
5"
6"
73
(A
2
3
5
7
9
10
12
Prop, parts of cols. •< B
(C
3
1
6
3
10
-4
13
6
16
7
19
9
22
10
TABLE ±±. [Page 815
Log. Sines, Tangents, and Secants.
43° A A B B C C 136°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
1
2
3
4
6 16 0
15 52
15 44
15 36
15 28
5 44 0
44 8
44 16
44 24
44 32
9. 83378
83392
83405
83419
83432
0
0
0
1
1
10. 16622
16608
16595
16581
16568
9. 96966
96991
97016
97042
97067
0
0
1
1
2
10. 03034
03009
02984
02958
02933
10. 13587
13599
13611
13623
13634
0
0
0
1
1
1
1
1
2
2
9. 86413
86401
86389
86377
86366
60
59
58
57
56
5
6
7
8
9
6 15 20
15 12
15 4
14 56
14 48
5 44 40
44 48
44 56
45 4
45 12
9. 83446
83459
83473
83486
83500
1
1
2
2
2
10. 16554
16541
16527
16514
16500
9. 97092
97118
97143
97168
97193
2
3
3
3
4
10. 02908
02882
02857
02832
02807
10. 13646
13658
13670
13682
13694
9. 86354
86342
86330
86318
86306
55
54
53
52
51
10
11
12
13
14
6 14 40
14 32
14 24
14 16
14 8
5 45 20
45 28
45 36
45 44
45 52
9. 83513
83527
83540
83554
83567
2
2
3
3
3
10. 16487
16473
16460
16446
16433
9. 97219
97244
97269
97295
97320
4
5
5
5
6
10. 02781
02756
02731
02705
02680
10. 13705
13717
13729
13741
13753
2
2
2
3
3
9. 86295
86283
86271
86259
86247
50
49
48
47
46
15
16
17
18
19
6 14 0
13 52
13 44 .j
13 36
13 28
5 46 0
46 8
46 16
46 24
46 32
9. 83581
83594
83608
83621
83634
3
4
4
4
4
10. 16419
16406
16392
16379
16366
9. 97345
97371
97396
97421
97447
6
7
7
8
8
10. 02655
02629
02604
02579
02553
10. 13765
13777
13789
13800
13812
3
3
3
4
4
9. 86235
86223
86211
86200
86188
45
44
43
42
41
20
21
22
23
24
6 13 20
13 12
13 4
12 56
12 48
5 46 40
46 48
46 56
47 4
47 12
9. 83648
83661
83674
83688
83701
4
5
5
5
5
10. 16352
16339
16326
16312
16299
9. 97472
97497
97523
97548
97573
8
9
9
10
10
10. 02528
02503
02477
02452
02427
10. 13824
13836
13848
13860
13872
4
4
4
5
5
9.86176
86164
86152
86140
86128
40
39
38
37
36
25
26
27
28
29
6 12 40
12 32
12 24
12 16
12 8
5 47 20
47 28
47 36
47 44
47 52
9. 83715
83728
83741
83755
83768
6
6
6
6
6
7
7
7
7
8
10. 16285
16272
16259
16245
16232
9. 97598
97624
97649
97674
97700
11
11
11
12
12
10. 02402
02376
02351
02326
02300
10. 13884
13896
13908
13920
13932
5
5
5
6
6
9.86116
86104
86092
86080
86068
35
34
33
32
31
30
31
32
33
34
6 12 0
11 52
11 44
11 36
11 28
5 48 0
48 8
48 16
48 24
48 32
9. 83781
83795
83808
83821
83834
10. 16219
16205
16192
16179
16166
9. 97725
97750
97776
97801
97826
13
13
13
14
14
10. 02275
02250
02224
02199
02174
10. 13944
13956
13968
13980
13992
6
6
6
7
7
9. 86056
86044
86032
86020-
86008
30
29
28
27
26
35
36
37
38
39
6 11 20
11 12
11 4
10 56
10 48
5 48 40
48 48
48 56
49 4
49 12
9. 83848
83861
83874
83887
83901
8
8
8
8
9
10. 16152
16139
16126
16113
16099
9. 97851
97877
97902
97927
97953
15
15
16
16
16
10. 02149
02123
02098
02073
02047
10.14004
14016"
14028
14040
14052
7
7
7
8
8
9.85996
85984
85972
85960
85948
25
24
23
22
21
40
41
42
43
44
6 10 40
10 32
10 24
10 16
10 8
5 49 20
49 28
49 36
49 44
49 52
9. 83914
83927
83940
83954
83967
9
9
9
10
10
10. 16086
16073
16060
16046
16033
9. 97978
98003
98029
98054
98079
17
17
18
18
19
10. 02022
01997
01971
01946
01921
10. 14064
14076
14088
14100
14112
8
8
8
9
9
9. 85936
85924
85912
85900
85888
20
19
18
17
16
45
46
47
48
49
6 10 0
9 52
9 44
9 36
9 28
5 50 0
50 8
50 16
50 24
50 32
9. 83980
83993
84006
84020
84033
10
10
10
11
11
10. 16020
16007
15994
15980
15967
9. 98104
98130
98155
98180
98206
19
19
20
20
21
10. 01896
01870
01845
01820
01794
10. 14124
14136
14149
14161
14173
9
9
9
10
10
9. 85876
85864
85851
85839
85827
15
14
13
12
11
50
51
52
53
54
6 9 20
9 12
9 4
8 56
8 48
5 50 40
50 48
50 56
51 4
51 12
9.84046
84059
84072
84085
84098
11
11
12
12
12
10. 15954
15941
15928
15915
15902
9. 98231
98256
98281
98307
98332
21
22
22
22
23
10. 01769
01744
01719
01693
01668
10. 14185
14197
14209
14221
14234
10
10
10
11
11
9. 85815
85803
85791
85779
85766
10
9
8
7
6
5
4
3
2
1
0
55
56
57
58
59
60
6 8 40
8 32
8 24
8 16
8 8
8 0
5 51 20
51 28
51 36
51 44
51 52
52 0
9. 84112
84125
84138
84151
84164
84177
12
12
13
13
13
13
10. 15888
15875
15862
15849
15836
15823
9. 98357
98383
98408
98433
98458
98484
23
24
24
24
25
25
10. 01643
01617
01592
01567
01542
01516
10. 14246
14258
14270
14282
14294
14307
11
11
11
12
12
12
9.85754
85742
85730
85718
85706
85693
M.
Hour P. M.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
133° A A B B C C 46°
Seconds of time
1« -2' 3' 4*
53
63
7'
i
(A
Prop, parts of colsxB
2 1 3 ' i 5 1 7
3 ! 6 i 9 13
2 i 3 5 | 6
8
16
10
•J
12
22
il
Page 816] TABLE M.
Log. Sines, Tangents, and Secants.
44° A A B B C C 135°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
59
58
57
56
0
1
2
3
4
680
7 52
7 44
7 36
7 28
5 52 0
52 8
52 16
52 24
52 32
9. 84177
84190
84203
84216
84229
0
0
0
1
1
10. 15823
15810
15797
15784
15771
9. 98484
98509
98534
98560
98585
0
0
1
1
2
10.01516
01491
01466
01440
01415
10. 14307
14319
14331
14343
14355
0
0
0
1
1
9. 85693
85681
85669
85657
85645
5
6
7
8
9
6 7 20
7 12
7 4
6 56
6 48
5 52 40
52 48
52 56
53 4
53 12
9. 84242
84255
84269
84282
84295
1
1
2
2
2
10. 15758
15745
15731
15718
15705
9. 98610
98635
98661
98686
98711
2
3
3
3
4
10. 01390
01365
01339
01314
01289
10. 14368
14380
14392
14404
14417
1
1
1
2
2
9. 85632
85620
85608
85596
85583
55
54
53
52
51
10
11
12
13
14
6 6 40
6 32
6 24
6 16
6 8
5 53 20
53 28
53 36
53 44
53 52
9. 84308
84321
84334
84347
84360
2
2
3
3
3
10. 15692
15679
15666
15653
15640
9. 98737
98762
98787
98812
98838
4
5
5
5
6
10. 01263
01238
01213
01188
01162
10. 14429
14441
14453
14466
14478
10. 14490
14503
14515
14527
14540
2
2
2
3
3
3
3
4
4
4.
9. 85571
85559
85547
85534
85522
50
49
48
47
46
15
16
17
18
19
660
5 52
5 44
5 36
5 28
5 54 0
54 8
54 16
54 24
54 32
9. 84373
84385
84398
84411
84424
3
3
4
4
4
10. 15627
15615
15602
15589
15576
9. 98863
98888
98913
98939
98964
6
7
7
8
8
10. 01137
01112
01087
01061
01036
9. 85510
85497
85485
85473
85460
45
44
43
42
41
40
39
38
37
i
20
21
22
23
24
6 5 20
5 12
5 4
4 56
4 48
5 54 40
54 48
54 56
55 4
55 12
9. 84437
84450
84463
84476
84489
4
5
5
5
5
10. 15563
15550
15537
15524
15511
9. 98989
99015
99040
99065
99090
8
9
9
10
10
10. 01011
00985
00960
00935
00910
10. 14552
14564
14577
14589
14601
4
4
5
5
5
9. 85448
85436
85423
85411
85399
25
26
27
28
29
6 4 40
4 32
4 24
4 16
4 8
5 55 20
55 28
55 36
55 44
55 52
9. 84502
84515
84528
84540
84553
5
6
6
6
6
10. 15498
15485
15472
15460
15447
9.99116
99141
99166
99191
99217
11
11
11
12
12
10. 00884
00859
00834
00809
00783
10. 14614
14626
14639
14651
14663
5
5
6
6
6
6.
6
7
7
7
9. 85386
85374
85361
85349
85337
35
34
33
32
31
30
31
32
33
34
640
3 52
3 44
3 36
3 28
5 56 0
56 8
56 16
56 24
56 32
9. 84566
84579
84592
84605
84618
6
7
7
7
7
10. 15434
15421
15408
15395
15382
9. 99242
99267
99293
99318
99343
13
13
13
14
14
10. 00758
00733
00707
00682
00657
10. 14676
14688
14701
14713
14726
9. 85324
85312
85299
85287
85274
30
29
28
27
26
35
36
37
38
39
6 3 20
3 12
3 4
2 56
2 48
5 56 40
56 48
56 56
57 4
57 12
9. 84630
84643
84656
84669
84682
8
8
8
8
8
10. 15370
15357
15344
15331
15318
9. 99368
99394
99419
99444
99469
15
15
16
16
16
10. 00632
00606
00581
00556
00531
10. 14738
14750
14763
14775
14788
7
7
8
8
8
9. 85262
85250
85237
85225
85212
25
24
23
22
21
40
41
42
43
44
6 2 40
2 32
2 24
2 16
2 8
5 57 20
57 28
57 36
57 44
57 52
9. 84694
84707
84720
84733
84745
9
9
9
9
9
10
10
10
10
11
10. 15306
15293
15280
15267
15255
9. 99495
99520
99545
99570
99596
17
17
18
18
19
10. 00505
00480
00455
00430
00404
10. 14800
14813
14825
14838
14850
8
a
9
9
9
9. 85200
85187
85175
85162
85150
20
19
18
17
16
45
46
47
48
49
620
1 52
1 44
1 36
1 28
5 58 0
58 8
58 16
58 24
58 32
9. 84758
84771
84784
84796
84809
10. 15242
15229
15216
15204
15191
9. 99621
99646
99672
99697
99722
19
19
20
20
21
10. 00379
00354
00328
00303
00278
10. 14863
14875
14888
14900
14913
9
10
10
10
10
9. 85137
85125
85112
85100
85087
15
14
13
12
11
50
51
52
53
54
6 1 20
1 12
1 4
0 56
0 48
5 58 40
58 48
58 56
59 4
59 12
9. 84822
84835
84847
84860
84873
11
11
11
11
12
10. 15178
15165
15153
15140
15127
9. 99747
99773
99798
99823
99848
21
21
22
22
23
23
24
24
24
25
25
10. 00253
00227
00202
00177
00152
10. 14926
14938
14951
14963
14976
10
11
11
11
11
9. 85074
85062
85049
85037
85024
10
9
8
7
6
55
56
57
58
59
60
6 0 40
0 32
0 24
0 16
0 8
0 0
5 59 20
59 28
59 36
59 44
59 52
600
9. 84885
84898
84911
84923
84936
84949
12
12
12
12
13
13
10. 15115
15102'
15089
15077
15064
15051
9. 99874
99899
99924
99949
99975
10. 00000
10. 00126
00101
00076
00051
00025
00000
10. 14988
15001
15014
15026
15039
15051
11
12
12
12
12
12
9. 85012
84999
84986
84974
84961
84949
5
4
3
2
1
0
M.
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
134° A A B B C C 45°
Seconds of time .
1s
9s
3s
4s
5"
6'
7"
(A
B
2
3
2
3
6
3
5
9
5
6
13
6
8
16
8
10
19
9
11
22
11
TABLE 45. [Page 817
Haversines.
B '
0* On 0° <K
0fcfmO°30/
Oh 4m 1° <K
Oh 6m 1° 3(K
0*8^2°^
s
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. iXat. Hav.
0 0
t
4+ 1
6
-00
1.72333
2.32539
2.67757
0.00000
.00000
.00000
.00000
5.27963
.29399
.30811
.32201
0.00002
.00002
.00002
.00002
5.88168
.88889
.89604
.90313
0.00008
.00008
.00008
.00008
6.23385
.23866
.24345
.24821
0.00017
.00017
.00018
.00018
6.48371
.48732
.49092
.49450
0.00030
.00031
.00031
.00031
60
58
56
54
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
2.92745
3.12127
3.27963
3.41353
3.52951
3.63182
3.72333
3.80612
0.00000
.00000
.00000
.00000
0.00000
.00000
.00000
.00000
5.33569
.34916
.36242
.37548
5.38835
.40103
.41352
.42585
0.00002
.00002
.00002
.00002
0.00002
.00003
.00003
.00003
5.91016
.91714
.92406
.93093
5.93774
.944-50
.95121
.95786
0.00008
.00008
.00008
.00009
0.00009
.00009
.00009
.00009
6. 25294
.25765
.26233
.26699
6.27162
.27623
.28081
.28537
0.00018
.00018
.00018
.00018
0.00019
.00019
.00019
.00019
6.49807
.50162
.50516
.50868
6.51219
.51568
.51916
.52263
0.00031
.00032
.00032
.00032
0.00033
.00033
.00033
.00033
d&
50
48
46
44
42
40
38
24+ 6
26
28+ 7
30
32+ 8
34
36+ 9
38
3.88169 0.00000
3.95122 .00000
4.01559 .00000
4.07551 i .00000
4.13157 ; 0.00000
.18423 .00000
.23388 : .00000
.28084 .00000
5.43799
.44997
.46179
.47345
5.48496
.49631
.50752
.51858
0.00003
.00003
.00003
.00003
0.00003
.00003
.00003
.00003
5.96447
.97102
.97753
.98399
5.99040
5.99676
6.00308
.00935
0.00009
.00009
.00010
.00010
0.00010
.00010
.00010
.00010
6.28991
29442
.29891
.30337
6.30781
.31223
.31663
.32101
0.00019
.00020
.00020
.00020
0.00020
.00021
.00021
.00021
6.52608
.52952
.53295
.53636
6.53976
.54315
.54652
.54988
0.00034
.00034
.00034
.00034
0.00035
.00035
.00035
.00035
36
34
32
30
28
26
24
22
40+10
42
44+11
46
48+12
50
52+13
54
4.32539 0.00000
.36777 , .00000
.40818 .00000
.44679 .00000
4.48375 0.00000
.51921 .00000
.55328 .00000
.58606 .00000
5.52951 0.00003
.54030 .00003
.55095 .00004
.56148 ! .00004
5.57189 1 0.00004
.58216 .00004
.59232 .00004
.60236 .00004
6.01557
.02176
.02789
.03399
6.04004
.04605
.05202
.05795
0.00010
.00011
.00011
.00011
0.00011
.00011
.00011
.00011
6.32536
.32969
.33400
.33829
6.34256
.34681
.35103
.35524
0.00021
.00021
.00022
.00022
0.00022
.00022
.00022
.00023
6.55323
.55656
.55988
.56319
6.56649
.56977
.57304
.57630
0.00036
.00036
.00036
.00037
0.00037
.00037
.00037
.00038
20
18
16
14
12
10
8
6
56+lt
58
4.61765 0.00000
4.64813 0.00000
5.61229 0.00004
5.62211 0.00004
6.06384 0.00012
6.06969 0.00012
6.35943
6.36359
0.00023
0.00023
6.57955
6.58278
0.00038
0.00038
4
2
23* 59^
23* 57^
23* 55m
23h 53m
23* 5im
8 '
0+15
2
4+16
(5
Oh im 0° 0/
Oh 3^ 0° 30"
Oh5ml° O'
Oh 7m 1° 307
Oh 9m 2° 0'
s
60
58
56
54
4.67757
.70605
.73363
.76036
0.00000
.00000
.00001
.00001
5.63181 I 0.00004
.64141 ! .00004
.65090! .00004
.66029 .00005
6.07550
.08127
.08700
.09270
0.00012
.00012
.00012
.00012
6.36774
.37186
.37597
.38006
0.00023
.00024
.00024
.00024
6.58600
.58921
.59241
.59560
0.00039
.00039
.00039
.00039
£+17
10
12+18
14
16+19
18
20+20
22
4.78629
.81147
.83594
.85973
4.88290
.90-546
.92745
.94890
0.00001
.00001
.00001
.00001
0.00001
.00001
.00001
.00001
5.66958
.67877
.68787
.69687
5.70578
.71460
.72332
.73197
0.00005
.00005
.00005
.00005
0.00005
.00005
.00005
.00005
6.09836
.10398
.10956
.11511
6.12063
.12611
.13155
.13696
0.00013
.00013
.00013
.00013
0.00013
.00013
.00014
.00914
6.38412
.38817
.39220
.39622
6.40021
.40418
.40814
.41208
0.00024
.00024
.00025
.00025
0.00025
.00025
.00026
.00026
6.59878
.60194
.60509
.60823
6.61136
.61448
.61759
.62068
0.00040
.00040
.00040
.00041
0.00041
.00041
.00041
.00042
52
50
48
46
44
42
40
38
24+21
26
28+22
30
32+23
34
36+24
38
4.96983
4.99027
5.01024
.02976
5.04885
.06753
.08581
.10372
0.00001
.00001
.00001
.00001
0.00001
.00001
.00001
.00001
5.74052
.74900
.75739
.76570
5.77394
.78209
.79017
.79818
0.00006
.00006
.00006
.00006
0.00006
.00006
.00006
.00006
6.14234
.14769
.15300
.15828
6.16353
.16874
.17393
.17908
0.00014
.00014
.00014
.00014
0.00015
.00015
.00015
.00015
6.41600 .
.41990
.42379
.42766
6.43151
.43534
.43916
.44296
0.00026
.00026
.00027
.00027
0.00027
.00027
.00027
.00028
6.62377
.62684
.62991
.63296
6.63600
.63903
.64205
.64504
0.00042
.00042
.00043
.00043
0.00043
.00044
.00044
.00044
36
34
32
30
28
26
24
22
40+25
42
44+26
46
48+21
50
52+28
54
5.12127
.13847
.15534
.17188
5.18812
.20406
.21971
.23508
0.00001
.00001
.00001
.00001
0.00002
.00002
.00002
.00002
5.80611 0.00006
.81397 .00007
.82176 .00007
.82948 i .00007
5.83713 0.00007
.84472 i .00007
.85224 .00007
.85969 .00007
6.18421
.18930
.19437
.19940
6.20441
.20938
.21433
.21925
0.00015
.00015
.00016
.00016
0.00016
.00016
.00016
.00017
6.44675
.45052
.45427
.45800
6.46172
.46543
.46911
.47279
0.00028
.00028
.00028
.00029
0.00029
.00029
.00029
.00030
6.64806
.65105
.65403
.65700
6.65996
.66291
.66585
.66878
0.00044
.00045
.00045
.00045
0.00046
.00046
.00046
.00047
20
18
16
14
12
10
8
6
4
2
0
56+29
58
60+30
5.25019
.26503
5.27963
0.00002
.00002
0.00002
5.86709 0.00007
.87442 .00008
5.88168 0.00008
6.22415
.22901
6.23385
0.00017
.00017
0.00017
6.47644
.48008
6.4S371
0.00030
.00030
0.00030
6.67170
.67461
6.67751
0.00047
.00047
0.00048
%3h 5Sm
2 3h 56m
23* 54m
23h 52m
23h 50m
Page 818] TABLE 45.
Haversines.
s '
Oh 10m 3° 30'
Oh 12m 3° ox
0^ 14™ 3° 30X
Oh iQrn 4° 0'
Oh 18m 4° 30X
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav.
0 0
2
4+ 1
6
6.67751
.68040
.68328
.68615
0.00048
.00048
.00048
.00049
6.83584
.83825
.84065
.84304
0.00069
.00069
.00069
.00070
6.96970
.97176
.97382
.97588
0.00093
.00094
.00094
.00095
7.08564
.08745
.08925
.09105
0.00122
.00122
.00123
.00123
7.18790
.18950
.19111
.19271
0.00154
.00155
.00155
.00156
60
58
56
54
8+ 3
10
12+ 3
14
16+ 4
18
20+ 5
22
6.68901
.69186
.69470
.69754
6.70036
.70318
.70598
.70878
0.00049
.00049
.00050
.00050
0.00050
.00050
.00051
.00051
6.84543
.84782
.85019
.85256
6.85492
.85728
.85963
.86197
0.00070
.00070
.00071
.00071
0.00072
.00072
.00072
.00073
6.97793
.97997
.98201
.98405
6.98608
.98811
.99013
.99214
0.00095
.00095
.00096
.00096
0.00097
.00097
.00098
.00098
7.09284
.09464
.09642
.09821
7.09999
.10177
.10354
.10531
0.00124
.00124
.00125
.00125
0.00126
.00126
.00127
.00127
7.19430
.19590
.19749
.19908
7.20066
.20225
.20383
.20540
0.00156
.00157
.00158
.00158
0.00159
.00159
.00160
.00160
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
~2~0~
18
16
14
12
10
8
6
24+ 6
26
28+ 7
30
32+ 8
34
36+ 9
38
6.71157
.71435
.71712
.71988
6.72263
.72537
.72811
.73084
0.00051
.00052
.00052
.00052
0.00053
.00053
.00053
.00054
6.86431
.86664
.86897
.87129
6.87360
.87591
.87821
.88050
0.00073
.00074
.00074
.00074
0.00075
.00075
.00076
.00076
6.99416
6.99616
6.99817
7.00017
7.00216
.00415
.00613
.00811
0.00099
.00099
.00100
.00100
0.00101
.00101
.00101
.00103
7.10708
.10884
.11060
.11236
7.11411
.11586
.11760
.11934
0.00128
.00128
.00129
.00130
0.00130
.00131
.00131
.00132
7.20698
.20855
.21012
.21168
7.21325
.21481
.21636
.21792
0.00161
.00162
.00163
.00163
0.00163
.00164
.00165
.00165
40+10
42
44+11
46
48+12
50
52+13
54
6.73355
.73626
.73896
.74166
6.74434
.74702
.74969
.75235
6.75500
6.75764
0.00054
.00054
.00055
.00055
0.00056
.00056
.00056
.00057
6.88279
.88507
.88735
.88962
6.89188
.89414'
.89639
.89864
0.00076
.00077
.00077
.00078
0.00078
.00078
.00079
.00079
7.01009
.01206
.01403
.01599
7.01795
.01990
.02185
.02379
0.00102
.00103
.00103
.00104
0.00104
.00105
.00105
.00106
7.12108
.12282
.12455
.12627
7.12800
.12972
.13144
.13315
0.00132
.00133
.00133
.00134
0.00134
.00135
.00135
.00136
7.21947
.22102
.22256
.22411
7.22565
.22718
.22872
.23025
0.00166
.00166
.00167
.00168
0.00168
.00169
.00169
.00170
56+14
58
0.00057
0.00057
6.90088
6.90312
0.00080
0.00080
7.02573
7.02767
0.00106
0.00107
7.13486
7.13657
0.00136
0.00137
7.23178
7.23331
0.00171
0.00171
4
2
2Sh 49^
23 h 47m
23h 45m
23h43m
23h 4im
s '
0+15
*
4+16
6
Oh urn 2° 30'
Oh 13m 3° Qx
Oh 15m 3° 30'
Oh nm 4° O7
Oh 19m 4° 30'
s
60
58
56
54
6.76028
.76290
.76552
.76814
0.00058
.00058
.00058
.00059
6.90535
.90757
.90979
.91200
0.00080
.00081
.00081
.00083
7.02960
.03153
.03345
.03537
0.00107
.00108
.00108
00108
7.13827
.13997
.14167
.14337
0.00137
.00138
.00139
.00139
7.23483
.23635
.23787
.23939
0.00173
.00173
.00173
.00174
£+17
10
12+18
14
16+1&
18 /
20+20
22
6.77074
.77334
.77592
.77851
6.78108
.78364
.78620
.78875
0.00059
.00059
.00060
.00060
0.00060
.00061
.00061
.00061
6.91421
.91641
.91860
.92079
6.92298
.92516
.92733
.92950
0.00083
.00083
.00083
.00083
0.00084
.00084
.00085
.00085
7.03729
.03920
.04110
.04300
7.04490
.04680
.04869
.05057
0.00109
.00109
.00110
.00110
0.00111
.00111
.00112
.00112
7.14506
.14674
.14843
.15011
7.15179
.15346
.15513
.15680
0.00140
.00140
.00141
.00141
0.00142
.00142
.00143
.00143
7.24090
.24241
.24392
.24543
7.24693
.24843
.24993
.25143
0.00174
.00175
.00175
.00176
0.00177
.00177
.00178
.00178
52
50
48
46
44
42
40
38
24+31
26
28+22
30
32+23
34
36+24:
38
6.79129
.79383
.79630
.79888
6.80139
.80390
.80640
.80889
0.00062
.00062
.00063
.00063
0.00063
.00064
.00064
.00064
6.93166
.93382
.93597
.93812
6.94026
.94239
.94453
.94665
0.00085
.00086
.00086
.00087
0.00087
.00088
.00088
.00088
7.05245
.05433
.05620
.05807
7.05994
.06180
.06366
.06551
0.00113
.00113
.00114
.00114
0.00115
.00115
.00116
.00116
7.15846
.16013
.16178
.16344
7.16509
.16674
.16839
.17003
0.00144
.00145
.00145
.00146
0.00146
.00147
.00147
.00148
7.25292
.25441
.25590
.25738
7.25886
.26034
.26182
.26330
0.00179
.00180
.00180
.00181
0.00181
.00183
.00183
.00183
36
34
32
30
28
26
24
22
40+25
42
44+36
46
48+21
50
52+38
54
6.81137
.81385
.81632
.81879
6.82124
' .82369
.82614
.82857
0.00065
.00065
.00066
.00066
0.00066
.00067
.00067
.00067
6.94877
.95089
.95300
.95510
6.95720
.95930
.96139
.96347
0.00089
.00089
.00090
.00090
0.00091
.00091
.00091
.00093
7.06736
.06920
.07105
.07288
7.07472
.07655
.07837
.08019
0.00117
.00117
.00118
.00118
0.00119
.00119
.00120
.00120
7.17167
.17331
.17494
.17657
7.17820
.17982
.18144
.18306
0.00148
.00149
.00150
.00150
0.00151
.00151
.00152
.00152
7.26477
.26624
.26771
.26917
7.27064
.27210
.27355
.27501
0.00184
.00185
.00185
.00186
0.00186
.00187
.00188
.00188
20
18
16
14
12
10
8
6
56+29
58
60+30
6.83100
.83342
6.83584
0.00068
.00068
0.00069
6.96555
.66763
6.96970
0.00093
.00093
0.00093
7.08201
.08383
7.08564
0.00121
.00121
0.00122
7.18468
.18629
7.18790
0.00153
.00154
0.00154
7.27646
.27791
7.27936
0.00189
.00190
0.00190
4
2
0
23 h 48m
23h 46^
23 h 44m
23h 42^
23h 40m
TABLE 45. [Page 819
Haversines.
s '
OA 20™ 5° V
0*2-2* 5° 30'
0* 24™ 6° O7
0* 26* 6° 3(K
0* 28* 7° 0"
s
60
58
56
54
Log. Hav.
Nat. Hav.
Log. Hav. Xat.Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0 0
o
4+ 1
6
7.27936
.28080
.28225
.28369
0.00190
.00191
.00192
.00192
7.36209
.36340
.36471
.36602
0.00230
.00231
.00232
.00232
7.43760
.43880
.44001
.44121
0.00274
.00275
.00275
.00276
7.50706
.50817
.50928
.51039
0.00321
.00322
.00323
.00324
7,57135
.57238
,57341
.57444
0.00373
.00374
.00374
.00375
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
7.28513
.28656
.28800
.28943
7.29086
.29228
.29371
.29513
0.00193
.00193
.00194
.00195
0.00195
.00196
.00197
.00197
7.36733
.36864
.36994
.37124
7.37254
.37384
.37514
.37643
0.00233
.00234
.00234
.00235
0.00236
.00237
.00237
.00238
7.44241
.44361
.44480
.44600
7.44719
.44838
.44957
.45076
0.00277
.00278
.00278
.00279
0.00280
.00281
.00282
.00282
7.51149
,51260
.51370
.51481
7.51591
.51701
.51811
.51921
0.00325
.00326
.00326
.00327
0.00328
.00329
.00330
.00331
0.00331
.00332
.00333
.00334
0.00335
.00336
.00336
.00337
7.57547
.57650
.57752
.57855
7.57957
,58060
.58162
.58264
7.58366
.58467
.58569
.58670
7.58772
,58873
.58974
.59075
0.00376
.00377
.00378
.00379
0.00380
.00381
.00382
.00383
52-
50
48
46
44
42
40
38
24+ 6
26
28+ 7
SO
32+ 8
34
36+ 9
38
7.29655
.29797
.29938
.30079
7.30220
.30361
.30502
.30642
0.00198
.00199
.00199
.00200
0.00201
.00201
.00202
.00203
7.37773
.37902
.38030
.38159
7.38288
.38416
.38544
.38672
0.00239
.00239
.00240
.00241
0.00241
.00242
.00243
.00244
7.45194
.45313
.45431
.45549
7.45667
.45785
.45903
.46020
0.00283
.00284
.00285
.00285
0.00286
.00287
.00288
.00289
7.52030
.52140
,52249
.52358
7.52467
.52576
,52685
.52794
0.00383
.00384
.00385
.00386
0.003S7
.00388
.00389
.00390
36
34
32
30
28
26
24
2 ?
40+10
42
44-1-11
46
4^+12
50
52+li
54
7.30782
.30922
.31062
.31201
7.31340
.31479
.31618
.31757
0.00203
.00204
.00204
.00205
0.00206
.00206
.00207
.00208
7.38800 0.00244
.38927 , .00245
.39054 i .00246
.39182 .00247
7.39309 0.00247
.39435 .00248
.39562 .00249
.39688 .00249
7.46138
.46255
.46372
.46489
7.46605
.46722
.46838
.46955
0.00289
.00290
.00291
.00292
0.00292
.00293
.00294
.00295
7,52902
.53011
.53119
.53227
7.53335
.53443
,53550
.53658
0.00338
.00339
.00340
.00341
0.00341
.00342
.00343
.00344
7,59176
.59277
.59378
.59478
7.59579
.59679
.59779
.59879
0.00391
.00392
.00392
.00393
0.00394
.00395
.00396
.00397
20
18
16
14
i>
10
8
6
56+14
58
7.31895
7.32033
0.00208
0.00209
7.39815 ; 0.00250
7.39941 0.00251
7.47071
7.47187
0.00296
0.00296
7.53766
7.53873
0.00345
0.00346
7.59979
7.60079
0.00398
0.00399
4
2
23* 39^
23 h .5;. -I
•23* 35"* '
23* 33m
23* 31m
s '
0*21" 5° V
0* 23* 5° 30X
0* 25m 6° O7
0* 27m 6° 307
0* 29m 7° <K
s
60
58
56
54
0+15
2
4+16
6
7.32171
.32309
.32446
,32583
0.00210
.00210
.00211
.00212
7.40067
.40192
.40318
.40443
0.00252
.00252
.00253
.00254
7.47302 0.00297
.47418 .00298
.47533 .00299
.47649 .00300
7.53980
,54087
,54194
,54301
0.00347
.00347
.00348
.00349
7.60179
.60279
.60378
.60478
0.00400
.00401
.00402
.00403
5+17
J70
12+lS
14
16+19
18
20+20
22
7.32720
.32857
.32994
.33130
7.33266
.33402
.33538
.33673
0.00212
.00213
.00214
.00214
0.00215
.00216
.00216
.002$
7.40568
.40693
.40818
.40943
7.41067
.41191
.41315
.41439
0.00255
.00255
.00256
.00257
0.00257
.00258
.00259
.Q0260
7.47764
.47879
.47994
.48109
7.48223
.48337
.48452
.48566
0.00300
.00301
.00302
.00303
0.00304
.00304
.00305
.00306
7,54407
,54514
.54620
,34727
7.54833
,54939
.55045
.55150
0.00350
.00351
.00352
.00353
0.00353
.00354
.00355
.00356
7.60577
.60676
.60775
.60874
7.60973
.61072
.61170
.61269
0.00403
.00404
.00405
.00406
0.00407
.00408
.00409
.00410
o2
50
48
46
44
42
40
38
24+21
26
28+22
30
32+23
34
36+24:
S8
7.33809
.33944
.34079
.34213
7.34348
.34482
.34616
.34750
0.00218
.00218
.00219
.00220
0.00221
.00221
.00222
.00223
7.41563
.41686
.41810
.41933
7.42056
.42179
.42301
.42424
0.00260
.00261
.00262
.00263
0.00263
.00264
.00265
.00266
7.48680
.48794
.48907
.49021
7.49134
.49247
.49360
.49473
0.00307
.00308
.00308
.00309
0.00310
.00311
.00312
.00312
7.55256
.55361
.55467
.55572
7.55677
.55782
.55887
.55992
0.00357
.00358
.00359
.00360
0.00360
.00361
.00362
.00363
7.61367
.61466
.61564
.61662
7.61760
.61858
.61955
.62053
0.00411
.00412
.00413
.00414
0.00415
.00416
.00416
.00417
36
34
32
30
28
26
24
22
40+2*
42
44+26
46
48+21
50
52+28
54
7.34884
.35017
.35150
.35283
7.35416
.35549
.35681
.35813
0.00223
.00224
.00225
.00225
0.00226
.00227
.00227
.00228
7.42546 ; 0.00266
.42668 .00267
.42790 .00268
.42912 .00269
7.43034 0.00269
.43155 i .00270
.43277 ! .00271
.43398 .00272
7.49586
.49699
.49811
.49923
7.50036
.50148
.50259
.50371
0.00313
.00314
.00315
.00316
0.00316
.00317
.00318
.00319
7,56096 0.00364
,56201 .00365
.56305 .00366
.56409 .00367
7.56513 0.00367
.56617 .00368
.56721 .00369
.56825 .00370
7.62151 0.00418
.62248 .00419
.62345 i .00420
.62442 : .00421
7.62540 ! 0.00422
.62636 .00423
.62733 .00424
.62830 .00425
20
18
16
14
12
10
8
6
56+29
58
60+30
7.35945 0.00229
.36077 .00229
7.36209 0.00230
7.43519
.43639
7.43760
0.00272
.00273
0.00274
7.50483
.50594
7.50706
0.00320
.00321
0.00321
7.56928 0.00371
,57032 .00372
7,57135 0.00373
7.62927 0.00426
.63023 i .00427
7.63120 0.00428
4
2
0
23* 38^
23* 36^
23* 34™
23* 32m
23* SO*
Page 820] TABLE 45.
Haversines.
s '
0* 30m 7° 30'
0* 32™ 8° 0'
Oh 34m 8° 30'
Oh 36m 9° 0'
0* 38m 9° 307
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0 0
2
4+ 1
6
7.63120
.63216
.63312
.63408
0.00428
.00429
.00430
.00431
7.68717
.68807
.68897
.68987
0.00487
.00488
.00489
.00490
7.73974
.74059
.74143
.74228
0.00549
.00550
.00551
.00552
7.78929
.79009
.79089
.79169
7.79249
.79329
.79409
.79489
7.79568
.79648
.79728
.79807
0.00616
.00617
.00618
.00619
0.00620
.00621
.00622
.00624
0.00625
.00626
.00627
.00628
7.83615
.83691
.83767
.83842
0.00686
.00687
.00688
.00689
60
58
56
54
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
7.63504
.63600
.63696
.63792
7.63887
.63983
.64078
.64173
0.00432
.00433
.00433
.00434
0.00435
.00436
.00437
.00438
7.69077
.69167
.69257
.69347
7.69437
.69526
.69616
.69705
0.00491
.00492
.00493
.00494
0.00495
.00496
.00497
.00498
7.74313
.74398
.74482
.74567
7.74651
74735
.74819
.74904
0.00554
.00555
.00556
.00557
0.00558
.00559
.00560
.00561
7.83918
.83994
.84070
.84145
7.84221
.84296
.84372
.84447
0.00691
.00692
.00693
.00694
0.00695
.00697
.00698
.00699
52
50
48
46
44
42
40
38
24+ 6
26
28+ 7
SO
32+ 8
34
36+ 9
38
7.64269
.64364
.64458
.64553
7.64648
.64743
.64837
.64932
0.00439
.00440
.00441
.00442
0.00443
.00444
.00445
.00446
7.69794
.69883
.69972
.70061
7.70150
.70239
.70328
.70416
0.00499
.00500
.00501
.00502
0.00503
.00504
.00505
.00506
7.74988
.75072
.75155
.75239
7.75323
.75407
.75490
.75574
0.00562
.00563
.00564
.00565
0.00567
.00568
.00569,
.00570
7.79886
.79966
.80045
.80124
7.80203
.80282
.80361
.80440
0.00629
.00630
.00632
.00633
0.00634
.00635
.00636
.00637
7.84522
.84597
.84672
.84747
7.84822
.84897
.84972
.85047
0.00700
.00701
.00703
.00704
0.00705
.00706
.00707
.00709
36
34
32
30
28
26
24
22
40+10
42
44+U
46
48+12
50
52+1$
54
7.65026
.65120
.65214
.65308
7.65402
.65496
.65590
.65683
0.00447
.00448
.00449
.00450
0.00451
.00452
.00453
.00454
7.70505
.70593
.70682
.70770
7.70858
.70946
.71034
.71122
0.00507
.00508
.00509
.00510
0.00511
.00512
.00513
.00514
7.75657
.75740
.75824
.75907
7.75990
.76073
.76156
.76239
0.00571
.00572
.00573
.00574
0.00575
.00576
.00578
.00579
7.80519
.80598
.80677
.80755
7.80834
.80912
.80991
.81069
0.00639
.00640
.00641
.00642
0.00643
.00644
.00646
.00647
0.00648
0.00649
7.85122
.85196
.85271
.85346
7.85420
.85494
.85569
.85643
0.00710
.00711
.00712
.00714
0.00715
.00716
.00717
.00719
0.00720
0.00721
20
18
16
14
12
10
8
6
56+14:
58
7.65777
7.65870
0.00455
0.00456
7.71210
7.71298
0.00515
0.00516
7.76321
7.76404
0.00580
0.00581
7.81147
7.81225
7.85717
7.85791
4
2
23* 29™
23* 27m
23* 25™
23 * 23m
23* 21m
s '
0+15
2
4+16
6
Oh 31^ 7° 30'
0* 33™ 8° O7
0* 35™ 8° 30'
0* 37m 9° 0'
0* 39m 9° 30'
s
60
58
56
54
7.65964
.66057
.66150
.66243
0.00457
.00458
.00459
.00460
7.71385
.71473
.71560
.71648
0.00517
.00518
.00520
.00521
7.76487
.76569
.76652
.76734
0.00582
.00583
.00584
.00585
7.81303
.81382
.81459
.81537
0.00650
.00651
.00653
.00654
7.85866
.85940
.86014
.86087
0.00722
.00723
.00725
.00726
8+11
10
12+18
14
16+19
18
20+2Q
22
7.66336
.66429
.66521
.66614
7.66706
.66799
.66891
.66983
0.00461
.00462
.00463
.00464
0.00465
.00466
.00467
.00468
7.71735
.71822
.71909
.71996
7.72083
.72170
.72257
.72343
0.00522
.00523
.00524
.00525
0.00526
.00527
.00528
.00529
7.76816
.76898
.76981
.77063
7.77145
.77227
.77308
.77390
0.00586
.00587
.00589
.00590
0.00591
.00592
.00593
.00594
7.81615
.81693
.81771
.81848
7.81926
.82003
.82081
.82158
0.00655
.00656
.00657
.00658
0.00660
.00661
.00662
.00663
7.86161
.86235
.86309
.86382
7.86456
.86530
.86603
.86676
0.00727
.00728
.00730
.00731
0.00732
.00733
.00735
.00736
52
50
48
46
44
42
40
38
24+21
26
28+22
30
32+23
34
3(5+24
38
7.67075
.67167
.67259
.67351
7.67443
.67535
.67626
.67718
0.00469
.00470
.00471
.00472
0.00473
.00474
.00475
.00476
7.72430
.72516
.72603
.72689
7.72775
.72861
.72948
.73034
0.00530
.00531
.00532
.00533
0.00534
.00535
.00536
.00537
7.77472
.77553
.77635
.77716
7.77798
.77879
.77960
.78041
0.00595
.00596
.00598
.00599
0.00600
.00601
.00602
.00603
7.82235
.82313
.82390
.82467
7.82544
.82621
.82698
.82774
0.00664
.00665
.00667
.00668
0.00669
.00670
.00671
.00673
7.86750
.86823
.86896
.86969
7.87042
.87115
.87188
.87261
0.00737
.00738
.00740
.00741
0.00742
.00743
.00745
.00746
36
34
32
30
28
26
24
22
40+25
42
44+26
46
48+21
50
52+28
54
7.67809
.67900
.67991
.68082
7.68173
.68264
.68355
.68445
0.00477
.00478
.00479
.00480
0.00481
.00482
.00483
.00484
7.73119
.73205
.73291
.73377
7.73462
.73548
.73633
.73718
0.00539
.00540
.00541
.00542
0.00543
.00544
.00545
.00546
7.78122
.78203
.78284
.78365
7.78446
.78526
.78607
.78688
0.00604
.00605
.00607
.00608
0.00609
.00610
.00611
.00612
7.82851
.82928
.83004
.83081
7.83157
.83234
.83310
.83386
0.00674
.00675
.00676
.00677
0.00679
.00680
.00681
.00682
7.87334
.87407
.87480
.87552
7.87625
.87697
.87770
.87842
0.00747
.00748
.00750
.00751
0.00752
.00753
.00755
.00756
20
18
16
14
12
10
8
6
56+29
58
60+30
7.68536
.68627
7.68717
0.00485
.00486
0.00487
7.73803
.73889
7.73974
0.00547
.00548
0.00549
7.78768
.78848
7.78929
0.00613
.00614
0.00616
7.83463
.83539
7.83615
0.00683
.00685
0.00686
7.87915
.87987
7.88059
0.00757
.00758
0.00760
4
0
23* 28^
23* 26™
23* 24m
23* 22^
23* 20m
TABLE 45.
Haversines.
[Page 821
s
0* 40^ 10° V
0* 42 m
10° 30'
0* 44m H° O7
0* 46m
11° 30'
Oh 48m 13° <K
s
Log. Hav.
Nat. Hav.
Log. Hav.' Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
0 0
-9
4+ 1
6
7.88059
.88131
.88203
.88276
0.00760
.00761
.00762
.00763
7.92286
.92354
.92423
.92492
0.00837
.00839
.00840
.00841
7.96315
.96380
.96446
.96511
0.00919
.00920
.00921
.00923
8.00163
.00226
.00289
.00351
0.01004
.01005
.01007
.01008
8.03847 0.01093
.03907 .01094
.03967 ! .01096
.04027 .01097
60
58
56
54
5+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
7.88348
.88419
.88491
.88563
7.88635
.88707
88778
.88850
0.00765
.00766
.00767
.00768
0.00770
.00771
.00772
.00774
7.92560
.92629
.92697
.92766
7.92834
.92902
.92970
.93039
0.00843
.00844
.00845
.00847
0.00848
.00849
.00851
.00852
7.96577
.96642
.96707
.96773
7.96838
.96903
.96968
.97033
0.00924
.00926
.00927
.00928
0.00930
.00931
.00933
.00934
8.00414
.00476
.00539
.00601
8.00664
.00726
.00788
.00851
0.01010
.01011
.01012
.01014
0.01015
.01017
.01018
.01020
8.04087
.04147
.04207
.04267
8.04326
.04386
.04446
.04506
0.01099
.01100
.01102
.01103
0.01105
.01106
.01108
.01109
0.01111
.01112
.01114
.01115
0.01117
.01118
.01120
.01122
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
24+ 6
26
25+ 7
30
32+ 8
34
36+ 9
38
7.88921
.88993
.89064
.89135
7.89207
.89278
.89349
• .89420
0.00775
.00776
.00777
.00779
0.00780
.00781
.00783
.00784
7.93107
.93175
.93243
.93311
7.93379
.93447
.93514
.93582
0.00853
.00855
.00856
.00857
0.00859
.00860
.00861
.00863
7.97093 0.00935
.97163 ! .00937
.97223 .00938
.97293 1 .00940
7.97358 0.00941
.97423 .00942
.97478 .00944
.97552 .00945
8.00913
.00975
.01037
.01099
8.01161
.01223
.01285
.01347
0.01021
.01023
.01024
.01026
0.01027
.01029
.01030
.01032
8.04565
.04625
.04684
.04744
8.04803
.04303
.04922
.04981
40+10
42
44+11
46
45+12
50
52+13
54
7.89491
.89562
.89633
.89704
7.89775
.39346
.89916
.89987
0.00785
.00786
.00788
. .00789
0.00790
.00792
.00793
.00794
7.93650
.93717
.93785
.93852
7.93920
.93987
.94055
.94122
7.94189
7.94257
0.00864
.00865
.00867
.00868
0.00869
.00871
.00872
.00873
7.97617 0.00947
.97681 .00948
.97746 .00949
.97810 : .00951
7.97875 0.00952
.97939 .00954
.98003 .00955
.98068 .00956
8.01409
.01471
.01532
.01594
8.01656
.01717
.01779
.01840
0.01033
.01034
.01036
.01037
0.01039
.01040
.01042
.01043
8.05041
.05100
.05159
.05218
8.05277
.05336
.05395
.05454
0.01123
.01125
.01126
.01128
0.01129
.01131
.01132
.01134
20
18
16
14
12
10
8
6
i
7.90057
7.90128
0.00795
0.00797
0.00875
0.00876
7.98132 0.00958
7.9S196 0.00959
8.01902
8.01963
0.01045
0.01046
8.05513 0.01135
8.05572 0.01137
4
2
23* 19m
23*
17m
23 h 15m
23* 13m
23* llm
s '
0+15
4+16
6
0* 41 m 10° O7
0* 43m
10° 30'
Oh 4om 11° O7
0* 4?'m
11° ^O7
0* 49m 12° O7
s
60
58
56
54
7.90198
.90269
.90339
.90409
0.00798
.00799
.00801
.00802
7.94324
.94391
.94458
.94525
0.00877
.00879
.00880
.00882
7.93260 0.00961
.93325 .00962
.98339 ' .00964
.93453 .00965
8.02025
.02086
.02148
.02209
0.01048
.01049
.01051
.01052
8.05631 0.01138
.05690 .01140
.05749; .01142
.05808 i .01143
5+17
10
14
16+19
18
2(9+20
22
7.90480
.90550
.90620
.90690
7.90760
.90830
.90900
.90970
0.00803
.00804
.00806
.00807
0.00808
.00810
.00811
.00812
7.94592
.94659
.94726
.94792
7.94859
.94926
.94992
.95059
0.00883
.00884
.00886
.00887
0.00888
.00890
.00891
.00892
7.98517
.98581
.98644
.98708
7.98772
.98836
.98899
.98963
0.00966
.00968
.00969
.00971
0.00972
.00974
.00975
.00976
8.02270
.02331
.02392
.02453
8.02515
.02576
.02637
.02697
0.01054
.01055
.01057
.01058
0.01060
.01061
.01063
.01064
8.05866 0.01145
.05925 .01146
.05984 I .01148
.06042 '•< .01149
8.06101 i 0.01151
.06159 .01152
.06218 | .01154
.06276 .01155
52
50
48
46
44
42
40
38
36
34
32
30
28
26
24
2 •*
20
18
16
14
12
10
8
6
24+21
26
28+22
30
32+23
34
36+24
38
7.91039
.91109
.91179
.91248
7.91318
.91387
.91457
.91526
0.00814
.00815
.00816
.00817
0.00819
.00820
.00821
.00823
7.95126
.95192
.95259
.95325
7.95391
.95458
.95524
.95590
0.00894
.00895
.00897
.00898
0.00899
.00901
.00902
.00903
7.99027
99090
.99154
.99217
7.99281
.99344
.99407
.99470
0.00978
.00979
.00981
.00982
0.00984
.00985
.00986
.00988
8.02758
.02819
.02880
.02941
8.03001
.03062
.03123
.03183
0.01066
.01067
.01069
.01070
0.01072
.01073
.01075
.01076
8.06335
.06393
.06451
.06510
8.06568
.06626
.06684
.06742
0.01157
.01159
.01160
.01162
0.01163
.01165
.01166
.01168
40+25
42
44+26
46
45+27
50
52+28
54
7.91596
.91665
.91734
.91803
7.91872
.91941
.92010
.92079
0.00824
.00825
.00827
.00828
0.00829
.00831
.00832
.00833
7.95656
.95722
.95788
.95854
7.95920
.95986
.96052
.96118
0.00905
.00906
.00908
.00909
0.00910
.00912
.00913
.00914
7.99534
.99597
.99660
.99723
7.99786
.99849
.99912
7.99975
0.00989
.00991
.00992
.00994
0.00995
.00997
.00998
.00999
8.03244
.03304
.03365
.03425
8.03486
.03546
.03606
.03666
0.01078
.01079
.01081
.01082
0.01084
.01085
.01087
.01088
8.06800
.06859
.06917
.06975
8.07032
.07090
.07148
.07206
0.01170
.01171
.01173
.01174
0.01176
.01177
.01179
.01180
56+29
58
60+30
7.92148
.92217
7.92286
0.00835
.00836
0.00837
7.96183
.96249
7.96315
0.00916
.00917
0.00919
8.00038
.00100
8.00163
0.01001
.01002
0.01004
8.03727
.03787
8.03347
0.01090
.01091
0.01093
8.07264
.07322
8.07379
0.01182
.01184
0.01185
4
2
0
23 * 18m
23 h
16m
23* 14m
23* 12™
23* 10m
Page 822] TABLE 45.
s '
(»' 50 »• 12" SO'
0* 52 '» 13° 0'
Oh ,54m 13° 30'
0*56«U°0'
Oh 58m 14° 30'
s
l.ti;;. ll:iv.
Nat. llav.
Log. Hav.
Nat.JIuv.
Log. Hav.
N.,l. llav.
Lor. llav.
Nat. llav.
Log. Hav.
Nat. llav.
0 0
8.07379
0.01185
8.10772
0.01282
8.14035
0.01382
8.17179
0.01 1S5
8.2021 1
0.01593
GO
t
.07437
.01 187
.10827
.01283
.14089
.01383
.172:50
.oils;
.20201
.01591
68
4+ 1
.07494
.011SS
.10883
.012S5
. 11 12
.01385
.17282
.014S9
.20310
.01590
f>6
6'
.07552
.01190
.10938
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. 4195
.01387
,17333
.01491
.20360
.01598
r>4
\v+ 2
8.07010
O.OllilS
8.10993
0.01288
8. 4248
0.0138H
8.17384
0.01492
8.20410
0.01000
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10
,07667
.01193
,11049
.01290
. 4302
.01390
.17430
.01494
.20459
.01002
60
./„'•!- ;{
.07728
.01195
.11101
.01291
. 1355
.01392
.!. 187
.01490
.20509
.01001
48
14
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.01190
.11159
.01293
. 4408
.01393
.17538
.01498
,20558
.01005
45
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8.0783!)
0.0 1198
8.1 1214
0.01295
8. 1401
0.01395
8.17590
0.0149!)
8.20008
0.01007
44
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.01199
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.01290
. 1514
.01397
.17843
.01501
,20657
.01009
42
20 + 5
.07954
.01201
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. 15(57
.01399
.17892
.01503
.20700
.01011
40
2 2
.08011
.01203
.1 137!)
.01300
. 1020
.01100
.17743
.01505
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.01013
AS'
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8.080(5!)
0.01201
8.11435
0.01301
8. 4(573
0.01402
8. 17794
0.01500
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so
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8. 082!) 7
0.01211
8. 1051
0.01308
8. 4885
0.01409
8.17998
0.01513
8.21002
0.01022
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54
.08354
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. 1709
.01309
. 4938
.01111
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24
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. 1819
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22
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8.08525
0.01217
8. 1873
0.01311
8. 5090
0.01410
8.18202
0.01521
8.21 199
0.01029
20
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.01117
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49+1)
8.08752
0.01223
8. 20!) 2
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8. 5307
0.01123
8.18405
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8.21396
0.01037
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. 5412
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8
54
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8.0897!)
0.01230
8 2310
0.0132S
8. 5517
0.01129
8.18007
0.01535
8.21590
0.01041
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8.09036
0.01231
8. 23(55
0.01329
8. 5569
0.01131
8.18058
0.01537
8.21(53!)
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2
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23 h 5"»
23* 8m
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0* 55« 13° V
Oh 5,V» 13° SO'
0* 57m 14° 0'
Oh 59m 14° SO'
s
0+15
8.09092
0.01233
8. 241!)
0.01331
8.15622
0.01433
8.18709
0.01538
8.21688
0.01018
50
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.01231
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.01540
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66
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64
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0.01239
8. 2(53(5
0.01338
8. 5831
0.01440
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0.01510
8.21883
0.01055
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70
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.0133!)
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.01112
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.01547
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60
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,0943]
.01243
. 2745
.01311
. 5935
.01113
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.01549
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.01059
48
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.01214
2799
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. 59S7
.01115
,19082
.01551
.22029 | .01001
45
K)-\-l9
8.09543
0.01240
8. 2853
0.01311
8.10040
0.01117
8.19112
0.01553
8.22077
0.01003
44
18
,09600
.01247
. 2907
.01310
.10092
.01448
.191(52
.01555
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.01001
4-'
20+20
.09656
.0124!)
. 2901
.01 SIS
.Kit 11
.01450
.19212
.01556
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40
22
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. 3015
.01349
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.01152
,19268
.01558
.22223
.01008
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2-$ | 21
8.09,1,8
0.01252
8. 300!)
0.01351
8.10248
0.01451
8.19313
0.01500
~8 22272
0.01070
Sti~
26
,09824
.01254
. 3123
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.10300
.01155
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.01072
34
. £,s'+23
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.01255
. 3177
.01351
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50
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30
52+23
8.09992
0.01259
8. 3285
0.0135S
8.10450
0.01101
8.19513
0.0(507
8.22466
0.01077
2<V
54
.10018
.01200
. 3339
.01300
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.01102
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.01101
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.01571
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.01081
84
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.01083
22
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8.10210
0.01205
8. 3500
0.01305
8.1(5003
0.01108
8.19713
0.01571
8.22058
0.01085
20
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.10271
.01207
. 3554
.01300
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.01109
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18
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. 3007
.01308
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.01171
.19813
.01578
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.01473
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14
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8.10439
0.01272
8. 37] 1
0.01371
8.10870
0.01175
8.1991:5
0.01582
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0.01092
12
60
.10494
.01273
. 37(58
.01373
.1692]
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.01091
10
52+28
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.01275
. 3822
.01375
.16978
.01178
.20012
.01585
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.01090
$
.10605
.01277
. 3875
.01370
.17024
.01180
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.01587
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6
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8.10001
0.01 27 S
8. 3928
0.01378
8.1707(5
0.0 1182
8.20112
0.01589
8.23044
0.01700
4
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.01280
3982
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.01183
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.01591
.23092
.01702
jj
60+30
8.10772
0.01282
8.14036
0.01383
8.17179
0.01185
8.20211
0.01593
8.23140
0.01701
0
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25M-
*3h2m
2Sh Om
TABLE 45. [Page 823
Jlaversinea.
s
1*0'« 15 0'
lh lm 15° 15'
lh 2* 15° 30'
IA 5^15° 45'
/*4"» 16° O7
s
Log. Hav.
Nal. l!:.v.
Log. Hav.
Log. Hav.
Nal. II:iv.
:
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Nut. Il:iv.
0
1
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8.23140
.23164
.23188
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.01704
.01705
.01706
.01707
.01707
.01708
.01709
.01710
8.24567
.24591
.24614
.24638
.01761
.01762
.01763
.01761
8.25971
.25994
.26017
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.01819
.01820
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8.27352
.27375
.27398
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.01878
.01879
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.01883
.01884
.01*85
.01886
.01887
.01888
.01889
.01890
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.01*96
8.28711
.28734
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.01937
.01938
.01939
.01940
60
69
68
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+ 1'
5
6
7
8.23236
.23259
.23283
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1
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.01764
.01765
.01766
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8.2000-1
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8.28X01
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66
66
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10
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8.23331
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8.24755
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8.26156
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8.28891
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8.290,0
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13
14
15
8.23427
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.23475
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8.24850
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.24897
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8.20249
.26272
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8.27626
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48
47
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46
44
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18
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8.23623
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8.26341
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8.23618
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8.25037
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8.26434
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8.26526
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8.26618
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1
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8.27989
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.01962
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40
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8.23904
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8.23999
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.24070
.01734
.01735
.017*6
.01737
.01738
.01739
.01740
.01741
.25.;! 2
.25365
.25389
8.25112
.26435
.25459
.25482
.01791
.01792
.01793
.01794
".0179.1
.01796
.01797
.01798
.0179?)
.01800
.01801
.01802
.01803
.01804
.01805
.01806
.01807
.01808
.01809
.01810
.01811
.01 SI 2
.01813
.01814
X.207IO
.20733
.20750
.20779
.01850
.01*51
.01*52
.01*53
8.28080
.28102
.28126
.28147
.01909
.01910
.01911
.01912
"01913
.01914
.01915
,01916
.01917
.01918
.01919
.01920
8.29127
.29449
.29172
.29194
.0196:1
.01970
.01971
.01972
t&
21
26
t6
u
S3
22
21
+ V
37
38
39
8.26802
.20825
.20848
.01*54
.01855
.01856
.01857
8.28170
.28183
.28215
.28238
8159516
.295:59
.29561
.295X3
8.29005
.29028
.29050
.29072
.01973
.01974
.01975
.01976
+ KK
41
42
4?
8.24094
.24118
.24141
.241(55
8.24189
.24212
.24236
.24260
.017*2
.01743
.01743
.01741
8.25505
.25529
.25552
.25575
8.255:*!)
.25022
.25015
.25009
8.25092'
.25715
.25738
.25702
8.20894
.26917
.26940
.26963
.01858
.01859
.01860
.01*61
.01*61
.01862
.01863
.01*6*
.28306
.28328
.01977
.01978
.01979
.019*0
to
19
18
17
+ 11'
4-5
4tf
47
.01715
.01746
.01747
.01718
8.20980
.27009
.27032
.27055
.28373
.28396
.28418
.01921
.01922
.01923
.0192*
T.01925
.01926
.01927
.01928
8.29094
.29716
.29739
.29761
.01981
.01982
.01983
.Olf)**
16
15
14
i.i
+ 12'
4-9
50
5J
Oi42§3
.24307
.24331
.24354
.017*9
.01750
.01751
.01752
8.27078
.27100
.2:12:;
.27146
.01865
.01866
.01867
.0186*
8.28441
.28464
.28509
.29806
.29827
.29X50
.019*5
.01986
.01987
.019*8
It
11
10
9
+ 13'
55
54
55
8.24378
.24402
.24425
.24449
.01753
.01754
.01755
.01756
8.25785
.26808
.25831
.25855
8127165
.27192
.27215
.27238
.01869
.01870
.01871
.01872
.2855-1
,28676
.2X5911
.28644
.2X089
.0192!)
.01930
.01931
.01932
8.20X72
.29894
.29916
.20938
.019*9
.01990
.01991
.01992
8
7
6
5
4- 14'
57
55
5.9
+ T57
8.24473
.24496
.24520
.24643
.01757
.01758
.01759
.017(50
8.25878
.25901
.25921
.25918
.01815
.01816
.01817
.01818
.01818
8.27261
.27283
.27306
.27:529
.01873
.01874
.01875
.01876
.01933
.01934
.01935
.01936
.01937
8.29900
.29982
.30005
.30027
.01993
.01994
.01995
.01997
4
3
2
1
.01701
£26971
8. 27352
.01*77
8.2S7II
8.30049
.01998
0
££»59*
22 * 58*
22* 57 «
22*
2£* .55 «
Page 824] TABLE 45.
Haversines.
s
1 * 5m 16° 15'
1*6*16° W
i A 7™ 16° 45'
lh$m 17° 0'
ihomins'
s
60
59
58
57
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
+ ^
5
6
7
8.30049
.30071
.30093
.30115
.01998
.01999
.02000
.02001
8.31366
.31388
.31410
.31431
.02059
.02060
.02061
.02062
8.32663
.32684
.32706
.32727
.02121
.02122
.02124
.02125
8.33940
.33962
.33983
.34004
.02185
.02186
.02187
.02188
8.35199
.35220
.35241
.35261
.02249
.02250
.02251
.02252
8.30137
.30159
.30182
.30204
.02002
.02003
.02004
.02005
8.31453
.31475
.31497
.31518
.02063
.02064
.02065
.02066
8.32749
.32770
.32792
.32813
.02126
.02127
.02128
.02129
8.34025
.34046
.34067
.34088
.02189
.02190
.02191
.02192
8.35282
.35303
.35324
.35345
.02253
.02254
.02255
.02257
56
55
54
53
+ V
9
10
11
8.30226
.30248
.30270
.30292
.02006
.02007
.02008
.02009
8.31540
.31562
.31584
.31605
.02067
.02068
.02069
.02070
8.32834
.32856
.32877
.32899
.02130
.02131
.02132
.02133
8.34109
.34130
.34152
.34173
.02193
.02194
.02195
.02196
8.35365
.35386
.35407
.35428
.02258
.02259
.02260
.02261
52
51
50
49
~48
47
46
45
+ &
13
14
15
8.30314
.30336
.30358
.30380
.02010
.02011
.02012
.02013
8.31627
.31649
.31670
.31692
.02071
.02072
.02074
.02075
8.32920
.32941
.32963
.32984
.02134
.02135
.02136
.02137
8.34194
.34215
.34236
.34257
.02198
.02199
.02200
.02201
8.35449
.35469
.35490
.35511
.02262
.02263
.02264
.02265
+ ¥
17
18
19
8.30402
.30424
.30446
.30468
.02014
.02015
.02016
.02017
8.31714
.31735
.31757
.31779
.02076
.02077
.02078
.02079
8.33006
.33027
.33048
.33070
.02138
.02139
.02140
.02141
8.34278
.34299
.34320
.34341
.02202
.02203
.02204
.02205
8.35532
.35552
.35573
.35594
.02266
.02267
.02268
.02270
44
43
42
41
+ 5/
21
22
23
8.30490
.30512
.30534
.30556
.02018
.02019
.02020
.02021
8.31800
.31822
.31844
.31865
.02080
.02081
.02082
.02083
8.33091
.33112
.33134
.33155
.02142
.02143
.02145
.02146
8.34362
.34383
.34404
.34425
.02206
.02207
.02208
.02209
8.35614
.35635
.35656
.35677
.02271
.02272
.02273
.02274
40
39
38
37
+ &
25
26
27
8.30578
.30600
.30622
.30644
.02022
.02023
.02024
.02025
8.31887
.31909
.31930
.31952
.02084
.02085
.02086
.02087
8.33176
.33198
.33219
.33240
.02147
.02148
.02149
.02150
8.34446
.34467
.34488
.34509
.02210
.02211
.02212
.02214
8.35697
.35718
.35739
.35759
.02275
.02276
.02277
.02278
36
35
34
33
+ ?'
29
30
31
8.30666
.30688
.30710
.30732
.02026
.02027
.02028
.02029
8.31974
.31995
.32017
.32039
.02088
.02089
.02090
.02091
8.33262
.33283
.33304
.33325
.02151
.02152
.02153
.02154
8.34530
.34551
.34572
.34593
.02215
.02216
.02217
.02218
8.35780
.35801
.35821
.35842
.02279
.02280
.02281
.02283
32
31
30
29
+ &
33
34
35
8.30754
.30776
.30798
.30820
.02030
.02031
.02032
.02033
8.32060
.32082
.32103
.32125
8.32147
.32168
.32190
.32211
.02092
.02093
.02094
.02095
8.33347
.33368
.33389
.33411
.02155
.02156
.02157
.02158
8.34614
.34635
.34656
.34677
.02219
.02220
.02221
.02222
8.35863
.35883
.35904
.35925
.02284
.02285
.02286
.02287
28
27
26
25
+ 9X
37
38
39
+ 107
41
42
43
8.30842
.30863
.30885
.30907
.02034
.02035
.02036
.02037
.02096
.02097
.02098
.02099
8.33432
.33453
.33474
.33496
.02159
.02160
.02161
.02162
8.34698
.34719
.34740
.34761
.02223
.02224
.02225
.02226
8.35945
.35966
.35987
.36007
.02288
.02289
.02290
.02291
24
23
22
21
8.30929
.30951
.30973
.30995
.02038
.02039
.02040
.02042
8.32233
.32254
.32276
.32297
.02101
.03102
.02103
.02104
8.33517
.33538
.33559
.33580
.02164
.02165
.02166
.02167
8.34782
.34803
.34823
.34844
.02227
.02229
.02230
.02231
8.36028
.36048
.36069
.36090
.02292
.02293
.02295
.02296
20
19
18
17
+ 11'
45
46
47
8.31017
.31039
.31060
.31082
.02043
.02044
.02045
.02046
8.32319
.32341
.32362
.32384
.02105
.02106
.02107
.02108
8.33602
.33623
.33644
.33665
.02168
.02169
.02170
.02171
8.34865
.34886
.34907
.34928
.02232
.02233
.02234
.02235
8.36110
.36131
.36151
.36172
.02297
.02298
.02299
.02300
16
15
14
13
+ 12'
49
50
51
8.31104
.31126
.31148
.31170
.02047
.02048
.02049
.02050
8.32405
.32427
.32448
.32470
.02109
.02110
.02111
.02112
8.33686
.33708
.33729
.33750
.02172
.02173
.02174
.02175
8.34949
.34970
.34991
.35011
.02236
.02237
.02238
.02239
8.36193
.36213
.36234
.36254
.02301
.02302
.02303
.02304
12
11
10
9
+ 13'
53
54
55
8.31192
.31213
.31235
.31257
.02051]
.02052
.02053
.02054
8.32491
.32513
.32534
.32556
.02113
.02114
.02115
.02116
8.33771
.33792
.33814
.33835
.02176
.02177
.02178
.02179
8.35032
.35053
.35074
.35095
.02240
.02241
.02243
.02244
8.36275
.36295
.36316
.36337
.02305
.02307
.02308
.02309
8
7
6
5
+ 14'
57
58
59
8.31279
.31301
.31322
.31344
.02055
.02056
.02057
.02058
8.32577
.32599
.32620
.32642
.02117
.02118
.02119
.02120
8.33856
.33877
.33898
.33919
.02181
.02182
.02183
.02184
8.35116
.35137
.35157
.35178
.02245
.02246
.02247
.02248
8.36357
.36378
.36398
.36419
.02310
.02311
.02312
.02313
4
3
2
1
+ 15'
8.31366
.02059
8.32663
.02121
8.33940
.02185
8.35199
.02249
8.36439
.02314
0
22* 54m
22* 53™
22* 52™
22* 51^
22* 50™
TABLE 45. [Page 825
Haversines.
i* 10*11 30'
1* llm 17°45/
1*12* 18° (K
J»Wmi8°15'
1* 14™18° W
s
s
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.j Nat. Hav.
Log. Hav. Nat. Hav.
0
1
2
3
8.36439
.36460
.36480
.36501
.02314
.02315
.02316
.02317
8.37662
.37682
.37702
.37722
.02380
.02381
.02382
.02384
8.38867
.38886
.38906
.38926
.02447
.02448
.02449
.02451
8.40055
.40074
.40094
.40114
.03515
.02516
.03517
.02518
8.41226
.41246
.41265
.41284
.03584
.03585
.02586
.03587
60
59
58
57
+ 1'
5
6
7
8.36521
.36542
.36562
.36583
.03319
.02320
.02321
.02322
8.37742
.37763
.37783
.37803
.02385
.02386
.02387
.02383
8.38946
.38966
.38986
.39006
.03452
.02453
.02454
.02455
8.40133
.40153
.40172
.40192
.03520
.03531
.02533
.03533
8.41304
.41323
.41343
.41362
.03588
.03590
.03591
.03593
56
55
54
53
+ 2'
9
10
11
8.36603
.36624
.36644
.36665
.02323
.02324
.02325
.02326
8.37823
.37843
.37864
.37884
.02389
.02390
.02391
.02392
8.39026
.39046
.39066
.39086
.02456
.02457
.02458
.02460
8.40212
.40231
.40251
.40271
.03534
.02525
.03536
.02528
8.41381
.41401
.41420
.41439
.03593
.03594
.03595
.02597
.03598
.02599
.03600
.03601
52
51
50
49
+ &
13
14
15 '
8.36685
.36706
.36726
.36746
.02327
.02328
.02329
.02331
8.37904
.37924
.37944
.37964
.02394
.02395
.02398
.02397
8.39105
.39125
.39145
.39165
.02461
.02402
.02463
.02464
8.40290 .03529
.40310 i .03530
.40329 i .02531
.40349 ; .03533
8.41459
.41478
.41497
.41517
48
47
46
45
+ *'
17
18
19
8.36767
.36787
.36808
.36828
.02332
.02333
.02334
.02335
8.37985
.38005
.38025
.38045
.02398
.02399
.02400
.02401
8.39185
.39205
.39225
.39245
.02465
.02468
.02467
.02489
8.40369
.40388
.40408
.40427
.03533
.03534
.03536
.03537
8.41536 I .02602
.41555 .03603
.41575 .03605
.41594 .03606
44
43
42
41
40
39
38
37
+ V
21
22
23
8.36849
.36869
.36889
.36910
.02330
.02337
.02338
.02339
8.38065
.38085
.33105
.38126
.02402
.02404
.02405
.02406
8.39264
.39284
.39304
.39324
.02470
.02471
.02473
.02473
8.40447
.40467
.40486
.40506
.03538
.03539
.03540
.03541
8.41613
.41632
.41652
.41671
.03607
.03608
.03609
.03610
+ 6'
25
26
27
8.36930
.36951
.36971
.36991
.02340
.02342
.02343
.02344
8.38146
.38166
.38186
.38206
.02407
.02408
.02409
.02410
8.39344
.39364
.39384
.39403
.02474
.02475
.02476
.02478
S. 40525
.40545
.40564
.40584
.03543
.03544
.03545
.03546
8.41690
.41710
.41729
.41748
.02612
.02613
.02614
.02615
36
35
34
33
+ r
• 29
30
31
8.37012
.37032
.37053
.37073
.02345
.02346
.02347
.02348
8.38226
.38246
.38266
.38286
.02411
.02412
.02114
.02415
8.39423
.39443
.39463
.39482
.02479
.02480
.02481
.02483
8.40603
.40623
.40642
.40662
.03547
.03548
.03549
.02550
8.41767
.41787
.41806
.41825
.02616
.03617
.03619
.03630
32
31
30
29
+ 8'
S3
34
35
8.37093
.37114
.37134
.37154
.02349
.02350
.02351
.02353
8.38306
.38320
.38346
.38367
.02416
.02417
.02418
.02419
8.39502
.39522
.39542
.39562
.02483
.02484
.02486
.02487
8.40681
.40701
.40721
.40740
.02552
.02553
.02554
.02555
8.41845
.41864
.41883
.41902
.03631
.03633
.02623
.02624
28
27
26
25
+ V
37
38
39
8.37175
.37195
.37215
.37236
.02354
.02355
.02356
.02357
8.38387
.38407
.38427
.38447
.02420
.02421
.02423
.02424
8.39581
.39601
.39621
.39641
.03488
.02489
.02490
.02491
8.40760
.40779
.40799
.40818
.03556
.03557
.03559
.03560
8.41921
.41941
.41960
.41979
.02636
.03637
.03838
.03639
24
23
22
21
+ W
41
42
43
8.37256
.37276
.37297
.37317
.02358
.02359
.02360
.02361
8.38467
.38487
.38507
.38527
.02425
.02426
.02427
.02428
8.39660
.39680
.39700
.39720
.02492
.03493
.02495
.02498
8.40837
.40857
.40876
.40896
.03561
.03563
.03563
.03564
8.41998
.42018
.42037
.42056
.02630
.02631
.02633
.02634
20
19
18
17
+ 11'
45
46
47
8.37337
.37358
.37378
.37398
.02363
.02364
.02365
.02366
8.38547
.38567
.38587
.38607
.02429
.02430
.02431
.02433
8.39739
.39759
.39779
.39799
.02497
.02498
.02499
.03500
8.40915
.40935
.40954
.40974
.03565
.03567
.03568
.03569
8.42075
.42095
.42114
.42133
.03635
.03636
.03637
.03638
16
15
14
13
+ 13'
49
50
51
8.37419
.37439
.37459
.37479
.02387
.02368
.02369
.02370
8.38627
.38647
.38667
.38687
.02434
.02435
.02436
.02437
8.39818
.39838
.39858
.39877
.02501
.03503
.03504
.03505
8.40993
.41013
.41032
.41052
.03570
.03571
.03573
.03573
8.42152
.42171
.42190
.42210
.03639
.03641
.03643
.03643
12
11
10
9
+ 13'
53
54
55
8.37500
.37520
.37540
.37560
.02371
.02372
.02374
.02375
8.38707
.38727
.38747
.38767
.02438
.02439
.02440
.02442
8.39897
.39917
.39937
.39956
.03506
.03507
.03508
.03509
8.41071
.41090
.41110
.41129
.03575
.03576
.03577
.03578
8.42229
.42248
.42267
.42286
.03644
.03645
.02646
.02648
8
7
6
5
+ ux
5?
58
59
8.37581
.37601
.37621
.37641
.02376
.02377
.02378
.02379
8.38787
.38807
.38827
.38847
.02443
.02444
.02445
.02446
8.39976
.39996
.40015
.40035
.03510
.03513
.03513
.03514
8.41149
.41168
.41187
.41207
.02579
.03580
.03583
.03583
8.42305
.42324
.42344
.42363
.02849
.02650
.02651
.02653
4
3
2
1
+ 15'
8.37662
.02380
8.38867
.02447
8.40055
.03515
8.41226
.03584
8.42382 I .03653
0
22* 49™
*t*48*
22* 4?m
22* 46*
22* 45m
61828°— 16 45
Page 826] TABLE 45.
Haversines.
s
lh ism 18° 45'
lh 16m 19° 0'
lh 17m 19° is/
lh ism 19° 30'
lh 19m 19° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
8.42382
.42401
.42420
.42439
.02653
.02655
.02656
.02657
8.43522
.43541
.43560
.43578
.02724
.02725
.02726
.02728
8.44647
.44665
.44684
.44703
.02796
.02797
.02798
.02799
8.45757
.45775
.45794
.45812
.02868
.02869
.02870
.02871
8.46852
.46871
.46889
.46907
.02941
.02942
.02944
.02945
60
59
58
57
+ 1'
5
6
7
8.42458
.42477
.42497
.42516
.02658
.02659
.02661
.02662
8.43597
.43616
.43635
.43654
.02729
.02730
.02731
.02732
8.44721
.44740
.44758
.44777
.02800
.02802
.02803
.02804
8.45830
.45849
.45867
.45885
.02873
.02874
.02875
.02876
8.46925
.46943
.46961
.46979
.02946
.02947
.02949
.02950
56
55
54
53
+ 2'
9
10
11
8.42535
.42554
.42573
.42592
.02663
.02664
.02665
.02666
8.43673
.43692
.43710
.43729
.02734
.02735
.02736
.02737
8.44796
.44814
.44833
.44851
.02805
.02806
.02808
.02809
8.45904
.45922
.45940
.45959
.02878
.02879
.02880
.02881
8.46998
.47016
.47034
.47052
.02951
.02952
.02954
.02955
52
51
50
49
+ &
13
14
15
8.42611
.42630
.42649
.42668
.02668
.02669
.02670
.02671
8.43748
.43767
.43786
.43805
.02738
.02739
.02741
.02742
8.44870
.44889
.44907
.44926
.02810
.02811
.02812
.02814
8.45977
.45995
.46014
.46032
.02883
.02884
.02885
.02886
8.47070
.47088
.47106
.47124
.02956
.02957
.02958
.02960
48
47
46
45
+ V
17
18
19
8.42687
.42706
.42725
.42745
.02672
.02673
.02675
.02676
8.43823
.43842
.43861
.43880
.02743
.02744
.02745
.02747
8.44944
.44963
.44981
.45000
.02815
.02816
.02817
.02818
8.46050
.46069
.46087
.46105
.02887
.02889
.02890
.02831
8.47142
.47160
.47178
.47197
.02961
.02962
.02963
.02965
44
43
42
41
+ &'
21
22
23
8.42764
.42783
.42802
.42821
.02677
.02678
.02679
.02680
8.43899
.43917
.43936
.43955
.02748
.02749
.02750
.02751
8.45018
.45037
.45055
.45074
.02820
.02821
.02822
.02823
8.4G124
.46142
.46160
.46179
.02892
.02893
.02895
.02896
8.47215
.47233
.47251
.47269
.02966
.02967
.02968
.02970
40
39
38
37
+ 6'
25
26
27
8.42840
.42859
.42878
.42897
.02682
.02683
.02684
.02685
8.43974
.43992
.44011
.44030
.02753
.02754
.02755
.02756
8.45093
.45111
.45130
.45148
.02824
.02826
.02827
.02828
8.46197
.46215
.46233
.46252
.02897
.02898
.02900
.02901
8.47287
.47305
.47323
.47341
.02971
.02972
.02973
.02974
36
35
34
33
+ v
29
30
31
8.42916
.42935
.42954
.42973
.02686
.02688
.02689
.02690
8.44049
.44067
.44086
.44105
.02757
.02759
.02760
.02761
8.45167
.45185
.45204
.45222
.02829
.02830
.02832
.02833
8.46270
.46288
.46306
.46325
.02902
.02903
.02904
.02906
8.47359
.47377
.47395
.47413
.02976
.02977
.02978
.02979
32
31
30
29
~W
27
26
25
+ 8'
33
34
35
8.42992
.43011
.43030
.43049
.02691
.02692
.02693
.02695
8.44124
.44142
.44161
.44180
.02762
.02763
.02764
.02766
8.45241
.45259
.45278
.45296
.02834
.02835
.02836
.02838
8.46343
,46361
.46379
.46398
.02907
.02908
.02909
.02911
8.47431
.47449
.47467
.47485
.02981
.02982
.02983
.02984
+ *'
37
38
39
8.43068
.43087
.43106
.43125
.02696
.02697
.02698
.02699
8.44199
.44217
.44236
.44255
.02767
.02768
.02769
.02771
8.45315
.45333
.45352
.45370
.02839
.02840
.02841
.02842
8.46416
.46434
.46452
.46471
.02912
,02913
.02914
.02915
8.47503
.47521
.47539
.47557
.02986
.02987
.02988
.02989
24
23
22
21
+ 10'
41
42
43
8.43144
.43163
.43181
.43200
.02700
.02702
.02703
.02704
8.44273
.44292
.44311
.44330
.02772
.02773
.02774
.02775
8.45388
.45407
.45425
.45444
.02844
.02845
.02846
.02847
8.46489
.46507
.46525
.46544
.02917
.02918
.02919
.02920
8.47575
.47593
.47611
.47629
.02991
.02992
.02993
.02994
20
19
18
17
+ 11'
45
46
47
8.43219
.43238
.43257
.43276
.02705
.02706
.02708
.02709
8.44348
.44367
.44386
.44404
.02776
.02778
.02779
.02780
8.45462
.45481
.45499
.45518
.02849
.02850
.02851
.02852
8.46562
.46580
.46598
.46616
.02922
.02923
.02924
.02925
8.47647
.47665
.47683
.47701
.02996
.02997
.02998
.02999
16
15
14
13
+ 12'
49
50
51
8.43295
.43314
.43333
.43352
.02710
.02711
.02712
.02713
8.44423
.44442
.44460
.44479
.02781
.02782
.02784
.02785
8.45536
.45554
.45573
.45591
.02853
.02855
.02856
.02857
8.46634
.46653
.46671
.46689
.02926
.02928
.02929
.02930
8.47719
.47737
.47755
.47773
.03000
.03002
.03003
.03004
12
11
10
9
+ 13'
53
54
55
8.43371
.43390
.43409
.43427
.02715
.02716
.02717
.02718
8.44498
.44516
.44535
.44554
.02786
.02787
.02788
.02790
8.45610
.45628
.45646
.45665
.02858
.02859
.02861
.02862
8.46707
.46725
.46744
.46762
.02931
.02933
.02934
.02935
8.47791
.47809
.47827
.47844
.03005
.03007
.03008
.03009
8
7
6
5
+ 14'
57
58
59
8.43446
.43465
.43484
.43503
.02719
.02721
.02722
.02723
8.44572
.44591
.44610
.44628
.02791
.02792
.02793
.02794
8.45683
.45702
.45720
.45738
.02863
.02864
.02866
.02867
8.46780
.46798
.46816
.46834
.02936
.02938
.02939
.02940
8.47862
.47880
.47898
.47916
.03010
.03012
.03013
.03014
4
S
2
1
+ 15'
8.43522
.02724
8.44647
.02796
8.45757 .02868
8.46852 .02941
8.47934 | .03015
0
22* 44™
ff»#»
22* 42™
22* 41m
M*40*
TABLE 45. [Page 827
Ilaversines.
s
1 A £0m 20° (K
IhZinZO0 15'
Jft£2n»20°30/
1 /' J.]m 20° 45'
Jft;24TO2100'
s
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
y
S
8.47934
.47952
.47970
.47988
.03015
.03017
.03018
.03019
8.49002
.49020
.49037
.49055
.03090
.03092
.03093
.03094
8.50056
.50074
.50091
.50109
.03166
.03168
.03169
.03170
8.51098
.51115
.51132
.51150
.03243
.03245
.03246
.03247
8.52127
.52144
.52161
.52178
.03321
.03322
.03324
.03325
60
59
58
57
+ lx
5
6
7
8.48006
.48024
.48041
.48059
.03020
.03022
.03023
.03024
8.49073
.49090
.49108
.49126
.03095
.03097
.03098
.03099
8.50126
.50144
.50161
.50179
.03171
.03173
.03174
.03175
8.51167
.51184
.51201
.51219
8.51236
.51253
.51270
.51287
.03248
.03250
.03251
.03252
8.52195
.52212
.52229
.52246
.03326
.03328
.03329
.03330
56
55
54
53
+ V
9
10
11
8.48077
.48095
.48113
.48131
.03025
.03027
.03028
.03029
8.49143
.49161
.49179
.49196
.03101
.03102
.03103
.03104
8.50196
.50214
.50231
.50248
.03177
.03178
.03179
.03180
.03254
.03255
.03256
.03257
8.52263
.52280
.52297
.52314
.03331
.03333
.03334
.03335
52
51
50
49
+ 3'
13
14
15
8.48149
.48167
.48184
.48202
.03030
.03032
.03033
.03034
8.49214
.49232
.49249
.49267
.03106
.03107
.03108
.03109
8.50266
.50283
.50301
.50318
.03182
.03183
.03184
.03186
8.51305
.51322
.51339
.51356
.03259
.03260
.03261
.03263
8.52331
.52348
.52365
.52382
.03337
.03338
.03339
.03341
4S
47
46
45
+ *'
17
18
19
8.48220
.48238
.48256
.48274
.03035
.03037
.03038
.03039
8.49284
.49302
.49320
.49337
.03111
.03112
.03113
.03114
8.50335
.50353
.50370
.50388
.03187
.03188
.03189
.03191
8.51374
.51391
.51408
.51425
.03264
.03265
.03266
.03268
8.52399
.52416
.52433
.52450
.03342
.03343
.03344
.03346
44
43
42
41
+ *'
21
22
23
8.48292
.48309
.48327
.48345
.03040
.03042
.03043
.03044
8.49355
.49373
.49390
.49408
.03116
.03117
.03118
.03119
8.50405
.50422
.50440
.50457
.03192
.03193
.03194
.03196
8.51442
.51459
.51477
.51494
.03269
.03270
.03272
.03273
8.52467
.52484
.52501
.52518
.03347
.03348
.03350
.03351
40
39
38
37
+ 6'
25
26
27
8.48363
.48381
.48399
.48416
.03045
.03047
.03048
.03049
8.49425
.49443
.49461
.49478
.03121
.03122
.03123
.03125
8.50475
.50492
.50509
.50527
.03197
.03198
.03200
.03201
8.51511
.51528
.51545
.51562
.03274
.03275
.03277
.03278
8.52535
.52552
.52569
.52585
.03352
.03354
.03355
.03356
36
35
34
33
+ r
29
SO
31
8.48434
.48452
.48470
.48488
.03050
.03052
.03053
.03054
8.49496
.49513
.49531
.49548
.03126
.03127
.03128
.03130
8.50544
.50561
.50579
.50596
.03202
.03204
.03205
.03206
8.51580
.51597
.51614
.51631
.03279
.03281
.03282
.03283
8.52602
.52619
.52636
.52653
.03358
.03359
.03360
.03361
32
31
30
29
+ 8'
S3
34
35
8.48505
.48523
.48541
.48559
.03055
.03057
.03058
.03059
8.49566
.49584
.49601
.49619
.03131
.03132
.03133
.03135
8.50614
.50631
.50648
.50666
.03207
.03209
.03210
.03211
8.51648
.51665
.51682
.51700
.03285
.03286
.03287
.03288
8.52670
.52687
.52704
.52721
.03363
.03364
.03365
.03367
28
27
26
25
+ V
37
38
39
8.48576
.48594
.48612
.48630
.03060
.03062
.03063
.03064
8.49636
.49654
.49671
.49689
.03136
.03137
.03138
.03140
8.50683
.50700
.50718
.50735
.03212
.03214
.03215
.03216
8.51717
.51734
.51751
.51768
.03290
.03291
.03292
.03294
8.52738
.52755
.52772
.52789
.03368
.03369
.03371
.03372
24
23
22
21
4- KK
41
42
43
8.48648
.48665
.48683
.48701
.03065
.03067
.03068
.03069
8.49706
.49724
.49742
.49759
.03141
.03142
.03144
.03145
8.50752
.50770
.50787
.50804
.03218
.03219
.03220
.03221
8.51785
.51802
.51819
.51836
.03295
.03296
.03298
.03299
8.52806
.52822
.52839
.52856
.03373
.03375
.03376
.03377
20
19
18
17
+ II7
45
46
47
8.48719
.48736
.48754
.48772
.03070
.03072
.03073
.03074
8.49777
.49794
.49812
.49829
.03146
.03147
.03149
.03150
8.50821
.50839
.50856
.50873
.03223
.03224
.03225
.03227
8.51854
.51871
.51888
.51905
.03300
.03301
.03303
.03304
8.52873
.52890
.52907
.52924
.03379
.03380
.03381
.03382
16
15
14
13
+ 12'
45
50
51
8.48789
.48807
.48825
.48843
.03075
.03077
.03078
.03079
8.49847
.49864
.49882
.49899
.03151
.03152
.03154
.03155
8.50891
.50908
.50925
.50943
.03228
.03229
.03230
.03232
8.51922
.51939
.51956
.51973
.03305
.03307
.03308
.03309
8.52941
.52958
.52974
.52991
.03384
.03385
.03386
.03388
12
11
10
9
+ 13'
53
J4
55
8.48860
.48878
.48896
.48914
.03080
.03082
.03083
.03084
8.49917
.49934
.49952
.49969
.03156
.03157
.03159
.03160
8.50960
.50977
.50994
.51012
.03233
.03234
.03236
.03237
8.51990
.52007
.52024
.52041
.03311
.03312
.03313
.03314
8.53008
.53025
.53042
.53059
.03389
.03390
.03392
.03393
8
7
6
5
+ 14'
57
55
59
8.48931
.48949
.48967
.48984
.03085
.03087
.03088
.03089
8.49987
.50004
.50022
.50039
.03161
.03163
.03164
.03165
8.51029
.51046
.51063
.51081
.03238
.03239
.03241
.03242
8.52058
.52076
.52093
.52110
.03316
.03317
.03318
.03320
8.53076
.53092
.53109
.53126
.03394
.03396
.03397
.03398
4
S
2
1
+ 15'
8.49002
.03090
8.50056
.03166
8.51098
.03243
8.52127
.03321
8.53143
.03400
0
22h 39™
£2 ft SB**
ggh sjm
g*h sem
22* S5m
Page 828] TABLE 45.
Haversines.
s
lh 25^ 21° 15'
lh 26m 21° 30'
lh 27m 21° 45'
lh 23™ 33° 0'
lh29mVZ° 15'
s
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
8.53143
.53160
.53177
.53193
.03400
.03401
.03403
.03404
8.54147
.54164
.54180
.54197
.03479
.03480
.03483
.03483
8.55139
.55156
55172
.55189
.03560
.03561
.03563
.03564
8.56120
.56136
.56152
.56169
.03641
.03643
.03644
.03645
8.57089
.57105
.57121
.57137
.03733
.03734
.03736
.03737
60
59
58
57
+ 1'
5
6
7
8.53210
.53227
.53244
.53261
.03405
.03406
.03408
.03409
8.54214
.54230
.54247
.54263
.03484
.03486
.03487
.03488
8.55205
.55221
55238
.55254
.03565
.03566
.03568
.03569
.03570
.03573
.03573
.03574
8.56185
.56201
.56217
.56233
.03646
.03648
.03649
.03650
8.57153
.57169
.57185
.57201
.03738
.03730
.03731
.03733
56
55
54
53
+ 3'
9
10
11
8.53277
.53294
.53311
.53328
.03410
.03411
.03413
.03414
8.54280
.54297
.54313
.54330
.03490
.03491
.03493
.03494
8.55271
.55287
.55303
.55320
8.55336
.55353
.55369
.55385
8.56250
.56266
.56282
.56298
.03653
.03653
.03654
.03656
8.57217
.57233
.57230
.57266
.03734
.03735
.03737
.03738
52
51
50
49
+ 3'
13
14
15
8.53345
.53361
.53378
.53395
.03415
.03417
.03418
.03419
8.54346
.54363
.54380
.54396
8.54413
.54429
.54446
.54462
.03495
.03496
.03498
.03499
.03576
.03577
.03578
.03580
8.56315
.56331
.56347
.56363
.03657
.03659
.03660
.03661
8.57282
.57298
.57314
.57330
.03740
.03741
.03743
.03744
48
47
46
45
+ 4'
17
18
19
+ 5'~
21
22
23
8.53412
.53429
.53445
.53462
.03431
.03433
.03433
.03435
.03500
.03503
.03503
.03504
8.55402
.55418
.55435
.55451
.03581
.03583
.03584
.03585
8.56379
.56396
.56412
.56428
.03663
.03664
.03665
.03667
8.57346
.57362
.57378
.57394
.03745
.03746
.03748
.03749
44
43
42
41
8.53479
.53496
.53512
.53529
.03436
.03437
.03439
.03430
8.54479
.54496
.54512
.54529
.03506
.03507
.03509
.03510
8.55467
.55484
.55500
.55516
.03587
.03588
.03589
.03591
8.56444
.56460
.56477
.56493
.03668
.03669
.03671
.03673
8.57410
.57426
.57442
.57458
.03751
.03753
.03753
.03755
40
39
38
37
+ V
25
26
27
8.53546
.53563
.53580
.53596
.03431
.03433
.03434
.03435
8.54545
.54562
.54578
.54595
.03511
.03513
.03514
.03515
8.55533
.55549
.55566
.55582
.03593
.03593
.03595
.03596
8.56509
.56525
.56541
.56557
.03674
.03675
.03676
.03678
8.57474
.57490
.57506
.57522
.03756
.03757
.03759
.03760
36
35
34
33
+ 7'
29
30
31
8.53613
.53630
.53646
.53663
8.53680
.53697
.53713
.53730
.03437
.03438
.03439
.03441
8.54612
.54628
.54645
.54661
.03517
.03518
.03519
.03531
8.55598
.55615
.55631
.55647
.03597
.03599
.03600
.03601
8.56574
.56590
.56606
.56622
.03679
.03680
.03683
.03683
8.57538
.57554
.57570
.57585
.03763
.03763
.03764
.03766
32
31
30
29
+ 8'
33
34
35
.03443
.03443
.03445
.03446
8.54678
.54694
.54711
.54727
.03533
.03533
.03535
.03536
8.55664
.55680
.55696
.55713
.03603
.03604
.03605
.03607
8.56638
.56654
.56670
.56687
.03685
.03686
.03687
.03689
8.57601
.57617
.57633
.57649
.03767
.03769
.03770
.03771
28
27
26
25
+ S7
37
38
39
8.53747
.53764
.53780
.53797
.03447
.03449
.03450
.03451
8.54744
.54760
.54777
.54793
.03537
.03539
.03530
.03531
8.55729
.55745
.55762
.55778
.03608
.03610
.03611
.03613
8.56703
.56719
.56735
.56751
.03690
.03691
.03693
.03694
8.57665
.57681
.57697
.57713
.03773
.03774
.03775
.03777
24
22
21
+ w
41
42
43
8.53814
.53830
.53847
.53864
.03453
.03454
.03455
.03457
8.54810
.54826
.54843
.54859
.03533
.03534
.03535
.03537
.03538
.03539
.03541
.03543
8.55794
.55811
.55827
.55843
.03614
.03615
.03616
.03618
8.56767
.56783
.56799
.56816
.03695
.03697
.03698
.03700
.03701
.03703
.03704
.03705
8.57729
.57745
.57761
.57777
.03778
.03780
.03781
.03783
20
19
18
17
+ 11'
45
46
47
8.53880
.53897
.53914
.53930
.03448
.03459
.03460
.03463
8.54876
.54892
.54909
.54925
8.55859
.55876
.55892
.55908
.03619
.03630
.03633
.03633
8.56832
.56848
.56864
.56880
8.57793
.57809
.57825
.57841
.03784
.03785
.03787
.03788
16
15
14
13
+ 13'
49
50
51
8.53947
.53964
.53980 .
.53997
.03463
.03464
.03466
.03467
8.54942
.54958
.54975
.54991
.03543
.03545
.03546
.03547
8.55925
55941
.55957
.55973
.03634
.03636
.03637
.03639
8.56896
.56912
56928
.56944
.03706
.03708
.03709
.03711
8.57856
.57872
.57888
.57904
.03789
.03791
.03793
.03794
12
11
10
9
+ 13'
53
54
55
8.54014
.54030
.54047
.45064
.03468
.03470
.03471
.03473
8.55008
.55024
.55041
.55057
.03549
.03550
.03551
.03553
8.55990
56006
.56022
.56039
.03630
.03631
.03633
.03634
8.56960
56977
.56993
.57009
.03713
.03713
.03715
.03716
8.57920
.57936
57952
.57968
.03795
.03796
.03798
.03799
8
7
6
5
+ 14'
57
58
59
8.54080
.54097
.54114
.54130
.03474
.03475
.03476
.03478
8.55073
.55090
.55106
.55123
.03554
.03555
.03557
.03558
8.56055
.56071
.56087
.56104
.03635
.03637
.03638
.03639
8.57025
.57041
.57057
.57073
.03717
.03719
.03730
.03733
8.57984
.58000
.58015
.58031
.03800
.03803
.03803
.03805
4
3
2
1
+ 15'
8.54147
.03479
8.55139
.03560
8.56120
.03641
8.57089
.03733
8.58047
.03806
0
22*> 34™
22h 33m
22h 32™
22* 3im
22~h 30m
TABLE 45. [Page 829 1
Haversines. <
s
1* SO™ 22° 30'
in Sim ^o^
1^3-2™ 23° V
lh S3™ 23° 15/
.7M4™23030/
s 1
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
8.58047
.58063
.58079
.58095
.03806
.03807
.03809
.03810
8.58994
.59010
.59026
.59042
.03890
.03891
.03893
.03894
8.59931
.59947
.59962
.59978
.03975
.03976
.03978
.03979
8.00867
.60873
.60888
.60903
8.60919
.60934
.60949
.60965
.04060
.04062
.04063
.04065
8.61773
61789
.61804
.61819
.04147
.04148
.04150
.04151
60
59
58 \
57 \
+ 1'
5
6
7
8.58111
.58127
.58142
.58158
.03812
.03813
.03814
.03816
8.59057
.59073
.59089
,59104
.03896
.03897
.03898
.03900
8.59993
.60009
.60024
.60040
.03980
.03982
.03983
.03985
.04066
.04068
.04069
.04070
8.61834
.61849
.61864
.61880
.04153
.04154
.04156
.04157
56
55
54
53
+ V
9
10
11
8.58174
.58190
.58206
.58222
.03817
.03819
.03820
.03821
8.59120
.59136
.59151
.59167
.03901
.03903
.03904
.03905
8.60055
.60071
.60086
.60102
.03986
.03988
.03989
.03990
8.60980
.60995
.61011
.61026
.04072
.04073
.04075
.04076
8.61895
.61910
.61925
.61940
.04159
.04160
.04162
.04163
52 \
51 \
50 \
49
+ *
IS
14
15
8.58238
.58253
.58269
.58285
.03823
.03824
.03826
.03827
8.59183
.59198
,59214
.59230
.03907
.03908
.03910
.03911
8.60117
.60133
.60148
.60164
.03992
.03993
.03995
.03998
8.61041
.61057
.61072
.61087
.01078
.04079
.04081
.04082
8.61955
.61971
.61986
.62001
.04164
.04166
.04167
.04169
48
47
46
45
+ 4'
17
18
19
8.58301
.58317
.58333
.58348
.03828
.03830
.03831
.03833
8.59245
.59261
,59277
.59292
.03912
.03914
.03915
.03917
8.60179
.60195
.60210
.60226
.03998
.03999
.04000
.04002
8.61103
.61118
.61133
.61149
.04083
.04085
.04088
.04088
8.62016
.62031
.62046
.62061
.04170
.04172
04173
.04175
44
43
42
41
40
39
38
_57j
36
35
34
33
+ 5'
21
22
23
8.58364
.58380
.58396
.58412
.03834
.03835
.03837
.03838
8.59308
.59323
.59339
.59355
.03918
.03920
.03921
.03922
8.60241
.60256
.60272
.60287
.04003
.04005
.04006
.04007
8.61164
.61179
.61194
.61210
.04089
.04091
.04092
.04094
8.62077
.62092
.62107
.02122
.04176
.04177
.04179
.04180
+ &
25
26
27
8.58427
.58443
.5S459
.58475
.03839
.03841
.03842
.03844
8.59370
.59386
.59402
.59417
.03924
.03925
.03927
.03928
8.60303
.60318
.60334
.60349
.04009
.04010
.04012
.04013
8.61225
.61240
.61256
.61271
.04095
.04096
.04098
.04099
8.62137
.62152
.62167
.62182
.04182
.04183
.04185
.04186
+ r
29
30
31
8.58491
.58506
.58522
.58538
.03845
.03846
.03848
.03849
8.59433
,59448
,59464
.59480
.03929
.03931
.03932
.03934
8.60365
.60380
.60396
.60411
.04015
.04016
.04017
.04019
8.61286
.61301
.61317
.61332
.04101
.04102
.04104
.04105
8.62197
.62213
.62228
.62243
.04188
.04189
.04191
.04192
32
31
30
29
+ 8'
33
34
35
8.58554
.58570
.58585
.58601
.03851
.03852
.03853
.03855
8.59495
.59511
.59527
.59542
.03935
.03938
.03938
.03939
8.60426
.60442
.60457
.60473
.04020
.04022
.04023
.04025
8.61347
.61362
.61378
.61393
.04106
.04108
.04109
.04111
8.62258
.62273
.62288
.62303
.04194
.04195
.04196
.04198
28
27
26
25
+ 9'
37
38
39
8.58617
.58633
,58648
.58664
.03856
.03858
.03859
.03860
8.59558
,59573
,59589
,59604
.03941
.03942
.03944
.03945
8.60488
.60504
.60519
.60534
.04026
.04027
.04029
.04030
8.61408
.61423
.61439
.61454
.04112
.04114
.04115
.04117
8.62318
.62333
.62348
.62363
.04199
.04201
.04202
.04204
24
23
22
21
+ W
41
42
49
8.58680
.58696
.58711
.58727
.03862
.03863
.03865
.03866
8.59620
.59636
,59651
.59667
.03946
.03948
.03949
.03951
8.60550
.60565
.60581
.60596
.04032
.04033
.04035
.04036
8.61469
.61484
.61500
.61515
.04118
.04119
.04121
.04122
8.62379
.62394
.62409
.62424
.04205
.04207
.04208
.04210
20
19
18
17
+ Hx
45
46
47
8.58743
.58759
.58774
,58790
.03867
.03869
.03870
.03872
8.59682
.59698
.59714
.59729
.03952
.03953
.03955
.03956
8.60611
.60627
.60642
.60658
.04038
.04039
.04040
.04042
8.61530
.61545
.61561
.61576
.04124
.04125
.04127
.04128
8.62439
.62454
.62469
.62484
.04211
.04212
.04214
.04215
16
15
14
13 \
~12\
11
10
9
~8~\
\
+ 12'
49
50
51
8.58806
.58822
.58837
.58853
.03873
.03875
.03876
.03877
8.59745
.59760
.59776
.59791
.03958
.03959
.03961
.03962
8.60673
.60688
.60704
.60719
.04043
.04045
.04046
.04048
8.61591
.61606
.61621
.61637
.04130
.04131
.04133
.04134
8.62499
.62514
.62529
.62544
.04217
.04218
.04220
.04221
+ 13'
53
54
55
8.58869 i .03879
.588851 .03880
.58900 ! .03883
.58916 .03883
8.59807
.59822
.59838
,59853
.03963
.03965
.03866
.03968
8.60734
.60750
.60765
.60781
.04049
.04050
.04052
.04053
8.61652
.61667
.61682
.61697
.04135
.04137
.04138
.04140
8.62559
.62574
.62589
.62604
.04223
.04224
.04226
.04227
+ 14'
57
58
59
8.58932
.58947
.58963
.58979
.03884
.03886
.03887
.03889
5.59869
.59885
.59900
.59916
.03969
.03971
.03972
.03973
8.60796
.60811
.60827
.60842
.04055
.04056
.04058
.04059
8.61713
.61728
.61743
.61758
.04141
.04143
.04144
.04146
8.62619
.62634
.62649
.62664
.04229
.04230
.04232
.04233
4
3
f
+ 15'
8.58994
.03890
8.59931
.03975
8.60857
.04060
8.61773
.04147
8.62680
.04234
0 I
22h 29m
%2h 28™
22^ 27m
2%h 26m
22*- 25Jn
Page 830] TABLE 45.
Haversines.
5
11*35™%%° 45'
IhSGmWV
IhSJm 24° 15'
lh 5#»24° 30'
^39™ 24° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
8.62680
.62695
.62710
.62725
.04234
.04236
.04237
.04239
8.63576
.63591
.63606
.63620
.04323
.04324
.04328
.04327
8.64463
.64477
.64492
.64507
.04412
..04413
.04415
.04416
8.65340
.65355
.65369
.65384
.04502
.04503
.04505
.04506
8.66208
.66223
.66237
.66251
.04593
.04594
.04596
.04597
60
59
58
57
56
55
54
53
+ 1'
5
6
7
8.62740
.62755
.62770
.62785
.04240
.04242
.04243
.04245
8.63635
.63650
.63665
.63680
.04329
.04330
.04332
.04333
8.64521
.64536
.64551
.64565
.04418
.04419
.04421
.04422
8.65398
.65413
.65427
.65442
.04508
.04509
.04511
.04512
8.66266
.66280
.66295
.66309
.04599
.04600
.04602
.04604
+ %'
9
10
11
8.62800
.62815
.62830
.62845
.04246
.04248
.04249
.04251
8.63695
.63709
.63724
.63739
.04335
.04336
.04338
.04339
8.64580
.64595
.64609
.64624
.04424
.04425
.04427
.04428
8.65456
.65471
.65485
.65500
.04514
.04516
.04517
.04519
8.66323
.66338
.66352
.66366
.04605
.04607
.04608
.04610
52
51
50
49
+ V
13
14
15
8.62860
.62875
.62890
.62904
.04252
.04253
.04255
.04256
8.63754
.63769
.63784
.63798
.04340
.04342
.04343
.04345
8.64639
.64653
.64668
.64683
.04430
.04431
.04433
.04434
8.65514
.65529
.65543
.65558
.04520
.04523
.04523
.04525
8.66381
.66395
.66409
.66424
.04611
.04613
.04614
.04616
48
47
46
45
+ *
17
18
19
8.62919
.62934
.62949
.62964
.04258
.04259
.04261
.04262
.04264
.04265
.04267
.04268
8.63813
.63828
.63843
.63858
.04346
.04348
.04349
.04351
8.64697
.64712
.64727
.64741
.04436
.04437
.04439
.04440
8.65572
.65587
.65601
.65616
.04526
.04528
.04529
.04531
8.66438
.66453
.66467
.66481
.04617
.04619
.04620
.04622
44
43
42
41
+ V
21
23
8.62979
.62994
.63009
.63024
8.63872
.63887
.63902
.63917
.04352
.04354
.04355
.04357
8.64756
.64771
.64785
.64800
.04442
.04443
.04445
.04446
8.65630
.65645
.65659
.65674
.04532
.04534
.04535
.04537
8.66496
.66510
.66524
.66539
.04623
.04625
.04626
.04628
40
39
38
37
+ 6X
25
26
27
8.63039
.63054
.63069
.63084
.04270
.04271
.04273
.04274
8.63932
.63946
.63961
.63976
.04358
.04360
.04361
.04363
8.64815
.64829
.64844
.64859
.04448
.04449
.04451
.04452
8.65688
.65703
.65717
.65732
.04538
.04540
.04541
.04543
8.66553
.66567
.66582
.66596
.046S9
.04631
.04633
.04634
36
35
34
33
+ r
29
30
31
8.63099
.63114
.63129
.63144
.04276
.04277
.04278
.04280
8.63991
.64006
.64020
.64035
.04364
.04366
.04367
,043€9
8.64873
.64888
.64902
.64917
.04454
.04455
.04457
.04458
8.65746
.65761
.65775
.65790
.04544
.04546
.04547
.04549
8.66610
.66625
.66639
.66653
.04636
.04637
.04639
.04640
32
30
29
+ 8'
33
34
35
8.63159
.63174
.63189
.63204
.04281.
.04283
.04284
.04286
8.64050
.64065
.64079
.64094
.01370
.04372
.04373
.04375
8.64932
.64946
.64961
.64976
.04460
.04461
.04463
.04464
8.65804
.65819
.65833
.65848
.04550
.04552
.04553
.04555
8.66668
.66682
.66696
.66710
.04642
.04643
.04645
.04646
28
27
26
25
+ 9'
37
38
39
8.63218
.63233
.63248
.63263
.04287
.04289
.04290
.04292
8.64109
.64124
.64139
.64153
.04376
.04378
.04379
.04381
8.64990
.65005
.65019
.65034
.04466
.04467
.04469
.04470
8.65862
.65876
.65891
.65905
.04556
.04558
.04559
.04561
8.66725
.66739
.66753
.66768
.04648
.04649
.04651
.04652
24
23
21
+ 10'
41
42
43
8.63278
.63293
.63308
.63323
.04293
.04295
.04296
.04298
8.64168
.64183
.64198
.64212
.04382
.04384
.04385
.04387
8.65049
.65063
.65078
.65092
.04472
.04473
.04475
.04476
8.65920
.65934
.65949
.65963
.04562
.04564
.04565
.04567
8.66782
.66796
.66811
.66825
.04654
.04655
.04657
.04659
20
19
18
17
+ 11'
45
46
47
8.63338
.63353
.63368
.63382
.04299
.04301
.04302
.04304
8.64227
.64242
.64257
.64271
.04388
.04390
.04391
.04393
8.65107
.65122
.65136
.65151
.04478
.04479
.04481
.04482
8.65978
.65992
.66006
.66021
.04569
.04570
.04572
.04573
8.66839
.66853
.66868
.66882
.04660
.04662
.04663
.04665
16
15
14
13
+ 12'
49
50
51
8.63397
.63412
.63427
.63442
.04305
.04306
.04308
.04309
8.64286
.64301
.64315
.64330
.04394
.04395
.04397
.04398
8.65165
.65180
.65194
.65209
.04484
.04485
.04487
.04488
8.66035
.66050
.66064
.66079
.04575
.04576
.04578
.04579
8.66896
.66911
.66925
.66939
.04666
.04668
.04669
.04671
12
11
10
9
+ 13'
53
54
55
8.63457
.63472
.63487
.63502
.04311
.04312
.04314
.04315
8.64345
.64360
.64374
.64389
.04400
.04401
.04403
.04404
8.65224
.65238
.65253
.65267
.04490
.04491
.04493
.04494
.04496
.04497
.04499
.04500
8.66093
.66107
.66122
.66136
.04581
.04582
.04584
.04585
8.66953
.66968
.66982
.66996
.04672
.04674
.04675
.04677
8
7
6
5
+ 14'
57
58
59
-+-w
8.63516
.63531
.63546
.63561
.04317
.04318
.04320
.04321
8.64404
.64418
.64433
.64448
.04405
.04407
.04409
.04410
8.65282
.65296
.65311
.65325
8.66151
.66165
.66179
.66194
.04587
.04588
.04590
.04591
8.67010
.67025
.67039
.67053
.04678
.04680
.04682
.04683
4
3
2
1
8.63576
.04323
8.64463
.04412
8.65340
.04502
8.66208
.04593
8.67067
.04685
0
22*> 24™
22^23™ •
22* 22m
22* 21™
22*20™
TABLE 45. [Page 831
Haversines.
lh 40m 25° O'
lh 41m
25° 15'
lh 42m 25° 30X
lh 43m 25° 45'
lh 44m 26° V
s
8
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.! Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
8.67067
.67082
.67096
.67110
.04685
.04686
.04688
.04689
8.67918
.67932
.67946
.67960
.04777
.04779
.04780
.04782
8.68760
.68773
.68787
.68801
.04871
.04872
.04874
.04875
8.69593
.69607
.69620
.69634
.04965
.04967
.04968
.04970
8.70418
.70431
.70445
.70459
.05060
.05062
.05063
.05065
60
59
58
57
+ 1'
5
6
7
8.67124
.67139
.67153
.67167
.04691
.04692
.04694
.04695
8.67974
.67988
.68002
.68016
.04783
.04785
.04787
.04788
8.6S815
.68829
.68843
.88857
.04877
.04879
.04880
.04882
8.69648
.69662
.69676
.69690
.04971
.04973
.04975
.04976
8.70472
.70486
.70500
.70513
.05067
.05068
.05070
.05071
56
55
54
53
9
10
11
8.67181
.67196
.67210
.67224
.04697
.04698
.04700
.04702
8.68030
.68045
.68059
.68073
.04790
.04791
.04793
.04794
8.68871
.68885
.68899
.68913
.04883
.04885
.04886
.04888
8.69703
.69717
.69731
.69745
.04978
.04979
.04981
.04982
8.70527
.70541
.70554
.70568
.05073
.05075
.05076
.05078
52
51
50
49
13
14
15
8.67238
.67252
.67267
.67281
.04703
.04705
.04706
.04708
8.68087
.68101
.68115
.68129
.04796
.04797
.04799
.04801
8.68927
.68941
.68955
.68969
.04890
.04891
.04893
.04894
8.69758 .04984
.69772 .04986
.69786 .04987
.69800 .04989
8.70582
.70595
.70609
.70623
.05079
.05081
.05083
.05084
48
47
46
45
17
18
19
8.67295
.67309
.67323
.67338
.04709
.04711
.04712
.04714
8.68143
.68157
.68171
.68185
.04802
.04804
.04805
.04807
8.68983
.68996
.69010
.69024
.04896
.04897
.04899
.04901
8.69814
.69827
.69841
.69855
.04990
.04992
.04994
.04995
8.70636
.70650
.70664
.70677
.05086
.05087
.05089
.05091
44
43
42
41
i e/
21
22
23
8.67352
.67366
.67380
.67394
.04715
.04717
.04718
.04720
8.68199
.68213
.68227
.68241
.04808
.04810
.04811
.04813
8.69038
.69052
.69066
.69080
8.69094
.69108
.69122
.69136
.04902
.04904
.04905
.04907
8.69869
.69882
.69896
.69910
.04997
.04998
.05000
.05001
8.70691
.70704
.70718
.70732
.05092
.05094
.05095
.05097
40
39
38
37
+ v
25 '
26
27
8.67409
.67423
.67437
.67451
.04722
.04723
.04725
.04726
8.68256
.68270
.68284
.68298
.04815
.04816
.04818
.04819
.04908
.04910
.04912
.04913
8.69924
.69937
.69951
.69965
.05003
.05005
.05006
.05008
8.70745
.70759
.70773
.70786
.05099
.05100
.05102
.05104
36
35
34
33
29
SO
31
8.67465
.67480
.67494
.67508
.04728
.04729
.04731
.04732
8.68312
.68326
.68340
.68354
.04821
.04822
.04824
.04825
8.69149
.69163
.69177
.69191
.049^5
.04916
.04918
.04919
8.69979
.69992
.70006
.70020
.05009
.05011
.05013
.05014
8.70800
.70813
.70827
.70841
.05105
.05107
.05108
.05110
32
31
30
29
28
27
26
25
+ 8'
S3
S4
35
8.67522
.67536
.67550
.67565
.04734
.04735
.04737
.04739
8.68368
.68382
.68396
.68410
.04827
.04829
.04830
.04832
8.69205
.69219
.69233
.69247
.04921
.04923
.04924
.04926
8.70034
.70047
.70061
.70075
.05016
.05017
.05019
.05021
8.70854
.70568
.70881
.70895
.05111
.05113
.05115
.05116
1 <V/
37
38
39
8.67579
.67593
.67607
.67621
.04740
.04742
.04743
.04745
8.68424
.68438
.68452
.68466
.04833
.04835
.04836
.04838
8.69260
.69274
.69288
.69302
.04927
.04929
.04930
.04932
8.70089
.70102
.70116
.70130
.05022
.05024
.05025
.05027
8.70909
.70922
.70936
.70949
.05118
.05119
.05121
.05123
24
23
22
21
-\- W
41
42
43
8.67635
.67649
.67664
.67678
.04746
.04748
.04749
.04751
8.68480
.68494
.68508
.68522
.04839
.04841
.04843
.04844
8.69316
.69330
.69344
.69358
.04934
.04935
.04937
.04938
8.70144
.70157
.70171
.70185
.05028
.05030
.05032
.05033
8.70963
.70977
.70990
.71004
.05124
.05126
.05127
.05129
20
19
18
17
+ Hx
45
46
47
8.67692
.67706
.67720
.67734
.04752
.04754
.04756
.04757
8.68536
' .68550
.68564
.68578
.04846
.04847
.04849
.04850
8.69371
.69385
.69399
.69413
.04940
.04941
.04943
.04945
8.70198
.70212
.70226
.70240
.05035
.05036
.05038
.05040
8.71017
.71031
.71045
.71058
.05131
.05132
.05134
.05135
16
15
14
13
49
50
51
8.67748
.67763
.67777
.67791
.04759
.04760
.04762
.04763
8.68592
.68606
.68620
.68634
; .04852
j .04854
.04855
.04857
8.69427
.69441
.69454
.69468
.04946
.04948
.04949
.04951
8.70253
.70267
.70281
.70294
.05041
.05043
.05044
.05046
8.71072
.71085
.71099
.71112
.05137
.05139
.05140
.05142
12
11
10
9
+ 13'
53
54
55
8.67805
.67819
.67833
.67847
.04765
.04766
.04768
.04769
8.68648
.68662
.68676
.68690
.04858
.04860
.04861
.04863
8.69482
.69496
.69510
.69524
.04952
.04954
.04956
.04957
8.70308
.70322
.70336
.70349
.0504S
.05049
.05051
.05052
8.71126
.71140
.71153
.71167
.05144
.05145
.05147
.05148
8
7
6
5
+ 14'
57
58
59
8.67861
.67875
.67890
.67904
.04771
.04773
.04774
.04776
8.68704
.68718
.68732
.68746
.04864
.04866
.04868
.04869
8.69537
.69551
.69565
.69579
.04959
.04960
.04962
.04964
8.70363
.70377
.70390
.70404
.05054
.05055
.05057
.05059
8.71180
.71194
.71207
.71221
.05150
.05152
.05153
.05155
4
3
2
1
+ 157
8.67918
.04777
8.68760
| .04871
8.69593
.04965
8.70418
.05060
8.71234
.05156
0
22^ 19^
2%h 18m
22h 17m
22* 16m
22h 15m
Page 832] TABLE 45.
Haversines.
s
lh 45m 2Q° 15'
in 46m 26° 30'
lh 47m 26° 45'
lh 4sm 21° (K
!*> 49m 21° 15'
8
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
8.71234
.71248
.71261
.71275
.05156
.05158
.05160
.05161
8.72043
.72057
.72070
.72083
.05253
.05255
.05257
.05258
8.72844
.72857
.72871
.72884
.05351
.05353
.05354
.05356
8.73637
.73650
.73663
.73677
.05450
.05451
.05453
.05455
8.74423
.74436
.74449
.74462
.05549
.05551
.05552
.05554
SO
59
58
57
+ ¥
5
6
7
8.71289
.71302
.71316
.71329
.05163
.05164
.05166
.05168
8.72097
.72110
.72124
.72137
.05260
.05261
.05263
.05265
8.72897
.72910
.72924
.72937
.05358
.05359
.05361
.05363
8.73690
.73703
.73716
.73729
.05456
.05458
.05460
.05461
8.74475
.74488
.74501
.74514
.05556
.05557
.05559
.05561
56
55
54
53
+ *
9
10
11
8.71343
.71356
.71370
.71383
.05169
.05171
.05172
.05174
8.72150
.72164
.72177
.72191
.05266
.05268
.05270
.05271
8.72950
.72963
.72977
.72990
.05364
.05366
.05367
.05369
8.73742
.73755
.73769
.73782
.05463
.05464
.05466
.05468
8.74527
.74540
.74553
.74566
.05562
.05564
.05566
.055G7
52
51
50
49
+ y
13
14
15
8.71397
.71410
.71424
.71437
.05176
.05177
.05179
.05181
8.72204
.72217
.72231
.72244
.05273
.05274
.05276
.05278
8.73003
.73016
.73030
.73043
.05371
.05372
.05374
.05376
8.73795
.73808
.73821
.73834
.05470
.05471
.05473
.05474
8.74579
.74592
.74605
.74618
.05569
.05571
.05572
.05574
48
47
46
45
+ v
17
18
19
8.71451
.71464
.71478
.71491
.05182
.05184
.05185
.05187
8.72257
.72271
.72284
.72298
.05279
.05281
.05233
.05284
8.73056
.73069
.73083
.73096
.05377
.05379
.05381
.05382
8.73847
.73860
.73874
.7388V
.05476
.05478
.05479
.05481
8.74631
.74644
.74657
.74670
.05576
.05577
.05579
.05581
44
43
42
41
+ &
21
22
8.71505
.71518
.71532
.71545
.05189
.05190
.05193
.05193
8.72311
.72324
.72338
.72351
.05286
.05287
.05289
.05291
8.73109
.73122
.73136
.73149
.05384
.05385
.05387
.05389
8.73900
.73913
.73926
.73939
.05483
.05484,:
.05486;
.05488
8.74683
.74696
.74709
.74722
.05582
.05584
.05586
.05587
40
39
38
37
+ 67
25
26
27
8.71559
.71572
.71586
.71599
.05195
.05197
.05198
.05200
8.72364
.72378
.72391
.72404
.05292
.05294
.05296
.05297
8.73162
.73175
.73189
.73202
.05390
.05392
.05394
.05395
8.73952
.73965
.73978
.73992
.05489
.05491
.05493
.05494
8.74735
.74748
.74761
.74774
.05589
.05591
.05593
.05594
.36
35
34
S3
+ r
29
30
31
8.71613
.71626
.71640
.71653
.05201
.05203
.05205
.05206
8.72418
.72431
.72445
.72458
.05299
.05300
.05302
.05304
8.73215
.73228
.73241
.73255
.05397
.05399
.05400
.05402
8.74005
.74018
.74031
.74044
.05496
.05498
.05499
.05501
8.74787
.74800
.74813
.74826
.05596
.05597
.05599
.05601
32
31
30
29
+ 8'
S3
34
35
8.71667
.71680
.71694
.71707
.05208
.05210
.05211
.05213
8.72471
.72485
.72498
.72511
.05305
.05307
.03309
.05310
8.73268
.73281
.73294
.73308
.05404
.05405
.05407
.05408
8.74057
.74070
.74083
.74096
.05503
.05504
.05506
.05508
8.74839
.74852
.74864
.74877
.05603
.05604
.05606
.05607
28
27
26
+sO
+ 9'
37
38
39
8.71721
.71734
.71748
.71761
.05214
.05216
.05218
.05219
8.72525
.72538
.72551
.72565
.05312
.05314
.05315
.05317
8.73321
.73334
.73347
.73360
.05410
.05412
.05413
.05415
8.74109
.74122
.74135
.74149
.05509
.05511
.05513
.05514
8.74890
.74903
.74916
.74929
.05609
.05611
.05613
.05614
24
23
21
+ 10'
41
42
43
8.71774
.71788
.71801
.71815
.05221
.05222
.05224
.05226
8.72578
.72591
.72605
.72618
.05318
.05320
.05322
.05323
8.73374
.73387
.73400'
.73413
.05417
.05418
.05420
.05422
8.74162
.74175
.74188
.74201
.05516
.05518
.05519
.05521
8.74942
.74955
.74968
.74981
.05616
.05618
.05619
.05621
20
19
18
17
16
15
14
13
+ 11'
45
46
47
8.71828
.71842
.71855
.71869
.05227
.05229
.05231
.05232
8.72631
.72644
.72658
.72671
.05325
.05326
.05328
.05330
8.73426
.73440
.73453
.73466
.05423,
.05425'
.05427
.05428
8.74214
.74227
.74240
.74253
.05523
.05524
.05526
.05528
8.74994
.75007
.75020
.75033
.05623
.05624
.05626
.05628
+ 12'
49
50
51
8.71882
.71895
.71909
.71922
.05234
.05235
.05237
.05239
8.72684
.72698
.72711
.72724
.05331
.05333
.05335
.05336
8.73479
.73492
.73505
.73519
.05430
.05431
.05433
.05435
8.74266
.74279
.74292
.74305
.05529
.05531
.05533
.05534
8.75046
.75059
.75072
.75084
.05629
.05631
.05633
.05634
12
11
10
9
+ 13'
53
54
55
8.71936
.71949
.71963
.71976
.05240
.05242
.05244
.05245
8.72738
.72751
.72764
.72778
.05338
.05340
.05341
.05343
8.73532
.73545
.73558
.73571
.05436
.05438
.05440
.05441
8.74318
.74331
.74344
.74357
.05536
.05537
.05539
.05541
8.75097
.75110
.75123
.75136
.05636
.05638
.05639
.05641
8
7
6
5
+ 14'
54
58
59
8.71989
.72003
.72016
.72030
.05247
.05248
.05250
.05252
8.72791
.72804
.72817
.72831
.05345
.05346
.05348
.05349
8.73584
.73598
.73611
.73624
.05443
.05445
.05446
.05448
8.74371
.74384
.74397
.74410
.05542
.05544
.05546
.05547
8.75149
.75162
.75175
.75188
.05643
.05644
.05646
.05648
4
3
2
1
+ 15'
8.72043
.05253
8.72844
.05351
8.73637
.05450
8.74423
.05549
8.75201
.05649
0
22h 14™
2gh ism
22^ 12m
ggh Urn
vvJi iom
TABLE 45. [Page 833
Haversine?.
s
lh 50™ 27° 3<K
lh 51™ 21° 15'
lh J^28°0/
lh 53m 28° 15'
1* 54m 28° 30'
s
Log. Hav.
Nat. Hav
Log. Havj Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Xai.llav.
0
1
2
3
8.75201
.75214
.75227
.75239
.05649
.05651
.05653
.05655
8.75972 .05751
.75984 | .05752
.75997 .05754
.76010 .05756
8.76735
.76748
.76760
.76773
.05853
.05854
.05856
.05858
8.77492
.77504
.77517
.77528
.05955
.05957
.05959
.05961
8.78241
.78254
.78266
.78278
.06059
.06061
.06063
.06064
60
59
58
57
+ 1'
5
6
7
8.75252
.75265
.75278
.75291
.05656
.05658
.05660
.05661
8.76023
.76035
.76048
.76061
8.76074"
.76086
.76099
.76112
.05757
.05759
.05761
.05762
8.76786
.76798
76811
.76824
.05859
.05861
.05863
.05865
.77554
.77567
.77579
.05962
.05964
.05366
.059G8
8.78291
.78303
.78316
.78328
.06066
.06068
.06070
.06071
56
55
54
53
+ 2'
9
10
11
8.75304
.75317
.75330
.75343
.05663
.05665
.05666
.05668
.05670
.05671
.05673
.05675
.05764
.05766
.05768
.05769
8.76836
.76849
.76862
.76874
.05866
.05868
.05870
.05871
8.77592
.77604
.77617
.77630
.05969
.05971
.05973
.05974
8.78341
.78353
.78365
.78378
.06073
.06075
.06077
.06078
52
51
50
49
+ 3'
13
14
15
8.75355
.75368
.75381
.75394
8.76125
.76138
.76150
.76163
.05771
.05773
.05774
.05776
8.76887
.76900
.76912
.76925
.05873
.05875
.05877
.05878
8.77642
.77655
.77667
.77680
.05976
.05978
.05980
.05981
8.78390
.78403
.78415
.78428
.06080
.06082
.06083
.06085
48
47
46
45
+ *'
17
18
19
8.75407
.75420
.75433
.75446
.05676
.05678
.05680
.05681
8.76176
.76189
.76201
.76214
.05778
.05779
.05781
.05783
8.76938
.76950
.76963
.76975
.05880
.05882
.05883
.05885
8.77692
.77705
.77717
.77730
.05983
.05985
.05986
.05988
8.78440
.75452
.78465
.78477
.06087
.06089
.06090
.96092
44
43
42
41
+ 5'
-21
22
2S
8.75458
.75471
.75484
.75497
.05683
.05685
.05686
.05688
8.76227
.76240
.76252
.76265
.05785
.05786
.05788
.05790
8.76988
.77001
.77013
.77026
.05887
.05888
.05890
.05892
8.77742
.05990
.05992
.05993
.05995
8.78490
.78502
.78514
.78527
.06094
.08098
.06097
.06099
40
39
38
37
. , i , 00
.77767
.77780
+ v
25
26
tv
8.75510
.75523
.75536
.75548
.05690
.05691
.05693
.05695
8.76278
.76291
.76303
.76316
.05791
.05793
.05795
.05796
8.77039
.77051
.77064
.77076
.05894
.05895
.05897
.05899
8.77792
.77805
.77817
.77830
.05997
.05999
.06000
.06002
8.78539
.78551
.78564
.78576
.06101
.06103
.06104
.08106
36
35
34
33
+ v
29
30
31
8.75561
.75574
.75587
.75600
.05897
.05698
.05700
.05702
8.76329
.76341
.76354
.76367
.05793
.05800
.05802
.05803
8.77089
.77102
.77114
.77127
.05901
.05902
.05904
.05906
8.77842
.77855
.77867
.77880
.06004
.06005
.06007
.06009
8.78589
.76601
.78613
.78626
.06108
.06110
.06111
.06113
62,
31
30
29
+ 8'
33
34
35
8.75613
.75626
.75638
.75651
.05703
.05705
.05707
.05708
8.76380
.76392
.76405
.76418
.05805
.05807
.05808
.05810
8.77139
.77152
.77165
.77177
.05907
.05909
.05911
.05913
8.77892
.77905
.77917
.77930
.06011
.06012
.06014
.06016
8.78638
.78651
.78663
.78675
.06115
.06117
.06118
.06120
28
£7
26
25
+ »'
37
38
39
8.75664
.75677
.75690
.75703
.05710
.0571?
.05713
.05715
8.76431
.76443
.76456
.76469
.05812
.05813
.05815
.05817
8.77190
.77202
.77215
.77228
.05914
.05916
.05918
.05919
8.77942
.77955
.77967
.77980
.06018
.06019
.06021
.06023
8.78688
.78700
.78712
.78725
.06122
.06124
.06125
.06127
24
23
22
21
+ 1<K
41
42
43
8.75715
.75728
.75741
.75754
.05717
.05718
.05720
.05722
8.76481
.76494
.76507
.76519
.05819
.05820
.05822
.05824
8.77240
.77253
.77265
.77278
.05921
.05923
.05925
.05926
8.77992
.78005
.78017
.78029
.06024
.0602C
.06028
.06030
8.78737
.78749
.78762
.78774
.06129
.06130
.06132
.06134
to
19
18
17
+ 11'
45
46
47
8.75767
.75779
.75792
.75805
.05724
.05725
.05727
.05729
8.76532
.76545
.76558
.76570
.05825
.05827
.05829
.05830
8.77291
.77303
.77316
.77328
.05928
.05930
.05931
.05933
8.78042
.78054
.78067
.78079
.06031
.06033
.06035
.06037
8.78787
.78799
.78811
.78824
.06136
.06137
.06139
.06141
16
15
14
13
+ 12'
49
50
51
8.75818
.75831
.75844
.75856
.05730
.05732
.05734
.05735
8.76583
.76596
.76608
.76621
.05832
.05834
.05836
.05837
8.77341
.77353
.77366
.77379
.05935
.05936
.05938
.05940
8.78092
.78104
.78117
.78129
.06038
.06040
.06042
.06044
8.78836
.78848
.78861
.78873
.06143
.06144
.06146
.06148
12
11
10
9
+ 13'
53
54
55
8.75869
.75882
.75895
.75908
.05737
.05739
.05740
.05742
8.76634
.76646
.76659
.76672
.05839
.05841
.05842
.05844
8.77391
.77404
.77416
.77429
.05942
.05943
.05945
.05947
8.78142
.78154
.78167
.78179
.06045
.06047
.08049
.06050
8.78885
.78898
.78910
.78922
^8. 78935
.78947
.78959
.78972
.06150
.06151
.06153
.06155
8
7
6
5
+ I*7
57
58
59
8.75920
.75933
.75946
.75959
.05744
.05745
.05747
.05749
8.76684
.76697
.76710
.76722
.05846
.05847
.05849
.05851
S.77441
.77454
.77466
.77479
.05949
.05950
.05952
.05954
8.78191 .06052
.78204 .06054
.78216 .06056
.7S229 .06057
.06157
.06158
.06160
.06162
4
3
2
1
+ 15'
8.75972
.05751
8.76735
.05853
8.77492 j .05955
8.78241 i .06059
8.78984 . .06164
0
2-2* 9m
f**6m
ft* 7m
22 h 6m
2->h 5m
Page 834] TABLE 45.
Haversines.
s
^55™ 28° 45'
lh 56™ 29° 0'
lh 57m 29° 15'
IhSgm^0 30'
^59™ 29° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
8.78984
.78996
.79009
.79021
.08164
.06165
.06167
.06169
8.79720
.79732
.79744
.79757
.06269
.06271
.06273
.06274
8.80449
.80462
.80474
.80486
.06375
.06377
.06379
.06381
8.81172
.81184
.81196
.81208
.06482
.06484
.06486
.06488
8.81889
.81901
.81913
.81925
.06590
.06592
.06594
.06595
60
59
58
57
+ V
5
6
7
8.79033
.79046
.79058
.79070
.06171
.06172
.06174
.06176
8.79769..
.797&D
.79793
.79805
K- .06276
.0622S-
.06280
.06281
8.80498
• .80510
.80522
.80534
.06382
.06384
.06386
.06388
8.81220
.81232
.81244
.81256
.06489
.06491
.06493
.06495
8.81937
.81948
.81960
.81972
.06597
.06599
.06601
.06603
56
55
54
53
+ 2'
9
10
11
8.79082
.79095
.79107
.79119
.06178
.06179
.06181
.06183
8.79818
.79830
.79842
.79854
.06283
.06285
.06287
.06288
8.80546
.80558
.80570
.80582
.06389
.06391
.06393
.06395
8.81268
.81280
.81292
.81304
.06497
.06498
.06500
.06502
8.81984
.81996
.82008
.82020
.06605
.06606
.06608
.06610
52
51
50
49
+ 3'
13
14
15
8.79132
.79144
.79156
.79169
.06185
.06186
.06188
.06190
8.79866
.79879
.79891
.79903
.06290
.06292
.06294
.06295
8.80595
.80607
.80619
.80631
.06397
.06398
.06400
.06402
8.81316
.81328
.81340
.81352
.06504
.06505
.06507
.06509
8.82032
.82043
.82055
.82067
.06612
.06614
.06615
.06617
48
47
46
45
+ V
17
18
19
8.79181
.79193
.79205
.79218
.06192
.06193
.06195
.06197
8.79915
.79927
.79940
.79952
.06297
.06299
.06301
.06303
8.80643
.80655
.80667
.80679
.06404
.06405
.06407
.06409
8.81364
.81376
.81388
.81400
.06511
.06513
.06514
.06516
8.82079
.82091
.82103
.82115
.06619
.06621
.06623
.06624
44
43
£2
41
+ 5'
21
22
23
8.79230
.79242
.79255
.79267
.06199
.06200
.06202
.06204
8.79964
.79976
.79988
.80000
.06304
.06306
.06308
.06310
8.80691
.80703
.80715
.80727
.06411
.06413
.06414
.06416
8.81412
.81424
.81436
.81448
.06518
.06520
.06522
.06523
8.82126
.82138
.82150
.82162
.06626
.06628
.06630
.06632
40
39
38
37
+ v
25
26
27
8.79279
. .79291
.79304
.79316
.06206
.06207
.06209
.06211
8.80013
.80025
.80037
.80049
.06311
.06313
.06315
.06317
8.80739
.80751
.80764
.80776
.06418
.06420
.06421
.06423
8.81460
.81472
.81484
.81496
.06525
.06527
.06529
.06531
8.82174
.82186
.82198
.82209
.06633
.06635
.06637
.06639
36
35
34
33
+ r
29
30
31
8.79328
.79341
.79353
.79365
.06213
.06214
.06216
.06218
8.80061
.80073
.80086
.80098
.06318
.06320
.06322
.06324
8.80788
.80800
.80812
.80824
.06425
.06427
.06429
.06430
8.81508
.81520
.81531
.81543
.06532
.06534
.06536
.06538
8.82221
.82233
.82245
.82257
.06641
.06642
.06644
.06646
32
31
30
29
+ 8'
33
34
35
8.79377
.79390
.79402
.79414
.06220
.06221
.06223
.06225
8.80110
.80122
.80134
.80146
.06326
.06327
.06329
.06331.
8.80836
.80848
.80860
.80872
.06432
.06434
.06436
.06438
8.81555
.81567
.81579
.81591
.06540
.06541
.06543
.06545
8.82269
. .82280
.82292
.82304
.06648
.06650
.06652
.06653
28
27
26
25
+ 9/
37
38
39
8.79426
.79439
.79451
.79463
.06227
.06229
.06230
.06232
8.80158
.80171
.80183
.80195
.06333
.06334
.06336
.06338
8.80884
.80896
.80908
.80920
.06439
.06441
.06443
.06445
8.81603
.81615
.81627
.81639
.06547
.06549
.06550
.06552
8.82316
.82328
.82340
.82351
.06655
.06657
.06659
.06661
24
23
22
21
+ 107
41
42
43
8.79475
.79488
.79500
.79512
.06234
.06236
.06237
.06239
8.80207
.80219
.80231
.80243
.06340
.06341
.06343
.06345
8.80932
.80944
.80956
.80968
.06446
.06448
.06450
.06452
8.81651
.81663
.81675
.81687
.06554
.06556
.06558
.06559
8.82363
.82375
.82387
.82399
.06662
.06664
.06666
.06668
20
19
18
17
+ 11'
45
46
47
8.79524
.79537
.79549
.79561
.06241
.06243
.06244
.06246
8.80256
.80268
.80280
.80292
.06347
.06349
.06350
.06352
8.80980
.80992
.81004
.81016
.06454
.06455
.08457
.06459
8.81699
.81710
.81722
.81734
.06561
.06563
.06565
.06567
8.82410
.82422
.82434
.82446
.06670
.06671
.06673
.06675
16
15
14
13
+ 12'
49
50
51
8.79573
.79586
.79598
.79610
.06248
.06250
.06251
.06253
8.80304
.80316
.80328
.80340
.06354
.06356
.08357
.06359
8.81028
.81040
.81052
.81064
.06461
.06463
.06464
.06466
8.81746
.81758
.81770
.81782
.06568
.06570
.06572
.06574
8.82458
.82470
.82481
.82493
.06677
.06679
.06681
.06682
12
11
10
9
+ 13'
53
54
55
8.79622
.79634
.79647
.79659
.06255
.06257
.06258
.06260
8.80353
.80365
.80377
.80389
.06361
.06363
.06365
.06366
8.81076
.81088
.81100
.81112
.06468
.06470
.06471
.06473
8.81794
.81806
.81818
.81830
.06576
.06577
.06579
.06581
8.82505
.82517
.82529
.82540
.06684
.06686
.06688
.OG690
8
7
6
5
+ 14'
57
58
59
8.79671
.79683
.79696
.79708
.06262
.06264
.06265
.06267
8.80401
.80413
.80425
.80437
.08368
.06370
.06372
.06373
8.81124
.81136
.81148
.81160
.06475
.06477
.06479
.06480
8.81841
.81853
.81865
.81877
.06583
.06585
.06586
.06588
8.82552
.82564
.82576
.82588
.06691
.06693
.06695
.06697
4
3
2
1
+ 15'
8.79720
.06269
8.80449
.06375
8.81172
.06482
8.81889
.06590
8.82599
.06699
0
2%h 4m
tZhfm
gfhgm
22h I'm-
%®h Qm
TABLE 45. [Page 835
Haversines.
s
£& 0m 30° O*7
2h im 30° 15'
gh om 30° 30'
2* 3m 30° 45' j 2 *> 4m 31° <K
s
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav/ Log. Hav. Nat. Hav.
0
1
2
3
8.82599
.82611
.82623
.82635
.06699
.06701
.06702
.06704
8.83303
.83315
.83327
.83338
.06808
.06810
.06812
.06814
8.84002 .06919
.84013 .06920
.84025 .06922
.84036 .06924
8.84694 .07030
.84705 .07032
.84717 .07033
.84728 : .07035
8.85380
.85391
.85403
.85414
.07142
.07144
.07145
.07147
60
59
58
57
+ 1'
5
6
7
8.82646
.82658
.82670
.82682
.06706
.06708
.06710
.06711
8.83350
.83362
.83374
.83385
.06816
.06817
.06819
.06821
8.84048 .06926
.84059 j .06928
.84071 .06930
.84083 ! .06931
8.84740 ! .07037
.84751 .07039
.84762 .07041
.84774 .07043
8.85425
.85437
.85448
.85459
.07149
.07151
.07153
.07155
56
55
54
53
+ 2'
9
10
11
8.82694
.82705
.82717
.82729
.06713
.06715
.06717
.06719
8.83397
.83409
.83420
.83432
.06823
.06825
.06826
.06828
8.84094 i .06933
.84106 .06935
.84117 .06937
.84129 .06939
8.84785 ] .07045
.84797 .07046
.84808 .07048
.84820 .07050
8.85471
.85482
.85494
.85505
.07157
.07158
.07160
.07162
52
51
50
49
+ 3'
13
14
15
8.82741
.82752
.82764
.82776
.06721
.06722
.06724
.06726
8.83444
.83455
.83467
.83479
.06830
.06832
.06834
.06836
8.84140
.84152
.84164
.84175
.06941
.06943
.06944
.06946
8.84831
.84843
.84854
.84866
.07P52
.07054
.07056
.07058
.07059
.07061
.07063
.07065
8.85516
.85528
.85539
.85550
.07164
.07166
.07168
.07170
48
47
46
45
44
4-3
42
41
17
19
8.82788
.82799
.82811
.82823
.06728
.06730
.06731
.06733
8.83490
.83502
.83513
.83525.
.06838
.06839
.06841
.06843
8.84187
.84198
.84210
.84221
.06948
.06950
.06952
.06954
8.84^77
.84889
.84900
.84912
8.85562
.85573
.85585
.85596
.07172
.07173
.07175
.07177
+ 5'
21
ftj
8.82835
.82846
.82858
.82870
.06735
.06737
.06739
.06741
8.83537
.83548
.83560
.83572
.06845
.06847
.06849
.06850
8.84233
.84244
.84356
.84268
.06956
.06957
.06959
.06961
8.84923
.84934
.84946
.84957
.07067
.07069
.07071
.07073
8.85607
.85619
.85630
.85641
.07179
.07181
.07183
.07185
40
39
38
37
+ 6'
i'o
26
27
8.82882
.82893
.82905
.82917
.06742
.06744
.06746
.06748
8.83583
.83595
.83607
.83618
.06852
.06854
.06856
.06858
8.84279
.84291
.84302
.84314
.06963
.06965
.06967
.06968
8.84969 .07074
.84980 .07076
.84992 .07078
.85003 .07080
8.85653
.85664
.85675
.85687
.07187
.07189
.07190
.07192
36
35
34
33
+ v
29
30
31
S. 82929
.82940
.82952
.82964
.06750
.06752
.06753
.06755
8.83630
.83642
.83653
.83665
.06860
.06861
.06863
.06865
8.84325
.84337
.84348
.84360
.06970
.06972
.06974
.06976
8.85015
.85026
.85037
.85049
.07082
.07084
.07086
.07087
8.85698
.85709
.85721
.85732
.07194
.07196
.07198
.07200
32
31
30
29
+ 8'
33
24
35
8.82976
.82987
.82999
.83011
.06757
.06759
.06761
.06763
8.83676
.83688
.83700
.83711
.06867
.06869
.06871
.06872
8.84371
.84383
.84394
.84406
.06978
.06980
.06981
.06983
8.85060
.85072
.85083
.85095
.07089
.07091
.07093
.07095
8.85743
.85755
.85766
.85777
.07202
.07204
.07205
.07207
26
25
37
38
39
8.83023
.83034
.83046
.83058
.06764
.08766
.06788
.06770
8.83723
.83735
.83746
.83758
.06874
.06876
.06878
.06880
8.84417
.84429
.84441
.84452
.06985
.06987
.06989
.06991
8.85106
.85117
.85129
.85140
.07097
.07099
.07100
.07102
8.85789
.85800
.85811
.85823
.07209
.07211
.07213
.07215
24
23
21
+ W
41
42
43
8.83069
.83081
.83093
.83105
.06772
.06773
.06775
.06777
8.83769
.83781
.83793
.83804
.06882
.06884
.06885
.06887
8.84464
.84475
.84487
.84498
.06993
.06994
.06996
.06998
8.85152
.85163
.85175
.85186
.07104
.07106
.07108
.07110
8.85834 ! .07217
.85845 .07219
.85857 .07220
.85868 .07222
20
19
18
17
45
46
47
8.83116
.83128
.83140
.83151
.06779
.06781
.06783
.06784
8.83816
.83828
.83839
.83851
.06889
.06891
.06893
.06895
8.84510
.84521
.84533
.84544
.07000
.07002
.07004
.07006
8.85197
.85209
.85220
.85232
.07112
.07114
.07115
.07117
8.85879 .07224
.85891 l .07226
.85902 .07228
.85913 ! .07230
16
15
14
13
+ 12'
49
50
51
8.83163
.83175
.83187
.83198
.06786
.06788
.06790
.06792
8.83862
.83874
.83886
.83897
.06896
.06898
.06900
.06902
8.84556
.84567
.84579
.84590
.07007
.07009
.07011
.07013
8.85243
.85254
.85266
.85277
.07119
.07121
.07123
.07125
8.85925 ; .07232
.85936 .07234
.85947 .07238
.85959 ! .07237
12
11
10
9
+ 13'
54
55
8.83210
.83222
.83233
.83245
.06794
.06795
.06797
.06799
8.83909
.83920
.83932
.83944
.06904
.06906
.06907
.06909
8.84602
.84613
.84625
.84636
.07015
.07017
.07019
.07020
8.85289
.85300
.85311
.85323
.07127
.07129
.07130
.07132
8.85970 .07239
.85981 .07241
.85992 ! .07243
.86004 .07245
8
7
6
5
+ 1*
57
58
59
8.83257 .06801
.83268 .06803
.83280 .06805
.83292 .06806
8.83955
.83967
.83978
.83990
.06911
.06913
.06915
.06917
8.84648 .07022
.84659 .07024
.84671 ' .07026
.84682 j .07028
8.85334
.85346
.85357
.85368
.07134
.07136
.07138
.07140
8.86015 .07247
.86026 .07249
.86038 .07251
.86049 .07253
4
3
1
+ 15'
8.83303 .06808
8.84002
.06919
8.84694 .07030
8.85380
.07142
8.86060 1 .07254
0
M*59-
21* 58m
tl*&»
21*56*
21* 55m
Page 836] TABLE 45.
Haversines.
s
2* 5™ 31° 15'
%U Qm 31° 30'
%h 7m 31° 45/
2h s™ 32° 0'
gh 9m 32° is/
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
8.86060
.86072
.86085
.86094
.07254
.07256
.07358
.07260
8.86735
.86746
.86757
.86769
.07368
.07370
.07372
.07374
8.874Q4
.87415
.87426
.87437
.07482
.07484
.07486
.07488
8.88068
.88079
.88090
.88101
.07598
.07600
.07601
.07603
8.88726
.88737
.88748
.88759
.07714
.07716
.07717
.07719
60
59
58
57
+ 1'
5
6
7
8.86105
.86117
.86128
.86139
.07262
.07264
.07266
.07268
8.86780
.86791
.86802
.86813
.07376
.07377
.07379
.07381
8.87448
.87460
.87471
.87482
.07490
.07492
.07494
.07496
8.88112
.88123
.88134
.88145
.07605
.07607
.07609
.07611
8.88769
.88780
.88791
.88802
.07721
.07723
.07725
.07727
56
55
54
53
+ *
9
10
11
8.86151
.86162
.86173
.86184
.07270
.07271
.07273
.07275
8.86825
.86836
.86847
.86858
.07383
.07385
.07387
.07389
8.87493
.87504
.87515
.87526
.07498
.07500
.07502
.07503
8.88156
.88167
.88178
.88189
.07613
.07615
.07617
.07619
8.88813
.88824
.88835
.88846
.07729
.07731
.07733
.07735
52
51
50
49
+ v
13
14
15
8.86196
.86207
.86218
.86229
.07277
.07279
.07281
.07283
8.86869
.86880
.86892
.86903
.07391
.07393
.07395
.07397
8.87537
.87548
.87559
.87570
.07505
.07507
.07509
.07511
8.88200
.88211
.88222
.88233
.07621
.07623
.07625
.07627
8.88857
.88868
.88879
.88890
.07737
.07739
.07741
.07743
48
47
46
45
+ ¥
17
18
19
8.86241
.86252
.86263
.86275
.07285
.07287
.07288
.07290
8.86914
.86925
.86936
.86947
.07398
.07400
.07402
.07404
8.87582
.87593
.87604
.87615
.07513
.07515
.07517
.07519
8.88244
.88255
.88266
.88277
.07628
.07630
.07632
.07634
8.88900
.88911
.88922
.88933
.07745
.07747
.07749
.07751
44
43
42
41
4- 5X
21
22
23
8.86286
.86297
.86308
.86320
.07292
.07294
.07296
.07298
8.86959
.86970
.86981
.86992
.07406
.07408
.07410
.07412
8.87626
.87637
.87648
.87659
.07521
.07523
.07525
.07527
8.88288
.88299
.88310
.88321
.07636
.07638
.07640
.07642
8.88944
.88955
.88966
.88977
.07752
.07754
.07756
.07758
40
39
38
37
+ v
25
26
27
8.86331
.86342
.86353
.86365
.07300
.07302
.07304
.07305
8.87003
.87014
.87026
.87037
.07414
.07416
.07417
.07419
8.87670
.87681
.87692
.87703
.07528
.07530
.07532
.07534
8.88332
.88343
.88354
.88364
.07644
.07646
.07648
.07650
8.88988
.88998
.89009
.89020
.07760
.07762
.07764
.07766
36
35
34
33,
+ V
29
30
31
8.86376
.86387
.86398
.86410
.07307
.07309
.07311
.07323
8.87048
.87059
.87070
.87081
.07421
.07423
.07425
.07427
8.87714
.87725
.87737
.87748
.07536
.07538
.07540
.07542
8.88375
.88386
.88397
.88408
.07652
.07654
.07656
:07657
8.89031
.89042
.89053
.89064
.07768
.07770
.07772
.077^4
32
31
30
29
+ 8'
33
34
35
8.86421
.86432
.86443
.86455
.07315
.07317
.07319
.07321
8.87093
.87104
.87115
.87126
.07429
.07431
.07433
.07435
8.87759
.87770
.87781
.87792
.07544
.07546
.07548
.07549
8.88419
.88430
.88441
.88452
.07659
.07661
.07663
.07665
8.89075
.89086
.89096
.89107
.07776
.07778
.07780
.07782
28
27
26
25
+ »x
37
38
39
8.86466
.86477
.86488
.86499
.07332
.07324
.07326
.07328
8.87137
.87148
.87159
.87171
.07437
.07438
.07440
.07442
8.87803
.87814
.87825
.87836
.07551
.07553
.07555
.07557
8.88463
.88474
.88485
.88496
.07667
.07669
.07671
.07673
8.89118
.89129
.89140
.89-151
.07784
.07786
.07788
.07789
24
23
22
21
+ W
41
42
43
8.86511
.86522
.86533
.86544
.07330
.07332
.07334
.07336
8.87182
.87193
.87204
.87215
.07444
.07446
.07448
.07450
8.87847
.87858
.87869
.87880
.07559
.07561
.07563
.07565
8.88507
.88518
.88529
.88540
.07675
.07677
.07679
.07681
8.89162
.89172
.89183
.89194
.07791
.07793
.07795
.07797
20
19
18
17
+ 11'
45
46
47
8.86556
.86567
.86578
.86589
8.86600
.86611
.86623
.86634
.07338
.07340
.07341
.07343
8.87226
.87237
.87248
.87260
.07452
.07454
.07456
.07458
8.87891
.87902
.87913
.87924
.07567
.07569
.07571
.07573
8.88551
.88562
.88573
.88584
.07683
.07685
.07686
.07688
8.89205
.89216
.89227
.$9238
.07799
.07801
.07803
.07805
16
15
14
13
+ 12'
49
50
51
.07345
.07347
.07349
.07351
8.87271
.87282
.87293
.87304
.07459
.07461
.07463
.07465
8.87935
.87946
.87957
.87968
.07574
.07576
.07578
.07580
8.88595
.88606
.8861G
.88627
.07690
.07692
.07694
.07696
8.89248
.89259
.89270
.89281
.07807
.07809
.07811
.07813
12
11
10
9
+ 13'
53
54
55
8.86645
.86657
.86668
.86679
.07353
.07355
.07357
.07359
8.87315
.87326
.87337
.87349
.07467
.07469
.07471
.07473
8.87980
.87991
.88002
.88013
.07582
.07584
.07586
.07588
8.88638
.88649
.88660
.88671
.07698
.07700
.07702
.07704
8.89292
.89303
.89314
.89324
.07815
.07817
.07819
.07821
8
7
6
5
+ W
57
58
59
8.86690
.86701
.86713
.86724
.07360
.07362
.07364
.07366
8.87360
.87371
.87382
.87393
.07475
.07477
.07479
.07480
8.88024
.88035
.88046
.88057
"8.88068
.07590
.07592
.07594
.07590
8.88682
.88693
.88704
.88715
.07706
.07708
.07710
.07712
8.89335
.89346
.89357
.89368
.07823
.07825
.07827
.07829
4
3
2
1
+ 15'
8.86735
.07368
8.87404
.07482
.07598
8.88726
.07714
8.89379
.07830
0
21 h 54m
2J* &m
fj*£f*
2in sim
21h 50™
TABLE 45.
Haversines.
[Page 837
s
2* J0m 33° 3(K
2* lim 32° 45X
2h izm 33° Q>
2h 13m 33' 15'
2h 14m 33° 3Q/
s
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
o
3
8.89379 ! .07830
.89389 .0783?
.89400 .07834
.89411 .07836
8.90026
.90037
.90048
.90058
.07948
.07950
.07952
.07954
8.90668
.90679
.90690
.90700
.08066
.08068
.08070
.08072
8.91306 i .08186
.91316 .08188
.91327 ! .08190
.91337 i .08192
8.91938 i
.91948 i
.91959 !
.91969 !
.08306
.08308
.08310
.08312
60
59
58
57
4- 1'
5
6
7
8.89422 .07838
.89433 ! .07840
.89444 i .07842
.894541 .07844
8.90069
.90080
.90091
.90101
.07956
.07958
.07960
.07962
8.90711
.90722
.90732
.90743
.08074
.08076
.08078
.08080
8.91348
.91358
.91369
.91380
.08194
.08196
.08198
.08200
8.91980 !
.91990
.92001
.92011
.08314
.08316
.08318
.08320
56
55
54
53
+ V
9
10
11
8.89465
.89476
.89487
.89498
.07846
.07848
.07850
.07852
1T90112
.90123
.90134
.90144
.07964
.07966
.07968
.07970
8.90754
.90764
.90775
.90786
.08082
.08084
.08086
.08088
8.91390
.91401
.91411
.91422
.08202
.08204
.08206
.08208
8.92022
.92032
.92043
.92053
.08322
.08324
.08326
.08328
5-2
51
50
49
+ 3'
13
U
15
8.89509
.89519
.89530
.89541
.07854
.07856
.07858
.07860
8.90155
.90166
.90176
.90187
.07972
.07974
.07976
.07978
8.90796
.90807
.90818
.90828
.08090
.08092
.08094
.08096
8.91432
.91443
.91454
.91464
.08210
.08212
.08214
.08216
8.92064
.92074
.92084
.92095
.oswo
.08332
.08334
.08336
48
47
46
46
+ *
17
18
19
8.89552
.89563
.89573
.89584
.07862
.07864
.07866
.07868
8.90198
.90209
.90219
.90230
.07980
.07982
.07983
.07985
8.90839
.90849
.90860
.90871
.08098
.08100
.08102
.08104
8.91475
.91485
.91496
.91506
.08218
.08220
.08222
.08224
8.92105
.92116
.92126
.92137
.08338
.08340
.08342
.08344
44
43
41
41
+ 5'
il
*f
, 23
8.89595
.89606
.89617
.89627
.07870
.07872
.07873
.07875
8.90241
.90252
.90262
.90273
.07987
.07989
.07991
.07993
8.90881
.90892
.90903
.90913
.08106
.08108
.08110
.08112
8.91517
.91527
.91538
.91549
.08226
.08228
.08230
.08232
8.92147
.92158
.92168
.92179
.08346
.08348
.08350
.08352
40
39
38
37
+ 6'
£5
26
27
8.S9638
.89649
.89660
.89671
.07877
.07879
.07881
.07883
8.90284
.90294
.90305
.90316
.07995
.07997
.07999
.08001
8.90924
.90935
.90945
.90956
.08114
.08116
.08118
.08120
8.91559
.91570
.91580
.91591
.08234
.08236
.08238
.08240
8.92189
.92200
.92210
.92221
.08354
.08356
.08358
.08360
36
35
34
33
+ r
29
30
31
8.89681
.89692
.89703
.89714
.07885
.07887
.07889
.07891
8.90326
.90337
.90348
.90359
.08003
.08005
.08007
.08009
8.90966 j .08122
.90977 | .08124
.90988 i .08126
.90998 | .08128
8.91601
.91612
.91622
.91633
.08242
.08244
.08246
.08248
8.92231
.92241
.92252
.92262
.08362
.08364
.08366
.08368
3-2
31
30
29
+ &
33
34
35
8.89725
.89735
.89746
.89757
.07893
.07895
.07897
.07899
8.90369
.90380
.90391
.90401
.08011
.08013
.08015
.08017
8.91009 ! .08130
.91019 i .08132
.91030 .08134
.91041 ! .08136
8.91643
.91654
.91664
.91675
.08250
.08252
.08254
.08256
8.92273
.92283
.92294
.92304
.08370
.08372
.08374
.08376
28
f?
*6
25
+ *
37
38
39
8.89768
.89779
.89789
.89800
.07901
.07903
.07905
.07907
8.90412
.90423
.90433
.90444
.08019
.08021
.08023
.08025
8.91051 .08138
.91062 .08140
.91073 .08142
.91083 .08144
8.91685
.91696
.91707
.91717
.08258
.08260
.08262
.08264
8.92315
.92325
.92335
.92346
.08378
.08380
.08382
.08384
24
23
09
~il
+ W
41
42
43
8.89811
.89822
.89832
.89343
.07909
.07911
.07913
.07915
8.90455
.90466
.90476
.90487
.08027
.08029
.08031
i .08033
8.91094 .08146
.91104 .08148
.91115 .08150
.91126 .08152
8.91728
.91738
.91749
.91759
.08266
.08268
.08270
.08272
8.92356
.92367
.92377
.92388
.08386
.08388
.08390
.08392
20
19
18
17
+ 11'
46
46
47
8.89854
.89865
.89875
.89886
.07917
.07919
.07921
.07923
8.90498
.90508
.90519
.90530
.08035
.08037
.08039
.08041
8.91136
.91147
.91157
.91168
.08154
.08156
.08158
.08160
8.91770
.91780
.91791
.91801
.08274
.08276
.08278
.08280
8.92398
.92409
.92419
.92429
.08394
.08396
.08398
.08400
16
15
14
13
+ 12'
49
50
51
8.89897
.89908
.89919
.89929
.07924
.07926
.07928
.07930
8.90540
.90551
.90562
.90572
.08043
.08045
.08047
.08049
8.91179 .08162
.91189 .08164
.91200 .08166
.91210 .08168
8.91812
.91822
.91833
.91843
.08282
.08284
.08286
.08288
8.92440
.92450
.92461
.92471
.08402
.08404
.08406
.08408
12
11
10
9
+ 13'
,53
54
55
8.89940
.89951
.89962
.89972
.07932
.07934
.07936
.07938
8.90583
.90594
.90604
.90615
.08051
.08053
.08055
.08057
8.91221
.91232
.91242
.91253
.08170
.08172
.08174
.08176
8.91854
.91864
.91875
.91885
.08290
.08292
.08294
.08296
8.92482
^92492
.92502
.92513
.08410
.08412
.08414
.08416
8
7
6
5
+ l*x
57
55
59
8.89983
.89994
.90005
.90015
.07940
.07942
.07944
.07946
8.90626
.90636
.90647
.90658
.08059
.08061
.08063
.08065
8.91263
.91274
.91284
.91295
.08178
.08180
.08182
.08184
8.91896
.91906
.91917
.91927
.08298
.08300
.08302
.08304
8.92523
.92534
.92544
.92554
.08418
.08420
.08422
.08425
4
S
2
1
4- 15'
8.90026
.07948
8.90668
.08066
8.91306 .08186
8.91938
.08306
8.92566
.08427
0
tl*49*
•21 h 48™
Ml 47*
21*46™
Ml
43*
Page 838] TABLE 45.
Haversines.
.
* S
2^ 15^ 33° 45'
2* iem 34° 0'
2h 17m 34° 15'
2U igm 34° 30'
2h 19m 34° 45'
s
Log. Hav.j Nat. Hav.
Log. Hav
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
!
3
8.92565
.92575
.92586
.92596
.08427
.08429
.08431
.08433
8.93187
.93197
.93208
.93218
.08548
.08550
.08552
.08554
8.93805
.93815
.93825
.93835
.08671
.08673
.08675
.08677
8.94417
.94427
.94438
.94448
.08794
.08796
.08798
.08800
.08802"
.08804
.08806
.08808
8.95025
.95035
.95045
.95055
.08918
.08920
.08922
.08924
60
59
58
57
+ 1'
5
\
+ %'
9
10
11
8.92607
.92617
.92627
.92638
.08435
.08437
.08439
.08441
8.93228
.93239
.93249
.93259
.08556
.08558
.08560
.08562
8.93846
.93856
.93866
.93876
.08679
.08681
.08683
.08685
8.94458
.94468
.94478
.94488
8.95065
.95076
.95086
.95096
.08926
.08928
.08930
.08932
56
55
54
53
8.92648
.92659
.92669
.92679
.08443
.08445
.08447
.08449
.08451
.08453
.08455
.08457
8.93270
.93280
.93290
.93301
8.93311
.93321
.93332
.93342
.08564
.08563
.08568
.08571
8.93886
.93897
.93907
.93917
.08687
.08689
.08691
.08693
8.94498
.94509
.94519
.94529
.08810
.08812
.08814
.08816
8.95106
.95116
.95126
.95136
.08934
.08936
.08938
.08940
52
51
50
49
+ &
13
14
15
8.92690
.92700
.92710
.92721
.08573
.08575
.08577
.08579
8.93927
.93938
.93948
.93958
.08695
.08697
.08699
.08701
8.94539
.94549
.94559
.94570
.08818
.08820
.08823
.08825
8.95146
.95156
.95166
.95176
.08943
.08945
.08947
.08949
48
47
46
45
+ 4'
17
18
19
8.92731
.92742
.92752
.92762
.08459
.08461
.08463
.08465
8.93352
.93363
.93373
.93383
.08581
.08583
.08585
.08587
8.93968
.93979
.93989
.93999
.08703
.08705
.08707
.08709
8.94580
.94590
.94600
.94610
.08827
.08829
.08831
.08833
8.95186
.95197
.95207
.95217
.08951
.08953
.08955
.08957
44
43
42
41
40
39
38
37
36
35
34
33
+ 5'
21
22
23
8.92773
.92783
.92794
.92804
.08467
.08469
.08471
.08473
8.93393
.93404
.93414
.93424
.08589
.08591
.08593
.08595
.08597
.08599
.08601
.08603
8.94009
.94019
.94030
.94040
.08711
.08714
.08716
.08718
.08720
.08722
.08724
.08726
8.94620
.94630
.94641
.94651
.08835
.08837
.08839
.08841
8.95227
.95237
.95247
.95257
.08959
.08981
.08963
.08965
+ 6'
25
26
27
8.92814
.92825
.92835
.92845
.08475
.08477
.08479
.08481
8.93435
.93445
.93455
.93466
8.94050
.94060
.94071
.94081
8.94661
.94671
.94681
.94691
.08843
.08845
.08847
.08849
8.95267
.95277
.95287
.95297
.08967
.08970
.08972
.08974
+ r
29
30
31
8.92856
.92866
.92877
.92887
.08483
.08485
.08487
.08489
8.93476
.93486
.93496
.93507
.08605
.08607
.08609
.08611
8.94091
.94101
.94111
.94122
.08728
.08730
.08732
.08734
8.94701
.94712
.94722
.94732
.08851
.08853
.08856
.08858
8.95307
.95317
.95327
.95337
.08976
.08978
.08980
.08982
32
31
30
29
+ 8/
33
34
35
+37*'
38
39
8.92897
.92908
.92918
.92928
.08491
.08493
.08495
.08497
8.93517
.93527
.93538
.93548
.08613
.08615
.08617
.08619
8.94132
.94142
.94152
.94162
.08736
.08738
.08740
.08742
8.94742
.94752
.94762
.94772
.08860
.08862
.08864
.08866
8.95347
.95357
.95368
.95378
.08984
.08986
.08988
.08990
28
27
26
25
8.92939
.92949
.92960
.92970
.08499
.08501
.08503
.08505
8.93558
.93568
.93579
.93589
.08621
.08624
.08626
.08628
8.94173
.94183
.94193
.94203
.08744
.08746
.08748
.08750
8.94782
.94793
.94803
.94813
.08868
.08870
.08872
.08874
8.95388
.95398
.95408
.95418
.08992
.08994
.08997
.08999
24
23
22
21
+ 10/
41
42
43
8.92980
.92991
.93001
.93011
.08508
.08510
.08512
.08514
8.93599
.93610
.93620
.93630
.08630
.08632
.08634
.08636
8.94213
.94224
.94234
.94244
.08753
.08755
.08757
.08759
8.94823
.94833
.94843
.94853
.08876
.08878
.08880
.08882
.08885
.08887
.08889
.08891
8.95428
.95438
.95448
.95458
.09001
.09003
.09005
.09007
20
19
18
17
+ 11'
45
46
47
+ W
49
50
51
8.93022
.93032
.93042
.93053
.08516
.08518
.08520
.08522
8.93640
.93651
.93661
.93671
.08638
.08640
.08642
.08644
8.94254
.94264
.94275
.94285
.08761
.08763
.08765
.08767
8.94863
.94874
.94884
.94894
8.95468
.95478
.95488
.95498
.09009
.09011
.09013
.09015
16
15
14
13
8.93063
.93073
.93084
.93094
.08524
.08526
.08528
.08530
8.93681
.93692
.93702
.93712
.08646
.08648
.08650
.08652
8.94295
.94305
.94315
.94326
.08769
.08771
.08773
.08775
8.94904
.94914
.94924
.94934
.08893
.08895
.08897
.08899
8.95508
.95518
.95528
.95538
.09017
.09019
.09022
.09024
12
11
10
9
+ 13'
53
54
55
+ 14'
57 .
58
59
8.93104
.93115
.93125
.93135
.08532
.08534
.08536
.08538
8.93722
.93733
.93743
.93753
.08654
.08656
.08658
.08660
8.94336
.94346
.94356
.94366
.08777
.08779
.08781
.08783
8.94944
.94954
.94965
.94975
.08901
.08903
.08905
.08907
8.95548
.95558
.95568
.95578
.09026
.09028
.09030
.09032
8
7
6
5
8.93146
.93156
.93166
.93177
.08540
.08542
.08544
.08546
8.93764
.93774
.93784
.93794
.08662
.08664
.08666
.08668
8.94376
.94387
.94397
.94407
.08785
.08788
.08790
.08792
8.94985
.94995
.95005
.95015
.08909
.08911
.08914
.08916
8.95588
.95598
.95608
.95618
.09034
.09036
.09038
.09040
4
S
2
1
+ 15'
8.93187
.08548
8.93805
.08671
8.94417 .08794
8.95025
.08918
8.95628 .09042
0
21*44™
ff*'44»
2 lh 42m
2in 4im
tl*4O*
TABLE 45. [Page 839
Havemnes.
s
2 * f 6"» 35° <K
2* 2im 35° 15'
«• 35° W
%h 2Sm 35° 45'
*» 24m 36° O7
s
Log. Hav.
Xat. Hav.
Log. Hav. Xar. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Xat.Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
8.95628
.95638
.95648
.95658
.0904?
.09044
.09047
.09049
8.96227
.96237
.96247
.96257
.09168
.09170
.09172
.09174
8.96821
.96831
.96841
.96851
.09294
.09296
.09298
.09301
8.97411
.97421
.97431
.97441
.09421
.09423
.09426
.09428
8.97997
.98006
.98016
.98026
.09549
.09551
.09553
.09556
60
59
58
57
+ *
5
6
7
8.95668
.95678
.95688
.95698
.09051
.09053
.09055
.09057
8.96267
.96277
.96287
.96297
.09176
.09178
.09181
.09183
8.96861
.96871
.96881
.96890
.09303
.09305
.09307
.09309
8.97450
.974GO
.97470
.97480
.09430
.0943-2
.09434
.09438
8.98035
.98045
.98055
.98065
.09558
.09560
.09562
.09564
56
55
54
53
+ 2'
9
10
11
8.95709
.95719
.95729
.95739
.09059
.09061
.09063
.09065
8.96307
.96317
.96326
.96336
.09185
.09187
.09189
.09191
8.96900
.96910
.96920
.96930
.09311
.09313
.09315
.09317
8.97489
.97499
.97509
.97519
.09433
.09440
.09443
.09445
8.98074
.98084
.98094
.98103
.09566
.09563
.09571
.09573
52
51
50
49
+ *'
IS
14
15
8.95749
.95759
.95769
.95779
.09067
.09070
.09072
.09074
8.96346
.96356
.96366
.96376
.09193
.09195
.09197
.09199
8.96940
.96950
.96959
.96969
.09320
.09322
.09324
.09326
8.97529
.97538
.97548
.97558
.09447
.09449
.09451
.09453
8.98113
.98123
.98132
.98142
.09575
.09577
.09579
.09581
48
47
46
45
+ *'
17
18
19
8.95789
.95799
.95809
.95819
.09076
.09078
.09080
.09082
8.96386
.96396
.96406
.96416
.09202
.09204
.09206
.09208
8.96979
.96989
.96999
.97009
.09328
.09330
.09332
.09334
8.97568
.97577
.97587
.97597
.09455
.09457
.09480
.09462
8.98152
.98162
.98171
.98181
.09583
.09586
.09588
.09590
44
43
42
41
+ &
21
'/-?
23
8.95S28
.95838
.95848
.95858
.09084
.09086
.09088
.09090
S. 96426
.96436
.96446
.96455
.09210
.09212
.09214
.09216
8.97018
.97028
.97038
.97048
.09337
.09339
.09341
.09343
8.97607
.97617
.97626
.97636
.09464
.09466
.09468
.09470
8.98191
.98200
.98210
.98220
.09592
.09594
.09596
.09598
40
39
38
37
+ 6/
25
26
';"*
8.95868
.95878
.95888
.95898
.09093
.09095
.09097
.09099
8.96465
.96475
.96485
.96495
.09218
.09220
.09223
.09225
8.97058
.97068
.97077
.97087
.09345
.09347
.09349
.09351
8.97646
.97656
.97665
.97675
.09472
.09474
.09477
.09479
8.9S229
.98239
.98249
.9S259
.09601
.09603
.09605
.09607
36
35
34
S3
+ r
29
30
31
8.95908
.95918
.95928
.95938
.09101
.09103
.09105
.09107
8.96505
.96515
.96525
.96535
.09227
.09229
.09231
.09233
8.97097
.97107
.97117
.97127
.09353
.09356
.09358
.09360
8.97685
.97695
.97704
.97714
.09481
.09483
.09485
.09487
8.98268
.9S278
.98288
.98297
.09609
.09611
.09613
.09616
32
31
30
29
+ V
33
34
S5
8.95948
.95958
.95968
.95978
.09109
.09111
.09113
.09116
8.96545
.96555
.96564
.96574
.09235
.09237
.09239
.09242
8.97136
.97146
.97156
.97166
.09362
.09364
.09366
.09368
8.97724
.97734
.97743
.97753
.09489
.09492
.09494
.09496
8.98307
.98317
.98326
.98336
.09618
.09620
.09622
.09624
28
27
26
25
+ V
37
38
39
8.95988
.95998
.96008
.96018
.09118
.09120
.09122
.09124
8.96584
.96594
.96604
.96614
.09244
.09246
.09248
.09250
8.97176
.97186
.97195
.97205
.09370
.09372
.09375
.09377
8.97763
.97773
.97782
.97792
.09498
.09500
.09502
.09504
8.98346
.98355
.98365
.98375
.09626
.09628
.09631
.09633
24
23
22
21
+ KK
41
42
43
8.96028
.96038
.96048
.96058
.09126
.09128
.09130
.09132
8.96624
.96634
.96644
.96653
.09252
.09254
.09256
.09258
8.97215
.97225
.97235
.97244
.09379
.09381
.09383
.09385
8.97802
.97812
.97821
.97831
.09506
.09509
.09511
.09513
8.98384
.98394
.98404
.98413
.09635
.09637
.09639
.09641
20
19
18
17
+ ii'
45
46
47
8.96068
.96078
.96088
.96098
.09134
.09136
.09139
.09141
8.96663
.96673
.96683
.96693
.09260
.09263
.09265
.09267
8.97254
.97264
.97274
.97284
.09387
.09389
.09392
.09394
8.97841
.97851
.97860
.97870
.09515
.09517
.09519
.09521
8.98423
.98433
.98442
.98452
.09643
.09646
.09648
.09650
16
15
14
13
+ 12'
49
50
51
8.96108
.96118
.96128
.96138
.09143
.09145
.09147
.09149
8.96703
.96713
.96723
.96733
.09269
.09271
.09273
.09275
8.97294
.97303
.97313
.97323
.09396
.09398
.09400
.09402
8.97880
.97890
.97899
.97909
.09524
.09526
.09528
.09530
8*98462
.98471
.98481
.98491
.09652
.09654
.09656
.09653
12
11
10
9
+ 13'
53
54
55
8.96148
.96158
.96167
.96177
.09151
.09153
.09155
.09157
8.96742
.96752
.96762
.96772
.09277
.09280
.09282
.09284
8.97333
.97343
.97352
.97362
.0940-1
.09406
.09409
.09411
8.97919
.97928
.97938
.97948
.09532
.09534
.09536
.09538
8.98500
.98510
.98520
.98529
.09661
.09683
.09665
.09667
8
7
6
5
+ 14'
57
58
59
8.96187
.96197
.96207
.96217
.09160
.09162
.09164
.09166
8.96782
.96792
.96802
.96812
.09286
.09288
.09290
.09292
8.97372
.97382
.97392
.97401
.09413
.09415
.09417
.09419
8.97958
.97967
.97977
.97987
.09541
.09543
.09545
.09547
8.98539
.98549
.98558
.98568
.09669
.09671
.09673
.09676
4
3
j
1
+ 15'
8.96227
.09168
8.96821
.09294
8.97411
.09421
8.97997
.09549
8.98578
.09678
0
21h 39^
%lh 3gm
2lh 37m
21h 36™
21h 35m
Page 840] TABLE 45.
Haversines.
s
2fc 25™ 36° 15'
2h 26m 36° 30'
2h 27^ 36° 45'
gh 2$™* 37° Ox
2 A 29^37° 157
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.j Nat. Hav.
Log. Hav.
Nat. Hav.
0
r
0
3.
8.98578
.98587
.98597
.98606
.09678
.09680
.09682
.09684
8.99154
.99164
.99173
.99183
.09807
.09809
.03811
.09814
8.99727
.99736
.99746
.99755
.09937
.09939
.09952
.09944
9.00295
.00305
.00314
.00324
.10068
.10070,
.10073
.10075
9.00860
.00869
.00878
.00888
.10200
.10202
.10204
.10206
60
59
58
57
+ lx
5
6
7' ..
8.98616
.98626
.98635
.98645
.09686
.09689
.09691
.09693
8.99193
.99202
.99212
.99221
.09816
.09818
.09820
.09822
8.99765
.99774
.99784
.99793
.09946
.09918
.09950
.09953
9.00333
.00342
.00352
.00361
.10077
.10079
.10081
.10084
9.00897
.00906
.00916
.00925
.10209
.10211
.10213
.10215
56
55
54
53
52
51
50
49
48
47
46
45
+ v
9
10
11
8.98655
.98664
.98674
.98684
.09695
.09697
.09699
.09701
8.99231
.99240
.99250
.99260
.09824
.09827
.09829
.09831
8.99803
.99812
.99822
.99831
.09955
.09957
.09959
.09961
9.00371
.00380
.00390
.00399
.10086
.10088
.10090
.10092
9.00935
.00944
.00953
.00963
.10218
.10220
.10222
.10224
+ &
13
U
15
8.98693
.98703
.98712
.98722
.09704
.09706
.09708
.09710
8.99269
.99279
.99288
.99298
.09833
.09835
.09837
.09840
8.99841
.99850
.99860
.99869
.09963
.09966
.09968
.09970
9.00408
.00418
.00427
.00437
.10095
.10097
.10099
.10101
9.00972
.00981
.00991
.01000
.10226
.10228
.10231
.10233
+ V
17
18
19
8.98732
.98741
.98751
.98761
.09712
.09714
.09717
.09719
8.99307
.99317
.99327
.99336
.09842
.09844
.09846
.09848
.09850
.09853
.09855
.09857
8.99879
.99888
.99898
.99907
.09972
.09974
.09977
.09979
9.00446
.00456
.00465
.00474
.10103
.10105
.10108
.10110
9.01009
.01019
.01028
.01037
.10235
.10237
.10240
.10242
44
43
42
41
+ -5'
21
22
23
8.98770
.98780
.98790
.98799
.09721
.09723
.09725
.09727
8.99346
.99355
.99365
.99374
8.99917
.99926
.99936
.99945
.09981
.09983
.09985
.09987
9.00484
.00493
.00503
.00512
.10112
.10114
.1011G
.10119
9.01047
.01056
.01065
.01075
.10244
.10246
.10248
.10251
40
39
38
37
+ v
25
26
27
8.98809
.98818
.98828
.98838
.09729
.09732
.09734
.09736
8.99384
.99393
.99403
.99412
.09859
.09881
.09803
.09866
8.99955
.99964
.99974
.99983
.09990
.09992
.09994
.09996
9.00522
.00531
.00540
.00550
.10121
.10123
.10125
.10127
9.01084
.01094
.01103
01112
.10253
.10255
.10257
.10259
36
35
34
33
+ 7'
29
30
31
8.98847
.98857
.98866
.98876
.09738
.09740
.09742
.09745
8.99422
.99432
.99441
.99451
.09868
.09870
.09872
.09874
8.99993
9.00002
.00012
.00021
.09998
.10000
.10003
.10005
9.00559
.00569
.00578
.00587
.10130
.10132
.10134
.10136
9.01122
.01131
.01140
.01150
.10262
.10264
.10266
.10268
32
31
30
29
+ 8/
33
34
35
8.98886
.98895
.98905
.98915
.09747
.09749
.09751
.09753
8.99460
.99470
.99479
.99489
.09876
.09879
.09881
.09883
9.00031
.00040
.00049
.00059
.10007
.10009
.10011
.10014
9.00597
.00606
.00616
.00625
.10138
.10141
.10143
.10145
9.01159
.01168
.01178
.01187
.10270
.10273
.10275
.10277
28
27
26
25
+ 9'
37
38
39
8.98924
.98934
.98943
.98953
.09755
.09757
.09760
.09762
8.99498
.99508
.99517
.99527
.09885
.09887
.09890
.09892
9.00068
.00078
.00087
.00097
.10016
.10018
.10020
.10022
9.00634
.00644
.00653
.00663
.10147
.10149
.10152
.10154
9.01196
.01206
.01215
.01224
.10279
.10281
.10284
.10286
24
23
22
21
+ 10/
41
42
43
8.98963
.98972
.98982
.98991
.09764
.09766
.09768
.09770
8.99536
.99546
.99556
.99565
.09894
.09896
.09898
.09900
9.00106
.00116
.00125
.00135
.10025
.10027
.10029
.10031
9.00672
.00681
.00691
.00700
.10156
.10158
.10160
.10163
.10165
.10167
.10169
.10171
9.01234
.01243
.01252
.01262
.10288
.10290
.10293
.10295
20
19
18
17
+ 11'
45
46
47
8.99001
.99011
.99020
.99030
.09773
.09775
.09777
.09779
8.99575
.99584
.99594
.99603
.09903
.09905
.09907
.09909
9.00144
.00154
.00163
.00172
.10033
.10035
.10038
.10040
9.00710
.00719
.00728
.00738
9.01271
.01280
.01289
.01299
.10297
.10299
.10301
.10304
16
15
14
13
+ 12'
49
50
51
8.99039
.99049
.99058
.99068
J09781
.09783
.09786
.09788
8.99613
.99622
.99632
.99641
.09911
.09913
.09916
.09918
9.00182
.00191'
.00201-
.00210
.10042
.10044
.10046
.10049
9.00747
.00756
.00766
.00775
.10174
.10176
.10178
.10180
9.01308
.01317
.01327
.01336
.10306
.10308
.10310
.10312
12
11
10
9
+ 13'
53
54
55
8.99078
.99087
.99097
.99106
.09790
.09792
.09794
.09796
8.99651
.99660
.99670
.99679
.09920
.09922
.09924
.09926
9.00220
.00229
.00239
.00248
.10051
.10053
.10055
.10057
9.00785
.00794
.00803
.00813
.10182
.10184
.10187
.10189
9.01345
.01355
.01364
.01373
.10315
.10317
.10319
.10321
8
7
6
5
+ 14'
57
58
59
8.99116
.99126
.99135
.99145
.09799
.09801
.09803
.09805
8.99689
.99698
.99708
.99717
.09929
.09931
.09933
.09935
9.00258
.00267
.00276
.00286
.10059
.10062
.10064
.10066
9.00822
.00831
.00841
.00850
.10191
.10193
.10196
.10198
9.01383
.01392
.01401
.01411
.10323
.10326
.10328
.10330
4
3
2
1
> + 15'
8.99154
.09807
8.99727
.09937
9.00295
.10068
9.00860
.10200
9.01420
.10332
0
21^34™
2 111 ssrn
2lh 32m
2lTi 31™
2 in som
TABLE 45. [Page 841
Haversines.
s
2h30m3rW
2* Sim 37° 45'
2* 32m 38° O7
2* 33^ 38° 15'
2 * 34™ 38° SO'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
9.01420
.01429
.01438
.01448
.10332
.10335
.10337
.10339
9.01976
.01985
.01995
.02004
.10466
.10468
.10470
.10472
9.02528
.02538
.02547
.02556
.10599
.10602
.10604
.10606
9.03077
.03086
.03095
.03104
.10734
.10736
.10739
.10741
9.03621
.03630
.03639
.03648
.10870
.10872
.10874
.10876
60
59
58
57
56
55
54
53
5
6
7
9.01457
.01466
.01476
.01485
.10341
.10343
.10346
.10348
9.02013
.02022
.02031
.02041
.10474
.10477
.10479
.10481
9.02565
.02574
.02583
.02593
.10608
.10611
.10613
.10615
9.03113
.03122
.03131
.03141
.10743
.10745
.10748
.10750
9.03657
.03667
.03676
.03685
.10879
.10881
.10883
.10885
+ v
9
10
11
9.01494
.01504
.01513
.01522
.10350
.10352
.10354
.10357
9.02050
.02059
.02068
.02078
.10483
.10486
.10488
.10490
9.02602
.02611
.02620
.02629
.10617
.10620
.10622
.10624
9.03150
.03159
.03168
.03177
.10752
.10754
.10757
.10759
9.03694
.03703
.03712
.03721
.10888
.10890
.10892
.10895
52
51
50
49
+ 3'
13
14
15
9.01531 ! .10359
.01541 i .10361
.01550 .10363
.01559 .10366
9.02087
.02096
.02105
.02115
.10492
.10494
.10497
.10499
9.02638
.02648
.02657
.02666
.10626
.10629
.10631
.10633
9.03186
.03195
.03204
.03213
.10761
.10763
.10766
.10768
9.03730
.03739
.03748
.03757
.10897
.10899
.10901
.10904
48
47
46
45
+ V
17
18
19
9.01569 .10368
.01578 i .10370
.01587 .10372
.01596 | .10374
9.02124
.02133
.02142
.02151
.10501
.10503
.10506
.10508
9.02675
.02684
.02693
.02702
.10635
.10638
.10640
.10642
9.03222
.03231
.03241
.03250
.10770
.10772
.10775
.10777
9.03766
.03775
.03784
.03793
.10906
.10908
.10910
.10913
44
43
42
41
+ 5'
21
22
23
9.01606 .10377
.01615 .10379
.01624 ! .10381
.01634 I .10383
9.02161
.02170
.02179
.02188
.10510
.10512
.10515
.10517
9.02712
.02721
.02730
.02739
.10644
.10647
.10649
.10651
9.03259
.03268
.03277
.03286
.10779
.10781
.10784
.10786
9.03802
.03811
.03820
.03829
.10915
.10917
.10919
.10922
40
39
38
37
+ v
25
26
27
9.01643
.01652
.01661
.01671
.10386
.10388
.10390
.10392
9.02197
.02207
.02216
.02225
.10519
.10521
.10523
.10526
9.02748
.02757
.02767
.02776
.10653
.10655
.10658
.10660
9.03295
.03304
.03313
.03322
.10788
.10790
.10793
.10795
9.03838
.03847
.03856
.03865
.10924
.10926
.10929
.10931
36
35
34
33
29
30
SI
9.01680 .10394
.01689 ! .10397
.01698 j .10399
.01708 .10401
9.02234
.02244
.02253
.02262
.10528
.10530
.10532
.10535
9.02785
.02794
.02803
.02812
.10662
.10664
.10667
.10669
9.03331
.03340
.03350
.03359
.10797
.10799
.10802
.10804
9.03874
.03883
.03892
.03901
.10933
.10935
.10938
.10940
32
31
30
29
S3
34
35
9.01717 ! .10403
.01726 ! .10405
.01736 ' .10408
.01745 ' .10410
9.02271
.02280
.02290
.02299
.10537
.10539
.10541
.10544
9.02821
.02830
.02840
.02849
.10671
.10673
.10676
.10678
9.03368
.03377
.03386
.03395
.10806
.10809
.10811
.10813
9.03910
.03919
.03928
.03937
.10942
.10944
.10947
.10949
28
27
26
25
+ V
37
38
39
9.01754
.01763
.01773
.01782
.10412
.10414
.10417
.10419
9.02308
.02317
.02326
.02336
.10546
.10548
.10550
.10552
9.02858
.02867
.02876
.02885
.10680
.10682
.10685
.10687
9.03404
.03413
.03422
.03431
.10815
.10818
.10820
.10822
9.03946
.03955
.03964
.03973
.10951
.10953
.10956
.10958
24
t$
22
21
41
42
4S
9.01791
.01800
.01810
.01819
.10421
.10423
.10425
.10428
9.02345
.023.54
.02363
.02372
.10555
.10557
.10559
.10561
9.02894 1 .106-89
.02904 .10691
.02913 .10694
.02922 .10696
9.03440
.03449
.03458
.03467
.10824
.10827
.10829
.10831
9.03982
.03991
.04000
.04009
.10960
.10963
.10965
.10967
20
19
18
17
+ 11'
45
46
47
9.01828
.01837
.01847
.01856
.10430
.10432
.10434
.10436
9.02381
.02391
.02400
.02409
.10564
.10568
.10568
.10570
9.02931 I .10698
.02940 .10700
.02949 i .10703
.02958 ! .10705
9.03476
03486
.03495
.03504
.10833
.10836
.10838
.10840
9.04018
.04027
.04036
.04045
.10969
.10972
.10974
.10976
16
15
14
13
49 "
50
51
9.01865
.01874
.01884
.01893
.10439
.10441
.10443
.10445
9.02418
.02427
.02437
.02446
.10573
.10575
.10577
.10579
9.02967 ; .10707
.02977 i .10709
.02986J .10712
.02995 .10714
9.03513
.03522
.03531
.03540
.10842
.10845
.10847
.10849
9.04054
.04063
.04072
.04081
.10978
.10981
.10983
.10985
n
11
10
9
+ 13'
53
54
55
9.01902
.01911
.01921
.01930
.10448
.10450
.10452
.10454
9.02455
.02464
.02473
.02483
.10582
.10584
.10586
.10588
9.03004
.03013
.03022
.03031
.10716
.10718
.10721
.10723
9.03549
.03558
.03567
.03576
.10851
.10854
.10856
.10858
9.04090
.04099
.04108
.04117
.10988
.10990
.10992
.10994
8
7
6
5
+ 14'
57
58
59
9.01939
01948
.01958
.01967
.10457
.10459
.10461
.10463
9.02492
.02501
.02510
.02519
.10591
.10593
.10595
.10597
9.03040
.03050
.03059
.03068
.10725
.10727
.10730
.10732
9.03585
.03594
.03603
.03612
.10861
.10863
.10865
.10867
9.04126
.04135
.04144
.04153
.10997
.10999
.11001
.11004
4
3
2
1
+ 15'
9.01976
.10466
9.02528
.10599
9.03077
.10734
9.03621
.10870
9.04162
.11006
0
21* 29m
21 h 28™ -
21*27*
,lh26m
•21*25m
61828°— 16 46
Page 842] TABLE 45.
Haversines.
s
2h 35m 38° 45'
2h 36m 39° (K
2^ 37m 39° 15'
2*> S8m 39° 3CK
2*> 39m 39° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.04162
.04171
.04180
.04189
.11006
.11008
.11010
.11013
9.04699
.04708
.04717
.04726
.11143
.11145
.11147
.11150
9.05232
.05241
.05250
.05259
.11280
.11283
.11285
.11287
9.05762
.05771
.05780
.05788
.11419
.11421
.11423
.11426
9.06288
.06297
.06305
.06314
.11558
.11560
.11563
.11565
60
59
58
57
+ lx
5
6
7
9.04198
.04207
.04216
.04225
.11015
.11017
.11019
.11023
9.04735
.04744
.04753
.04761
.11152
.11154
.11156
.11159
9.05268
.05277
.05285
.05294
.11290
.11292
.11294
.11296
9.05797
.05806
.05815
.05823
.11428
.11430
.11433
.11435
9.06323
.06332
.06340
.06349
.11567
.11569
.11572
.11574
.11577
.11579
.11581
.11584
56
55
54
53
52
51
50
49
+ v.
9
10
11
9.04234
/.04243
(.04252
.04261
.11024
.11026
.11029
.11031
9.04770
.04779
.04788
.04797
.11161
.11163
.11166
.11168
9.05303
.05312
.05321
.05330
.11299
.11301
.11303
.11306
9.05832
.05841
.05850
.05859
.11437
.11440
.11442
.11444
9.06358
.06367
.06375
.06384
+ 3'
13
14
15
9.04270
.04279
.04288
.04297
.11033
.11035
.11038
.11040
9.04806
.04815
.04824
.04833
.11170
.11172
.11175
.11177
9.05339
.05347
.05356
.05365
.11308
.11310
.11313
.11315
9.05867 .11447
.05876 .11449
.05885 .11451
.05894 .11453
9.06393
.06401
.06410
.06419
.11586
.11588
.11590
.11593
48
47
46
45
+ *'
17
18
19
9.04306
.04315
.04324
.04333
.11042
.11044
.11047
.11049
9.04842
.04851
.04859
.04868
.11179
.11182
.11184
11186
9.05374
.05383
.05392
.05400
.11317
.11320
.11322
.11324
9.05903
.05911
.05920
.05929
.11456
.11458
.11460
.11463
9.06428
.06436
.06445
.06454
.11595
.11597
.11600
.11602
44
43
42
41
+ &
21
22
23
9.04341
.04350
.04359
.04368
.11051
.11054
.11050
.11058
9.04877
.04886
.04895
.04904
.11189
.11191
.11193
.11195
9.05409
.05418
.05427
.05436
.11326
.11329
.11331
.11333
9.05938
.05946
.05955
.05964
.11465
.11467
.11470
.11472
9.06462
.06471
.06480
.06489
.11604
.11607
.11609
.11611
40
39
38
37
+ v
25
26
27
9.04377
.04386
.04395
.04404
.11060
.11063
.11065
.11067
9.04913
.04922
.04931
.04939
.11198
.11200
.11202
.11205
9.05445
.05453
.05462
.05471
.11336
.11338
.11340
.11343
9.05973
.05982
.05990
.05999
.11474
.11477
.11479
.11481
9.06497
.06506
.06515
.06523
.11614
.11616
.11518
.11621
36
35
34
33
32
31
30
29
+ 7'
29
30
31
9.04413
.04422
.04431
.04440
.11070
.11072
.11074
.11076
9.04948
.04957
.04966
.04975
.11207
.11209
.11211
.11214
9.05480
.05489
.05498
.05506
.11345
.11347
.11349
.11352
9.06008
.06017
.06025
.06034
.11484
.11486
.11488
.11491
9.06532
.06541
.06550
.06558
.11623
.11625
.11628
.11630
+ 8'
33
34
35
9.04449
.04458
.04467
.04476
.11079
.11081
.11083
.11086
9.04984
.04993
.05002
.05011
.11216
.11218
.11221
.11223
9.05515-
.05524-
.05533
.05542
.11354
.11356
.11359
.11361
9.06043
.06052
.06060
.06069
.11493
.11495
.11498
.11500
9.06567
.06576
.06584
.06593
.11632
.11635
.11637
.11639
28
27
26
25
+ 9'
37
38
39
9.04485
.04494
.04503
.04512
.11088
.11090
.11092
.11095
9.05019
.05028
.05037
.05046
.11225
.11228
.11230
.11232
9.05551
.05559
.05568
.05577
.11363
.11366
.11368
.11370
9.06078
.06087
.06095
.06104
.11502
.11504
.11507
.11509
9.06602
.06611
.06619
.06628
.11642
.11644
.11646
.11649
24
23
22
21
+ 10'
41
42
43
9.04520
.04529
.04538
.04547
.11097
.11099
.11102
.11104
9.05055
.05064
.05073
.05082
.11234
.11237
.11239
.11241
9.05586
.05595
.05603
.05612
.11373
.11375
.11377
.11379
9.06113
.06122
.06131
.06139
.11511
.11514
.11516
.11518
9.06637
.06645
.06654
.06663
.11651
.11653
.11656
.11658
20
19
18
17
+ 11'
45
46
47
9.04556
.04565
.04574
.04583
.11106
.11108
.11111
.11113
9.05090
.05099
.05108
.05117
.11244
.11246
.11248
.11251
9.05621
.05630
.05639
.05648
.11382
.11384
.11386
.11389
9.06148
.06157
.06166
.06174
.11521
.11523
.11525
.11528
9.06671
.06680
.06689
.06697
.11660
.11663
.11665
.11667
16
15
14
13
+ 12'
49
50
51
9.04592
.04601
.04610
.04619
.11115
.11117
.11120
.11122
9.05126
.05135
.05144
.05153
.11253
.11255
.11257
.11260
9.05656
.05665
.05674
.05683
.11391
.11393
.11396
.11398
9.06183
.06192
.06201
.06209
.11530
.11532
.11535
.11537
9.06706
.06715
.06724
.06732
.11670
.11672
.11674
.11677
12
11
10
9
+ 13'
53
54
55
9.04628
.04637
.04646
.04654
.11124
.11127
.11129
.11131
9.05161
.05170
.05179
.05188
.11262
.11264
.11267
.11269
9.05692
.05700
.05709
.05718
.11400
.11403
.11405
.11407
9.06218
.06227
.06235
.06244
.11539
.11542
.11544
.11546
9.06741
.06750
.06758
.06767
.11679
.11681
.11684
.11686
8
7
6
5
+ 14'
57
58
59
9.04663
.04672
.04681
.04690
.11134
.11136
.11138
.11140
9.05197
.05206
.05215
.05223
.11271
.11274
.11276
.11278
9.05727
.05736
.05744
.05753
.11410
.11412
.11414
.11416
9.06253 i .11549
.06262 .11551
.06270! .11553
.06279 .11556
9.06776
.06784
.06793
.06802
.11688
.11691
.11693
.11695
4
3
2
1
+ 15'
9.04699
.11143
9.05232
.11280
9.05762
.11419
9.06288 ; .11558
9.06810
.11698
0
21h 24m
21h 23m
21h 22m
glh 2im
21h 20m
TABLE 45.
Haversines.
[Page 843
S
2 h 40m 40° 0'
oh 4im 40° 15'
2h 42m 40° 30/
2* 43m 40° 45'
2h 44m 41° O7
s
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.06810
.06819
.06828
.06836
.11698
.11700
.11702
.11705
9.07329 .11838
.07338 j .11841
.07346 .11843
.07355 .11845
9.07845
.07853
.07862
.07870
.11980
.11982
.11984
.11987
9.08357
.08365
.08374
.08382
.12122
.12124
.12127
.12129
9.08865
.08874
.08882
.08890
.12265
.12267
.12269
.12272
60
59
58
57
56
55
54
53
+ v
5
6
7
9.06845
.06854
.06862
.06871
.11707
.11709
.11712
.11714
9.07364
.07372
.07381
.07390
.11848
.11850
.11852
.11855
9.07879
.07887
.07896
.07905
.11989
.11992
.11994
.11996
9.08391
.08399
.08408
.08416
.12131
.12134
.12136
.12138
9.08899
.08907
.08916
.08924
.12274
! 1227 9
.12281
9
10
11
9.06880
.06888
.06897
.06906
.11716
.11719
.11721
.11724
9.07398
.07407
.07415
.07424
.11857
.11860
.11862
.11864
9.07913
.07922
.07930
.07939
.11999
.12001
.12003
.12006
9.08425
.08433
.08442
.08450
.12141
.12143
.12146
.12148
9.08933
.08941
.08949
.08958
.12284
.12286
.12288
.12291
52
51
50
49
+ 3'
13
14
15
9.06914
.06923
.06932
.06940
.11726
.11728
.11731
.11733
9.07433
.07441
.07450
.07458
.11867
.11869
.11871
.11874
9.07947
.07956
.07964
.07973
.12008
.12010
.12013
.12015
9.08459
.08467
.08475
.08484
.12150
.12153
.12155
.12157
9.08966
.08975
.08983
.08992
.12293
.12296
.12298
.12300
48
47
46
45
+ v
17
18
19
9.06949
.06958
.06966
.06975
.11735
.11738
.11740
.11742
9.07467
.07476
.07484
.07493
.11876
.11878
.11881
.11883
9.07981
.07990
.07999
.08007
.12018
.12020
.12022
.12025
9.08492
.08501
.08509
.08518
.12160
.12162
.12165
.12167
9.09000
.09009
.09017
.09025
.12303
.12305
.12307
.12310
44
43
42
41
+ 5'
21
02
"is
9.06984
.06992
.07001
.07010
.11745
.11747
.11749
.11752
9.07501
.07510
.07519
.07527
.11885
.11888
.11890
.11892
9.08016
.08024
.08033
.08041
.12027
.12029
.12032
.12034
9.08526
.08535
.08543
.08552
.12169
.12172
.12174
.12176
9.09034
.09042
.09051
.09059
.12312
.12315
.12317
.12319
40
39
38
37
+ 6'
25
26
27
9.07018
.07027
.07036
.07044
.11754
.11756
.11759
.11761
9.07536
.07544
.07553
.07562
.11895
.11897
.11900
.11902
9.08050
.08058
.08067
.08075
.12036
.12039
.12041
.12044
.12046
.12048
.12051
.12053
9.08560
.08569
.08577
.08586
.12179
.12181
.12184
.12186
9.09068
.09076
.09084
.09093
.12322
.12324
.12327
.12329
36
35
34
33
+ 7'
29
30
31
9.07053
,07062
.07070
.07079
.11763
.11766
.11768
.11770
9.07570
.07579
.07587
.07596
.11904
.11907
.11909
.11911
9.08084
.08092
.08101
.08110
9.08594
.08603
.08611
.08620
.12188
.12191
.12193
.12195
9.09101
.09110
.09118
.09126
.12331
.12334
.12336
.12339
32
31
30
29
' 33
34
35
9.070S8
.07096
.07105
.07113
.11773
.11775
.11777
.11780
9.07605
.07613
.07622
.07630
.11914
.11916
.11918
.11921
9.08118
.08127
.08135
.08144
.12055
.12058
.12060
.12062
9.08628
.08637
.08645
.08654
.12198
.12200
.12203
.12205
9.09135
.09143
.09152
.09160
.12341
.12343
.12346
.12348
28
27
26
25
37
38
39
9.07122
.07131
.07139
.07148
.11782
.11784
.11787
.11789
9.07639
.07647
.07656
.07665
.11923
.11925
.11928
.11930
9.08152
.08161
.08169
.08178
.12065
.12067
.12070
.12072
9.08662
.08671
.08679
.08687
.12207
.12210
.12212
.12214
9.09169
.09177
.09185
.09194
.12351
.12353
.12355
.12:558
24
23
22
21
+ UK
41
41
43
9.07157
.07165
.07174
.07183
.11791
.11794
.11796
.11798
9.07673
.07682
.07690
.07699
.11933
.11935
.11937
.11940
9.08186
.08195
.08203
.08212
.12074
.12077
.12079
.12081
9.08696
.08704
.08713
.08721
.12217
.12219
.12222
.12224
9.09202
.09211
.09219
.09227
.12360
.12363
.12365
.12367
20
19
18
17
'45
46
47
9.07191
.07200
.07208
.07217
.11801
.11803
.11806
.11808
9.07708
.07716
.07725
.07733
.11942
.11944
.11947
.11949
9.08220
.08229
.08237
.08246
.12084
.12086
.12089
.12091
9.08730
.08738
.08747
.08755
.12226
.12229
.12231
.12233
9.09236
.09244
.09253
.09261
.12370
.12372
.12374
.12377
16
15
14
13
12
11
10
9
+ 12'
49
50
51
9.07226
.07234
.07243
.07252
.11810
.11813
.11815
.11817
9.07742
.07750
.07759
.07768
.11951
.11954
.11956
.11958
9.08254
.08263
.08271
.08280
.12093
.12096
.12098
.12100
9.08764
.08772
.08781
.08789
.12236
.12238
.12241
.12243
9.09269
.09278
.09286
.09295
.12379
.12382
.12384
.12386
+ 13'
53
54
55
9.07260
.07269
.07277
.07286
.11820
.11822
.11824
.11827
9.07776
.07785
.07793
.07802
.11961
.11963
.11966
.11968
9.08288
.08297
.08306
.08314
.12103
.12105
.12108
.12110
9.08797
.08806
.08814
.08823
.12245
.12248
.12250
.12253
9.09303
.09311
.09320
.09328
.12389
.12391
.12394
.12396
8
7
6
5
+ 14'
57
59
9.07295
.07303
.07312
.07321
.11829
.11831
.11834
.11836
9.07810
.07819
.07827
.07836
.11970
.11973
.11975
.11977
9.08323
.08331
.08340
.08348
.12112
.12115
.12117
.12119
9.08831
.08840
.08848
.08857
.12255
.12257
.12260
.12262
9.09337
.09345
.09353
.09362
.12398
.12401
.12403
.12406
4
S
2
1
+ 15'
9.07329 .11838
9.07845
.11980
9.08357
.12122
9.08865
.12265
9.09370
.12408
0
21h i$m
21h 18m
2 lh 17m
£1* 16m
21^ 15m
Page 844] TABLE 45.
Haversines.
%h 45m 41° 15'
%h 46m 41° 3r
%li 47m 41° 45'
2* 48™ 42° 0'
2h 49m 42° 15'
s
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
U>g. Hav.
Nat. Hav.
0
1
2
3
9.09370
.09379
.09387
.09395
.12408
.12410
.12413
.12415
9.09872
.09880
.09889
.09897
.12552
.12555
.12557
.12559
9.10371
.10379
.10387
.10395
.12697
.12700
.12702
.12704
9.10866
.10874
.10882
.10891
.12843
.12845
.12848
.12850
9.11358
.11366
.11374
.11382
.12989
.12992
.12994
.12998
60
59
58
57
+ 1'
5
6
7
9.09404
.09412
.09421
.09429
.12418
.12420
.12422
.12425
9.09905
.09914
.09922
.09930
.12562
.12564
.12567
.12569
9.10404
.10412
.10420
.10429
.12707
.12709
.12712
.12714
.12717
.12719
.12721
.12724
9.10899
.10907
.10915
.10923
.12852
.12855
.12857
.12860
9.11391
.11399
.11407
.11415
.12999
.13001
.13004
.13006
56
55
54
53
+ 2X
9
10
11
9,09437
.09446
.09454
.09462
.12427
.12430
.12432
.12434
9.09939
.09947
.09955
.09964
.12572
.12574
.12576
.12579
9.10437
.10445
.10453
.10462
9.10932
.10940
.10948
.10956
.12862
.12865
.12867
.12870
9.11423
.11431
.11440
.11448
.13009
.13011
.13014
.13016
52
51
50
49
+ &
13
14
15
9.09471
.09479
.09488
.09496
.12437
.12439
.12442
.12444
9.09972
.09980
.09989
.09997
.12581
.12584
.12586
.12588
9.10470
.10478
.10486
.10495
.12726
.12729
.12731
.12733
9.10965
.10973
.10981
.10989
.12872
.12874
.12877
.12879
9.11456
.11464
.11472
.11480
.13018
.13021
.13023
.13026
48
47
46
45
+ *'
17
18
19
9.09504
.09513
.09521
.09529
.12446
.12449
.12451
.12454
9.10005
.10014
.10022
.10030
.12591
.12593
.12596
.12598
9.10503
.10511
.10519
.10528
.12736
.12738
.12741
.12743
9.10997
.11006
.11014
.11022
.12882
.12884
.12887
.12889
9.11489
.11497
.11505
.11513
.13028
.13031
.13033
.13036
44
43
42
41
+ V
21
22
23
9.09538
.09546
.09555
.09563
.12456
.12458
.12461
.12463
9.10039
.10047
.10055
.10064
.12600
.12603
.12605
.12608
9.10536
.10544
.10553
.10561
.12746
.12748
.12750
.12753
9.11030
.11038
.11047
.11055
.12891
.12894
.12896
.12899
9.11521
.11529
.11538
.11546
.13038
.13041
.13043
.13045
40
39
38
37
+ v
25
26
27
9.09571
.09580
.09588
.09596
.12466
.12468
.12470
.12473
9.10072
.10080
.10088
.10097
.12610
.12613
.12615
.12617
9.10569
.10577
.10586
.10594
.12755
.12758
.12760
.12763
9.11063
.11071
.11079
.11088
.12901
.12904
.12906
.12909
9.11554
.11562
.11570
.11578
.13048
.13050
.13053
.13055
36
35
34
33
+ r
29
30
31
9.09605
.09613
.09622
.09630
.12475
.12478
.12480
.12482
9.10105
.10113
.10122
.10130
.12620
.12622
.12625
.12627
9.10602
.10610
.10619
.10627
.12765
.12767
.12770
.12772
9.11096
.11104
.11112
.11120
.12911
.12913
.12916
.12918
9.11586
.11595
.11603
.11611
.13058
.13060
.13063
.13065
32
31
30
29
+ 8'
33
34
35
9.09638
.09647
.09655
.09663
.12485
.12487
.12490
.12492
9.10138
.10147
.10155
.10163
9.10172
.10180
.10188
.10196
.12629
.12632
.12634
.12637
9.10635
.10643
.10652
.10660
.12775
.12777
.12780
.12782
9.11129
.11137
.11145
.11153
.12921
.12923
.12926
.12928
9.11619
.11627
.11635
.11643
.13067
.13070
.13072
.13075
28
27
26
25
+ 9'
37
38
39
9.09672
.09680
.09688
.09697
.12494
.12497
.12499
.12502
.12639
.12641
.12644
.12646
9.10668
,.10676
.10685
.10693
.12784
.12787
.12789
.12792
9.11161
.11170
.11178
.11186
.12930
.12933
.12935
.12938
9.11652
.11660
.11668
.11676
.13077
.13080
.13082
.13085
24
23
22
21
+ 10'
41
42
43
9.09705
.09713
.09722
.09730
.12504
.12506
.12509
.12511
9.10205
.10213
.10221
.10230
.12649
.12651
.12654
.12656
9.10701
.10709
.10718
.10726
.12794
.12797
.12799
.12801
9.11194
.11202
.11211
.11219
.12940
.12943
.12945
.12948
9.11684
.11692
.11700
.11709
.13087
.13090
.13092
.13095
20
19
18
17
+ 11'
45
46
47
9.09739
.09747
.09755
.09764
.12514
.12516
.12519
.12521
9.10238
.10246
.10255
.10263
.12658
.12661
.12663
.12666
9.10734
.10742
.10751
.10759
.12804
.12806
.12809
.12811
9.11227
.11235
.11243
.11252
.12950
.12952
.12955
.12957
9.11717
.11725
.11733
.11741
.13097
.13099
.13102
.13104
16
15
14
13
+ 12'
49
50
51
9.09772
.09780
.09789
.09797
.12523
.12526
.12528
.12531
9.10271
.10279
.10288
.10296
.12668
.12671
.12673
.12675
9.10767
.10775
.10784
.10792
.12814
.12816
.12818
.12821
9.11260
.11268
.11276
.11284
.12960
.12962
.12965
.12967
9.11749
.11757
.11766
.11774
.13107
.13109
.13112
.13114
12
11
10
9
+ 13'
53
54
55
9.09805
.09814
.09822
.09830
.12533
.12536
.12538
.12540
9.10304
.10313
.10321
.10329
.12678
.12680
.12683
.12685
9.10800
.10808
.10816
.10825
.12823
.12826
.12828
.12831
9.11292
.11301
.11309
.11317
.12970
.12972
.12974
.12977
9.11782
.11790
.11798
.11806
.13116
.13119
.13121
.13124
8
7
6
5
+ 14'
57
58
59
9.09839
.09847
.09856
.09864
.12543
.12545
.12547
.12550
9.10337
.10346
.10354
.10362
.12687
.12690
.12692
.12695
9.10833
.10841
.10849
.10858
.12833
.12836
.12838
.12840
9.11325
.11333
.11342
.11350
.12979
.12982
.12984
.12987
9.11814
.11822
.11831
.11839
.13126
.13129
.13131
.13134
4
3
1
~T
+ 15'
9.09872
.12552
9.10371
.12697
9.10866
.12843
9.11358
.12989
9.11847
.13136
SI* 14m
21* 13™>
21* 12™
21* llm
21* 10™-
TABLE 45. [Page 845
Haversines.
s
2 h 50™ 42° 307
2* 5V* 42° 45'
2* 52™ 43° O7
2* 5$™ 43° 15'
2h 54m 43° 307
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.; Nat. Hav.
Log. HavJ Nat. Hav.
0
1
2
S
9.11847
.11855
.11863
.11871
.13136
.13139
.13141
.13143
9.12332
.12341
.12349
.12357
.13284
.13286
.13289
.13291
9.12815
.12823
.12831
.12839
.13432
.13435
.13437
.13440
9.13295 .13581
.13303 ' .13584
.13311 i .13586
.13319 ' .13589
9.13771 .13731
.13779 ! .13734
.13787 i .13736
.13795 .13739
60
59
58
57
+ 1'
5
6
7
9.11879
.11887
.11895
.11904
.13146
.13148
.13151
.13153
9.12365
.12373
.12381
.12389
.13294
.13296
.13299
.13301
9.12847
.12855
.12863
.12871
.13442
.13445
.13447
.13450
9.13326 .13591
.13334 i .13594
.13342 ! .13596
.13350 1 .13599
9.13803
.13811
.13819
.13827
.13741
.13744
.13746
.13749
56
55
54
53
+ 2'
10
11
9.11912 s .13156
.11920 .13158
.11928 .13161
.11936 /.13163
9.12397
.12405
.12413
.12421
.13304
.13306
.13309
.13311
9.12879
.12887
.12895
.12903
.13452
.13455
.13457
.13460
9.13358
.13366
.13374
.13382
.13601
.13604
.13607
.13609
9.13834 .13751
.13842 .13754
.13850 .13756
.13858 .13759
52
51
50
49
^ i «»/
IS
14
15
9.11944,
.11952
.11960
.11968
.13168
.13171
.13173
9.12429
.12437
.12445
.12453
.13314
.13316
.13318
.13321
9.12911 .13462
.12919 ! .13465
.12927 i .13467
.12935 .13470
9.13390
.13398
.13406
.13414
.13611
.13614
.13616
.13619
9.13866
.13874
.13882
.13890
.13761
.13764
.13766
.13769
4$
47
46
45
17
18
19
9.11977
.11985
.11993
.12001
.13175
.13178
.13180
.13183
9.12461
.12470
.12478
.12486
.13323
.13326
.13328
.13331
9.12943
.12951
.12959
.12967
.13472
.13474
.13477
.13479
9.13422
.13430
.13438
.13446
.13621
.13624
.13626
.13629
9.13898
.13906
.13913
.13921
.13771
.13774
.13776
.13779
44
43
42
41
+ 5'
21
ti
23
9.12009
.12017
.12025
.12033
.13185
.13188
.13190
.13193
9.12494
.12502
.12510
.12518
.13333
.13336
.13338
.13341
9.12975
.12983
.12991
.12999
.13482
.13484
.13487
.13489
.13492
.13494
.13497
.13499
9.13454
.13462
.13470
.13478
.13631
.13634
.13636
.13639
9.13929
.13937
.13945
.13953
.13781
.13784
.13786
.13789
40
39
38
37
+ 6'
25
26
27
9.12041
.12050
.12058
.12066
.13195
.13198
.13200
.13203
9.12526
.12534
.12542
.12550
.13343
.13346
.13348
.13351
9.13007
.13015
.13023
.13031
9.13486
.13494
.13501
.13509
.13641
.13644
.13646
.13649
9.13961
.13969
.13977
.13985
.13791
.13794
.13796
.13799
36
35
34
33
+ r
29
30
SI
9.12074
.12082
.12090
.12098
.13205
.13207
.13210
.13212
9.1255S
.12566
.1257,4
.12582
.13353
.13356
.13358
.13360
9.13039
.13047
.13055
.13063
.13502
.13504
.13507
.13509
9.13517
.13525
.13533
.13541
.13651
.13654
.13656
.13659
9.13992
.14000
.14008
.14016
.13801
.13804
.13806
.13809
32
31
30
29
S3
34
35
9.12106
.12114
.12122
.12130
.13215
.13217
.13220
.13222
9.12590
.12598
.12606
.12614
.13363
.13365
.13368
.13370
9.13071
.13079
.13087
.13095
.13512
.13514
.13517
.13519
9.13549
.13557
.13565
.13573
.13661
.13664
.13666
.13669
9.14024
.14032
.14040
.14048
.13811
.13814
.13816
.13819
28
21
26
25
+ V
37
38
39
9.12139
.12147
.12155
.12163
.13225
.13227
.13230
.13232
9.12622
.12630
.12638
.12647
.13373
.13375
.13378
.13380
9.13103
.13111
.13119
.13127
.13522
.13524
.13527
.13529
9.13581
.13589
.13597
.13605
.13671
.13674
.13676
.13679
9.14056
.14063
.14071
.14079
.13822
.13824
.13827
.13829
24
22
21
41
42
43
9.12171
.12179
.12187
.12195
.13235
.13237
.13239
.13242
9.12655
.12663
.12671
.12679
.13383
.13385
.13383
.13390
9.13135
.13143
.13151
.13159
.13532
.13534
.13537
.13539
9.13613
.13621
.13628
.13636
.13681
.13684
.13686
.13689
9.14087
.14095
.14103
.14111
.13832
.13834
.13837
.13839
20
19
18
17
+ 11'
45
46
47
9.12203
.12211
.12219
.12228
.13244
.13247
.13249
.13252
9.12687
.12695
.12703
.12711
.13393
.13395
.13398
.13400
9.13167
.13175
.13183
.13191
.13542
.13544
.13547
.13549
9.13644
.13652
.13660
.13668
.13691
.13694
.13696
.13699
9.14119
.14127
.14134
.14142
.13842
.13844
.13847
.13849
16
15
14
13
+ 12'
49
50
51
9.12236
.12244
.12252
.12260
.13254
.13257
.13259
.13262
9.12719
.12727
.12735
.12743
.13403
.13405
.13408
.13410
9.13199
.13207
.13215
.13223
.13552
.13554
.13557
.13559
9.13676
.13684
.13692
.13700
.13701
.13704
.13706
.13709
9.14150
.14158
.14166
.14174
.13852
.13854
.13857
.138o9
12
11
10
9
+ 13'
53
54
55
9.12268
.12276
.12284
.12292
.13264
.132G7
.13269
.13272
9.12751
.12759
.12767
.12775
.13412
.13415
.13417
.13420
9.13231
.13247
.13255
.13562
.135G4
.13567
.13569
9.13708
.13716
.13724.
.13732
.13711
.13714
.13716
.13719
9.14182 j J3SG2
.14190 ! .13864
.14197 .13867
.14205 ,13869
S
6
5
+ 14'
57
58
59
9.12300
.12308
.12316
.12324
.13274
.13278
.13279
.13281
9.12783
.12791
.12799
.12S07
.13422
.13425
.13427
.13430
9.13263
.13271
.13279
.13287
.13571
.13574
.13576
.13579
9.13739
.13747
.13755
.13763
.13721
.13724
.1372S
.13729
9.14213 .13872
.14221 .13874
.14229 .13877
.14237 .13879
4
3
2
1
>+ 15'
9.12332
.13284
9.12815
.13432
9.13295 .13581
9.13771 ! .13731
9.14245 .13882
0
2lhgm
I***"
21h "m
2i~h, Qm
:>} h jm
|
Page 846] TABLE 45.
Haversines.
s
2* 55n 43° 45'
2h 56m 44° 0'
%h 57m 44° 15'
2*> 58m 44° 307
gh 59m 440 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
9.14245
.14252
.14260
.14268
.13883
.13884
.13887
.13889
9.14715
.14723
.14731
.14739
.14033
.14035
.14038
.14041
9.15183
.15190
.15198
.15206
.14185
.14187
.14190
.14192
9.15647
.15655
.15663
.15670
.14337
.14340
.14343
.14345
9.16109
.16117
.16124
.16132
.14491
.14493
.14496
.14498
60
59
58
57
+ 1'
5
6
7
9.14276
.14284
.14292
.14300
.13892
.13894
.13897
.13899
9.14746
.14754
.14762
.14770
.14043
.14046
.14048
.14051
9.15214
.15221
.15229
.15237
.14195
.14198
.14200
.14203
9.15678
.15686
.15694
.15701
.14348
.14350
.14353
.14355
9.16140
.16147
.16155
.16163
.14501
.14504
.14506
.14509
.14511
.14514
.14516
.14519
56
55
54
53
+ 3'
9
10
11
9.14307
.14315
.14323
.14331
.13902
.13904
.13907
.13909
9.14778
.14785
.14793
.14801
.14053
.14056
.14058
.14061
9.15245
.15253
.15260
.15268
.14205
.14208
.14210
.14213
9.15709
.15717
.15724
.15732
.14358
.14360
.14363
.14366
9.16170
.16178
.16186
.16193
(52
51
50
49
+ 3'
13
14
15
9.14339
.14347
.14355
.14362
.13912
.13914
.13917
.13920
9.14809
.14817
.14824
.14832
.14063
.14066
.14068
.14071
9.15276
.15284
.15291
.15299
.14215
.14218
.14220
.14223
9.15740
.15748
.15755
.15763
.14368
.14371
.14373
.14376
9.16201
.16209
.16216
.16224
.14521
.14524
.14527
.14529
48
47
46
45
+ *'
17
18
19
9.14370
.14378
.14386
.14394
.13922
.13925
.13927
.13930
9.14840
.14848
.14856
.14863
.14073
.14076
.14079
.14081
9.15307
.15315
.15322
.15330
.14226
.14228
.14231
.14233
9.15771
.15778
.15786
.15794
.14378
.14381
.14383
.14386
9.16232
.16239
.16247
.16255
.14532
.14534
.14537
.14539
44
43
42
41
+ $'
21
22
23
9.14402
.14410
.14417
.14425
.13932
.13935
.13937
.13940
9.14871
.14879
.14887
.14895
.14084
.14086
.14089
.14091
9.15338
.15346
.15353
.15361
.14236
.14238
.14241
.14243
9.15802
.15809
.15817
.15825
.14388
.14391
.14394
.14396
9.16262
.16270
.16278
.16285
.14542
.14545
.14547
.14550
40
39
38
37
36
35
34
33
+ 6'
25
26
27
9.14433
.14441
.14449
.14457
.13942
.13945
.13947
.13950
9.14902
.14910
.14918
.14926
.14094
.14096
.14099
.14101
9.15369
.15377
.15384
.15392
.14246
.14248
.14251
.14253
9.15832
.15840
.15848
.15855
.14399
.14401
.14404
.14406
9.16293
.16301
.16308
.16316
.14552
.14555
.14557
.14560
+ r
29
30
31
9.14465
.14472
.14480
.14488
.13952
.13955
.13957
.13960
9.14934
.14941
.14949
.14957
.14104
.14106
.14109
.14111
9.15400
.15408
.15415
.15423
.14256
.14259
.14261
.14264
9.15863
.15871
.15879
.15886
.14409
.14411
.14414
.14417
9.16324
.16331
.16339
.16346
.14562
.14565
.14568
.14570
32
31
30
29
28
27
26
25
+ 8'
33
34
35
9.14496
.14504
.14512
.14519
.13962
.13965
.13967
.13970
9.14965
.14973
.14980
.14988
.14114
.14116
.14119
.14122
9.15431
.15439
.15446
.15454
.14266
.14269
.14271
.14274
9.15894
.15902
.15909
.15917
.14419
.14422
.14424
.14427
9.16354
.16362
.16369
.16377
.14573
.14575
.14578
.14580
+ V
37
38
39
9.14527
.14535
.14543
.14551
.13972
.13975
.13977
.13980
9.14996
.15004
.15012
.15019
.14124
.14127
.14129
.14132
9.15462
.15470
.15477
.15485
.14276
.14279
.14281
.14284
9.15925
.15932
.15940
.15948
.14429
.14432
.14434
.14437
9.16385
.16392
.16400
.16408
.14583
.14586
.14588
.14591
24
23
21
+ 10'
41
42
43
9.14559
.14566
.14574
.14582
.13983
.13985
.13988
.13990
9.15027
.15035
J5043
.15050
.14134
.14137
.14139
.14142
9.15493
.15500
.15508
.15516
.14287
.14289
.14292
.14294
9.15955
.15963
.15971
.15978
.14440
.14442
.14445
.14447
9.16415
.16423
.16431
.16438
.14593
.14596
.14598
.14601
20
19
18
17
+ ir
45
46
47
9.14590
.14598
.14606
.14613
.13993
.13995
.13998
.14000
9.15058
.15066
.15074
.15082
.14144
.14147
.14149
.14152
9.15524
.15531
.15539
.15547
.14297
.14299
.14302
.14304
9.15986
.15994
.16002
.16009
.14450
.14452
.14455
.14457
9.16446
.16453
.16461
.16469
.14604
.14606
.14609
.14611
16
15
14
13
+ 12'
49
50
51
9.14621
.14629
.14637
.14645
.14003
.14005
.14008
.14010
9.15089
.15097
.15105
.15113
.14154
.14157
.14160
.14162
9.15555
.15562
.15570
.15578
.14307
.14309
.14312
.14315
9.16017
.16025
.16032
.16040
.14460
.14463
.14465
.14468
9.16476
.16484
.16492
.16499
.14614
.14616
.14619
.14622
12
11
10
9
+ 13'
53
54
55
9.14653
.14660
.14668
.14676
.14013
.14015
.14018
.14020
9.15120
.15128
.15136
.15144
.14165
.14167
.14170
.14172
9.15585
.15593
.15601
.15609
.14317
.14320
.14322
.14325
9.16048
.16055
.16063
.16071
.14470
.14473
.14475
.14478
9.16507
.16515
.16522
.16530
.14624
.14627
.14629
.14632
8
7
6
5
+ 14'
57
58
59
9.14684
.14692
.14699
.14707
.14023
.14025
.14028
.14030
9.15152
.15159
.15167
.15175
.14175
.14177
.14180
.14182
9.15616
.15624
.15632
.15640
.14327
.14330
.14332
.14335
9.16078
.16086
.16094
.16101
.14480
.14483
.14486
.14488
9.16537
.16545
.16553
.16560
.14634
.14637
.14639
.14642
4
3
2
1
+ 15'
9.14715
.14033
9.15183
.14185
9.15647
.14337
9.16109
.14491
9.16568
.14645
0
i**4»
21h3™
&*£•
21h lm
21h Om
TABLE 45. [Page 847
Haversines.
s
3* G™ 45° 0'
Jfc im 45° 15'
3h em 45° 30'
Sh sm 45° 45^
3h 4m 46° O7
s
Log. Hav. Nat. Hay.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
0
1
2
3
9.16568
.16576
.16583
.16591
.14645
.14647
.14650
.14652
9.17024
.17032
.17039
.17047
.14799
.14802
.14804
.14807
9.17477
.17485
.17492
.17500
.14955
.14957
.14960
.14962
9.17928
.17935
.17943
.17950
.15110
.15113
.15116
.15118
9.18376
.18383
.18390
.18398
.15267
.1527D
.15272
.15275
60
59
58
57
+ lx
5
6
7
9.16598
.16606
.16614
.16621
.14655
.14658
.14660
.14663
9.17054
.17062
.17069
.17077
.14810
.14812
.14815
.14817
9.17507
.17515
.17522
.17530
.14965
.14968
.14970
.14973
9.17958
.17965
.17973
.17980
.15121
.15123
.15126
.15129
9.18405
.18413
.18420
.18428
.15278
.15280
.15283
.15285
56
55
54
53
+ V
9
10
11
9.16629
.16637
.16644
.16652
.14665
.14668
.14670
.14673
9.17085
.17092
.17100
.17107
.14820
.14822
.14825
.14828
9.17538
.17545
.17553
.17560
.14975
.14978
.14981
.14983
9.17988
.17995
.18003
.18010
.15131
.15134
.15137
.15139
9.18435
.18443
.18450
.18457
.15288
.15291
.15293
.15296
52
51
50
49
+ *
IS
14
15
9.16659
.16667
.16675
.16682
.14676
.14678
.14681
.14683
9.17115
.17122
.17130
.17138
.14830
.14833
.14835
.14838
9.17568
.17575
.17583
.17590
.14986
.14988
.14991
.14993
9.18018
.18025
.18033
.18040
.15142
.15144
.15147
.15150
9.18465
.18472
.18480
.18487
.15298
.15301
.15304
.15306
48
47
46
45
+ 4'
17
18
19
9.16690
.16697
.16705
.16713
.14686
.146S8
.14691
.14693
9.17145
.17153
.17160
.17168
.14841
.14843
.14846
.14848
9.17598
.17605
.17613
.17620
.14996
.14999
.15001
.15004
9.18048
.18055
.18062
.18070
.15152
.15155
.15157
.15160
9.18495
.18502
.18509
.18517
.15309
.15312
.15314
.15316
44
43
42
41
+ 5/
21
22
23
9.16720
.16728
.16735
.16743
.14696
.14699
.14701
.14704
9.17175
.17183
.17191
.17198
.14851
.14853
.14856
.14859
9.17628
.17635
.17643
.17650
.15006
.15009
.15012
.15014
9.18077
.18085
.18092
.18100
.15163
.15165
.15168
.15170
9.18524
.18532
.18539
.18547
.15319
.15322
.15325
.15327
40
39
38
37
+ 6'
25
26
27
9.16751
.16758
.16766
.16774
.14706
.14709
.14712
.14714
9.17206
.17213
.17221
.17228
.14861
.14864
.14866
.14869
9.17658
.17665
.17673
.17680
.15017
.15019
.15022
.15025
9.18107
.18115
.18122
.18130
.15173
.15176
.15178
.15181
9.18554
.18561
.18569
.18576
.15330
.15333
.15335
.15337
36
35
34
33
+ v
29
30
31
9.16781
.16789
.16796
.16804
.14717
.14719
.14722
.14724
9.17236
.17243
.17251
.17259
.14872
.14874
.14877
.14879
9.17688
.17695
.17703
.17710
.15027
.15030
.15032
.15035
9.18137
.18145
.18152
.18160
.15183
.15186
.15189
.15191
9.18584
.18591
.18598
.18606
.15340
.15343
.15346
.15348
32
31
30
29
+ 8'
33
34
35
9.16812
.16819
.16827
.16834
.14727
.14730
.14732
.14735
9.17266
.17274
.17281
.17289
.14882
.14885
.14887
.14890
9.17718
.17725
.17733
.17740
.15038
.15040
.15043
.15045
9.18167
.18174
.18182
.18189
.15194
.15197
.15199
.15202
9.18613
.18621
.18628
.18636
.15351
.15353
.15356
.15359
28
27
26
25
+ v
37
38
39
9.16842
.16850
.16857
.16865
.14737
.14740
.14743
.14745
9.17296
.17304
.17311
.17319
.14892
.14895
.14898
.14900
9.17748
.17755
.17763
.17770
.15048
.15051
.15053
.15056
9.18197
.18204
.18212
.18219
.15204
.15207
.15210
.15212
9.18643
.18650
.18658
.18665
.15361
.15364
.15367
.15369
24
23
22
21
+ 10'
41
42
43
9.16872
.16880
.16887
.16895
.14748
.14750
.14753
.14755
9.17327
.17334
.17342
.17349
.14903
.14905
.14908
.14910
9.17778
.17785
.17793
.17800
.15058
.15061
.15064
.15066
9.18227
.18234
.18242
.18249
.15215
.15217
.15220
'.15222
9.18673
.18680
.18687
.18695
.15372
.15374
.15377
.15379
20
19
18
17
+ 11'
45
46
47
9.16903
.16910
.16918
.16925 ^
.14758
.14760
.14763
.14766
9.17357
.17364
.17372
.17379
.14913
.14916
.14918
.14921
9.17808
.17815
.17823
.17830
.15069
.15071
.15074
.15077
9.18256
.18264
.18271
.18279
.15225
.15228
.15230
.15233
9.18702
.18710
.18717
.18724
.15382
.15385
.15388
.15390
16
15
14
13
+ 12'
49
50
51
9. 16933 ^
.16941
.16948
.16956
.14768
.14771
.14773
.14776
9.17387
.17394
.17402
.17409
.14923
.14926
.14929
.14931
9.17838
.17845
.17853
.17860
.15079
.15082
.15084
.15087
9.18286
.18294
.18301
.18309
.15236
.15238
.15241
.15244
9.18732
.18739
.18747
.18754
.15393
.15395
.15398
.15401
12
11
10
9
+ 13'
53
54
55
9.16963
.16971
.16979
.16986
.14779
.14781
.14784
.14786
9.17417
.17425
.17432
.17440
.14934
.14936
.14939
.14942
9.17868
.17875
.17883
.17890
.15090
.15092
.15095
.15097
9.18316
.18324
.18331
.18338
.15246
.15249
.15251
.15254
9.18762
.18769
.18776
.18784
.15403
.15406
.15409
.15411
8
7
6
5
+ 14'
57
58
59
9.16994
.17001
.17009
.17016
.14789
.14791
.14794
.14797
9.17447
.17455
.17462
.17470
.14944
.14947
.14949
.14952
9.17898
.17905
.17913
.17920
.15100
.15103
.15105
.15108
9.18346
.18353
.18361
.18368
.15257
.15259
.15262
.15264
9.18791
.18798
.18806
.18813
.15414
.15416
.15419
.15422
4
3
2
1
' + 15'
9.17024
.14799
9.17477 .14955
9.17928 .15110
9.18376
.15267
9.18821
.15424
0
2Qh 59m
2Qh 5Sm
2Qh J7?»
20^ 56m
•20* 55m
Page 848] TABLE 45.
Haversines.
s
Sh 5m 46° 15'
Sh em 46° SO7
3h jm 46° 45'
Sh 8-m 47° 0'
3h 9m 47° 15'
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
s
0
1
2
8
9.18821
.18828
.18835
.18843
.15424
.15427
.15430
.15433
9.19263
.19270
.19278
.19285
.15582
.15585
.15588
.15590
9.19703
.19710
.19717
.19725
.15741
.15743
.15746
.15748
9.20140
.20147
.20154
.20162
.15900
.15903
.15905
.15908
9.20574
.20582
.20589
.20596
.16060
.16063
.16065
.16068
60
59
58
57
+ 1'
5
6
7
9.18850
.18858
.18865
.18872
.15435
.15437
.15440
.15443
9.19292
.19300
.19307
.19315
.15593
.15595
.15598
.15601
9.19732
.19739
.19747
.19754
.15751
.15754
.15757
.15759
9.20169
.20176
.20184
.20191
.15911
.15913
.15916
.15919
9.20603
.20611
.20618
.20625
.16071
.16073
.16076
.16079
56
55
54
53
+ %'
9
10
11
9.18880
.18887
.18895
.18902
.15445
.15448
.15451
.15453
9.19322
.19329
.19337
.19344
.15603
.15606
.15609
.15611
9.19761
.19769
.19776
.19783
.15762
.15765
.15767
.15770
9.20198
.20205
.20213
.20220
.15921
.15924
.15927
.15929
9.20632
.20639
.20647
.20654
.16081
.16084
.16087
.16089
52
51
50
49
+ 3'
13
14
15
9.18909
.18917
.18924
.18932
.15456
.15458
.15461
.15464
9.19351
.19359
.19366
.19373
.15614
.15617
.15619
.15622
9.19790
.19798
.19805
.19812
.15773
.15775
.15778
.15781
9.20227
.20234
.20242
.20249
.15932
.15935
.15937
.15940
9.20661
.20668
.20675
.20683
.16092
.16095
.16097
.16100
48
47
46
45
+ A'
17
18
19
9.18939
.18946
.18954
.18961
.15466
.15469
.15472
.15474
9.19381
.19388
.19395
.19403
.15625
.15627
.15630
.15632
9.19820
.19827
.19834
.19842
.15783
.15786
.15789
.15791
9.20256
.20263
.20271
.20278
.15943
.15945
.15948
.15951
9.20690
.20697
.20704
.20712
.16103
.16105
.16108
.16111
44
43
42
41
+ 5'
21
22
28
9.18968
.18976
.18983
.18991
.15477
.15479
.15482
.15485
9.19410
.19417
.19425
.19432
.15635
.15638
.15640
.15643
9.19849
.19856
.19863
.19871
.15794
.15796
.15799
.15802
9.20285
.20292
.20300
.20307
.15953
.15956
.15959
.15961
9.20719
.20726
.20733
.20740
.16113
.16116
.16119
.16121
40
39
38
37
+ 6/
25
26
27
9.18998
.19005
.19013
.19020
.15487
.15490
.15493
.15495
9.19439
.19447
.19454
.19461
.15646
.15648
.15651
.15654
9.19878
.19885
.19893
.19900
.15804
.,15807
.15810
.15812
.9.20314
.20321
.20329
.20336
.15964
.15967
.15969
.15972
9.20748
.20755
.20762
.20769
.16124
.16127
.16129
.16132
36
35
34
33
+ ?'
29 .
30
31
9.19027
.19035
.19042
.19050
.15498
.15501
.15503
.15506
9.19469
.19476
.19483
.19491
.15656
.15659
.15662
.15664-
9.19907
.19914
.19922
.19929
.15815
.15818
.15820
.15823
9.20343
.20350
.20358
.20365
.15975
.15977
.15980
.15983
9.20776
.20784
.20791
.20798
.16135
.16137
.16140
.16143
32
31
30
29
+ 8'
38
34
35
9.19057
.19064
.19072
.19079
.15509
.15511
.15514
.15516
9.19498
.19505
.19513
.19520
.15667
.15670
.15672
.15675
9.19936
.19944
.19951
.19958
.15826
.15828
.15831
.15834
9.20372
.20379
.20386
.20394
.15985
.15988
.15991
.15993
9.20805
.20812
.20820
.20827
.16146
.16148
.16151
.16154
28
27
26
25
+ 9'
37
38
39
9.19086
.19094
.19101
.19109
.15519
.15522
.15524
.15527
9.19527
.19535
.19542
.19549
.15677
.15680
.15683
.15685
9.19965
.19973
.19980
.19987
.15836
.15839
.15842
.15844
9.20401
.20408
.20415
.20423
.15996
.15999
.16001
.16004
9.20834
.20841
.20848
.20856
.16156
.16159
.16162
.16164
24
23
22
21
20
19
18
17
+ iox
41
42
43
9.19116
.19123
.19131
.19138
.15530
.15532
.15535
.15537
9.19557
.19564
.19571
.19579
.15688
.15691
.15693
.15686
9.19995
.20002
.20009
.20016
.15847
.15850
.15852
.15855
9.20430
.20437
.20444
.20452
.16007
.16009
.16012
.16015
9.20863
.20870
.20877
.20884
.16167
.16170
.16172
.16175
+ 11'
45
46
47
9.19145
.19153
.19160
.19167
.15540
.15543
.15545
.15548
9.19586
.19593
.19600
.19608
.15699
.15701
.15704
.15706
9.20024
.20031
.20038
.20045
.15858
.15860
.15863
.15866
9.20459
.20466
.20473
.20481
.16017
.16020
.16023
.16025
9.20891
.20899
.20906
.20913
.16178
.16180
.16183
.18186
16
15
14
13
+ 12'
49
50
51
9.19175
.19182
.19190
.19197
.15551
.15553
.15556
.15559
9.19615
.19622
.19630
.19637
.15709
.15712
.15714
.15717
9.20053
.20060
.20067
.20075
.15868
.15871
.15874
.15876
9.20488
.20495
.20502
.20509
.16028
.16031
.16033
.16036
9.20920
.20927
.20935
.20942
.16188
.16191
.16194
.16196
12
11
10
9
+ 13X
53
* 54
55
9.19204
.19212
.19219
.19226
.15561
.15564
.15566
.15569
9.19644
.19652
.19659
.19666
.15720
.15722
.15725
.15728
9.20082
.20089
.20096
.20104
.15879
.15881
.15884
.15887
9.20517
.20524
.20531
.20538
.16039
.16041
.16044
.16047
9.20949
.20956
.20963
.20971
.16199
.16202
.16204
.16207
8
7
6
5
+ 14'
57
58
59
9.19234
.19241
.19248
.19256
.15572
.15574
.15577
.15580
9.19674
.19681
.19688
.19696
.15730
.15733
.15736
.15738
9.20111
.20118
.20125
.20133
.15889
.15892
.15895
.15898
9.20546
.20553
.20560
.20567
.16049
.16052
.16055
.16057
9.20978
.20985
.20992
.20999
.16210
.16212
.16215
.16218
4
3
2
1
+ 15'
9.19263
.15582
9.19703
.15741
9.20140
.15900
9.20574 .16060
9.21006 .16220
0
j?0ft 54™
2Qh 53m
jg0A sgm
20^ 51m
20~h 5Qm
TABLE 45. [Page 849
Haversines.
s
jfc j0m 47° 3(K
Sh llm 47° 45'
Sh Jim 48° o'
Sh ism 48° 15'
Sh 14m 48° 30X
s
Log. Hav.j Nat. Hav.
Log. Hav.l Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
0
1
2
S
9.21006 .16220
.21014 i .16223
.21021 .16226
.21028 .16229
9.21436 | .16382
.21443 .16384
.21450 1 .16387
.21457 | .16390
9.21863 .16543
.21870 .16546
.21877 .16549
.21884 : .16552
9.22287
.22294
.22301
.22308
.16706
.16709
.16711
.16714
9.22709
.22716
.22723
.22730
.16889
.16872
.16874
.16877
60
59
58
57
+ I7
5
6
9.21035 : .16231
.21042 .16234
.21049 .16237
.21057 .16239
9.21464
.21471
.21479
.21486
.16392
.16395
.16398
.164C1
9.2d891 .16554
.21898 i .16557
.21905 i .16560
.21912 | .16562
9.22315
.22322
^22329
.2*336
.16711
.16720
.16722
.16725
9.22737
.22744
.22751
.22758
.16880
.16883
.16885
.16888
56
55
54
53
+ *'
9
10
11
9.21064 .16242/
.21071 .16245-
.21078 c 16247
.21085 .16250
9.21493 i .16403
.21500 .16406
.21507J .16409
.21514 .16411
9.21919 | .16565
.21926 .16568
.21934 .16571
.21941 i .16573
9.22343
.22350
.22358
.22365
.16728
.16730
.16733
.16736
9.22765
.22772
.22779
.22786
.13381
.16893
.16896
.16899
52
51
50
49
+ 3'
IS
14
15
9.21092
.21100
.21107
.21114
.16253
.16255
.16258
.16261
0.21521 i .16414
.21529 ; .16417
.21536 .16419
.21543 1 .10422
9.21948 .16576
.21955 .16579
.21962 .16581
.21969 .16584
9.22372
.22379
.22386
.22393
.16738
.16741
.16744
.16747
9.22793
.22800
.22807
.22814
.16902
.16904
.16907
.16910
48
47
46
45
+ ±'
17
18
19
9.21121 I .16263
.21128 .16266
.21135 ' .16269
.21143 i .16271
9.21550 ' .16425
.21557 .16427
.21564 .16430
21571 .16433
9.21976
.21983
.21990
.21997
.16587
.16589
.16592
.16595
9.22400
.22407
.22414
.22421
.16749
.16752
.16755
.16757
9.22821
.22828
.22835
.22842
.16913
.16915
.16918
.16921
44
43
42
41
+ *'
21
23
9.21150 .16274
.21157 ! .16277
.21164 .16280
.21171 | .16282
9.21578
.21585
.21593
.21600
.16436
.16438
.16441
.16444
9.22004
.22011
.22019
.22026
.16598
.16600
.16603
.16606
9.2242S .16760
.22435 .16763
.22442 .16766
.22449 .16768
9.22849 .16924
.22856 .16926
.22863 .16929
.22870 .16932
40
39
3S
37
36
35
34
33
+ 6'
25
26
27
9.21178
.21186
.21193
.21200
.16285
.16288
.16290
.16293
9.21607
.21614
.21621
.21628
.16446
.16449
.16452
.16454
9.22033
.22040
.22047
.22054
.16608
.16611
.16614
.16616
9.22456 .16771
.22463 ! .16774
.22470 .16777
.22477 \ .16779
9.22877 .16934
.22884 .16937
.22891 i .16940
.22898 .16943
+ 7'
29
30
31
9.21207 .16296
.21214 ! .16298
.21221 | .16301
.21229 .16304
9.21635
.21642
.21650
.21657
.16457
.16460
.16462
.16465
9.22061
.22068
.22075
.22082
.16619
.16622
.16625
.16627
9.22484 .16782
.22491 ' .16785
.22498 i .16787
.225054 .16790
9.22905
.22912
.22919
.22926
.16945
.16948
.16951
.16953
32
31
30
29
+ 8/
ft
35
9.21236
.21243
.21250
.21257
.16306
.16309
.16312
.16314
9.21664
.21671
.21678
.21685
.16468
.16471
.16473
.16476
9.22089
.22096
.22103
.22111
.16630
.16633
.16635
.16638
9.22512
.22519
.22526
.22533
.16793
.16795
.16798
.16801
9.22933 .16956
.22940 i .16959
.22947 .16962
.22954 .16964
28
27
26
25
+ V
37
38
39
9.21264
.21272
.21279
.21286
.16317
.16320
.16323
.16325
9.21692
.21699
.21706
.21714
.16479
.16481
.16484
.10487
9.22118
.22125
2^132
^22139
.16641
.16644
.16646
.16649
9.22540 .16804
.22547 .16806
.22555 .16809
.22562 .16812
9.22961
.22968
.22975
.22982
.16967
.16970
.16973
.16975
24
23
22
21
+ 10'
41
42
43
9.21293
.21300
.21307
.21314
.16328
.16331
.16333
.16336
9.21721
.21728
.21735
,21742
.16489
.16492
.16495
.16498
9.22146
.22153
.22160
.22167
.16652
.10654
.10657
.16660
9.22569
.22576
.2258$
.22590
.16815
.16817
.16820
.16823
9.22989
.22996
.23003
.23010
.16978
.16981
.16984
.16986
to
19
18
17
+ 11'
45
46
47
9.21322
.21329
.21336
.21343
.1633S
.16311
.16344
.16347
9.21749
.21756
.21763
.21770
.16500
.16503
.16506
.16508
9.22174
.22181
.22188
.22195
.16663
.16665
.16668
.16671
9.22597
.22604
.22611
.22618
.16825
.16828
.16831
.16834
9.23017 ; .16989
.23024 .16992
.23031 .16994
.23038 .18997
16
15
14
13
+ 12'
49
50
51
9. 21350 '
.21357
.21364
.21372
.16349
.16352
.16355
.16357
9.21778 .16511
.21785 .16514
.21792 .16510
.21799 .16519
9.22202
.22209
.22216
.22224
.18673
.16676
.16679
.16681
9.22625
.22632
.22639
.226^'i
.16836
.16839
.16842
.16844
9.23045 .17000
.23052 .17003
.23059 .17005
.23066 .17008
12
11
10
9
-f 13'
si,
54
55
9.21379
.21380
.21393
.21400
.16360
.16363
.16366
.16368
9.21806
.21813
.21820
.21827
.16522
.16524
.16527
.16533
9.22231
.22238
.22245
.22252
.16684
.16687
.16690
.16692
9.22653 .16847
.22660 .16850
.22667 ! .16853
.22674 .16855
9.23073 .17011
.23080 .17014
.23087 .17016
.23094 .17019
8
.7
6
5
+ 14
57
5S
59
9.21407
.21414
.21422
.21429
.16371
.1-3371
.1G376
.16379
9.21834
.21841
.21848
.21856
.16533
.16535
.16538
.16541
:, 22259
.22266
.22273
.22280
.16695
.16698
.16701
.18703
9.22681 .16858
.22688 .16861
.22695 .16864
.22702 .16866
9.23100 .17022
.23107 .17024
.23114 .17027
.23121 : .17030
4
3
2
1
-f 15'
9.21436
.10382
9.21S63 .16543
9.22287 | .16706
9.22709 .16869
9.2312S .17033
0
20^ 49m
oQh jgm
OQh ^jm
20* 46^
20^ 45™
Page 850] TABLE 45.
Haversines.
s
5fc 15m 48° 45'
3h 16m 49° 0'
Sh 17m 49° 15/
gh ism 49° 30'
3h 19m 49° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
0
1
|
3
9.23128
.23135
.23142
.23149
.17033
.17035
.17038
.17041
9.23545
.23552
.23559
.23566
.17197
.17200
.17203
.17205
9.23960
.23967
.23974
.23981
.17362
.17365
.17368
.17370
9.24372
.24379
.24386
.24393
.17528
.17530
.17533
.17536
9.24782
.24789
.24796
.24803
.17694
.17697
.17699
.17702
60
59
58
57
+ 1'
5
6
7
9.23156
.23163
.23170
.23177
.17044
.17046
.17049
.17052
9.23573
.23580
.23587
.23594
.17208
.17211
.17214
.17216
9.23988
.23994
.24001
.24008
.17373
.17376
.17379
.17381
9.24400
.24406
.24413
.24420
.17539
.17541
.17544
.17547
9.24809
.24816
.24823
.24830
.17705
.17708
.17710
.17713
56
55
54
53
+ %'
9
10
11
9.23184
.23191
.23198
.23205
.17055
.17057
.17060
.17063
9.23601
.23608
.23615
.23622
.17219
.17222
.17225
.17227
9.24015
.24022
.24029
.24036
.17384
.17387
.17390
.17392
9.24427
.24434
.24441
.24448
.17550
.17552
.17555
.17558
9.24837
.24843
.24850
.24857
.17716
.17719
.17722
.17724
52
51
50
49
+ 3'
13
14
15
9.23212
.23219
.23226
.23233
.17066
.17068
.17071
.17074
9.23629
.23635
.23642
.23649
.17230
.17233
.17235
.17238
9.24043
.24050
.24056
.24063
.17395
.17398
.17401
.17403
9.24454
.24461
.24468
.24475
.17561
.17563
.17566
.17569
9.24864
.24871
.24877
.24884
.17727
.17730
.17733
.17735
48
47
46
45
+ 4'
17
15
19
9.23240
.23247
.23254
.23261
.17076
.17079
.17082
.17085
9.23656
.23663
.23670
.23677
.17241
.17244
.17246
.17249
9.24070
.24077
.24084
.24091
.17406
.17409
.17412
.17414
9.24482
.24489
.24495
.24502
.17572
.17575
.17577
.17580
9.24891
.24898
.24905
.24911
.17738
.17741
.17744
.17746
44
43
42
41
+ 5/
*j
JW
9.23268
.23275
.23282
.23289
.17087
.17090
.17093
.17096
9.23684
.23691
.23698
.23705
.17252
.17255
.17257
.17260
9.24098
.24105
.24111
.24118
.17417
.17420
.17423
.17425
9.24509
.24516
.24523
.24530
.17583
.17586
.17588
.17591
9.24918
.24925
.24932
.24939
.17749
.17752
.17755
.17758
40
39
38
37
+ 6'
25
26
27
9.23295
.23302
.23309
.23316
.17098
.17101
.17104
.17107
9.23712
.23718
.23725
.23732
.17263
.17266
.17268
.17271
9.24125
.24132
.24139
.24146
.17428
.17431
.17434
.17436
9.24536
.24543
.24550
.24557
.17594
.17597
.17600
.17602
9.24945
.24952
.24959
.24966
.17760
.17763
.17766
.17769
36
35
34
33
+ r
29
30
31
9.23323
.23330
.23337
.23344
.17109
.17112
.17115
.17117
9.23739
.23746
.23753
.23760
.17274
.17277
.17279
.17282
9.24153
.24160
.24166
.24173
.17439
.17442
.17445
.17447
9.24564
.24571
.24577
.24584
.17605
.17608
.17611
.17613
9.24973
.24979
.24986
.24993
.17772
.17774
.17777
.17780
32
31
30
29
+ 8'
33
34
35
9.23351
.23358
.23365
.23372
.17120
.17123
.17126
.17128
9.23767
.23774
.23781
.23788
.17285
.17288
.17290
.17293
9.24180
.24187
.24194
.24201
.17450
.17453
.17456
.17458
9.24591
.24598
.24605
.24612
.17616
.17619
.17622
.17624
9.25000
.25007
.25013
.25020
.17783
.17785
.17788
.17791
28
27
26
25
+ V
37
38
39
9.23379
.23386
.23393
.23400
.17131
.17134
.17137
.17139
9.23794
.23801
.23808
.23815
.17296
.17299
.17301
.17304
9.24208
.24215
.24221
.24228
.17461
.17464
.17467
.17470
9.24618
.24625
.24632
.24639
.17627
.17630
.17633
.17636
9.25027
.25034
.25040
.25047
.17794
.17797
.17799
.17802
24
23
22
21
+ 10'
41
43
9.23407
.23414
.23421
.23427
.17142
.17145
.17148
.17150
9.23822
.23829
.23836
.23843
.17307
.17310
.17313
.17315
9.24235
24242
]24249
.24256
.17472
.17475
.17478
.17481
9.24646
.24653
.24659
.24666
.17638
.17641
.17644
.17647
9.25054
.25061
.25068
.25074
.17805
.17808
.17811
.17813
20
19
18
17
+ 11'
45
46
47
9.23434
.23441
.23448
.23455
.17153
.17156
.17159
.17161
9.23850
.23857
.23863
.23870
.17318
.17321
.17323
.17326
9.24263
.24269
.24276
.24283
.17483
.17486
.17489
.17492
9.24673
.24680
.24687
.24694
.17649
.17652
.17655
.17658
9.25081
.25088
.25095
.25102
.17816
.17819
.17822
.17824
16
15
14
13
+ 12'
49
50
51
9.23462
.23469
.23476
.23483
.17164
.17167
.17170
.17172
9.23877
.23884
.23891
.23898
.17329
.17333
.17335
.17337
9.24290
.24297
.24304
.24311
.17494
.17497
.17500
.17503
9.24700
.24707
.24714
.24721
.17661
.17663
.17666
.17669
9.25108
.25115
.25122
.25129
.17827
.17830
.17833
.17836
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
53
54
55
9.23490
.23497
.23504
.23511
.17175
.17178
.17181
.17183
9.23905
.23912
.23919
.23926
.17340
.17343
.17346
.17348
9.24317
.24324
.24331
.24338
.17505
.17508
.17511
.17514
9.24728
.24734
.24741
.24748
.17672
.17674
.17677
.17680
9.25135
.25142
.25149
.25156
.17838
.17841
.17844
.17847
+ 14'
57
58
59
9.23518
.23525
.23532
.23538
.17186
.17189
.17192
.17194
9.23932
.23939
.23946
.23953
.17351
.17354
.17357
.17359
9.24345
.24352
.24359
.24365
.17517
.17519
.17522
.17525
9.24755
.24762
.24768
.24775
.17683
.17686
.17688
.17691
9.25163
.25169
.25176
.25183
.17849
.17852
.17855
.17858
+ 15'
9.23545
.17197
9.23960
.17362
9.24372
.17528
9.24782
.17694
9.25190
.17861
0
20* 44m
20h 43™
20h 42m
20* 41™
20* 40™
TABLE 45. [Page 851
Haversines.
s
J» f 0"» 50° <K
5* ft"
50° 15'
3* 2?™ 50* 30"
S* 2.3™ 50° 45'
jh 24™ 51° V
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.'Nat. Hav.
Log. Hav.! Nat. Hav.
Log. Hav. Nat. Hav.
s
0
1
2
3
9.25190
.25196
.25203
.25210
.17861
.17863
.17866
.17869
9.25595
.25602
.25608
.25615
.18028
.18031
.18034
.18036
9.25998
.26005
.26011
.26018
.18196
.18199
.18202
.18205
9.26398
.26405
.26412
.26418
.18365
.18368
.18370
.18373
9.26797
.26804
.26810
.26817
.18534
.18537
.18540
.18542
60
59
58
57
+ 1'
5
6
/y
/
9.25217
.25224
.25230
.25237
.17872
.17875
.17877
.17880
9.25622
.25629
.25635
.25642
.18039
.18042
.18045
.18048
9.26025
.26031
.26038
.26045
9.26051
.26058
.26065
.26071
.18207
.18210
.18213
.18216
9.26425
.26432
.26438
.26445
.18376
.18379
.18382
.18384
9.26823
.26830
.26837
.26843
.18545
.18548
.18551
.18554
56
55
54
53
+ 2'
9
10
11
9.25244
.25251
.25257
.25264
.17883
.17886
.17888
.17891
9.25649
.25655
.25662
.25669
.18050
.18053
.18056
.18059
.18219
.18221
.18224
.18227
9.26452
.26458
.26465
.26472
.18387
.18390
.18393
.18396
9.26850
.26856
.26863
.26870
.18557
.18559
.18562
.18565
52
51
50
49
+ 3'
.tf
J4
.?5
9.25271
.25278
.25284
.25291
.17894
.17897
.17900
.17902
9.25676
.25682
.25689
.25696
.18062
.18064
.18067
.18070
9.26078
.26085
.26091
.26098
.18230
.18233
.18235
.18238
9.26478
.26485
.26492
.26498
.18399
.18401
.18404
.18407
9.26876
.26883
.26890
.26896
.18568
.18571
.18574
.18576
48
47
46
45
+ *'
.77
IS
J9
9.25298
.25305
.25311
.25318
.17905
.17908
.17911
.17914
9.25703
.25709
.25716
.25723
.18073
.18076
.18078
.18081
9.26105
.26112
.26118
.26125
.18241
.18244
.18247
.18249
9.26505
.26512
.26518
.26525
.18410
.18413
.18415
.18418
9.26903
.26909
.26916
.26923
.18579
.18582
.18585
.18588
44
4-3
42
41
+ 5'
2.7
ff
25
9.25325
.25332
.25339
.25345
.17916
.17919
.17922
.17925
9.25729
.25736
.25743
.25750
.18084
.18087
.18090
.18092
9.26132
.26138
.26145
.26152
.18252
.18255
.18258
.18261
9.26532
.26538
.26545
.26551
.18421
.18424
.18427
.18430
9.26929
.26936
.26942
.26949
.18591
.18593
.18596
.18599
40
39
38
37
+ &
25
26
27
9.25352
.25359
.25366
.25372
.17928
.17930
.17933
.17936
9.25756
.25763
.25770
.25776
.18095
.18098
.18101
.18104
9.26158
.26165
.26172
.26178
.18263
.18266
.18269
.18272
9.26558
.26565
.26571
.26578
.18432
.18435
.18438
.18441
9.26956
.26962
.26969
.26975
.18602
.18605
.18608
.18610
36
35
34
33
4- ?'
29
30
«
9.25379
.25386
.25393
.25399
.17939
.17941
.17944
.17947
9.25783
.25790
.25797
.25803
.18106
.18109
.18112
.18115
9.26185
.26192
.26198
.26205
.18275
.18277
.18280
.18283
9.265S5
.26591
.26598
.26605
.18444
.18446
.18449
.18452
9.26982
.26989
.26995
.27002
.18613
.18616
.18619
.18622
32
31
30
29
+ 8'
Ail
34
55
9.25406 j .17950
.25413 ; .17953
.25420 | .17955
.25426 .17958
9.25810
.25817
.25823
.25830
.18118
.18120
.18123
.18126
9.26212
.26218
.26225
.26232
.18286
.18289
.18292
.18294
9.26611
.26618
.26625
.26631
.18455
.18458
.18461
.18463
.18466
.18469
.18472
.18475
9.27008
.27015
.27022
.27028
.18624
.18627
.18630
.18633
28
27
26
25
+ v
37
38
39
9.25433
.25440
.25447
.25453
.17961
.17964
.17967
.17969
9.25837
.25844
.25850
.25857
.18129
.18132
.18134
.18137
9.26238
.26245
.26252
.26259
.18297
.18300
.18303
.18306
9.26638
.26644
.26651
.26658
9.27035
.27041
.27048
.27055
.18636
.18639
.18641
.18644
24
23
-.:
21
+ W
41
42
43
9.25460
.25467
.25474
.25480
.17972
.17975
.17978
.17981
9.25864
.25870
.25877
.25884
.18140
.18143
.18146
.18148
9.26265
.26272
.26279
.26285
.18308
.18311
.18314
.18317
9.26664
.26671
.26678
.26684
.18478
.18480
.18483
.18486
9.27061
.27068
.27074
.27081
.18647
.18650
.18653
.18656
20
19
18
17
+ 11'
45
46
47
9.25487
.25494
.25500
.25507
.17983
.17986
.17989
.17992
9.25891
.25897
.25904
.25911
.18151
.18154
.18157
.18160
9.26292
.26299
.26305
.26312
.18320
.18323
.18325
.18328
9.26691
.26697
.26704
.26711
.18489
.18492
.18494
.18497
9.27088
.27094
.27101
.27107
.18658
.18661
.18664
.18667
16
15
14
13
+ 12'
49
50
51
9.25514
.25521
.25528
.25534
.17995
.17997
.18000
.18003
9.25917
.25924
.25931
.25938
.18162
.18165
.18168
.18171
9.26319
.26325
.26332
.26339
.18331
.18334
.18337
.18339
9.26717
.26724
.26731
.26737
.18500
.18503
.18506
.18509
9.27114
.27121
.27127
.27134
.18670
.18673
.18675
.18678
12
11
10
9
+ 13'
53
54
55
9.25541
.25548
.25544
.25561
.18006
.18008
.18011
.18014
9.25944
.25951
.25958
.25964
.18174
.18176
.18179
.18182
9.26345
.26352
.26359
.26365
.18342
.18345
.18348
.18351
9.26744
.26751
.26757
.26764
.18511
.18514
.18517
.18520
9.27140
.27147
.27154
.27160
.18681
.18684
.18687
.18690
8
7
6
5
+ 14'
57
55
59
9.25568
.25575
.25581
.25588
.18017
.18020
.18022
.18025
9.25971
.25978
.25984
.25991
.18185
.18188
.18190
.18193
9.26372
.26378
.26385
.26392
.18353
.18356
.18359
.18362
9.26770
.26777
.26784
.26790
.18523
.18526
.1852S
.18531
9.27167
.27173
.27180
.27186
.18692
.18695
.18698
.18701
4
3
2
1
+ 15'
9.25595
.18028
9.25998
.18196
9.26398
.18365
9.26797 .18534
9.27193
.18704
0
20h 39™>
SO* 38m
20* 37m
*0*J9>
£0* S5m
Page 852] TABLE 45.
Haversines.
3h 25™ 51° 15'
S* 26™ 51° 30'
3h 27m 51° 45'
3h 28^ 52° O7
3*> 29™ 52° 15'
s
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
9.27193
.27200
.27206
.27213
.18704
.18707
.18710
.18712
9.27587
.27594
.27600
.27607
.18874
.18877
.18880
.18883
9.27979
.27985
.27992
.27998
.19045
.19048
.19051
.19054
9.28368
.28375
.28381
.28388
.19217
.19220
.19223
.19226
9.28756
.28762
.28769
.28775
.19389
.19392
.19395
.19398
60
59
58
57
+ 1'
5
6
7
9.27219
.27226
.27233
.27239
.18715
.18718
.18721
.18724
9.27613
.27620
.27626
.27633
.18886
.18888
.18891
.18894
9.28005
.28011
.28018
.28024
.19057
.19060
.19062
.19065
9.28394
.28401
.28407
.28414
.19228
.19231
.19234
.19237
9.28782
.28788
.28794
.28801
.19401
.19404
.19406
.19409
56
55
54
53
+ V
9
10
11
9.27246
.27252
.27259
.27265
.18727
.18729
.18732
.18735
9.27639
.27646
.27652
.27659
.18897
.18900
.18903
.18906
9.28031
.28037
.28044
.28050
.19068
.19071
.19074
.19077
9.28420
.28427
.28433
.28440
.19240
.19243
.19246
.19248
9.28807
.28814
.28820
.28827
.19412
.19415
.19418
.19421
52
51
50
49
+ &
13
14
15
9.27272
.27279
.27285
.27292
.18738
.18741
.18744
.18746
9.27666
.27672
.27679
.27685
.18908
.18912
.18914
.18917
9.28057
.28063
.28070
.28076
.19080
.19082
.19085
.19088
9.28446
.28453
.28459
.28465
.19251
.19254
.19257
.19260
9.28833
.28840
.28846
.28852
.19424
.19427
.19429
.19432
48
47
46
45
+ v
17
18
19
9.27298
.27305
.27311
.27318
.18749
.18752
.18755
.18758
9.27692
.27698
.27705
.27711
.18920
.18923
.18926
.18928
9.28083
.28089
.28096
.28102
.19091
.19094
.19097
.19100
9.28472
.28478
.28485
.28491
.19263
.19266
.19269
.19271
9.28859
.28865
.28872
.28878
.19435
.19438
.19441
.19444
44
43
42
41
+ V
21
22
23
9.27325
.27331
.27338
.27344
.18761
.18763
.18766
.18769
9.27718
.27724
.27731
.27737
.18931
.18934
.18937
.18940
9.28109
.28115
.28112
.28128
.19102
.19105
.19108
.19111
9.28498
.28504
.28511
.28517
.19274
.19277
.19280
.19283
9.28885
.28891
.28897
.28904
.19447
.19450
.19452
.19455
40
39
38
37
+ v
25
26
27
9.27351
.27357
.27364
.27371
.18772
.18775
.18778
.18780
9.27744
.27751
.27757
.27764
.18943
.18945
.18948
.18951
9.28135
.28141
.28148
.28154
.19114
.19117
.19120
.19122
9.28524
.28530
.28537
.28543
.19286
.19289
.19291
.19294
9.28910
.28917
.28923
.28930
.19458
.19461
.19464
.19467
36
35
34
33
+ V
29
30
31
9.27377
.27384
.27390
.27397
.18783
.18786
.18789
.18792
9.27770
.27777
.27783
.27790
.18954
.18957
.18960
.18963
9.28161
.28167
.28174
.28180
.19125
.19128
.19131
.19134
9.28549
.28556
.28562
.28569
.19297
.19300
.19303
.19306
9.28936
.28942
.28949
.28955
.19470
.19473
.19475
.19478
32
31
30
29
+ &
33
34
35
9.27403
.27410
.27417
.27423
.18795
.18797
.18800
.18803
9.27796
.27803
.27809
.27816
.18965
.18968
.18971
.18974
9.28187
.28193
.28200
.28206
.19137
.19140
.19142
.19145
9.28575
.28582
.28588
.28595
.19309
.19311
.19314
.19317
9.28962
.28968
.28974
.28981
.19481
.19484
.19487
.19490
28
27
26
25
+ 9'
37
38
39
9.27430
.27436
.27443
.27449
.18806
.18809
.18812
.18815
9.27822
.27829
.27835
.27842
.18977
.18980
.18983
.18985
9.28213
.28219
.28226
.28232
.19148
.19151
.19154
.19157
9.28601
.28608
.28614
.28620
.19320
.19323
.19326
.19329
9.28987
.28994
.29000
.29007
.19493
.19496
.19499
.19501
24
23
22
21
+ W
41
42
43
9.27456
.27463
.27469
.27476
.18817
.18820
.18823
.18826
9.27848
.27855
.27861
.27868
.18988
.18991
.18994
.18997
9.28239
.28245
.28252
.28258
.13160
.19163
.19165
.19168
9 28627
.28633
.28640
.28646
.19332
.19335
.19337
.19340
9.29013
.29019
.29026
.29032
.19504
.19507
.19510
.19513
20
19
18
17
+ 11'
45
46
47
9.27482
.27489
.27495
.27502
.18829
.18832
.18834
.18837
9.27875
.27881
.27888
.27894
.18000
.18002
.19005
.19008
9.28265
.28271
.28278
.28284
.19171
.19174
.19177
.19180
9.28653
.28659
.28666
.28672
.19343
.19346
.19349
.19352
9.29039
.29045
.29051
.29058
.19516
.19519
.19532
.19524
16
15
14
13
+ 12'
49
50
51
9.27508
.27515
.27522
.27528
.18840
.18843
.18846
.18849
9.27901
.27907
.27914
.27920
.19011
.19014
.19017
.19020
9.28291
.28297
.28304
.28310
.19183
.19185
.19188
.19191
9.28679
.28685
.28691
.28698
.19355
.19358
.19360
.19303
9.29064
.29071
.29078
.29084
.19527
.19530
.19533
.19536
^12
11
10
9
+ 13'
53
54
55
9.27535
.27541
.27548
.27554
.18852
.18854
.18857
.18860
9.27927
.27933
.27940
.27946
.13022
.19025
.19028
.19031
9.28317
.28323
.28330
.28336
.19194
.19197
.19200
.19203
9.28704
.28711
.28717
.28724
.19366
.19369
.19372
.19375
9.29090
.29096
.29103
.29109
.19539
.19542
.19545
.19548
8
7
6
5
+ 14'
57
58
59
9.27561
.27567
.27574
.27580
.18863
.18866
.18869
.18871
9.27953
.27959
.27966
.27972
.19034
.19037
.19040
.19042
9.28342
.28349
.28355
.28362
.19205
.19208
.19211
.19214
9.28730
.28737
.28743
.28749
.19378
.19381
.19383
.19386
9.29116
.29122
.29128
.29135
.19550
.19553
.19556
.19559
4
3
2
1
+ 15'
9.27587
.18874
9.27979
.19045
9.28368
.19217
9.28756
.19389
9.29141
.19562
0
SO* 34^
2Qh S3m
20 fc 32™
2Qh Sim
20h 30™
TABLE 45. [Page 853
Haversines.
s
3* 30m 52° 30'
3* Si™ 52° 45'
3* 32m 53° o'
3* 33^ 53° 15'
3* 34™ 53° 30'
s
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.29141
.29148
.29154
.29160
.19562
.19565
.19568
.19571
9.29524 .19735
.29531 i .19738
.29537 .19741
.29543 .19744
9.29906
.29912
.29918
.29925
.19909
.19912
.19915
.19918
9.30285
.30291
.30207
.30303
.20084
.20087
.20090
.20093
9.30662
.30668
.30674
.30680
.20259
.20202
.20265
.20268
60
59
58
57
+ 1'
5'
6
7
9.29167
.29173
.29180
.29186
.19573
.19576
.19579
.19582
9.29550
.29556
.29565*
.29569
.19747
.19750
.19753
.19756
9.29931
.29937
.29943
.29950
.19921
.19924
.19927
.19930
9.30310
;30316
.30322
.30329
.20095
.20098
.20101
.20104
9.30687
.30693
.30699
.30705
.20271
.20273
.20276
.20279
56
55
54
53
+ *'
9
10
11
9.29192
.29199
.29205
.29212
.19585
.19588
.19591
.19594
9.29575
.29582
.29588
.29594
.19758
.19761
.19764
.19767
9.29956
.29962
.29969
.29975
.19932
.19935
.19938
.19941
9.30335
.30341
.30348
.30354
.20107
.20110
.20113
.20116
9.30712
.30718
.30724
.30730
.20282
.20285
.20288
.20291
52
51
50
49
+ &
13
14
15
9.29218
.29224
.29231
.29237
.19597
.19599
.19602
.19605
9.29601
.29607
.29614
.29620
.19770
.19773
.19776
.19779
9.29981
.29988
.29994
.30000
.19944
.19947
.19950
.19953
9.30360
.30366
.30373
.30379
.20119
.20122
.20125
.20127
9.30737
.30743
.30749
.30755
.20294
.20297
.20300
.20303
43
47
46
45
+ *
17
18
19
9.29244
.29250
.29256
.29263
.19608
.19611
.19614
.19617
9.29626
.29633
.29639
.29645
.19782
.19785
.19787
.19790
9.30007
.30013
.30019
.30026
.19956
.19959
.19962
.19964
9.30385
.30392
.30398
.30404
.20130
.20133
.20136
.20139
9.30762
.30768
.30774
.30780
.20306
.20309
.20312
.20314
44
43
42
41
+ $'
21
22
23
9.29269
.29276
.29282
.29288
.19620
.19623
.19625
.19628
9.29652
.29658
.29664
.29671
.19793
.19796
.19799
.19802
9.30032
.30038
.30045
.30051
.19967
.19970
.19973
.19976
9.30410
.30417
.30423
.30429
.20142
.20145
.20148
.20151
9.30787
.30793
.30799
.30805
.20317
.20320
.20323
.20326
40
39
38
37
+ 6'
25
26
27
9.29295
.29301
.29307
.29314
.19631
.19634
.19637
.19640
9.29677
.29683
.29690
.29696
.19805
.19808
.19811
.19814
9.30057
.30064
.30070
.30076
.19979
.19982
.19985
.19988
9.30436
.30442
.30448
.30454
.20154
.20157
.20160
.20162
9.30812
.30818
.30824
.30830
.20329
.20332
.20335
.20338
36
35
34
33
+ r
29
SO
SI
9.29320
.29327
.29333
.29339
.19643
.19646
.19649
.19651
9.29703
.29709
.29715
.29722
.19816
.19819
.19822
.19825
9.30083
.30089
.30095
.30102
.19991
.19994
.19996
.19999
9.30461
.30467
.30473
.30480
.20165
.20168
.20171
.20174
9.30837
.30843
.30849
.30855
.20341
.20344
.20347
.20350
32
31
30
29
+ 8X
33
34
35
9.29346
.29352
.29359
.29365
.19654
.19657
.19660
.19663
9.29728
.29734
.29741
.29747
.19828
.19831
.19834
.19837
9.30108
.30114
.30121
.30127
.20002
.20005
.20008
.20011
9.30486
.30492
.30498
.30505
.20177
.20180
.20183
.20186
9.30862
.30868
.30874
.30880
.20352
.20355
.20358
.20361
28
27
26
25
+ V
37
38
39
9.29371
.29378
.29384
.29391
.19666
.19669
.19672
.19675
9.29753
.29760
.29766
.29772
.19840
.19842
.19845
.19848
9.30133
.30139
.30146
.30152
.20014
.20017
.20020
.20023
9.30511
.30517
.30524
.30530
.20189
.20192
.20195
.20198
9.30887
.30893
.30899
.30905
.20364
.20367
.20370
.20373
24
23
22
21
+ W
41
42
43
9.29397
.29403
.29410
.29416
.19677
.19680
.19683
.19686
9.29779
.29785
.29791
.29798
.19851
.19854
.19857
.19860
9.30158
.30165
.30171
.30177
.20026
.20028
.20031
.20034
9.30536
.30542
.30549
.30555
.20200
.20203
.20206
.20209
9.30912
.30918
.30924
.30930
.20376
.20379
.20382
.20385
20
19
18
17
+ 11'
45
46
47
9.29422
.29429
.29435
.29442
.19689
.19692
.19695
.19698
9.29804
.29810
.29817
.29823
.19863
.19866
.19869
.19872
9.30184
.30190
.30196
.30203
.20037
.20040
.20043
.20046
9.30561
.30567
.30574
.30580
.20212
.20215
.20218
.20221
9.30937 i .20388
.30943 .20391
.30949 .20393
.30955 .20396
16
15
14
13
'+ 12'
49
50
51
9.29448
.29454
.29461
.29467
.19701
.19703
.19706
.19709
9.29829
.29836
.29842
.29848
.19874
.19877
.19880
.19883
9.30209
.30215
.30222
.30228
.20049
.20052
.20055
.20058
9.30586
.30593
.30599
.30605
.20224
.20227
.20230
.20233
9.30962
.30968
.30974
.30980
.20399
.20402
.20405
.20408
11
11
10
9
+ 13'
53
54
55
9.29473
.29480
.29486
.29493
.19712
.19715
.19718
.19721
9.29855
.29861
.29867
.29874
.19886
.19889
.19892
.19895
9.30234
.30240
.30247
.30253
.20060
.20063
.20066
.20069
9.30611
.30618
.30624 i
.30630
.20235
.20238
.20241
.20244
9.30987
.30993
.30999
.31005
.20411
.20414
.20417
.20420
8
7
6
5
+ 14'
57
58
59
9.29499
.29505
.29512
.29518
.19724
.19727
.19730
.19732
9.29880
.29886
.29893
.29899
.19898
.19901
.19903
.19906
9.30259
.30266
.30272
.30278
.20072
.20075
.20078
.20081
9.30636 .20247
.30643 ! .20250
.30649; .20253
.30655 i .20256
9.31012
.31018
.31024
.31030
.20423
.20426
.20429
.20432
4
3
2
1
+ 15'
9.29524
.19735
9.29906 j .19909
9.30285
.20084
9.30662 j .20259
9.31036
.20435
0
20* 29™
*0fc«8«
20* %7m
20*26™
20* 25™
Page 854] TABLE 45.
Haversines.
s
$h 35m 53° 45'
3U sem 54° 0'
Sh 37m 54° 15'
3h 38m 54° 30'
Sh 39m 540 45/
s
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav.
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
0
1
3
9.31036
.31043
.31049
.31055
.20435
.20437
.20440
.20443
9.31409
.31416
.31422
.31428
.20611
.20614
.20617
.20620
9.31780
.31786
.31793
.31799
.20788
.20790
.20793
.20796
9.32149
.32155
.32161
.32168
.20965
.20968
.20971
.20974
9.32516
.32522
.32528
.32534
.21143
.21146
.21149
.21152
60
59
58
57
+ V
5
6
7
9.31061
.31068
.31074
.31080
.20446
.20449
.20452
.20455
9.31434
.31440
.31447
.31453
.20623
.20626
.20629
.20631
9.31805
.31811
.31817
.31823
.20799
.20802
.20805
.20808
9.32174
.32180
.32186
.32192
.20977
.20980
.20983
.20986
9.32541
.32547
.32553
.32559
.21155
.21158
.21161
.21164
56
55
54
53
+ w
9
10
11
9.31086
.31093
.31099
.31105
.20458
.20401
.20464
.20467
9.31459
.31465
.31471
.31478
.20634
.20637
.20640
.20643
9.31830
.31836
.31842
.31848
.20811
.20814
.20817
.20820
9.32198
.32204
.32210
.32217
.20989
.20991
.20994
.20997
9.32565
.32571
.32577
.32583
.21167
.21169
.21172
.21175
52
51
50
49
+ *'
13
14
15
9.31111
.31117
.31124
.31130
.20470
.20473
.20476
.20479
9.31484
.31490
.31496
.31502
.20646
.20649
.20652
.20655
9.31854
.31860
.31867
.31873
.20823
.20826
.20829
.20832
9.32223
.32229
.32235
.32241
.21000
.21003
.21006
.21009
9.32589
.32595
.32601
.32608
.21178
.21181
.21184
.21187
48
47
46
45
+ *'
17
18
19
9.31136
.31142
.31149
.31155
.20481
.20484
.20487
.20490
.20493
.20496
.20499
.20502
9.31508
.31515
.31521
.31527
.20658
.20661
.20664
.20667
9.31879
.31885
.31891
.31897
.20835
.20838
.20841
.20844
9.32247
.32253
.32259
.32266
.21012
.21015
.21018
.21021
9.32614
.32620
.32626
.32632
.21180
.21193
.21196
.21199
44
43
42
41
+ 5/
21
22
23
9.31161
.31167
.31173
.31180
9.31533
.31539
.31546
.31552
.20670
.20673
.20675
.20678
9.31903
.31910
.31916
.31922
.20847
.20850
.20852
.20855
9.32272
.32278
.32284
.32290
.21024
.21027
.21030
.21033
9.32638
.32644
.32650
.32656
.21202
.21205
.21208
.21211
40
39
38
37
+ 6'
25
26
27
9.31186
.31192
.31198
.31205
.20505
.20508
.20511
.20514
9.31558
.31564
.31570
.31577
.20681
.20684
.20687
.20690
9.31928
.31934
.31940
.31947
.20858
.20861
.20864
.20867
9.32296
.32302
.32308
.32315
.21036
.21039
.21042
.21045
9.32662
.32668
.32675
.32681
.21214
.21217
.21220
.21223
36
35
34
33
+ r
29
30
31
9.31211
.31217
.31223
.31229
.20517
.20520
.20523
.2G525
9.31583
.31589
.31595
.31601
.20693
.20696
.20699
.20702
9.31953
.31959
.31965
.31971
.20870
.20873
.20876
.20879
9.32321
.32327
.32333
.32339
.21048
.21051
.21054
.21057
9.32687
.32693
.32699
.32705
.21226
.21229
.21232
.21235
32
31
30
29
+ 8'
33
34
35
9.31236
.31242
.31248
.31254
.20528
.20531
.20534
.20537
9.31607
.31614
.31620
.31626
9.31632
.31638
.31644
• .31651
.20705
.20708
.20711
.20714
9.31977
.31983
.31990
.31996
9.32002
.32008
.32014
.32020
.20882
.20885
.20888
.20891
9.32345
.32351
.32357
.32363
.21060
.21063
.21066
.21069
9.32711
.32717
.32723
.32729
.21238
.21241
.21244
.21247
28
27
26
25
+ 9"
37
38
39
9.31260
.31267
.31273
.31279
.20540
.20543
.20546
.20549
.20717
.20720
.20723
.20726
.20894
.20897
.20900
.20903
9.32370
.32376
.32382
.32388
.21072
.21074
.21077
.21080
9.32735
.32741
.32748
.32754
.21250
.21253
.21256
.21259
24
23
22
21
+ 10'
41
42
43
9.31285
.31291
.31298
.31304
.20552
.20555
.20558
.20561
9.31657
.31663
.31669
.31675
.20729
.20731
.20734
.20737
9.32026
.32033
.32039
.32045
.20906-
.20909
.20912
.20915
9.32394
.32400
.32406
.32412
.21083
.21086
.21089
.21092
9.32760
.32766
.32772
.32778
.21262
.21265
.21268
.21271
20
19
18
17
+ 11'
45
46
47
9.31310
.31316
.31323
.31329
.20564
.20567
.20570
.20573
9.31682
.31688
.31694
.31700
.20740
.20743
.20746
.20749
9.32051
.32057
.32063
.32069
.20918
.20920
.20923
.20926
9.32418
.32425
.32431
.32437
.21095
.21098
.21101
.21104
9.32784
.32790
.32796
.32802
.21274
.21277
.21280
.21282
16
15
14
IS
+ 12'
49
50
51
9.31335
.31341
.31347
.31354
.20575
.20578
.20581
.20584
9.31706
.31712
.31719
.31725
.20752
.20755
.20758
.20761
9.32076
.32082
.32088
.32094
.20929
.20932
.20935
.20938
9.32443
.32449
.32455
.32461
.21107
.21110
.21113
.21116
9.32808
.32814
.32820
.32827
.21285
.21288
.21291
.21294
12
11
10
9
+ 13'
53
54
55
9.31360
.31366
.31372
.31378
.20587
.20590
.20593
.20596
9.31731
.31737
.31743
.31749
.20764
.20767
.20770
.20773
9.32100
.32106
.32112
.32119
.20941
.20944
.20947
.20950
9.32467
.32473
.32480
.32486
.21119
.21122
.21125
.21128
.21131
.21134
.21137
.21140
9.32833
.32839
.32845
.32851
.21297
.21300
.21303
.21306
8
7
6
5
+ U'
57
58
59
9.31385
.31391
.31397
.31403
.20599
.20602
.20605
.20608
9.31756
.31762
.31768
.31774
.20776
.20779
.20782
.20785
9.32125
.32131
.32137
.32143
.20953
.20956
.20959
.20962
9.32492
.32498
.32504
.32510
9.32857
.32863
.32869
.32875
.21309
.21312
.21315
.21318
4
3
2
1
+ 15'
9.31409
.20611
9.31780
.20788
9.32149
.20965
9.32516
.21143
9.32881
.21321
0
20*> 24m
20^ 23m
20^ 22m
20* 21**
20*>20m
TABLE 45. [Page 855
Haversines.
s
1 3* 40™ 55° V
3h 4im 55° 15'
3* 4?™ 55° W
Sk 43™ 55° 45'
3k 44m 56° 0'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav. Nat. Hav.
Log. Hav.! Xat. Hav
Log. Hav.
Nat. Hav
0
1
2
3
9.32881
.32887
.32893
.32899
.21321
.21324
.21327
.21330
9.33244
.33250
.33256
.33262
.21500
.21503
.21506
.21509
9.33605
.33611
.33617
.33623
.21680
.21683
.21686
.21689
9.33965
.33971
.33976
.33982
.21860
.21863
.21866
i .21869
9.34322
.34328
.34334
.34340
.22040
.22043
.22046
.22049
60
59
58
57
+ 1'
5
6
7
9.32905
.32911
.32918
.32924
.21333
.21336
.21339
.21342
9.33268- .21512
.33274 .21515
.33280 .21518
.33286 .21521
9.33629
.33635
.33641
.33647
.21692
.21695
.21G98
.21701
9.33988
.33994
.34000
.34006
.21872
.21875
.21878
.21881
9.34346
.34352
.34358
.34363
.22052
.22055
.22058
.22061
56
55
54
53
+ V
9
10
11
9.32930
.32936
.32942
.32948
.21345
.21348
.21351
.21354
9.33292 .21524
.33298 .21527
.33305 .21530
.33311 .21533
9.33653
.33659
.33665
.33671
.21704
.21707
.21710
.21713
9.34012 ! .21884
.34018 ! .21887
.34024 ! .21890
.34030 ! .21893
9.34369
.34375
.34381
.34387
.22064
.22067
.22071
.22074
52
51
50
49
+ 3'
13
14
15
9.32954
.32960
.32966
.32972
.21357
.21360
.21363
.21366
9.33317 .21536
.33323 .21539
.33329 .21542
.33335 .21545
9.33677
.33683
.33689
.33695
.21716
.21719
.21722
.21725
9.34036
.34042
.34048
.34054
.21896
.21899
.21902
.21905
9.34393
.34399
.34405
.34411
.22077
.22080
.22083
.22086
48
47
46
45
+ 4'
17
18
19
9.32978
.32984
.32990
.32996
.21369
.21372
.21375
.21378
9.33341
.33347
.33353
.33359
.21548
.21551
.21554
.21557
9.33701
.33707
.33713
.33719
.21728
.21731
.21734
.21737
9.34060
.34066
.34072
.34078
.21908
.21911
.21914
.21917
9.34417
.34423
.34429
.34435
.22089
.22092
.22095
.22098
44
43
42
41
+ 5'
21
22
23
9.33002
.33008
.33014
.33021
.21381
.21384
.21387
.21390
9.33365
.33371
.33377
.33383
.21560
.21563
.21566
.21569
9.33725
.33731
.33737
.33743
.21740
.21743
.21746
.21749
9.34084
.34090
.34096
.34102
.21920
.21923
.21926
.21929
9.34441
.34446
.34452
.34458
.22101
.22104
.22107
.22110
40
39
38
37
+ 6'
25
26
27
9.33027
.33033
.33039
.33045
.21393
.21396
.21399
.21402
9.33389
.33395
.33401
.33407
.21572
.21575
.21578
.21581
9.33749
.33755
.33761
.33767
.21752
.21755
.21758
.21761
9.34108
.34114
.34120
.34126
.21932
.21935
.21938
.21941
9.34464
.34470
.34476
.34482
.22113
.22116
.22119
.22122
36
35
34
33
+ v
29
. 30
31
9.33051
.33057
.33063
.33069
.21405
.21408
.21411
.21414
9.33413
.33419
.33425
.33431
.21584
.21587
.21590
.21593
9.33773
.33779
.33785
.33791
.21764
.21767
.21770
.21773
9.34132
.34137
.34143
.34149
.21944
.21947
.21950
.21953
9.34488
.34494
.34500
.34506
.22125
.2212.a
!22131
.22134
St
31
30
29
+ 8'
33
34
35
9.33075
.33081
.33087
.33093
.21417
.21420
.21423
.21426
9.33437
.33443
.33449
.33455
.21596
.21599
.21602
.21605
9.33797
.33803
.33809
.33815
.21776
.21779
.21782
.21785
9.34155
.34161
.34167
.34173
.21956
.21959
.21962
.21965
9.34512
.34518
.34524
.34529
.22137
.22140
.22143
.22146
28
27
26
25
+ 9'
37
38
39
9.33099
.33105
.33111
.33117
.21429
.21431
.21434
.21437
9.33461
.33467
.33473
.33479
.21608
.21611
.21614
.21617
9.33821
.33827
.33833
.33839
.21788
.21791
.21794
.21797
9.34179
.34185
.34191
.34197
.21968
.21971
.21974
.21977
9.34535
.34541
.34547
.34553
.22149
.22152
.22155
.22158
t4
23
22
21
+ W
41
42 '
43
9.33123
.33129
.33135
.33142
.21440
.21443
.21446
.21449
9.33485
.33491
.33497
.33503
.21620
.21623
.21626
.21329
9.33845
.33851
.33857
.33863
.21800
.21803
.21806
.21809
9.34203
.34209
.34215
.34221
.21980
.21983
.21986
.21989
9.34559
.34565
.34571
.34577
.22161
.22164
.22167
.22170
20
19
18
17
+ 11'
45
46
47
9.33148
.33154
.33160
.33166
.21452
.21455
.21458
.21461
9.33509
.33515
.33521
.33527
.21632
.21635
.21638
.21641
9.33869
.33875
.33881
.33887
.21812
.21815
.21818
.21821
9.34227
.34233
.34239
.34245
.21992
.21995
.21998
.22001
9.34583
.34589
.34595
.34600
.22173
.22176
.22179
.22182
16
15
14
13
+ 12'
49
50
51
9.33172
.33178
.33184
.33190
.21464
.21467
.21470
.21473
9.33533
.33539
.33545
.33551
.21644
.21647
.21650
.21653
9.33893
.33899
.33905
.33911
.21824
.21827
.21830
.21833
9.34251
.34256
.34262
.34268
.22004
.22007
.22010
.22013
9.34606
.34612
.34618
.34624
.22185
.22188
.22191
.22194
12
11
10
9
+ 13'
53
54
55
9.33196
.33202
.33208
.33214
.21476
.21479
.21482
.21485
9.33557
.33563
.33569
.33575
.21656
.21659
.21662
.21665
9.33917
.33923
.33929
.33935
.21836
.21839
.21842
.21845
9.34274
.34280
.34286
.34292
.22016
.22019
.22022
.22025
9.34630
.34636
.34642
.34648
.22197
.22200
.22203
.22206
8
7
6
5
+ 14'
57
58
59
9.33220
.33226
.33232
.33238
.21488
.21491
.21494
.21497
9.33581
.33587
.33593
.33599
.21668
.21671
.21674
.21677
9.33941
.33947
.33953
.33959
.21848
.21851
.21854
.21857
9.34298
.34304
34310
.34316
.22028
.22031
.22034
.22037
9.34654
.34660
.34666
.34671
.22209
.22212
.22215
.22218
4
3
o
1
+ 15'
9.33244
.21500
9.33605 .21680
9.33965
.21860
9.34322 .22040
9.34677
.22221
0
•20k igm
20k 18™
20^ ijm
20k i&n
20k ism
Page 856] TABLE 45.
Haversines.
s
3k 45™ 56° 15'
3k 46^ 56° 307
Sh 47m 56° 45'
3k 43™ 57° 0'
3k 49m 57° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat .Hav.
0
1
2
3
9.34677
.34683
.34689
.34695
.22221
.22225
.22228
.22231
9.35031
.35037
.35043
.35049
.22403
.22406
.22409
.22412
9.35383
.35389
.35394
.35400
.22585
.22588
.22591
.22594
9.35733
.35738
.35744
.35750
.22768
.22771
.22774
.22777
9.36081
.36086
.36092
.36098
.22951
.22954
.22957
.22960
60
59
58
57
+ 1'
5
6
7
9.34701
.34707
.34713
.34719
.22234
.22237
.22240
.22243
9.35054
.35060
.35066
.35072
.22415
.22418
.22421
.22424
9.35406
.35412
.35418
.35424
.22598
.22601
.22604
.22607
9.35756
.35762
.35767
.35773
.22780
.22783
.22786
.22789
9.36104
.36110
.36115
.36121
.22964
.22967
.22970
.22973
56
55
54
53
+ v
9
10
11
9.34725
.34730
.34736
.34742
.22246
.22249
.22252
.22255
9.35078
.35084
.35090
.35096
.22427
.22430
.22433
.22437
9.35429
.35435
.35441
.35447
.22610
.22613
.22616
.22619
9.35779
.35785
.35791
.35797
.22792
.22795
.22799
.22802
9.36127
.36133
.36139
.36144
.22976
.22979
.22982
.22985
52
51
50
49
+ v
13
14
15
9.34748
.34754
.34760
.34766
.22258
.22261
.22264
.22267
9.35101
.35107
.35113
.35119
.22440
.22443
.22446
.22449
9.35453
.35459
.35464
.35470
.22622
.22625
.22628
.22631
9.35802
.35808
.35814
.35820
.22805
.22808
.22811
.22814
9.36150
.36156
.36162
.36167
.22988
.22991
.22994
.22997
48
47
46
45
+ 4'
11
18
19
9.34772
.34778
.34784
.34789
.22270
.22273
.22276
.22279
9.35125
.35131
.35137
.35143
.22452
.22455
.22458
.22461
9.35476
.35482
.35488
.35494
.22634
.22637
.22640
.22643
9.35826
.35831
.35837
.35843
.22817
.22820
.22823
.22826
9.36173
.36179
.36185
.36191
.23000
.23003
.23006
.23009
44
43
42
41
+ 5'
21
22
23
9.34795
.34801
.34807
.34813
.22282
.22285
.22288
.22291
9.35148
.35154
.35160
.35166
.22464
.22467
.22470
.22473
9.35500
.35505
.35511
.35517
.22646
.22649
.22652
.22655
9.35849
.35855
.35860
.35866
.22829
.22832
.22835
.22838
9.36196
.36202
.36208
.36214
.23012
.23016
.23019
.23022
40
39
38
37
+ &
25
26
27
9.34819
.34825
.34831
.34837
.22294
.22297
.22300
.22303
9.35172
.35178
.35184,
.35189
.22476
.22479
.22482
.22485
9.35523
.35529
.35535
.35540
.22658
.22661
.22664
.22667
9.35872
.35878
.35884
.35889
.22841
.22844
.22847
.22850
9.36219
.36225
.36231
.36237
.23025
.23028
.23031
.23034
36
35
34
33
+ v
29
30
31
9.34843
.34848
.34854
.34860
.22306
.22309
.22312
.22315
9.35195
.35201
.35207
.35213
.22488
.22491
.22494
.22497
9.35546
.35552
.35558
.35564
.22671
.22674
.22677
.22680
9.35895
.35901
.35907
.35913
.22853
.22857
.22860
.22863
9.36243
.36248
.36254
.36260
.23037
.23040
.23043
.23046
32
31
30
29
+ 8'
33
34
35
9.34866
.34872
.34878
.34884
.22318
.22321
.22324
.22327
9.35219
.35225
.35230
.35236
.22500
.22503
.22506
.22509
9.35570
.35575
.35581
.35587
.22683
.22686
.22689
.22692
9.35918
.35924
.35930
.35936
.22866
.22869
.22872
.22875
9.36266
.36271
.36277
.36283
.23049
.23052
.23055
.23058
28
27
26
25
+ - 9'
37
38
39
9.34890
.34896
.34901
.34907
.22330
.22333
.22336
.22340
9.35242
.35248
.35254
.35260
.22512
.22515
.22518
.22522
.22525
.22528
.22531
.22534
9.35593
.35599
.35604
.35610
.22695
.22698
.22701
.22704
9.35942
.35947
.35953
.35959
.22878
.22881
.22884
.22887
9.36289
.36294
.36300
.36306
.23061
.23065
.23068
.23071
24
23
22
21
+ 10'
41
42
43
9.34913
.34919
.34925
.34931
.22343
.22346
.22349
.22352
9.35266
.35271
.35277
.35283
9.35616
.35622
.35628
.35634
.22707
.22710
.22713
.22716
9.35965
.35971
.35976
.35982
.22890
.22893
.22896
.22899
9.36312
.36318
.36323
.36329
.23074
.23077
.23080
.23083
20
19
18
17
+ 11'
45
46
47
9.34937
.34943
.34949
.34954
.22355
.22358
.22361
.22364
9.35289
.35295
.35301
.35307
.22537
.22540
.22543
.22546
9.35639
.35645
.35651
.35657
.22719
.22722
.22725
.22728
9.35988
.35994
.36000
.36005
.22902
.22905
.22908
.22912
9.36335
.36341
.36346
.36352
.23086
.23089
.23092
.23095
16
15
14
13
+ 12'
49
50
51
9.34960
.34966
.34972
.34978
.22367
.22370
.22373
.22376
9.35312
.35318
.35324
.35330
.22549
.22552
.22555
.22558
9.35663
.35669
.35674
.35680
.22731
.22735
.22738
.22741
9.36011
.36017
.36023
.36029
.22915
.22918
.22921
.22924
9.36358
.36364
.36369
.36375
.23098
.23101
.23104
.23107
12
11
10
9
+ 13'
53
54
55
9.34984
.34990
.34996
.35002
.22379
.22382
.22385
.22388
9.35336
.35342
.35348
.35353
.22561
.22564
.22567
.22570
9.35686
.35692
.35698
.35703
.22744
.22747
.22750
.22753
9.36034
.36040
.36046
.36052
9736058
.36063
.36069
.36075
.22927
.22930
.22933
.22936
9.36381
.36387
.36392
.36398
.23110
.23114
.23117
.23120
8
7
6
5
+ 14'
57
58
59
9.35007
.35013
.35019
.35025
.22391
.22394
.22397
.22400
9.35359
.35365
.35371
.35377
.22573
.22576
.22579
.22582
9.35709
.35715
.35721
.35727
.22756
.22759
.22762
.22765
.22939
.22942
.22945
.22948
.22951
9.36404
.36410
.36415
.36421
.23123
.23126
.23129
.23132
4
3
2
1
+ 15'
9.35031
.22403
9.35383
.22585
9.35733
.22768
9.36081
9.36427
.23135
0
20*> i4m
2Qk 13m
20^ 12m
20k urn
20k iom
TABLE 45. [Page 857
Haversines.
<?& 50m 57° 307
3* 5im 57° 45'
3* 52m 58° <K
3* 53m 58° 15'
S* 54m 58° 3(K
s
s
Log.Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav.
Log.Hav. Nat. Hav.
Log. Hav.
Nat Hav.
0
1
2
3
9.36427
.36433
.36439
.36444
.23135
.23138
.23141
.23144
9.36772
.36777
.36783
.36789
.23319
.23322
.23325
.23329
9.37114
.37120
.37126
.37131
.23504
.23507
.23510
.23513
9.37455
.37461
.37467
.37472
.23689
.23692
.23695
.23699
9.37794
.37800
.37806
.37811
.23875
.23878
.23881
.23884
60
59
58
57
56
55
54
53
+ 1'
5
6
7
9.36450
.36456
.36462
.36467
.23147
.23150
.23153
.23156
9.36794
.36800
.36806
.36812
.23332
.23335
.23338
.23341
9.37137
.37143
.37148
.37154
.23516
.23519
.23523
.23526
9.37478
.37484
.37489
.37495
.23702
.23705
.23708
.23711
9.37817
.37823
.37828
.37834
.23887
.23891
.23894
.23897
+ y
9
10
11
9.36473
.36479
.36485
.36490
.23160
.23163
.23166
.23169
9.36817
.36823
.36829
.36834
.23344
.23347
.23350
.23353
9.37160
.37166
.37171
.37177
.23529
.23532
.23535
.23538
9.37501
.37506
.37512
.37518
.23714
.23717
.23720
.23723
9.37840
.37845
.37851
.37856
.23900
.23903
.23906
.23909
52
51
50
49
+ 3'
13
14
15
9.36496
.36502
.36508
.36513
.23172
.23175
.23178
.23181
9.36840
.36846
.36852
.36857
.23356
.23359
.23362
.23365
9.37183
.37188
.37194
.37200
.23541
.23544
.23547
.23550
9.37523
.37529
.37535
.37540
.23726
.23729
.23733
.23736
9.37862
.37868
.37873
.37879
.23912
.23915
.23918
.23922
48
47
46
45
+ 4'
17
18
19
9.36519
.36525
.36531
.36536
.23184
.23187
.23190
.23193
9.36863
.36869
.36875
.36880
.23368
.23372
.23375
.23378
9.37205
.37211
.37217
.37222
.23553
.23556
.23560
.23563
9.37546
.37552
.37557
.37563
.23739
.23742
.23745
.23748
9.37885
.37890
.37896
.37902
.23925
.23928
.23931
.23934
44
43
42
41
+ V
21
22
23
9.36542
.36548
.36554
.36559
.23196
.23199
.23203
.23206
9.36886
.36892
.36897
.36903
.23381
.23384
.23387
.23390
9.37228
.37234
.37239
.37245
.23566^
.23569
.23572
.23575
9.37569
.37574
.37580
.37585
.23751
.23754
.23757
.23760
9.37907
.37913
.37918
.37924
.23937
.23940
.23943
.23946
40
39
38
37
+ 6'
25
26
27
9.36565
.36571
.36577
.36582
.23209
.23212
.23215
.23218
9.36909
.36915
.36920
.36926
.23393
.23396
.23399
.23402
9.37251
.37257
.37262
.37268
.23578
.23581
.23584
.23587
9.37591
.37597
.37602
.37608
.23764
.23767
.23770
.23773
9.37930
.37935
.37941
.37947
.23950
.23953
.23956
.23959
36
35
34
33
+ v
•29
30
31
9.36588 i .23221
.36594 .23224
.36599 .23227
.36605 1 .23230
9.36932
.36937
.36943
.36949
.23405
.23409
.23412
.23415
9.37274
.37279
.37285
.37291
.23590
.23594
.23597
.23600
9.37614
.37619
.37625
.37631
.23776
.23779
.23782
.23785
9.37952
.37958
.37963
.37969
.23962
.23965
.23968
.23971
32
31
SO
29
+ 8'
34
35
9.36611
.36617
.36622
.36628
.23233
.23236
.23239
.23242
9.36955
.36960
.36966
.36972
.23418
.23421
.23424
.23427
9.37296
.37302
.37308
.37313
.23603
.23606
.23609
.23612
9.37636
.37642
.37648
.37653
.23788
.23791
.23795
.23798
9.37975
.37980
.37986
.37992
.23974
.23977
.23981
.23984
28
27
26
25
24
23
.:
21
+ r
37
38
39
9.36634
.36640
.36645
.36651
.23246
.23249
.23252
.23255
9.36977
.36983
.36989
.36995
.23430
.23433
.23436
.23439
9.37319
.37325
.37330
.37336
.23615
.23618
.23621
.23624
9.37659
.37665
.37670
.37676
.23801
.23804
.23807
.23810
9.37997
.38003
.38008
.38014
.23987
.23990
.23993
.23996
+ W
41
42
43
9.36657
.36663
.36668
.36674
.23258
.23261
.23204
.23267
9.37000
.37006
.37012
.37017
.23442
.23445
.23449
.23452
9.37342
.37347
.37353
.37359
.23627
.23631
.23634
.23637
9.37682
.37687
.37693
.37699
.23813
.23816
.23819
.23822
9.3S020
.38025
.38031
.38037
.23999
.24002
.24005
.24009
20
19
18
17
+ 11'
45
46
47
9.36680
.36686
.36691
.36697
.23270
.23273
.23276
.23279
9.37023 i .23455
.37029: .23458
.37034: .23461
.37040 .23464
9.37364 ! .23640
.37370 .23643
.37376 .23646
.37382 .23649
9.37704
.37710
.37715
.37721
.23825
.23829
.23832
.23835
9.38042
.38048
.38053
.38059
.24012
.24015
.24018
.24021
16
15
14
13
+ 12'
49
50
51
9.36703 .23282
.36708 .232,85
.36714 .23239
.36720; .23292
9.37046 .23467
.37052 .23470
.37057 .23473
.37063 .23476
9.37387 .23652
.37393 .23655
.37399: .23658
.37404 .23661
9.37727
.37732
.37738
.37744
.23838
.23841
.23844
.23847
9.38065
.38070
.38076
.38081
.24024
.24027
.24030
.24033
.24036
.24040
.24043
.24046
12
11
10
9
+ 13'
53
54
55
9.36726
.36731
.36737
.36743
.23295
.23298
.23301
.23304
9.37069 .23479
.37074 .23482
.37080 .23486
.370S6 .23489
9.37410 .23665
.37416 .23668
.37421 .23671
.37427 .23674
9.37749
.37755
.37761
.37766
.23850
.23853
.23856
.23860
9.38087
.38093
.38098
.38104
8
7
6
5
+ 14'
57
58
59
9.36749
.36754
.36760
.36766
.23307
.23310
.23313
.23316
9.37091 .23492
.37097 .23495
.37103 .23498
.37109 .23501
9.37433 .23677
.37438 .23680
.37444 .23683
.37450 .23686
9.37772
.37778
.37783
.37789
.23863
.23866
.23869
.23872
9.38110
.38115
.38121
.38126
.24049
.24052
.24055
.24058
4
3
2
1
+ 15'
9.36772
.23319
9.37114 .23504
9.37455 i .23689
9.37794
.23875
9.38132
.24061
0
20* 9^
20* 8™>
20* 7m
20* 6^
20* 5m
61828°— 16 47
Page 858] TABLE 45.
Haversines.
s
3h 55™ 58° 45'
3fc 56™ 59° 0'
3*> 57m 59° 15'
3* 58™ 59° 30'
3h 59^ 59° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
9.38132
.38138
.38143
.38149
.24061
.24064
.24068
.24071
9.38468
.38473
.38479
.38485
.24248
.24251
.24254
.24257
9.38802
.38807
.38813
.38819
.24435
.24438
.24442
.24445
9.39134
.39140
.39145
.39151
.24623
.24626
.24629
.24633
9.39465
.39470
.39476
.39481
.24811
.24814
.24818
.24821
60
59
58
57
+ 1'
5
6
7
9.38154
.38160
.38166
.38171
.24074
.24077
.24080
.24083
9.38490
.38496
.38501
.38507
.24261
.24264
.24267
.24270
9.38824
.38830
.38835
.38841
.24448
.24451
.24454
.24457
9.39156
.39162
.39167
.39173
.24636
.24639
.24642
.24645
9.39487
.39492
.39498
.39503
.24824
.24827
.24830
.24833
56
55
54
53
+ %'
9
10
11
9.38177
.38182
.38188
.38194
.24086
.24089
.24092
.24096
9.38512
.38518
.38524
.38529
.24273
.24276
.24279
.24282
9.38846
.38852
.38857
.38863
.24460
.24463
.24467
.24470
9.39178
.39184
.39189
.39195
.24648
.24651
.24654
.24658
.24661
.24664
.24667
.24670
9.39509
.39514
.39520
.39525
.24836
.24840
.24843
.24846
52
51
50
49
+ 3'
13
14
15
9.38199
.38205
.38210
.38216
.24099
.24102
.24105
.24108
9.38535
.38540
.38546
.38551
.24286
.24289
.24292
.24295
9.38868
.38874
.38880
.38885
.24473
.24476
.24479
.24482
9.39201
.39206
.39212
.39217
9.39531
.39536
.39542
.39547
.24849
.24852
.24855
.24858
48
47
46
45
+ 4'
17
18
19
9.38222
.38227
.38233
.38239
.24111
.24114
.24117
.24120
9.38557
.38563
.38568
.38574
.24298
.24301"
.24304
.24307
9.38891
.38896
.38902
.38907
.24485
.24488
.24492
.24495
9.39223
.39228
.39234
.39239
.24673
.24676
.24680
.24683
9.39553
.39558
.39564
.39569*
.24862
.24865
.24868
.24871
44
43
42
41
+ $'
21
22
23
9.38244
.38250
.38255
.38261
.24124
.24127
.24130
.24133
9.38579
.38585
.38590
.38596
.24310
.24314
.24317
.24320
9.38913
.38918
.38924
.38929
.24498
.24501
.24504
.24507
9.39245
.39250
.39256
.39261
.24686
.24689
.24692
.24695
9.39575
.39580
.39586
.39591i
.24874
.24877
.24880
^•-.24884
40
39
38
37
+ v
25
26
27
9.38267
.38272
.38278
.38283
.24136
.24139
.24142
.24145
9.38602
.38607
.38613
.38618
.24323
.24326
.24329
.24332
9.38935
.38941
.38946
.38952
.24510
.24514
.24517
.24520
9.39267
.39272
.39278
.39283
.24698
.24701
.24705
.24708
9.39597
.39602
.39608
.39613
.24887
.24890
.24893
.24896
36
35
34
33
+ v
29
30
31
9.38289
.38295
.38300
.38306
.24148
.24152
.24155
.24158
9.38624
.38629
.38635
.38641
.24335
.24339
.24342
.24345
9.38957
.38963
.38968
.38974
.24523
.24526
.24529
.24532
9.39289
.39294
.39300
.39305
.24711
.24714
.24717
.24720
9.39619
.39624
.39630
.39635
.24899
.24902
.24906
.24909
32
31
30
29
+ 8'
33
34
35
9.38311
.38317
.38322
.38328
.24161
.24164
.24167
.24170
9.38646
.38652
.38657
.38663
.24348
.24351
.24354
.24357
9.38979
.38985
.38990
.38996
.24535
.24539
.24542
.24545
9.39311
.39316
.39322
.39327
.24723
.24727
.24730
.24733
9.39641
.39646
.39652
.39657
.24912
.24915
.24918
.24921
28
27
26
25
+ 9'
37
38
39
9.38334
.38339
.38345
.38350
.24173
.24176
.24180
.24183
.24186
.24189
.24192
.24195
9.38668
.38674
.38680
.38685
.24360
.24364
.24367
.24370
9.39002
.39007
.39013
.39018
.24548
.24551
.24554
.24557
9.39333
.39338
.39344
.39349
.24736
.24739
.24742
.24745
9.39663
.39668
.39674
.39679
.24924
.24928
.24931
.24934
24
23
22
21
+ 10'
41
42
43
9.38356
.38362
.38367
.38373
9.38691
.38696
.38702
.38707
.24373
.24376
.24379
.24382
9.39024
.39029
.39035
.39040
.24560
.24564
.24567
.24570
9.39355
.39360
.39366
.39371
.24749
.24752
.24755
.24758
9.39685
.39690
.39695
.39701
.24937
.24940
.24943
.24946
20
19
18
17
+ llx
45
46
47
9.38378
.38384
.38390
.38395
.24198
.24201
.24204
.24208
9.38713
.38719
.38724
.38730
.24385
.24388
.24392
.24395
9.39046
.39051
.39057
.39062
.24573
.24576
.24579
.24582
9.39377
.39382
.39388
.39393
.24761
.24764
.24767
.24770
9.39706
.39712
.39717
.39723
.24950
.24953
.24956
.24959
16
15
14
13
+ 13'
49
50
51
9.38401
.38406
.38412
.38418
.24211
.24214
.24217
.24220
9.38735
.38741
.38746
.38752
.24398
.24401
.24404
.24407
9.39068
.39073
.39079
.39085
.24586
.24589
.24592
.24595
9.39399
.39404
.39410
.39415
.24774
.24777
.24780
.24783
9.39728
.39734
.39739
.39745
.24962
.24965
.24969
.24972
12
11
10
9
+ 13'
53
54
55
9.38423
.38429
.38434
.38440
.24223
.24226
.24229
.24233
9.38757
.38763
.38769
.38774
.24410
.24413
.24417
.24420
9.39090
.39096
.39101
.39107
.24598
.24601
.24604
.24607
9.39421
.39426
.39432
.39437
,24786
.24789
.24792
.24796
9.39750
.39756
.39761
.39767
.24975
.24978
.24981
.24984
8
7
6
5
+ 14'
57
58
59
9.38445
.38451
.38457
.38462
.24236
.24239
.24242
.24245
9.38780
.38785
.38791
.38796
.24423
.24426
.24429
.24433
9.39112
.39118
.39123
.39129
.24611
.24614
.24617
.24620
9.39443
.39448
.39454
.39459
.24799
.24802
.24805
.34808
9.39772
.39778
.39783
.39789
.24987
.24991
.24994
.24997
4
3
2
1
+ 15'
9.38468
.24248
9.38802
.24435
9.39134
.24623
9.39465
.24811
9.39794
.25000
0
20*4™
zo^s™
20^2™
2 Oh lm
20*>0™
TABLE 45. [Page 859
Haversines.
s
4 ft tfw 60° (K
4h im 60° 15'
4h 2m 60° 30'
4* Sm 60° 45'
4* 4m 61° 0/
s
Los. Hav. Nat. Hav.
Log.HavJXat.Hav.
Log. Hav.; Nat. Hav.
Log.Hav. Nat. Hav.
Log. Hav. Nat. Hav.
0
1
2
S
9.39794
.39799
.39805
.39810
.25000
.25003
.25006
.25009
9.40121 .25189
.40127 ! .25192
.40132 .25195
.40138 .25199
9.40447
.40453
.40458
.40463
.25379
.25382
.25385
.25388
9.40771 .25569
.40777 .25572
.40782 .25575
.40787 .25578
9.41094
.41099
.41105
.41110
.25760
.25763
.25766
.25769
60
59
58
57
+ 1'
5
6
7
9.39816
.39821
.39827
.39832
.25013
.25016
.25019
.25022
9.40143 .25202
.40149 .25205
.40154 .35208
.40159 .25211
9.40469
.40474
.40480
.40485
.25391
.25395
.25398
.25401
9.40793
.40798
.40804
.40809
.25582
.25585
.25588
.25591
9.41115
.41121
.41126
.41131
.25772
.25775
.25779
.25782
56
55
54
53
-f 2'
9
10
11
9.39838
.39843
.39849
.39854
.25025
.25028
.25032
.25035
9.40165 j .25214
.40170 i .25218
.40176 .25221
.40181 .25224
9.40490
.40496
.40501
.40507
.25404
.25407
.25410
.25414
9.40814
.40820
.40825
.40831
.25594
.25597
.25601
.25604
9.41137
.41142
.41147
.41153
.25785
.25788
.25791
.25795
52
51
50
49
+ -*-
15
14
15
9.39860
.39865
.39871
.39876
.25038
.25041
.25044
.25047
9.40187
.40192
.40198
.40203
.25227
.25230
.25233
.25237
9.40512
.40518
.40523
.40528
.25417
.25420
.25423
.25426
9.40836
.40841
.40847
.40852
.25607
.25610
.25613
.25617
9.41158
.41163
.41169
.41174
.25798
.25801
.25804
.25807
4£
47
46
45
+ *'-•
17
15
19
9.39881
.39887
.39892
.39898
.25050
.25054
.25057
.25060
9.40208
.40214
.40219
.40225
.25240
.25243
.25246
.25249
9.40534
.40539
.40545
.40550
.25429
.25433
.25436
.25439
9.40858
.40863
.40868
.40874
.25620
.25623
.25626
.25629
9.41180
.41185
.41190
.41196
.25810
.25814
.25817
.25820
44
43
42
41
+ 5/
;?!
22
23
9.39903
.39909
.39914
.39920
.25063
.25066
.25069
.25072
9.40230
.40236
.40241
.40246
.25252
.25255
.25259
.25262
9.40555
.40561
.40566
.40572
.25442
.25445
.25448
.25452
9.40879
.40884
.40890
.40895
.25632
.25636
.25639
.25642
9.41201
.41206
.41212
.41217
.25823
.25826
.25830
.25833
40
39
38
37
+ &
25
26
27
9.39925
.39931
.39936
.39942
.25076
.25079
.25082
.25085
9.40252
.40257
.40263
.40268
.25265
.25268
.25271
.25274
9.40577
.40582
.40588
.40593
.25455
.25458
.25461
.25464
9.40900
.40906
.40911
40917
.25645
.25648
.25651
.25655
9.41222
.41228
.41233
.41238
.25836
.25839
.25842
.25845
36
35
34
33
+ V
29
30
31
9.39947
.39952
.39958
.39963
.25088
.25091
.25095
.25098
9.40274
.40279
.40284
.40290
.25278
.25281
.25284
.25287
9.40590
.40604
.40609
.40615
.25467
.25471
.25474
.25477
9.40922
.40927
.40933
.40938
.25658
.25661
.25664
.25667
9.41244
.41249
.41254
.41260
.25849
.25852
.25855
.25858
St
31
30
29
+ 8'
S3
34
35
9.39969
.39974
.39980
.39985
.25101
.25104
.25107
.25110
9.40295
.40301
.40306
.40312
.25290
.25293
.25297
.25300
9.40620
.40626
.40631
.40636
.25480
.25483
.25487
.25490
9.40943
.40949
.40954
.40960
.25671
.25674
.25677
.25680
9.41265
.41270
.41276
.41281
.25861
.25865
.25868
.25871
28
27
26
25
+ &
37
38
39
9.39991
.39996
.40002
.40007
.25113
.25117
.25120
.25123
9.40317
.40322
.40328
.40333
.25303
.25306
.25309
.25312
9.40642
.40647
.40653
.40658
.25493
.25496
.25499
.25502
9.40965
.40970
.40976
.40981
.25683
.25686
.25690
.25693
9.41287
.41292
.41297
.41303
.25874
.25877
.25880
.25884
24
23
22
21
+ KK
41
4~?
43
9.40012
.40018
.40023
.40029
.25126
.25129
.25132
.25136
9.40339
.40344
.40350
.40355
.25316
.25319
.25322
.25325
9.40663
.40669
.40674
.40680
.25506
.25509
.25512
.25515
9.40986
.40992
.40997
.41003
.25696
.25699
.25702
.25705
9.4130S
.41313
.41319
.41324
.25887
.25890
.25893
.25896
20
19
18
17
+ llx
45'
4£
47
9.40034
.40040
.40045
.40051
.25139
.25142
.25145
.25148
9.40360
.40366
.40371
.40377
.25328
.25331
.25335
.25338
9.40685
.40690
.40696
.40701
.25518
.25521
.25525
.25528
9.41008
.41013
.41019
.41024
.25709
.25712
.25715
.25718
9.41329 ' .25900
.41335 i .25903
.41340 i .25906
.41345 .25909
16
15
14
13
+ 12'
49
50
51
9.40056
.40062
.40067
.40071!
.25151
.25154
.25158
.25161
9.40382
.40388
.40393
.40398
.25341
.25344
.25347
.25350
9.40707
.40712
.40717
.40723
.25531
.25534
.25537
.25540
9.41029
.41035
.41040
.41046
.25721
.25724
.25728
.25731
9.41351
.41356
.41361
.41367
.25912
.25915
.25919
.25922
It
11
10
9
+ 13'
55
54
55
9.40078
.40083
.40089
.40094
.25164
.25167
.25170
.25173
9.40404
.40409
.40415
.40420
.25354
.25357
.25360
.25363
9.4072S
.40734
.40739
.40744
.25544
.25547
.25550
.25553
9.41051
.41056
.41062
.41067
.25734
.25737
.25740
.25744
9.41372
.41377
.41383
.41388
.25925
.25928
.25931
.25935
8
M
/
6
5
+ 14'
57
55
59
9.40100
.40105
.40111
.40116
.25177
.25180
.25183
.25186
9.40425
.40431
.40436
.40442
.25366
.25369
.25372
.25376
9.40750
.40755
.40761
.40766
.25556
.25559
.25563
.25566
9.41072
.41078
.41083-
.41088
.25747
.25750
.25753
.25756
9.41393
.41399
.41404
.41409
.25938
.25941
.25944
.25947
4
3
o
1
+ 15'
9.40121
.25189
9.40447
.25379
9.40771
.25569
9.41094
.25760
9.41415 .25951
0
19* 59^
19* 58m
19* 57m
19* 56m
19* 55m
Page 860] TABLE 45.
Haversines.
s
4h sm 61° 15'
4h em 61° 30'
4h 7m 61° 45'
4*> 8^ 62° (K
4h 9m 62° 15'
s
Log. Ha v.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.41415
.41420
.41425
.41431
.25951
.25954
.25957
.25960
9.41734
.41739
.41745
.41750
.26142
.26145
.26148
.26152
9.42052
.42057
.42062
.42068
.26334
.26337
.26340
.26344
9.42368
.42373
.42378
.42384
.26526
.26530
.26533
.26536
9.42682
.42688
.42693
.42698
.26719
.26722
.26726
.26729
60
59
58
57
+ V
5
6
7
9.41436
.41441
.41447
.41452
.25963
.25966
.25970
.25973
9.41755
.41761
.41766
.41771
.26155
.26158
.26161
.26164
9.42073
.42078
.42083
.42089
.26347
.26350
.26353
.26356
9.42389
.42394
.42399
.42405
.26539
.26543
.26546
.26549
9.42703
.42709
.42714
.42719
.26732
.26735
.26739
.26742
56
55
54
53
+ 3'
9
10
11
9.41457
.41463
.41468
.41473
.25976
.25979
.25982
.25986
9.41776
.41782
.41787
.41792
.26168
.26171
.26174
.26177
9.42094
.42099
.42105
.42110
.26360
.26363
.26366
.26369
9.42410
.42415
.42420
.42426
.26552
.26555
.26559
.26562
9.42724
.42730
.42735
.42740
.26745
.26748
.26751
.26755
52
51
50
49
+ v
13
14
15
9.41479
.41484
.41489
.41495
.25989
.25992
.25995
.25998
9.41798
.41803
.41808
.41814
.26180
.26184
.26187
.26190
9.42115
.42120
.42126
.42131
.26372
.26376
.26379
.26382
9.42431
.42436
.42441
.42447
.26565
.26568
.26571
.26575
9.42745
.42750
.42756
.42761
.26758
.26761
.26764
.26768
48
47
46
45
+ *'
17
18
19
9.41500
.41505
.41511
.41516
.26002
.26005
.26008
.26011
9.41819
.41824
.41829
.41835
.26193
.26196
.26200
.26203
9.42136
.42141
.42147
.42152
.26385
.26389
.26392
.26395
9.42452
.42457
.42462
.42468
.26578
.26581
.26584
.26587
9.42766
.42771
.42777
.42782
.26771
.26774
.26777
.26780
44
43
42
41
+ *'
21
22
23
9.41521
.41527
.41532
.41537
.26014
.26017
.26021
.26024
9.41840
.41845
.41851
.41856
.26206
.26209
.26212
.26216
9.42157
.42163
.42168
.42173
.26398
.26402
.26405
.26408
9.42473
.42478
.42483
.42489
.26591
.26594
.26597
.26600
9.42787
.42792
.42797
.42803
.26784
.26787
.26790
.26793
40
39
38
37
+ 6'
25
26
27
+ r
29
30
31
9.41543
.41548
.41553
.41559
.26027
.26030
.26033
.26037
9.41861
.41867
.41872
.41877
.26219
.26222
.26225
.26228
9.42178
.42184
.42189
.42194
.26411
.26414
.26417
.26421
9.42494
.42499
.42504
.42510
.26604
.26607
.26610
.26613
9.42808
.42813
.42818
.42824
.26797
.26800
.26803
.26806
36
35
34
33
9.41564
.41569
.41575
.41580
.26040
.26043
.26046
.26049
9.41882
.41888
.41893
.41898
.26232
.26235
.26238
.26241
9.42199
.42205
.42210
.42215
.26424
.26427
.26430
.26433
9.42515
.42520
.42525
.42531
.26616
.26620
.26623
.26626
9.42829
.42834
.42839
.42844
.26809
.26813
.26816
.26819
.26822
.26826
.26829
.26832
32
31
30
29
+ 8'
33
34
35
9.41585
.41590
.41596
.41601
.26053
.26056
.26059
.26062
9.41904
.41909
.41914
.41920
.26244
.26248
.26251
.26254
9.42221
.42226
.42231
.42236
.26437
.26440
.26443
.26446
9.42536
.42541
.42546
.42552
.26629
.26632
.26836
.26639
9.42850
.42855
.42860
.42865
28
27
26
25
+ w9'
38
39
9.41606
.41612
.41617
.41622
.26065
.26069
.26072
.26075
9.41925
.41930
.41935
.41941
.26257
.26260
.26264
.26267
9.42242
.42247
.42252
.42257
.26449
26453
.26456
.26459
9.42557
.42562
.42567
.42573
.26642
.26645
.26649
.26652
9.42870
.42876
.42881
.42886
.26835
.26838
.26842
.26845
24
23
22
21
+ 10'
41
42
43
9.41628
.41633
41638
.41644
.26078
.26081
.26085
.26088
9.41946
.41951
.41957
.41962
.26270
.26273
.26276
.26280
9.42263
.42268
.42273
.42278
.26462
.26465
.26469
.26472
9.42578
.42583
.42588
.42593
.26655
.26658
.26661
.26665
9.42891
.42897
.42902
.42907
.26848
.26851
.26855
.26858
20
19
18
17
+ 11'
45
46
47
9.41649
.41654
.41660
.41665
.26091
.26094
.26097
.26101
9.41967
.41972
.41978
.41983
.26283
.26286
.26289
.26292
9.42284
.42289
.42294
.42300
.26475
.26478
.26481
.26485
9.42599
.42604
.42609
.42614
.26668
.26671
.26674
.26677
9.42912
.42917
.42923
.42928
.26861
.26864
.26867
.26871
16
15
14
13
+ 12'
19
5<9
5J
9.41670
.41676
.41681
.41686
.26104
.26107
.26110
.26113
9.41988
.41994
.41999
.42004
.26296
.26299
.26302
.26305
9.42305
.42310
.42315
.42321
.26488
.26491
.26494
.26498
9.42620
.42625
.42630
.42635
.26681
.26684
.26687
.26690
9.42933
.42938
.42943
.42949
.26874
.26877
.26880
.26883
12
11
10
9
8
7
6
5
+ 13'
53
54
55
9.41692
.41697
.41702
.41707
.26117
.26120
.26123
.26126
.26129
.26132
.26136
.26139
9.42009
.42015
.42020
.42025
.26308
.26312
.26315
.26318
9.42326
.42331
.42336
.42342
.26501
.26504
.26507
.26510
9.42641
.42646
.42651
.42656
.26694
.26697
.26700
.26703
9.42954
.42959
.42964
.42969
.26887
.26890
.26893
.26896
+ 14'
57
58
59
9.41713
.41718
.41723
.41729
9.42031
. .42036
.42041
.42046
.26321
.26324
.26328
.26331
9.42347
.42352
.42357
.42363
.26514
.26517
.26520
.26523
.26526
9.42662
.42667
.42672
.42677
9.42682
.26706
.26710
.26713
.26716
9.42975
.42980
.42985
.42990
.26900
.26903
.26906
.26909
4
3
2
1
+ 15'
9.41734
.26142
9.42052
.26334
9.42368
.26719
9.42996
.26913
0
19U 54m
19h 53^
197t 52m
19h 5im
19h 5Qm
TABLE 45. [Page 861
Haversinee.
4* 10m 62° 30'
4h um 62° 45'
4* 12m 63° <K
4h ism 63° 15'
4h Um 63° 307
s
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.42996
.43001
.43006
.43011
.26913
.26916
.26919
.26922
9.43307
.43312
.43317
.43323
.27106
.27110
.27113
.27116
9.43617
.43622
.43627
.43632
.27300
.27304
.27307
.27310
9.43926
.43931
.43936
.43941
.27495
.27498
.27502
.27505
9.44232
.44238
.44243
.44248
.27690
.27693
.27697
.27700
60
59
58
57
+ V
5
6
7
9.43016
.43022
.43027
.43032
.26925
.26929
.26932
.26935
9.43328
.43333
.43338
.43343
.27119
.27122
.27126
.27129
9.43638
.43643
.43648
.43653
.27313
.27317
.27320
.27323
9.43946
.43951
.43956
.43961
.27508
.27511
.27515
.27518
9.44253
.44258
.44263
.44268
.27703
.27706
.27710
.27713
06
55
54
53
+ V
9
10
11
9.43037
.43042
.43048
.43053
.26938
.26942
.26945
.26948
9.43348
.43354
.43359
.43364
.27132
.27135
.27139
.27142
9.43658
.43663
.43669
.43674
.27326
.27330
.27333
.27336
9.43967
.43972
.43977
.43982
.27521
.27524
.27528
.27531
9.44273
.44278
.44283
.44289
.2771«
.27719
.27723
.27726
52
51
50
49
+ &
IS
14
15
9.43058
.43063
.43068
.43074
.26951
.26955
.26958
.26961
9.43369
.43374
.43380
.43385
.27145
.27148
.27152
.27155
9.43679
.43684
.43689
.43694
.27339
.27343
.27346
.27349
9.439S7
.43992
.43997
.44002
.27534
.27537
.27541
.27544
9.44294
.44299
.44304
.44309
.27729
.27732
.27736
.27739
4S
47
46
45
+ *'
17
18
19
9.48079
.43084
.43089
.43094
.26064
.26967
.26971
.26974
9.43390
.43395
.43400
.43405
.27158
.27161
.27165
.27168
9.43699
.43705
.43710
.43715
.27352
.27356
.27359
.27362
9.44008
.44013
.44018
.44023
.27547
.27550
.27554
.27557
9.44314
.44319
.44324
.44329
.27742
.27745
.27749
.27752
44
43
42
41
+ &
21
22
t8
9.43100
.43105
.43110
.43115
.26977
.26980
.26984
.26987
9.43411
.43416
.43421
.43426
.27171
.27174
.27177
.27181
9.43720
.43725
.43730
.43735
.27365
.27369
.27372
.27375
9.44028
.44033
.44038
.44043
.27560
.27563
.27567
.27570
9.44334
.44340
.44345
.44350
.27755
.27758
.27762
.27765
40
39
38
37
+ V
25
26
27
9.43120
.43126
.43131
.43136
.26990
.26993
.26996
.27000
9.43431
.43436
.43442
.43447
.27184
.27187
.27190
.27194
9.43741
.43746
.43751
.43756
.27378
.27382
.27385
.27388
9.44048
.44054
.44059
.44064
.27573
.27576
.27580
.27583
9.44355
.44360
.44365
.44370
.27768
.27772
.27775
.27778
36
35
34
33
+ r
29
30
SI
9.43141
.43146
.43151
43157
.27003
.27006
.27009
.27013
9.43452
.43457
.43462
.43467
.27197
.27200
.27203
.27207
9.43761
.43766
.43771
.43777
.27391
.27394
.27398
.27401
9.44069
.44074
.44079
.44084
.27586
.27589
.27593
.27596
9.44375
.44380
.44385
.44390
.27781
.27785
.27788
.27791
32
31
30
29
+ S'
w
34
35
9.43162
.43167
.43172
.43177
.27016
.27019
.27022
.27025
9.43473
.43478
.43483
.43488
.27210
.27213
.27216
.27220
9.437S2
.43787
.43792
.43797
.27404
.27407
.27411
.27414
9.44089
.44095
.44100
.44105
.27599
.27602
.27606
.27609
9.44396
.44401
.44406
.44411
.27794
.27798
.27801
.27804
28
27
26
25
+ &
37
38
39
9.43183
.43188
.43193
.43198
.27029
.27032
.27035
.27038
9.43493
.43498
.43504
.43509
.27223
.27226
.27229
.27232
9.43802
.43807
.43813
.43818
.27417
.27420
.27424
.27427
9.44110
.44115
.44120
.44125
.27612
.27615
.27619
.27622
9.44416
.44421
.44426
.44431
.27807
.27811
.27814
.27817
24
23
-?-?
J}
+ W
k
42
43
9.43203
.43209
.43214
.43219
.27042
.27045
.27048
.27051
9.43514
.43519
.43524
.43529
.27236
.27239
.27242
.27245
9.43823
.43828
.43833
.43838
.27430
.27433
.27437
.27440
9.44130
.44135
.44141
.44146
.27625
.27628
.27632
.27635
9.44436
.44441
.44446
.44452
.27820
.27824
.27827
.27830
to
19
18
17
+ 11'
45
46
47
9.43224
.43229
.43234
.43240
.27055
.27058
.27061
.27064
9.43535
.43540
.43545
.43550
.27249
.27252
.27255
.27258
9.43S43
.43849
.43854
.43859
.27443
.27446
.27450
.27453
9.44151
.44156
.44161
.44166
.27638
.27641
.27645
.27648
9.44457
.44462
.44467
.44472
.27833
.27837
.27840
.27843
16
15
14
13
12
11
10
9
+ 12'
49
50
51
9.43245
.43250
.43255
.43260
.27068
.27071
.27074
.27077
9.43555
.43560
.43565
.43571
.27262
.27265
.27268
.27271
9.43864
.43869
.43874
.43879
.27456
.27459
.27463
.27466
9.44171
44176
.44181
.44187
.27651
.27654
.27658
.27661
9.44477 .27846
.44482 .27850
.44487 .27853
.44492 ' .27856
+ 13'
53
54
55
9.43266
.43271
.43276
.43281
.27080
.27084
.27087
.27090
9.43576
.43581
.43586
.43591
.27275
.27278
.27281
.27284
9.43884
.43890
.43895
.43900
.27469
.27472
.27476
.27479
9.44192
.44197
.44202
.44207
.27664
.27667
.27671
.27674
9.44497 .27859
.44502 .27863
.44507 i .27866
.44513 ! .27869
8
7
6
5
+ 14'
57
58
59
9.43286
.43291
.43297
.43302
.27093
.27097
.27100
.27103
9.43596
.43602
.43607
.43612
.27288
.27291
.27294
.27297
9.43905
.43910
.43915
.43920
.27482
.27485
.27489
.27492
9.44212
.44217
.44222
.44227
.27677
.27680
.27684
.27687
9.44518 .27873
.44523 .27876
.44528 .27879
.44533 .27882
4
3
o
1
+ 15'
9.43307
.27106
9.43617 .27300
9.43926
.27495
9.44232
.27690
9.44538 .27886
0
19h 49m
19*48™
19h 47m
igh 46m
19^ 45™
Page 862] TABLE 45.
Haversines.
s
4^ 15™ 63° 45'
4h ism 64° 0'
4h 17m 64° 15'
4h ism 64° 30'
4h idm 64° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.44538
.44543
.44548
.44553
.27886
.27889
.37892
.27895
9.44842
.44847
.44852
.44857
.28081
.28085
.28088
.28091
9.45144
.45149
.45155
.45160
.28278
.28281
.28284
.28288
9.45446
.45451
.45456
.45461
.28474
.28478
.28481
.28484
9.45745
.45750
.45755
.45760
.28672
.28675
.28678
.28681
60
59
58
57
+ 1'
5
6
7
9.44558
.44563
.44568
.44573
.27899
.27902
.27905
.27908
9.44862
.44867
.44872
.44877
.28095
.28098
.28101
.28104
9.45165
.45170
.45175
.45180
.28291
.28294
.28297
.28301
9.45466
.45471
.45476
.45481
.28488
.28491
.28494
.28497
9.45765
.45770
.45775
.45780
.28685
.28688
.28691
.28695
56
55
54
53
+ %'
9
10
11
9.44579
.44584
.44589
.44594
.27912
.27915
.27918
.27921
9.44882
.44887
.44892
.44898
.28108
.28111
.28114
.28117
9.45185
.45190
.45195
.45200
.28304
.28307
.28310
.28314
9.45486
.45491
.45496,
.45501
.28501
.28504
.28507
.28511
9.45785
.45790
.45795
.45800
.28698
.28701
.28704
.28708
52
51
50
49
+ 3'
13
14
15
9.44599
.44604
.44609
.44614
.27925
.27928
.27931
.27935
9.44903
.44908
.44913
.44918
.28121
.28124
.28127
.28130
9.45205
.45210
.45215
.45220
.28317
.28320
.28324
.28327
9.45506
.45511
.45516
.45521
.28514
.28517
.28520
.28524
9.45805
.45810
.45815
.45820
.28711
.28714
.28718
.28721
48
47
46
45
+ *'
17
18
19
9.44619
.44624
.44629
.44634
.27938
.27941
.27944
.27948
9.44923
.44928
.44933
.44938
.28134
.28137
.28140
.28144
9.45225
.45230
.45235
.45240
.28330
.28333
.28337
.28340
9.45526
.45531
.45536
.45541
.28527
.28530
.28534
.28537
9.45825
.45830
.45835
.45840
.28724
.28727
.28731
.28734
44
43
42
41
+ &'
21
23
9.44639
.44645
.44650
.44655
.27951
.27954
.27957
.27961
9.44943
.44948
.44953
.44958
.28147
.28150
.28153
.28157
9.45245
.45250
.45255
.45260
.28343
.28347
.28350
.28353
9.45546
.45551
.45556
.45561
.28540
.28543
.28547
.28550
9.45845
.45850
.45855
.45860
.28737
.28741
.28744
.28747
40
39
38
37
+ 6'
25
26
27
9.44660
.44665
.44670
.44675
.27964
.27967
.27970
.27974
9.44963
.44968
.44973
.44978
.28160
.28163
.28166
.28170
9.45265
.45270
.45275
.45280
.28356
.28360
.28363
.28366
9.45566
.45571
.45576
.45581
.28553
.28557
.28560
.28563
9.45865
.45870
.45875
.45879
.28751
.28754
.28757
.28760
36
35
34
33
32
31
30
29
+ v
29
30
31
9.44680
.44685
.44690
.44695
.27977
.27980
.27983
.27987
9.44983
.44988
.44993
.44998
.28173
.28176
.28180
.28183
9.45285
.45290
.45295
.45300
.28369
.28373
.28376
.28379
9.45586
.45591
.45596
.45601
.28566
.28570
.28573
.28576
9.45884
.45889
.45894
.45899
.28764
.28767
.28770
.28774
+ 8'
33
34
35
9.44700
.44705
.44710
.44715
.27990
.27993
.27997
.28000
9.45003
.45009
.45014
.45019
.28186
.28189
.28193
.28196
9.45305
.45310
.45315
.45320
.28383
.28386
.28389
.28392
9.45606
.45610
.45615
.45620
.28580
.28583
.28586
.28589
9.45904
.45909
.45914
.45919
.28777
.28780
.28783
.28787
28
27
26
25
+ V
37
38
39
9.44721
.44726
.44731
.44736
.28003
.28006
.28010
.28013
9.45024
.45029
.45034
.45039
.28199
.28202
.28206
.28209
9.45325
.45330
.45335
.45340
.28396
.28399
.28402
.28406
9.45625
.45630
.45635
.45640
.28593
.28596
.28599
.28603
9.45924
.45929
.45934
.45939
.28790
.28793
.28797
.28800
24
23
22
21
+ W
41
43
9.44741
.44746
.44751
.44756
.28016
.28019
.28023
.28026
9.45044
.45049
.45054
.45059
.28212
.28216
.28219
.28222
9.45345
.45350
.45355
.45360
.28409
.28412
.28415
.28419
9.45645
.45650
.45655
.45660
.28606
.28609
.28612
.28616
9.45944
.45949
.45954
.45959
.28803
.28807
.28810
.28813
20
19
18
17
+ 11'
45
46
47
9.44761
.44766
.44771
.44776
.28029
.28032
.28036
.28039
9.45064
.45069
.45074
.45079
.28225
.28229
.28232
.28235
9.45365
.45370
.45375
.45380
.28422
.28425
.28429
.28432
9.45665
.45670
.45675
.45680
.28619
.28622
.28626
.28629
9.45964
.45969
.45974
.45979
.28816
.28820
.28823
.28826
16
15
14
13
+ 12'
49
50
51
9.44781
.44786
.44791
.44796
.28042
.28046
.28049
.28052
9.45084
.45089
.45094
.45099
.28238
.28242
.28245
.28248
9.45385
.45390
.45395
.45400
.28435
.28438
.28442
.28445
9.45685
.45690
.45695
.45700
.28632
.28635
.28639
.28642
9.45984
.45989
.45994
.45999
.28830
.28833
.28836
.28839
12
11
10
9
+ 13'
53
54
55
9.44801
.44807
.44812
.44817
.28055
.28059
.28062
.28065
9.45104
.45109
.45114
.45119
.28252
.28255
.28258
.28261
9.45405
.45410
.45415
.45420
.28448
.28451
.28455
.28458
9.45705
.45710
.45715
.45720
.28645
.28649
.28652
.28655
9.46004
.46009
.46014
.46019
.28843
.28846
.28849
.28853
8
7
6
5
+ 14'
57
58
59
9.44822
.44827
.44832
.44837
.28068
.28072
.28075
.28078
9.45124
.45129
.45134
.45139
.28265
.28268
.28271
.28274
9.45426
.45431
.45436
.45441
.28461
.28465
.28468
.28471
9.45725
.45730
.45735
.45740
.28658
.28662
.28665
.28668
9.46023
.46028
.46033
.46038
.28856
.28859
.28863
.28866
4
3
2
1
+ 15'
9.44842
.28081
9.45144
.28278
9.45446
.28474
9.45745
.28672
9.46043
.28869
0
19*> 44™
19* 43m
19h 42m
19* 41™
19*40*
TABLE 45. [Page 863
Haversines.
s
4* £#m 65° O7
4h 2im 65° 15'
4* 2*™ 65° 307
4* 23m 65° 45'
4* 24m 66° (K
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.j Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
s
0
1
2
3
9.46043
.46048
.46053
.46058
.28869
.28872
.28876
.28879
9.46340
.46345
.46350
.46355
.29067
.29070
.29074
.29077
9.46635
.46640
.46645
.46650
.29265
.29269
.29272
.29275
9.46929
.46934
.46939
.46944
.29464
.29467
.29471
.29474
9.47222
.47227
.47231
.47236
.29663
.29666
.29670
.29673
60
59
58
57
+ 1'
5
6
7
9.46063
.46068
.46073
.46078
.28882
.28886
.28889
.28892
9.46360
.46365
.46370
.46375
.29080
.29084
.29087
.29090
9.46655
.46660
.46665
.46670
.29279
.29282
.29285
.29289
9.46949
.46954
.46959
.46963
.29477
.29481
.29484
.29487
9.47241
.47246
.47251
.47256
.29676
.29680
.29683
.29686
56
55
54
53
+ V
9
10
11
9.46083
.46088
.46093
.46098
.28895
.28899
.28902
.28905
9.46380 .21*093
.46384 .29097
.46389 .29100
.46394 .29103
9.46675
.46680
.46684
.46689
.29292
.29295
.29298
.29302
9.46968
.46973
.46978
.46983
.29491
.29494
.29497
.29501
9.47261
.47266
.47270
.47275
.29690
.29693
.29696
.29700
52
51
50
49
+ 3'
IS
14
15
9.46103
.46108
.46113
.46118
.28909
.28912
.28915
.28918
9.46399 1 .29107
.46404 .29110
.46409| .29113
.46414 i .29117
9.46694
.46699
.46704
.46709
.29305
.29308
.29312
.29315
9.46988
.46993
.46998
.47003
.29504
.29507
.29510
.29514
9.47280
.47285
.47290
.47295
.29703
.29706
.29710
.29713
48
47
46
45
+ 47
17
15
19
9.46123
.46128
.46132
.46137
.28922
.28925
.28928
.28932
9.46419
.46424
.46429
.46434
.29120
.29123
.29126
.29130
9.46714
.46719
.46724
.46729
.29318
.29322
.29325
.29328
9.47007
.47012
.47017
.47022
.29517
.29520
.29524
.29527
9.47306
.47304
.47309
.47314
.29716
.29720
.29723
.29726
44
43
42
41
+ 5'
fl
f*
W
9.46142
.46147
.46152
.46157
.28935
.28938
.28942
.28945
9.46439
.46444
.46448
.46453
.29133
.29136
.29140
.29143
9.46733
.46738
.46743
.46748
.29332
.29335
.29338
.29341
9.47027
.47032
.47037
.47042
.29530
.29534
.29537
.29540
9.47319
.47324
.47329
.47334
.29730
.29733
.29736
.29740
40
39
38
37
36
35
34
33
+ «'
£5
£tf
«7
9.46162
.46167
.46172
.46177
.2894$
.28952
.28955
.28958
9.4645S
.46463
.46468
.46473
.29146
.29150
.29153
.29156
9.46753
.46758
.46763
.46768
.29345
.29348
.29351
.29355
9.47046
.47051
.47056
.47061
.29544
.29547
.29550
.29554
9.47338
.47343
.47348
.47353
.29743
.29746
.29750
.29753
+ 1'
29
SO
SI
9.46182
.46187
.46192
.46197
.28961
.28965
.28968
.28971
9.46478
.46483
.46488
.46493
.29160
.29163
.29166
.29169
9.46773
.46778
.46782
.46787
.29358
.29361
.29365
.29368
9.47066
.47071
.47076
.47081
.29557
.29560
.29564
.29567
9.47358
.47363
.47367
.47372
.29756
.29760
.29763
.29766
32
31
30
29
+ 8X
S3
34
S5
9.46202
.46207
.46212
.46217
.28975
.28978
.28981
.28985
9.46498
.46503
.46508
.46512
.29173
.29176
.29179
.29183
9.46792
.46797
.46802
.46807
.29371
.29375
.29378
.29381
9.47085
.47090
.47095
.47100
.29570
.29573
.29577
.29580
9.47377
.47382
.47387
.47392
.29770
.29773
.29776
.29779
28
27
,26
25
+ 9/
37
38
39
9.46222
.46226
.46231
.46236
.28988
.28991
.28994
.28998
9.46517
.46522
.46527
.46532
.29186
.29189
.29193
.29196
9.46812
.46817
.46822
.46827
.29385
.29388
.29391
.29394
9.47105
.47110
.47115
.47120
.29583
.29587
.29590
.29593
9.47397
.47401
.47406
.47411
.29783
.29786
.29789
.29793
24
23
22
21
+ W
41
42
4S
9.46241
.46246
.46251
.46256
.29001
.29004
.29008
.29011
9.46537
.46542
.46547
.46552
.29199
.29202
.29206
.29209
9.46831
.46836
.46841
.46846
.29398
.29401
.29404
.29408
9.47124
.47129
.47134
.47139
.29597
.29600
.29603
.29607
9.47416
.47421
.47426
.47431
.29796
.29799
.29803
.29806
20
19
18
17
+ ir
45
46
47
9.46261
.46266
.46271
.46276
.29014
.29017
.29021
.29024
9.46557
.46562
.46567
.46571
.29212
.29216
.29219
.29222
9.46851
.46856
.46861
.46866
.29411
.29414
.29418
.29421
9.47144
.47149
.47154
.47159
.29610
.29613
.29617
.29620
9.47435
.47440
.47445
.47450
.29809
.29813
.29816
.29819
16
15
14
13
+ 12'
49
50
51
9.46281
.46286
.46291
.46296
.29027
.29031
.29034
.29037
9.46576
.46581
.46586
.46591
.29226
.29229
.29232
.29236
9.46871 | .29424
.46875 ! .29428
.46880 I .29431
.46885 .29434
9.47163
.47168
.47173
.47178
.29623
.29627
.29630
.29633
9.47455
.47460
.47464
.47469
.29823
.29826
.29829
.29833
12
11
10
9
+ 13'
53
54
55
9.46301
.46305
.46310
.46315
.29041
.29044
.29047
.29051
9.46596
.46601
.46606
.46611
.29239
.29242
.29245
.29249
9.46890 .29438
.46895 ! .29441
.46900 i .29444
.46905! .29447
9.47183 .29637
.47188 .29640
.47193 .29643
.47197 .29647
9.47474
.47479
.47484
.47489
.29836
.29839
.29843
.29846
8
6
5
+ 14'
57
55
59
9.46320
.46325
.46330
.46335
.29054
.29057
.29060
.29064
9.461516
.46621
.46626
.46630
.29252
.29255
.29259
.29262
9.46910 i .29451
.46915 ' .29454
.46919! .29457
.46924 .29461
9.47202 .29650
.47207 .29653
.47212 .29657
.47217 .29660
9.47493
.47498
.47503
.47508
.29849
.29853
.29856
.29859
4
S
2
1
+ 15'
9.46340
.29067
9.46635
.29265
9.46929 | .29464
9.47222 .29663
9.47513
.29863
0
19* 39™
19*38™
19 * 37^
19*36?"
19* S5m
Page 864] TABLE 45.
Haversines.
s
4h 25™ 66° 15'
4h 26m 66° 30'
4*> 27m 66° 45'
4h ssm 67° 0'
4h 29m 67° 15'
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.47513
.47518
.47523
.47527
.29863
.29806
.29869
.29873
9.47803
.47807
.47812
.47817
.30063
.30066
.30069
.30073
9.48091
.48096
.48101
.48105
.30263
.30266
.30269
.30273
9.48378
.48383
.48387
.48392
.30463
.30467
.30470
.30473
9.48664
.48668
.48673
.48678
.30664
.30668
.30671
.30675
60
59
58
57
56
55
54
53
+ 1'
5
6
7
9.47532
.47537
.47542
.47547
.29876
.29879
.29883
.29886
9.47822
.47827
.47831
.47836
.30076
.30079
.30083
.30086
9.48110
.48115
.48120
.48124
.30276
.30280
.30283
.30286
9.48397
.48402
.48407
.48411
.30477
.30480
.30484
.30487
9.48683
.48687
.48692
.48697
.30678
.30681
.30685
.30688
+ %'
9
10
11
9.47552
.47556
.47561
.47566
.29889
.29893
.29896
.29899
9.47841
.47846
.47851
.47856
.30089
.30093
.30096
.30099
9.48129
.48134
.48139
.48144
.30290
.30293
.30236
.30300
9.48416
.48421
.48426
.48430
.30490
.30494
.30497
.30500
9.48702
.48706
.48711
.48716
.30691
.30695
.30698
.30701
52
51
50
49
+ &
13
14
15
9.47571
.47576
.47581
.47585
.29903
.29906
.29909
.29913
9.47860
.47865
.47870
.47875
.30103
.30106
.30109
.30113
9.48148
.48153
.48158
.48163
.30303
.30306
.30310
.30313
9.48435
.48440
.48445
.48449
.30504
.30507
.30510
.30514
9.48720
.48725
.48730
.48735
.30705
.30708
.30711
.30715
48
47
46
45
+ ¥
17
18
19
9.47590
.47595
.47600
.47605
.29916
.29919
.29923
.29926
9.47880
.47884
.47889
.47894
.30116
.30119
.30123
.30126
9.48168
.48172
.48177
.48182
.30316
.30320
.30323
.30326
9.48454
.48459
.48464
.48468
.30517
.30520
.30524
.30527
9.48739
.48744
.48749
.48754
.30718
.30721
.30725
.30728
44
43
42
41
+ &'
21
22
23
9.47610
.47614
.47619
.47624
.29929
.29933
.29936
.29939
9.47899
.47904
.47908
.47913
.30129
.30133
.30136
.30139
9.48187
.48192
.48196
.48201
.30330
.30333
.30336
.30340
9.48473
.48478
.48483
.48488
.30530
.30534
.30537
.30540
9.48758
.48763
.48768
.48773
.30732
.30735
.30738
.30742
40
39
38
37
+ 6'
25
26
27
9.47629
.47634
.47639
.47643
.29943
.29946
.29949
.29953
9.47918
.47923
.47928
.47933
.30143
.30146
.30149
.30153
9.48206
.48211
.48215
.48220
.30343
.30346
.30350
.30353
9.48492
.48497
.48502
.48507
.30544
.30547
.30551
.30554
9.48777
.48782
.48787
.48792
.30745
.30748
.30752
.30755
36
35
34
33
+ r
29
30
31
9.47648
.47653
.47658
.47663
.29956
.29959
.29963
.29966
9.47937
.47942
.47947
.47952
.30156
.30159
.30163
.30166
9.48225
.48230
.48235
.48239
.30356
.30360
.30363
.30366
9.48511
.48516
.48521
.48526
.30557
.30561
.30564
.30567
9.48796
.48801
.48806
.48811
.30758
.30762
.30765
.30768
32
31
30
29
+ &
S3
34
35
9.47668
.47672
.47677
.47682
.29969
.29973
.29976
.29979
9.47957
.47961
.47966
.47971
.30169
.30173
.30176
.30179
9.48244
.48249
.48254
.48258
.30370
.30373
.30376
.30380
9.48530
.48535
.48540
.48545
.30571
.30574
.30577
.30581
9.48815
.48820
.48825
.48830
.30772
.30775
.30779
.30782
28
27
26
25
+ 9'
37
38
39
9.47687
.47692
.47697
.47701
.29983
.29986
.29989
.29993
9.47976
.47981
.47985
.47990
.30183
.30186
.30189
.30193
.30196
.30199
.30203
.30206
9.48263
.48268
.48273
.48278
.30383
.30386
.30390
.30393
9.48549
.48554
.48559
.48564
.30584
.30587
.30591
.30594
9.48834
.48839'
.48844
.48848
.30785
.30789
.30792
.30795
24
23
22
21
+ 10'
41'
42
43
9.47706
.47711
.47716
.47721
.29996
.29999
.30003
.30006
9.47995
.48000
.48005
.48009
9.48282
.48287
.48292
.48297
.30397
.30400
.30403
.30407
9.48568
.48573
.48578
.48583
.30597
.30601
.30604
.30607
9.48853
.48858
.48863
.48867
.30799
.30802
.30805
.30809
20
19
18
17
+ 11'
45
46
47
9.47725
.47730
.47735
.47740
.30009
.30013
.30016
.30019
9.48014
.48019
.48024
.48029
.30209
.30213
.30216
.30219
9.48302
.48306
.48311
.48316
.30410
.30413
.30417
.30420
9.48587
.48592
.48597
.48602
.30611
.30614
.30618
.30621
9.48872
.48877
.48882
.48886
.30812
.30815
.30819
.30822
16
15
14
13
+ 12'
49
50
51
9.47745
.47750
.47754
.47759
.30023
.30026
.30029
.30033
9.48033
.48038
.48043
.48048
.30223
.30226
.30229
.30233
9.48321
.48325
.48330
.48335
.30423
.30427
.30430
.30433
9.48607
.48611
.48616
.48621
.30624
.30628
.30631
.30634
9.48891
.48896
.48901
.48905
.30826
.30829
.30832
.30836
12
11
10
9
+ 13'
53
54
55
9.47764
.47769
.47774
.47778
.30036
.30039
.30043
.30046
9.48053
.48057
.48062
.48067
.30236
.30239
.30243
.30246
9.48340
.48344
.48349
.48354
.30437
.30440
.30443
.30447
9.48626
.48630
.48635
.48640
.30638
.30641
.30644
.30648
9.48910
.48915
.48919
.48924
.30839
.30842
.30846
.30849
8
7
6
5
+ 14'
57
58
59
9.47783
.47788
.47793
.47798
.30049
.30053
.30056
.30059
9.48072
.48077
.48081
.48086
.30249
.30253
.30256
.30259
9.48359
.48364
.48368
.48373
.30450
.30453
.30457
.30460
9.48645
.48649
.48654
.48659
.30651
.30655
.30658
.30661
9.48929
.48934
.48938
.48943
.30852
.30856
.30859
.30862
4
S
2
1
+ I*'
9.47803
.30063
9.48091
.30263
9.48378
.30463
9.48664
.30664
9.48948
.30866
0
19*> 34m
igh ssm
igh 32m
19h 3lm
19*>30m
TABLE 45. [Page 865
Haversines.
4*$0»67°30''
4h sim 67° 45'
471 S2n 68° <K
4hSSm 68° ly
4&«?4"»68°30/
s
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
,9
3
9.4S94S
.48953
.48957
.48962
.30866
.30869
.30873
.30876
9.49231
.49235
.49240
.49245
.31068
.31071
.31074
.31078
9.49512
.49517
.49522
.49526
.31270
.31273
.31276
.31280
9.49793
.49797
.49802
.49807
.31472
.31475
.31479
.31482
9.50072
.50076
.50081
.50085
.31675
.31678
.31682
.31685
60
59
58
57
+ v
5
6
7
9.48967
.48971
.48976
.48981
.30879
.30883
.30886
.30889
9.49250
.49254
.49259
.49264
.31081
.31084
.31088
.31091
9.49531
.49536
.49540
.49545
.31283
.31287
.31290
.31293
9.49811
.49816
.49821
.49825
.31486
.31489
.31492
.31496
9.50090
.50095
.50099 1
.50104
.31688
.31692
.31695
.31699
56
55
54
53
+ 2X
9
10
11
9.48986
.48990
.48995
.49000
.30893
.30896
.30899
.30903
9.49268
.49273
.49278
.49282
.31095
.31098
.31101
.31105
9.49550
.49554
.49559
.49564
.31297
.31300
.31303
.31307
9.49b30
.49835
.49839
.49844
.31499
.31503
.31506
.31509
9.50109
.50113
.50118
.50123
.31702
.31J05
.31709
.31712
52
51
50
49
+ 3'
13
14
15
9.49004
.49009
.49014
.49019
.30906
.30910
.30913
.30916
9.49287
.49292
.49297
.49301
.31108
.31111
.31115
.31118
9.49568
.49573
.49578
.49583
.31310
.31314
.31317
.31320
9.49849
.49853
.49858
.49862
.31513
.31516
.31519
.31523
9.50127
.50132
.50136
.50141
.31716
.31719
.31722
.31726
4$
47
46
45
+ 4'
17
18
19
9.49023
.49028
.49033
.49038
.30920
.30923
.30926
.30930
9.49306
.49311
.49315
.49320
.31121
.31125
.31128
.31132
9.49587
.49592
.49597
.49601
.31324
.31327
.31330
.31334
9.49867
.49872
.49876
.49881
.31526
.31530
.31533
.31536
9.50146
.50150
.50155
.50160
.31729
.31732
.31736
.31739
44
43
42
41
+ &'
21
22
5}
9.49042
.49047
.49052
.49056
.30933
.30936
.30940
.30943
9.49325
.49329
.49334
.49339
.31135
.31138
.31142
.31145
9.49606
.49611
.49615
.49620
.31337
.31341
.31344
.31347
9.49886
.49890
.49895
.49900
.31540
.31543
.31546
.31550
9.50164
.50169
.50174
.50178
.31742
.31746
.31749
.31753
40
39
38
37
4- 6'
2$
££
£7
9.49061
.49066
.49071
.49075
.30946
.30950
.30953
.30957
9.49344
.49348
.49353
.49358
.31148
.31152
.31155
.31158
9.49625
.49629
.49634
.49639
.31351
.31354
.31357
.31361
9.49904
.49909
.49914
.49918
.31553
.31557
.31560
.31563
9.50183
.50187
.50192
.50197
.31756
.31760
.31763
.31766
36
35
34
33
+ r
29
30
31
9.49080
.49085
.49069
.49094
.30960
.30963
.30967
.30970
9.493G2
.49367
.49372
.49376
.31162
.31165
.31169
.31172
9.49643
.49648
.49653
.49G57
.31364
.31367
.31371
.31374
9.49923
.49928
.49932
.49937
.31567
.31570
.31573
.31577
9.50201
.50206
.50211
.50215
.31770
.31773
.31776
.31780
32
31
30
29
+ 8X
33
34
35
9.49099
.49104
.49108
.49113
.30973
.30977
.30980
.30983
.49386
.49390
.49395
.31175
.31179
.31182
.31185
9.49662
.49667
.49671
.49676
.31378
.31381
.31384
.31388
9.49942
.49946
.49951
.49956
.31580
.31584
.31587
.31590
9 50220
.50224
.50229
.50234
.31783
.31787
.31790
.31793
A.O
26
25
-f V
37
38
39
9.49118
.49122
.49127
.49132
.30987
.30990
.30994
.309S7
9.49400
.49405
.49409
.49414
.31189
.31192
*.311%
.31199
9.49681
.49685
.49690
.49695
.31391
.31394
.31398
.31401
9.49960
.49965
.49969
.49974
.31594
.31597
.31601
.31604
9.50238
.50243
.50248
.50252
.31797
.31800
.31804
.31807
24
23
22
21
+ 1(K
4.7
4?
4,?
9.49137
.49141
.49146
.49151
.31000
.31004
.31007
.31010
9.49419
.49-123
.49-128
.49433
.31202
.31206
.31209
.31212
9.49699
.49704
.49709
.49713
.31405
.31408
.31411
.31415
9.49979
.49983
.49988
.49993
.31607
.31611
.31614
.31617
9.50257
.50261
.50266
.50271
.31810
.31814
.31817
.31820
fft
19
18
17
+ 11'
45
46
47
9.49155
.49160
.49165
.49170
.31014
.31017
.31020
.31024
9.49437
.49442
.49447
.49451
.31216
.31219
.3122?
.31226
9.49718
.49723
.49727
.49732
.31418
.31421
.31425
.31428
9.49997
.50002
.50007
.50011
.31621
.31624
.31628
.31631
9.50275
.50280
.50284
.50289
.31824
.31827
.31831
.31834
16
15
14
13
+ «'
45
50
51
9.49174
.49179
.49184
.49188
.31027
.31031
.31034
.31037
9.49456
.49461
.49465
.49470
.31229
.31233
.31236
.31239
9.49737
.49741
.49746
.49751
.31432
.31435
.31438
.31442
9.50016
.50021
.50025
.50030
.31634
.31638
.31641
.31644
9.50294
.50298
.50303
.50308
.31837
.31841
.31844
.31848
12
11
10
9
8
7
6
5
+ 13'
53
54
55
9.49193
.49198
.49202
.49207
.31041
.31044
.31047
.31051
9.49475
.49480
.49484
.49489
.31-243
.31246
.31249
.31253
9.49755
.49760
.49765
.49769
.31445
.31448
.31452
.31455
9.50034
.50039
.50044
.50048
.31648
.31651
.31655
.31658
9.50312
.50317
.50322
.50326
.31851
.31854
.31858
.31861
+ 14'
57
5S
59
9.49212
.49217
.49221
.49226
.31054
.31057
.31061
.31064
9.49494
.49498
.49503
.49508
.31256
.31260
.31263
.31266
9.49774
.49779
.49783
.49788
.31459
.31462
.31465
.31469
9.50053
.50058
.50062
.50067
.31661
.31665
.31668
.31672
9.50331
.50335
.50340
.50345
.31865
.31868
.31871
.31875
4
S
2
1
+ 15/
9.49231
.31068
9.49512
.31270
9.49793
.31472
9.50072
.31675
9.50349
.31878
0
29h 2Qm
19* 28™
19h 2jm
19* 26m
19h 2sm
Page 866] TABLE 45.
Haversines.
s
4* 35^ 68° 45'
4* 36m 69° 0'
4* 37m 69° 15'
4h ssm 69° 30'
4h 39^ 69° 45'
s
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
9.50349
.50354
.50358
.50363
.31878
.31881
.31885
.31888
.31893
.31895
.31898
.31903
9.50626
.50630
.50635
.50639
.33083
.33085
.33088
.33093
9.50901
.50905
.50910
.50914
.33385
.33389
.33393
.33396
9.51174
.51179
.51184
.51188
.33490
.33493
.33496
.33500
9.51447
.51452
.51456
.51461
.33694
.33698
.33701
.33704
60
59
58
57
+ V
5
6
7
9.50368
.50372
.50377
.50382
9.50644
.50649
.50653
.50658
.33095
.33099
.33103
.33105
9.50919
.50924
.50928
.50933
.33399
.33303
.33306
.33309
9.51193
.51197
.51202
.51206
.33503
.33507
.33510
.33513
9.51465
.51470
.51474
.51479
.33708
.33711
.33715
.33718
56
55
54
53
+ *
9
10
11
9.50386
.50391
.50395
.50400
.31905
.31909
.31913
.31915
9.50662
.50667
.50672
.50676
.33109
.33113
.33116
.33119
9.50937
.50942
.50946
.50951
.33313
.33316
.33319
.33333
9.51211
.51215
.51220
.51225
.33517
.33530
.33534
.33537
9.51483
.51488
.51492
.51497
.33731
.33735
.33738
.33733
52
51
50
49
+ &
13
14
15
9.50405
.50409
.50414
.50418
.31919
.31933
.31936
.31939
9.50681
.50685
.50690
.50694
.33133
.33136
.33139
.33133
9.50956
.50960
.50965
.50969
.33336
.33330
.33333
.33336
9.51229
.51234
.51238
.51243
.33531
.33534
.33537
.33541
9.51501
.51506
.51510
.51515
.33735
.33738
.33743
.33745
48
47
46
45
+ *'
17
18
19
9.50423
.50428
.50432
.50437
.31933
.31936
.31939
.31943
9.50699
.50704
.50708
.50713
.33136
.33139
.33143
.33146
9.50974
.50978
.50983
.50988
.33340
.33343
.33347
.33350
9.51247
.51252
.51256
.51261
.33544
.33547
.33551
.33554
9.51519
.51524
.51529
.51533
.33749
.33753
.33756
.33759
44
43
42
41
+ &
21
22
23
9.50442
.50446
.50451
.50455
.31946
.31949
.31953
.31956
9.50717
.50722
.50727
.50731
.33150
.33153
.33156
.33160
9.50992
.50997
.51001
.51006
.33353
.33357
.33360
.33364
9.51265
.51270
.51275
.51279
.33558
.33561
.33565
.33568
9.51538
.51542
.51547
.51551
.33763
.33766
.33769
.33773
40
39
38
37
+ *'
25
26
27
9.50460
.50465
.50469
.50474
.31959
.31963
.31966
.31970
9.50736
.50740
.50745
.50750
.33163
.33166
.33170
.33173
9.51010
.51015
.51019
.51024
.33367
.33370
.33374
.33377
9.51284
.51288
.51293
.51297
.33571
.33575
.33578
.33583
9:51556
.51560
.51565
.51569
.33776
.33779
.33783
.33786
36
35
34
S3
+ r
29
30
31
9.50478
.50483
.50488
.50492
.31973
.31976
.31980
.31983
9.50754
.50759
.50763
.50768
.33177
.33180
.33183
.33187
9.51029
.51033
.51038
.51042
.33381
.33384
.33388
.33391
9.51302
.51306
.51311
.51315
.33585
.33588
.33593
.33595
9.51574
.51578
.51583
.51587
.33790
.33793
.33797
.33800
32
31
30
29
+ 8'
S3
34
35
9.50497
.50501
.50506
.50511
.31987
.31990
.31993
.31997
9.50772
.50777
.50782
.50786
.33190
.33194
.33197
.33300
9.51047
.51051
.51056
.51061
.33394
.33398
.33401
.33405
9.51320
.51325
.51329
.51334
.33599
.33603
.33605
.33609
9.51592
.51596
.51601
.51605
.33803
.33807
.33810
.33814
28
27
26
25
+ 9X
37
38
39
9.50515
.50520
.50524
.50529
.33000
.33004
.33007
.33010
9.50791
.50795
.50800
.50805
.33304
.33307
.33311
.33314
9.51065
.51070
.51074
.51079
.33408
.33411
.33415
.33418
9.51338
.51343
.51347
.51352
.33613
.33616
.33619
.33633
9.51610
.51614
.51619
.51623
.33817
.33830
.33834
.33837
24
23
22
21
+ 10'
41
42
43
9.50534
.50538
.50543
.50547
.33014
.33017
.33031
.33034
9.50809
.50814
.50818
.50823
.33317
.33331
.33334
.33338
9.51083
.51088
.51092
.51097
.33433
.33435
.33438
.33433
9.51356
.51361
.51365
.51370
.33636
.33639
.33633
.33636
9.51628
.51633
.51637
.51642
.33831
.33834
.33838
.33841
20
19
18
17
+ 11'
45
46
47
9.50552
.50557
.50561
.50566
.33037
.33031
.33034
.33037
9.50827
.50832
.50837
.50841
.33331
.33335
.33338
.33341
9.51102
.51106
.51111
.51115
.33435
.33438
.33443
.33445
9.51374
.51379
.51384
.51388
.33640
.33643
.33646
.33650
9.51646
.51651
.51655
.51660
.33844
.33848
.33851
.33855
16
15
14
13
+ 13'
49
50
51
9.50570
.50575
.50580
.50584
.33041
.33044
.33048
.33051
9.50846
.50850
.50855
.50860
.33345
.33348
.33351
.33355
9.51120
.51124
.51129
.51133
.33449
.33453
.33456
.33459
9.51393
.51397
.51402
.51406
.33653
.33657
.33660
.33663
9.51664
.51669
.51673
.51678
.33858
.33861
.33865
.33868
12
11
10
9
8
7
6
5
+ 13'
53
54
55
9.50589
.50593
.50598
.50603
.33054
.33058
.33061
.33065
9.50864
.50869
.50873
.50878
.33358
.33363
.33365
.33368
9.51138
.51143
.51147
.51152
.33463
.33466
.33469
.33473
9.51411
.51415
.51420
.51424
.33667
.33670
.33674
.33677
9.51682
.51687
.51691
.51696
.33873
.33875
.33878
.33883
+ 14'
57
58
59
9.50607
.50612
.50616
.50621
.33068
.33071
.33075
.33078
9.50882
.50887
.50892
.50896
.33373
.33375
.33379
.33383
9.51156
.51161
.51165
.51170
.33476
.33479
.33483
.33486
9.51429
.51433
.51438
.51442
.33681
.33684
.33687
.33691
9.51700
.51705
.51709
.51714
.33885
.33889
.33893
.33896
4
3
2
1
+ 15'
9.50626
.33083
9.50901
.33385
9.51174
.33490
9.51447
.33694
9.51718
.33899
0
19*> 24™
19h 23™
19^22™
19h 21m
19h20™
TABLE 45. [Page 867
Haver-sines.
s
4^ 40™ 70° (K
4h 4im 70° 15'
4h 42m 70° 307
4h 4sm 70° W
4h 44m 71° (K
s
60
59
58
57
56
55
54
53
Log. Hav.i Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.51718
.51723
.51727
.51732
.32899
.32902
.32906
.32909
9.51988
.51993
.51997
.52002
.33104
.33108
.33111
.33114
9.52257
.52261
.52266
.52270
.33310
.33313
.33317
.33320
9.52525
.52529
.52533
.52538
.33515
.33519
.33522
.33526
9.52791
.52795
.52800
.52804
.33722
.33725
.33728
.33732
+ lx
5
6
7
9.51736
.51741
.51745
.51750
.32913
.32916
.32920
.32923
9.52006
.52011
.52015
.52020
.33118
.33121
.33125
.33128
9.52275
.52279
.52284
.52288
.33323
.33327
.33330
.33334
9.52542
.52547
.52551
.52556
.33529
.33533
.33536
.33540
9.52809
.52813
.52817
.52822
.33735
.33739
.33742
.33746
+ v
9
10
11
9.51754
.51759
.51763
.51768
.32926
.32930
.32933
.32937
9.52024
.52029
.52033
.52038
.33132
.33135
.33138
.33142
9.52293
.52297
.52302
.52306
.33337
.33341
.33344
.33347
9.52560
.52565
.52569
.52573
.33543
.33546
.33550
.33553
9.52826
.52831
.52835
.52839
.33749
.33753
.33756
.33759
52
51
50
49
+ V
13
14
15
9.51772
.51777
.51781
.51786
.32940
.32943
.32947
.32950
9.52042
.52047
.52051
.52056
.33145
.33149
.33152
.33156
9.52311
.52315
.52320
.52324
.33351
.33354
.33358
.33361
9.52578
.52582
.52587
.52591
.33557
.33560
.33564
.33567
9.52844
.52848
.52853
.52857
.33763
.33766
.33770
.33773
48
47
46
45
+ *'
17
18
19
9.51790
.51795
.51799
.51804
.32954
.32957
.32961
.32964
9.52060
.52065
.52069
.52074
.33159
.33162
.33166
.33169
9.52328
.52333
.52337
.52342
.33365
.33368
.33371
.33375
9.52596
.52600
.52605
.52609
.33570
.33574
.33577
.33581
9.52862
.52866
.52870
.52875
.33777
.33780
.33783
.33787
44
43
42
41
+ 5'
21
22
23
9.51808
.51813
.51817
.51822
.32967
.32971
.32974
.32978
9.52078
.52082
.'52087
.52091
.33173
.33176
.33179
.33183
9.52346
.52351
.52355
.52360
.33378
.33382
.33385
.33389
9.52613
.52618
.52622
.52627
.33584
.33588
.33591
.33594
9.52879
.52884
.52888
.52893
.33790
.33794
.33797
.33801
40
39
38
37
36
35
34
33
+ 6'
25
26
27
9.51826
.51831
.51835
.51840
.32981
.32984
.32988
.32991
9.52096
.52100
.52105
.52109
.33186
.33190
.33193
.33197
9.52364
.52369
.52373
.52378
.33392
.33395
.33399
.33402
9.52631
.52636
.52640
.52645
.33598
.33601
.33605
.33608
9.52897
.52901
.52906
.52910
.33804
.33808
.33811
.33814
+ r
29
SO
31
9.51844
.51849
.51853
.51858
.32995
.32998
.33002
.33005
9.52114
.52118
.52123
.52127
.33200
.33203
.33207
.33210
9.52382
.52386
.52391
.52395
.33406
.33409
.33413
.33416
9.52649
.52653
.52658
.52662
.33612
.33615
.33618
.33622
9.52915
.52919
.52923
.52928
.33818
.33821
.33825
.33828
3-2
31
30
29
+ 8/
33
34
35
9.51862
.51867
.51871
.51876
.33008
.33012
.33015
.33019
9.52132
.52136
.52141
.52145
.33214
.33217
.33221
.33224
9.52400
.52404
.52409
.52413
.33419
.33423
.33426
.33430
9.52667
.52671
.52676
.52680
.33625
.33629
.33632
.33636
9.52932
.52937
.52941
.52946
.33832
.33835
.33839
.33842
28
27
26
25
+ v
37
38
39
9.51880
.51885
.51889
.51894
.33022
.33025
.33029
.33032
9.52150
.52154
.52159
.52163
.33227
.33231
.33234
.33238
9.52418 ! .33433
.52422 i .33436
.52427 ; .33440
.52431 l .33444
9.52684
.52689
.52693
.52698
.33639
.33642
.33646
.33649
9.52950
.52954
.52959
.52963
.33845
.33849
.33852
.33856
24
23
22
21
+ 10'
41
42
43
9.51898 .33036
.51903 .33039
.51907 ! .33043
.51912 .33046
9.52168
.52172
.52177
.52181
.33241
.33245
.33248
.33251
9.52436 .33447
.52440 ! .33450
.52444 i .33454
.52449 .33457
9.52702
.52707
.52711
.52715
.33653
.33656
.33660
.33663
9.52968
.52972
.52976
.52981
.33859
.33863
.33866
.33869
20
19
18
17
+ 11'
45
46
47
9.51916
.51921
.51925
.51930
.33049
.33053
.33056
.33060
9.52185
.52190
.52194
.52199
.33255
.33258
.33262
.33265
9.52453 i .33461
.52458 j .33464
.52462 .33467
.52467 .33471
9.52720
.52724
.52729
.52733
.33667
.33670
.33673
.33677
9.52985
.52990
.52994
.52999
.33873
.33876
.33880
.33883
16
15
14
13
+ 12'
49
50
51
9.51934
.51939
.51943
.51948
.33063
.33067
.33070
.33073
9.52203 ! .33269
.52208 .33272
.52212 .33275
.52217 .33279
9.52471
.52476
.52480
.52484
.33474
.33478
.33481
.33485
9.52738
.52742
.52747
.52751
.33680
.33684
.33687
.33691
9.53003 .33887
.53007 .33890
.53012 \ .33894
.53016 .33897
12
11
10
9
8
7
6
5
+ 13'
53
54
55
9.51952
.51957
.51961
.51966
.33077
.33080
.33084
.33087
9.52221
.52226
.52230
.52235
.33282
.33286
.33289
.33293
9.52489
.52493
.52498
.52502
.33488
.33491
.33495
.33498
9.52755
.52760
.52764
.52769
.33694
.33698
.33701
.33704
9.53021 .33900
.53025 .33904
.53029 .33907
.53034 .33911
+ 14'
57
58
59
9.51970
.51975
.51979
.51984
.33090
.33094
.33097
.33101
9.52239
.52244
.52248
.52253
.33296
.33299
.33303
.33306
9.52507
.52511
.52516
.52520
.33502
.33505
.33509
.33512
9.52773
.52778
.52782
.52786
.33708
.33711
.33715
.33718
9.53038 .33914
.53043 .33918
.53047 .33921
.53051 .33925
4
3
2
1
0
+ 15'
9.51988
.33104
9.52257 .33310
9.52525
.33515
9.52791
.33722
9.53056 .33928
19h igm
19* 18m
19*17**
13*16*
19h 15m
Page 868] TABLE 45.
Haversines.
4>* 45^ 71° 15'
4& 46™ 71° 30'
4h 47m 71° 45'
4h 48™ 72° 0'
4*> 49™ 72° 15'
s
i s
Log. Hav.
Nat. Kav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.53056
.53060
.53065
.53069
.33928
.33931
.33935
.33938
9.53320
.53324
.53328
.53333
.34135
.34138
.34142
.34145
9.53582
.53587
.53591
.53595
.34342
.34345
.34349
.34352
9.53844
.53848
.53852
.53857
.34549
.34553
.34556
.34560
9.54104
.54108
.54113
.54117
.34757
.34760
.34764
.34767
60
59
58
57
+ 1'
5
6
7
9.53073
.53078
.53082
.53087
.33942
.33945
.33949
.33952
9.53337
.53342
.53346
.53350
.34149
.34152
.34155
.34159
9.53600
.53604
.53609
.53613
.34356
.34359
.34363
.34366
9.53861
.53865
.53870
.53874
.34563
.34566
.34570
.34573
9.54121
.54126
.54130
.54134
.34771
.34774
.34778
.34781
56
55
54
53
+ V
9
10
11
9.53091
.53096
.53100
.53104
.33956
.33959
.33962
.33966
9.53355
.53359
.53364
.53368
.34162
.34166
.34169
.34173
9.53617
.53622
.53626
.53630
.34369
.34373
.34376
.34380
9.53879
.53883
.53887
.53892
.34577
.34580
.34584
.34587
9.54139
.54143
.54147
.54152
.34784
.34788
.34791
.34795
52
51
50
49
+ 3'
13
14
15
9.53109
.53113
.53118
.53122
.33969
.33973
.33976
.33980
9.53372
.53377
.53381
.53385
.34176
.34180
.34183
.34186
9.53635
.53639
.53643
.53648
.34383
.34387
.34390
.34394
9.53896
.53900
.53905
.53909
.34591
.34594
.34598
.34601
9.54156
.54160
.54165
.54169
.34798
.34802
.34805
.34809
48
47
46
45
+ 4'
17
18
19
9.53126
.53131
.53135
.53140
.33983
.33986
.33990
.33993
9.53390
.53394
.53399
.53403
.34190
.34193
.34197
.34200
9.53652
.53657
.53661
.53665
.34397
.34400
.34404
.34407
9.53913
.53918
.53922
.53926
.34604
.34608
.34611
.34615
9.54173
.54177
.54182
.54186
.34812
.34816
.34819
.34823
44
43
42
41
+ 5X
21
22
23
9.53144
.53148
.53153
.53157
.33997
.34000
.34004
.34007
9.53407
.53412
.53416
.53421
.34204
.34207
.34211
.34214
9.53670
.53674
.53678
.53683
.34411
.34414
.34418
.34421
9.53931
.53935
.53939
.53944
.34618
.34622
.34625
.34629
9.54190
.54195
.54199
.54203
.34826
.34830
.34833
.34836
40
39
38
37
+ 6'
25
26
27
9.53162
.53166
.53170
.53175
.34011
.34014
.34018
.34021
9.53425
.53429
.53434
.53438
.34218
.34221
.34224
.34228
9.53687
.53691
.53696
.53700
.34425
.34428
.34432
.34435
9.53948
.53952
.53957
.53961
.34632
.34636
.34639
.34643
9.54208
.54212
.54216
.54221
.34840
.34843
.34847
.34850
36
35
34
33
+ 1'
29
30
31
9.53179
.53184
.53188
.53192
.34024
.34028
.34031
.34035
9.53442
.53447
.53451
.53456
.34231
.34235
.34238
.34242
9.53704
.53709
.53713
.53718
.34439
.34442
.34445
.34449
9.53966
.53970
.53974
.53978
.34646
.34649
.34653
.31656
9.54225
.54229
.54234
.54238
.34854
.34857
.34861
.34864
32
31
30
29
+ 8'
33
34
35
9.53197
.53201
.53206
.53210
.34038
.34042
.34045
.34049
9.53460
.53464
.53469
.53473
.34245
.34249
.34252
.34256
9.53722
.53726
.53731
.53735
.34152
.34456
.34459
.34463
9.53983
.53987
.53991
.53996
.34660
.34663
.34667
.34670
9.54242
.54247
.54251
.54255
.34868
.34871
.34875
.34878
28
27
26
25
+ 9/
37
38
39
9.53214
.53219
.53223
.53228
.34052
.34055
.34059
.34062
9.53477
.53482
.53486
.53491
.34259
.34262
.34266
.34269
9.53739
.53744
.53748
.53752
.34466
.34470
.34473
.34477
9.54000
.54004
.54009
.54013
.34674
.34677
.34681
.34684
9.54260
.54264
.54268
.54272
.34882
.34885
.34888
.34892
24
23
22
21
+ 10'
41
42
43
9.53232
.53236
.53241
.53245
.34066
.34069
.34073
.34076
9.53495
.53499
.53504
.53508
.34273
.34276
.34280
.34283
9.53757
.53761
.53765
.53770
.34480
.34483
.34487
.34490
9.54017
.54022
.54026
.54030
.34688
.34691
.34694
.34698
9.54277
.54281
.54285
.54290
.34895
.34899
.34902
.34906
20
19
18
17
+ 11'
45
46
47
9.53249
.53254
.53258
.53263
.34080
.34083
.34087
.34090
9.53512
.53517
.53521
.53526
.34287
.34290
.34293
.34297
9.53774
.53778
.53783
.53787
.34494
.34497
.34501
.34504
9.54035
.54039
.54043
.54048
.34701
.34705
.34708
.34712
9.54294
.54298
.54303
.54307
.34909
.34913
.34916
.34920
16
15
14
13
+ 12'
49
5(9
5*
9.53267
.53271
.53276
.53280
.34093
.34097
.34100
.34104
9.53530
.53534
.53539
.53543
.34300
.34304
.34307
.34311
9.53792
.53796
.53800
.53805
.34508
.34511
.34515
.34518
9.54052
.54056
.54061
.54065
.34715
.34719
.34722
.34726
9.54311
.54316
.54320
.54324
.34923
.34927
.34930
.34933
12
11
10
9
+ 13'
55
54
55
9.53285
.53289
.53293
.53298
.34107
.34111
.34114
.34118
9.53547
.53552
.53556
.53560
.34314
.34318
.34321
.34325
9.53809
.53813
.53818
.53822
.34521
.34525
.34528
.34532
9.54069
.54074
.54078
.54082
.34729
.34733
.34736
.34739
9.54329
.54333
.54337
.54341
.34937
.34940
.34944
.34947
8
7
6
5
'+ 14'
57
55
59
9.53302
.53307
.53311
.53315
.34121
.34124
.34128
.34131
9.53565
.53569
.53574
.53578
.34328
.34331
.34335
.34338
9.53826
.53831
.53835
.53839
.34535
.34539
.34542
.34546
9.54087
.54091
.54095
.54100
.34743
.34746
.34750
.34753
9.54346
.54350
.54354
.54359
.34951
.34954
.34958
.34961
4
3
2
1
+ 15'
9.53320
.34135
9.53582
.34342
9.53844
.34549
9.54104
.34757
9.54363
.34965
0
19*> 14™
19h 13™
19h 12™
19h urn
19*> 10™
TABLE 45. [Page 869
Haversines.
s
4* 50m 12° 307
4h sim 72° 45'
4h 5%™ 73° O7
4h 53™ 73° 15'
4* 54™ 73° 3(K
s
Log. Hav., Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.; Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.; Nat. Hav.
0
1
2
3
9.54363
.54367
.54372
.54376
.34965
.34968
.34972
.34975
9.54621
.54625
.54629
.54634
.35173
.35176
.35180
.35183
9.54878
.54882
.54886
.54890
.35381
.35385
.35388
.35392
9.55133
.55137
.55142
.55146
.35590
.35594
.35597
.35601
9.55337
.55392
.55396
.55400
.35799
.35803
.35806
.35810
60
59
58
57
+ 1'
5
6
7
9.54380
.54385
.54389
.54393
.34979
.34982
.34986
.34989
9.54638
.54642
.54647
.54651
.35187
.35190
.35194
.35197
9.54895
.54899
.54903
.54907
.35395
.35399
.35402
.35406
9.55150
.55154
.55159
.55163
.35604
.35608
.35611
.35615
9.55404
.55409
.55413
.55417
.35813
.35817
.35820
.35824
56
55
54
53
+ ¥
9
10
11
9.54397
.54402
.54406
.54410
.34992
.34996
.34999
.35003
9.54655
.54659
.54664
.54668
.35201
.35204
.35208
.35211
9.54912
.54916
..54920
.54924
.35409
.35413
.35416
.35420
9.55167
.55171
.55176
.551SO
.35618
.35622
.35625
.35628
9.55421
.55425
.55430
.55434
.35827
.35831
.35834
.35838
52
51
50
49
+ 3'
13
14
15
9.54415
.54419
.54423
.54428
.35006
.35010
.35013
.35017
9.54672
.54677
.54681
.54685
.35215
.35218
.35222
,35225
9.54929
.54933
.54937
.54942
.35423
.35427
.35430
.35434
9.55184
.55188
.55192
.55197
.35632
.35635
.35639
.35642
9.5543S
.55442
.55447
.55451
.35841
.35845
.35848
.35852
48
47
46
45
+ *'
17
18
19
9.54432
.54436
.54440
.54445
.35020
.35024
.35027
.35031
9.54689
.54694
.54698
.54702
.35228
.35232
.35235
.35239
9.54946
.54950
.54954
.54959
.35437
.35441
.35444
.35448
9.55201
.55205
.55209
.55214
.35646
.35649
.35653
.35656
9.55455
.55459
.55463
.55468
.35855
.35859
.35862
.35865
44
43
42
41
+ 5/
21
22
.?.}
9.54449
.54453
.54458
.54462
.35034
.35038
.35041
.35044
9.54707
.54711
.54715
.54719
.35242
.35246
.35249
.35253
9.54963
.54967
.54971
.54976
.35451
.35454
.35458
.35461
9.55218
.55222
.55226
.55231
.35660
.35663
.35667
.35670
9.55472
.55476
.55480
.55485
.35869
.35872
.35876
.35879
40
39
38
37
+ &
25
26
27
9.54466
.54471
.54475
.54479
.35048
.35051
.35055
.35058
9.54724
.54728
.54732
.54736
.35256
.35260
.35263
.35267
9.54980
.54984
.54988
.54993
.35465
.35468
.35472
.35475
9.55235
.55239
.55243
.55248
.35674
.35677
.35681
.35684
9.55489 i .35883
.55493 i .35886
.55497 i .35890
.55501 .35893
36
35
34
33
+ v
29
SO
31
9.54483
.54488
.54492
.54496
.35062
.35065
.35069
.35072
9.54741
.54745
.54749
.54754
.35270
.35274
.35277
.35281
9.54997
.55001
.55005
.55010
.35479
.35482
.35486
.35489
9.55252
.55256
.55260
.55265
.35688
.35691
.35695
.35698
9.55506
.55510
.55514
.55518
.35897
.35900
.35904
.35907
32
31
30
29
+ 8'
S3
34
35
9.54501
.54505
.54509
.54514
.35076
.35079
.35083
.35086
9.54758
.54762
.54766
.54771
.35284
.35288
.35291
.35294
9.55014
.55018
.55022
.55027
.35493
.35496
.35500
.35503
9.55269
.55273
.55277
.55282
.35702
.35705
.35709
.35712
9.55523 1 .35911
.55527 .35914
.55531 i .35918
.55535! .35921
28
27
26
25
+ 9'
37
S8
39
9.54518
.54522
.54526
.54531
.35090
.35093
.35097
.35100
9.54775
.54779
.54784
.54788
.35298
.35301
.35305
.35308
9.55031 ; .35507
.55035 .35510
.55039 ; .35514
.55044 i .35517
9.55286
.55290
.55294
.55298
.35716
.35719
.3^723
.35726
9.55539 .35925
.55544 i .35928
.55548 .35932
.55552 j .35935
24
23
22
21
+ W
41
42
43
9.54535 .35103
.54539 : .35107
.54544 .35110
.54548 i .35114
9.54792
.54796
.54801
.54805
.35312
.35315
.35319
.35322
9.55048 .35521
.55052 .35524
.55057 .35528
.55061 .35531
9.55303
.55307
.55311
.55315
.35730
.35733
.35737
.35740
9.55556
.55561
.55565
.55569
.35939
.35942
.35946
.35949
20
19
18
17
+ 11'
45
46
47
9.54552
.54556
.54561
.54565
.35117
.35121
.35124
.35128
9.54809
.54813
.54818
.54822
.35326
.35329
.35333
.35336
9.55065 ' .35534
.55069 .35538
.55074 .35541
.55078 .35545
9.55320
.55324
.55328
.55332
.35743
.35747
.35750
.35754
9.55573
.55577
.55582
.55586
.35953
.35956
.35960
.35963
16
15
14
13
+ 12'
49
50
51
9.54569
.54574
.54578
.54582
.35131
.35135
.35138
.35142
9.54826
.54831
.54835
.54839
.35340
.35343
.35347
.35350
9.550S2
.55086
.55091
.55095
.35548
.35552
.35555
.35559
9.55337
.55341
.55345
.55349
.35757
.35761
.35764
.35768
9.55590
.55594
.55598
.55603
.35967
.35970
.35974
.35977
12
11
10
9
+ 13'
53
54
55
9.54587
.54591
.54595
.54599
.35145
.35149
.35152
.35156
9.54843
.54848
.54852
.54856
.35354
.35357
.35361
.35364
9.55099
.55103
.55108
.55112
.35562
.35566
.35569
.35573
9.55354
.55358
.55362
.55366
.35771
.35775
.35778
.35782
9.55607
.55611
.55615
.55620
.35981
.35984
.35988
.35991
8
7
6
5
+ W
57
58
59
9.54604
.54608
.54612
.54617
.35159
.35162
.35166
.35169
9.54860
.54865
.54869
.54873
.35368
.35371
.35374
.35378
9.55116
.55120
.55125
.55129
.35576
.35580
.35583
.35587
9.55370 .35785
.55375 .35789
.55379 i .35792
.55383 i .35796
9.55624
.55628
.55632
.55636
.35995
.35998
.36002
.36005
4
3
2
1
+ 15'
9.54621
.35173
9.54878 .35381
9.55133
.35590
9.55387 .35799
9.55641 | .36009
0
19h9m
19^ 8m
19* 7m
19h Qm
IQh JT7J
Page 870] TABLE 45.
Haversines.
s
4h 55™ 73° 45'
4h 53™ 74° 0'
4h 5jm 74° 15'
4h 58m 74° 3<K
4h 59™ 74° 45'
3
60
59
58
57
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.55641
.55645
.55649
.55653
.36009
.36012
.36016
.36019
9.55893
.55897
.55901
.55905
.36218
.36222
.36225
.36229
9.56144
.56148
.56152
.56156
.36428
.36431
.36435
.36438
9.56393
.56397
.56402
.56406
.36638
.36642
.36645
.36649
9.56642
.56646
.56650
.56654
.36848
.36852
.36855
.36859
+ v
5
6
7
9.55657
.55662
.55666
.55670
.36023
.36026
.36030
.36033
9.55909
.55914
.55918
.55922
.36232
.36236
.36239
.36243
9.56160
.56164
.56169
.56173
.36442
.36445
.36449
.36452
9.56410
.56414
.56418
.56422
.36652
.36656
.36659
.36663
9.56658
.56663
.56667
.56671
.36862
.36866
.36869
.36873
56
55
54
53
+ 2'
9
10
11
9.55674
.55678
.55683
.55687
.36036
.36040
.36043
.36047
9.55926
.55930
.55935
.55939
.36246
.36250
.36253
.36257
9.56177
.56181
.56185
.56189
.36456,
.36459
.36463
.36466
9.56426
.56431
.56435
.56439
.36666
.36670
.36673
.36677
9.56675
.56679
.56683
.56687
.36877
.36880
.36884
.36887
52
51
50
49
+ &
13
14
15
9.55691
.55695
.55699
.55704
.36050
.36054
.36057
.36061
9.55943
.55947
.55951
.55955
.36260
.36264
.36267
.36271
9.56194
.56198
.56202
.56206
.36470
.36473
.36477
.36480
9.56443
.56447
.56451-
.56456
.36680
.36684
.36687
.36691
9.56692
.56696
.56700
.56704
.36891
.36894
.36898
.36901
48
47
46
45
+ *'
17
18
19
9.55708
.55712
.55716
.55721
.36064
.36068
.38071
.36075
9.55960
.55964
.55968
.55972
.36274
.36278
.36281
.36285
9.56210
.56214
.56219
.56223
.36484
.36487
.36491
.36494
9.56460
.56464
.56468
.56472
.36694
.36698
.36701
.36705
9.56708
.56712
.56716
.56720
.36905
.36908
.36912
.36915
44
43
42
41
+ &
21
22
23
9.55725
.55729
.55733
.55737
.26078
.36082
.36085
.36089
9.55976
.55981
.55985
.55989
.36288
.36292
.36295
.36299
9.56227
.56231
.56235
.56239
.36498
.36501
.36505
.36508
9.56476
.56480
.56485
.56489
.36708
.36712
.36715
.36719
9.56725
.56729
.56733
.56737
.36919
.36922
.36926
.36929
40
39
38
37
+ V
25
26
27
9.55742
.55746
.55750
.55754
.36092
.36096
.36099
.36103
9.55993
.55997
.56001
.56006
.36302
.36306
.36309
.36313
9.56244
.56248
.56252
.56256
.36512
.36515
.36519
.36522
9.56493
.56497
.56501
.56505
.36722
.36726
.36729
.36733
9.56741
.56745
.56749
.56753
.36933
.36936
.36940
.36943
36
35
34
33
+ r
29
30
31
9.55758
.55763
.55767
.55771
.36106
.36110
.36113
.36117
9.56010
.56014
.56018
.56022
.36316
.36320
.36323
.36327
9.56260
.56264
.56269
.56273
.36526
.36529
.36533
.36536
9.56509
.56514
.56518
.56522
.36736
.36740
.36743
.36747
9.56758
.56762
.56766
.56770
.36947
.36950
.36954
.36957
32
31
30
29
+ 8'
33
34
35
9.55775
.55779
.55784
.55788
.36120
.36124
.36127
.36131
9.56027
.56031
.56035
.56039
.36330
.36334
.36337
.36341
9.56277
.56281
.56285
.56289
.36540
.36543
.36547
.36551
9.56526
.56530
.56534
.56538
.36750
.36754
.36757
.36761
9.56774
.56778
.56782
.56786
.36961
.36964
.36968
.36971
28
27
26
25
+ v
37
38
39
9.55792
.55796
.55800
.55805
.36134
.36138
.36141
.36145
9.56043
.56047
.56052
.56056
.36344
.36348
.36351
.36355
9.56294
.56298
.56302
.56306
.36554
.36558
.36561
.36565
~T86568
.36572
.36575
.36579
9.56543
.56547
.56551
.56555
.36764
.36768
.36771
.36775
9.56791
.56795
.56799
.56803
.36975
.36978
.36982
.36985
24
23
22
21
+ 10'
41
42
43
9.55809
.55813
.55817
.55821
.36148
.36152
.36155
.36159
9.56060
.56064
.56068
.56073
.36358
.36362
.36365
.36368
9.56310
.56314
.56318
.56323
9.56559
.56563
.56567
.56572
.36778
.36782
.36785
.36789
9.56807
.56811
.56815
.56819
.36989
.36992
.36996
.369819
20
19
18
17
+ 11'
45
46
47
9.55826
.55830
.55834
.55838
.36162
.36166
.36169
.36173
9.56077
.56081
.56085
.56089
.36372
.36376
.36379
.36382
9.56327
.56331
.56335
.56339
.36582
.36586
.36589
.36593
9.56576
.56580
.56584
.56588
.36792
.36796
.36799
.36803
9.56824
.56828
.56832
.56836
.37003
.37006
.37010
.37013
16
15
14
13
+ 12'
49
50
51
9.55842
.55846
.55851
.55855
.36176
.36180
.36183
.36187
9.56093
.56098
.56102
.56106
.36386
.36389
.36393
.36396
9.56343
.56348
.56352
.56356
.36596
.36600
.36603
.36607
9.56592
.56596
.56601
.56605
.36806
.36810
.36813
.36817
9.56840
.56844
.56848
.56852
.37017
.37020
.37024
.37027
11
10
9
+ 13'
53
54
55
9.55859
.55863
.55867
.55872
.36190
.36194
.36197
.36201
9.56110
.56114
.56118
.56123
.36400
.36403
.36407
.36410
9.56360
.56364
.56368
.56373
.36610
.36614
.36617
.36621
9.56609
.56613
.56617
.56621
.36820
.36824
.36827
.36831
9.56856
.56861
.56865
.56869
.37031
.37034
.37038
.37041
8
7
6
5
+ 14'
57
58
59
9.55876
.55880
.55884
.55888
.36204
.36208
.36211
.36215
9.56127
.56131
.56135
.56139
.36414
.36417
.36421
.36424
9.56377
.56381
.56385
.56389
.36624
.36628
.36631
.36635
9.56625
.56630
.56634
.56638
.36834
.36838
.36841
.36845
9.56873
.56877
.56881
.56885
.37045
.37049
.37052
.37055
4
3
2
1
+ 15'
9.55893
.36218
9.56144
.36428
9.56393
.36638
9.56642
.36848
9.56889
.37059
0
19*1,4™,
igtigm
19h 2m
19*> im
IdhQfn
TABLE 45. [Page 871
Haversines.
s
5h Qm 75° O7
5h im 75° 15'
5h om 750 30/
5* s™ 75° 45'
5* 4m 76° V
s
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.| Nat. Hav.
Log. Hav.j Nat. Hav.
Log. Hav.j Nat. Hav.
0
1
2
S
9.56889
.56893
.56898
.56902
.37059
.37063
.37066
.37070
9.57136 .37270
.57140 .37273
.57144 .37277
.57148 .37280
9.57381
.57385
.57389
.57393
.37481
.37485
.37488
.37492
9.57625
.57629
.57633
.57637
.37692
.37696
.37699
.37703
9.57868
.57872
.57876
.57881
.37904
.37907
.37911
.37914
60
59
58
57
+ 1'
5
6
7
9.56906
.56910
.56914
.56918
.37073
.37077
.37080
.37084
9.57152
.57156
.57160
.57165
.37284
.37287
.37291
.37295
9.57397
.57402
.57406
.57410
.37495
.37499
.37502
.37506
9.57642 .37706
.57646 .37710
.57650 .37713
.57654 • .37717
9.57885
.57889
.57893
.57897
.37918
.37922
.37925
.37929
56
55
54
53
+ 2'
9
10
11
9.56922
.56926
.56931
.56935
.37087
.37091
.37094
.37098
9.57169 .37298
.57173 .37302
.57177 .37305
.57181 .37309
9.57414
.57418
.57422
.57426
.37509
.37513
.37516
.37520
9.57658 .37721
.57662 i .37724
.57666 ! .37728
.57670 .37731
9.57901
.57905
.57909
.57913
.37932
.37936
.37939
.37943
52
51
50
49
48
47
46
45
+ &
13
14
15
9.56939
.56943
.56947
.56951
.37101
.37105
.37108
.3711?
9.57185 .37312
.57189 .37316
.57193 .37319
.57197! .37323
9.57430
.57434
.57438
.57442
.37523
.37527
.37530
.37534
9.57674
.57678
.57682
.57686
.37735
.37738
.37742
.37745
9.57917
.57921
.57925
.57929
.37946
.37950
.37953
.37957
+ *'
17
18
19
9.56955
.56959
.56963
.56968
.37115
.37119
.3712?
.37126
9.57201 .37326
.57205 .37330
.57210 .37333
.572141 .37337
9.57446
.57450
.57454
.57459
.37537
.37541
.37544
.37548
9.57690
.57694
.57698
.57702
.37749
.37752
.37756
.37759
9.57933
.57937
.57941
.57945
.37960
.37964
.37987
.37971
44
43
42
41
+ 5'
21
22
23
9.56972
.56976
.56980
.56984
.37129
.37133
.37136
.37140
9.57218
.57222
.57226
.57230
.37340
.37344
.37347
.37351
9.57463-
.57467
.57471
.57475
.37551
.37555
.37558
.37562
9.57706
.57711
.57715
.57719
.37763
.37766
.37770
.37773
9.57949
.57953
.57957
.57961
.37974
.37978
.37982
.37985
40
39
38
37
+ *'
25
26
27
9.56988
.56992
.56996
.57000
.37143
.37147
.37150
.37154
9.57234 .37354
.57238 .37358
.57242 .37361
.57246 • .37365
9.57479
.57483
.57487
.57491
.37566
.37569
.37573
.37576
9.57723
.57727
.57731
.57735
.37777
.37780
.37784
.37788
9.57965
.57969
.57973
.57977
.37989
.37992
.37996
.37999
36
35
34
33
+ v
29
30
31
9.57005
.57009
.57013
.57017
.37157
.37161
.37164
.37168
9.57250
.57255
.57259
.57263
.37368
.37372
.37375
.37379
9.57495
.57499
.57503
.57507
.37580
.37583
.37587
.37590
9.57739
.57743
.57747
.57751
.37791
.37794
.37798
.37802
9.57981
.57986
.57990
.57994
.38003
.38006
.38010
.38013
32
31
30
29
+ 8'
S3
34
35
9.57021
.57025
.57029
.57033
.37171
.37175
.37179
.37182
9.57267
.57271
.57275
.57279
.37382
.37386
.37389
.37393
9.57511
.57516
.57520
.57524
.37594
.37597
.37601
.37604
9.57755
.57759
.57763
.57767
.37805
.37809
.37812
.37816
9.57998
.58002
.58006
.58010
.38017
.38020
.38024
.38027
28
27
26
25
+ *
37
38
39
9.57037
.57042
.57046
.57050
.37186
.37189
.37193
.37196
9.57283
.57287
.57291
.57295
.37397
.37400
.37404
.37407
9.57528
.57532
.57536
.57540
.37608
.37611
.37615
.37618
9.57771
.57775
.57779
.57783
.37819
.37823
.37826
.37830
9.58014
.58018
.58022
.58026
.38031
.38034
.38038
.38042
24
23
22
"~21
+ KK
41
42
43
9.57054
.57058
.57062
.57066
.37200
.37203
.37207
.37210
9.57299
.57304
.57308
.57312
.37411
.37414
.37418
.37421
9.57544
.57548
.57552
.57556
.37622
.37625
.37629
.37632
9.57787
.57792
.57796
.57800
.37833
.37837
.37840
.37844
9.58030
.58034
.58038
,58042
.38045
.38049
.38052
.38056
20
19
18
17
+ 11'
45
46
47
9.57070
.57074
.57078
.57083
.37214
.37217
.37221
.37224
9.57316
.57320
.57324
.57328
.37425
.37428
.37432
.37435
9.57560
.57564
.57568
.57572
.37636
.37639
.37643
.37647
9.57804
.57808
.57812
.57816
.37847
.37851
.37855
.37858
9.58046
.58050
.58054
.58058
.38059
.38063
.38066
.38070
16
15
14
13
+ 12'
49
50
51
9.57087
.57091
.57095
.57099
.37228
.37231
.37235
.37238
9.57332
.57336
.57340
.57344
.37439
.37442
.37446
.37449
9.5/5 1 i
.57581
.57585
.57589
.37650
.37654
.37657
.37661
9.57820
.57824
.57828
.57832
.37862
.37865
.37869
.37872
9,58062
.58066
.58070
.58074
.38073
.38077
.38080
.38084
U
11
10
9
+ 13'
53
54
55
9.57103
.57107
.57111
.57115
.37242
.37245
.37249
.37252
9.57348
.57353
.57357
.57361
.37453
.37456
.37460
.37463
9.57593
.57597
.57601
.57605
.37664
.37668
.37671
.37675
9.57836
.57840
.57844
.57848
.37876
.37879
.37883
.37886
9.58078
.58082
,58086
,58090
.38087
.38091
.38095
.38098
8
7
6
5
+ 1*'
57
58
59
9.57119
.57124
.57128
.57132
.37256
.37259
.37263
.3726G
9.57365
.57369
.57373
.57377
.37467
.37470
.37474
.37477
9.57609
.57613
.57617
.57621
.37678
.37682
.37685
.37689
9.57852
.57856
.57860
.57864
.37890
.37893
.37897
.37900
9,58094
.58098
.58102
.58106
.38102
.38105
.38109
.38112
4
3
2
1
+ 15'
9.57136
.37270
9.57381
.37481
9.57625
.37692
9.57868 | .37904
9.58110
.38116
0
18* 59m
18*68*
18* 57"»
18*56™
18* 55"»
Page 872] TABLE 45.
Haversines.
s
£fc 5™ 76° 15'
5h em 76° 3(K
5h 7m 76° 45'
5h sm 77° (K
5& pro 770 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.58110
.58114
.58118
.58122
.38116
.38119
.38123
.38126
9.58351
.58355
.58359
.58363
.38328
.38331
.38335
.38338
9.58591
.58595
.58599
.58603
.38540
.38544
.38547
.38551
9.58830
.58834
.58838
.58842
.38752
.38756
.38760
.38763
9.59068
.59072
.59076
.59079
.38965
.38969
.38972
.38976
60
59
58
57
+ lx
5
6
7
9.58126
.58131
.58135
.58139
.38130
.38133
.38137
.38140
9.58367
.58371
.58375
.58379
.38342
.38345
.38349
.38352
9.58607
.58611
.58615
.58619
.38554
.38558
.38561
.38565
9.58846
.58850
.58854
.58858
.38767
.38770
.38774
.38777
9.59083
.59087
.59091
.59095
.38979
.38983
.38986
.38990
56
55
54
53
+ V
9
10
11
9.58143
.58147
.58151
.58155
.38144
.38148
.38151
.38155
9.58383
.58387
.58391
.58395
.38356
.38360
.38363
.38367
9.58623
.58627
.58631
.58635
.38568
.38572
.38575
.38579
9.58862
.58866
.58870
.58874
.38781
.38784
.38788
.38791
9.59099
.59103
.59107
.59111
.38994
.38997
.39001
**>*/'MlTC
52
51
50
49
+ 3'
13
14
15
9.58159
.58163
.58167
.58171
.38158
.38162
.38165
.38169
9.58399
.58403
.58407
.58411
.38370
.38374
.38377
.38381
9.58639
.58643
.58647
.58651
.38582
.38586
.38590
.38593
9.58878
.58882
.58885
.58889
.38795
.38799
.38802
.38806
9.59115
.59119
.59123
.59127
.39008
.39011
.39015
.39018
48
47
46
45
+ V
17
18
19
9.58175
.58179
.58183
.58187
.38172
.38176
.38179
.38183
9.58415
.58419
.58423
.58427
.38384
.38388
.38391
.38395
9.58655
.58659
.58663
.58667
.38597
.38600
.38604
.38607
9.58893
.58897
.58901
.58905
.38809
.38813
.38816
.38820
9.59131
.59135
.59139
.59143
.39022
.39025
.39029
.39033
44
43
42
41
+ &
21
22
23
9.58191
.58195
.58199
.58203
.38186
^38190
.38193
.38197
9.58431
.58435
.58439
' .58443
.38398
.38402
.38406
.38409
9.58671
.58675
.58679
.58683
.38611
.38614
.38618
.38621
9.58909
.58913
.58917
.58921
.38823
.38827
.38830
.38834
9.59147
.59151
.59155
.59158
.39036
.39040
.39043
.39047
40
39
38
37
+ *
25
JW
£7
9.58207
.58211
.58215
.58219
.38200
.38204
.38208
.38211
9.58447
.58451
.58455
.58459
.38413
.38416
.38420
.38423
9.58687
.58691
.58695
.58699
.38625
.38628
.38632
.38636
9.58925
.58929
.58933
.58937
.38837
.38841
.38845
.38848
9.59162
.59166
.59170
.59174
.39050
.39054
.39057
.39061
36
35
34
33
+ 1'
29
30
31 •
9.58223
.58227
.58231
.58235
.38215
.38218
.38222
.38225
9.58463
.58467
.58471
.58475
.38427
.38430
.38434
.38437
9.58703
.58707
.58711
.58715
.38639
.38643
v.38646
.38650
9.58941
.58945
.58949
.58953
.38852
.38855
.38859
.38862
9.59178
.59182
.59186
.59190
.39064
.39068
.39072
.39075
32
31
30
29
+ 8'
33
34
35
9.58239
.58243
.58247
.58251
.38229
.38232
.38236
.38239
9.58479
.58483
.58487
.58491
.38441
.38444
.38448
.38451
9.58719
.58723
.58727
.58731
.38653
.38657
.38660
.38664
9.58957
.58961
.58965
.58969
.38866
.38869
.38873
.38876
9.59194
.59198
.59202
.59206
.39079
.39082
.39086
.39089
28
27
26
25
+ 9X
57
55
££
9.58255
.58259
.58263
.58267
.38243
.38246
.38250
.38254
9.58495
.58499
.58503
.58507
.38455
.38459
.38462
.38466
9.58735
.58739
.58742
.58746
.38667
.38671
.38675
.38678
9.58973
.58977
.58981
.58985
.38880
.38884
.38887
.38891
9.59210
.59214
.59218
.59222
.39093
.39096
.39100
.39103
24
23
22
21
+ 10'
41
42
43
9.58271
.58275
.582V9
.58283
.38257
.38261
.38264
.38268
9.58511
.58515
.58519
.58523
.38469
.38473
.38476
.38480
9.58750
.58754
.58758
.58762
.38682
.38685
.38689
.38692
9.58989
.58992
.58996
.59000
.38894
.38898
.38901
.38905
9.59225
.59229
.59233
.59237
.39107
.39111
.39114
.39118
20
19
18
17
+ H'
45
46
47
9.58287
.58291
.58295
.58299
.38271
.38275
.38278
.38282
9.58527
.58531
.58535
.58539
.38483
.38487
.38490
.38494
9.58766
.58770
.58774
.58778
.38696
.38699
.38703
.38706
9.59004
.59008
.59012
.59016
.38908
.38912
.38915
.38919
9.59241
.59245
.59249
.59253
.39121
.39125
.39128
.39132
16
15
14
13
+ 12'
49
,50
£?
9.58303
.58307
.58311
.58315
.38285
.38289
.38292
.38296
9.58543
.58547
.58551
.58555
.38498
.38501'
.38505
.38508
9.58782
.58786
.58790
.58794
.38710
.38713
,38717
.38721
9.59020
.59024
.59028
.59032
.38923
.38926
.38930
.38933
9.59257
.59261
.59265
.59269
.39135
.39139
.39143
.39146
12
11
10
9
+ 13'
53
54
55
9.58319
.58323
.58327
.58331
.38299
.38303
.38307
.38310
9.58559
.58563
.58567
.58571-
.38512
.38515
.38519
.38522
9.58798
.58802
.58806
.58810
.38724
.38728
.38731
:38735
9.59036
.59040
.59044
.59048
.38937
.38940
.38944
.38947
9.59273
.59277
.59281
.59285
.39150
.39153
.39157
.39160
8
7
6
5
+ 14'
57
5S
59
9.58335
.58339
.58343
.58347
.38314
.38317
.38321
.38324
9.58575
.58579
.58583
.58587
.38526
.38529
.38533
.38536
9.58814
.58818
.58822
.58826
.38738
.38742
.38745
.38749
9.59052
.59056
.59060
.59064
.38951
.38954
.38958
.38962
9.59289
.59292
.59296
.59300
.39164
.39167
.39171
.39174
4
3
2
1
+ 15'
9.58351
.38328
9.58591
.38540
9.58830
.38752
9.59068
.38965
9.59304
.39178
0
18* 54m
18* 53m
18* 52^
18* 51™>
18* 50m
TABLE 45. [Page 873
Haversines.
s
oh iQm 77° 30'
5h urn 77° 45'
5h i2m 78° <K
5* is™ 78° 15'
5h 14m 78° 307
3
60
59
58
57
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.; Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
>3
9.59304
.59308
.59312
.59316
.39178
.39182
.39185
.39189
9.59540
.59544
.59548
.59552
.39391
.39395
.39398
.39402
9.59774
.59778
.59782
.59786
.39604
.39608
.39612
.39615
9.60008
.60012
.60016
.60020
.39818
.39821
.39825
.39829
9.60240
.60244
.60248
.60252
.40032
.40035
.40039
.40042
j_ -^/
5
6
7
9.593'20
.59324
.59328
.59332
.39192
.39196
.39199
.39203
9.59556
.59559
.59563
.59567
.39405
.39409
.39412
.39416
9.59790
.59794
.59798
.59802
.39619
.39622
.39626
.39629
9.60023
.60027
.60031
.60035
.39832
.39836
.39839
.39843
9.60256
.60260
.60263
.60267
.40046
.40049
.40053
.40057
56
55
54
53
+ *
9
10
11
9.59336
.59340
.59344
.59348
.39206
.39210
.39214
.39217
9.59571
.59575
.59579
.59583
.39420
.39423
.39427
.39430
9.59S06
.59809
.59813
.59817
.39633
.39636
.39640
.39644
9.60039
.60043
.60047
.60051
.39846
.39850
.39854
.39857
9.60271
.60275
.60279
.60283
.40060
.40064
.40067
.40071
52
51
50
49
+ 3'
13
14
15
9.59351
.59355
.59359
.59363
.39221
.39224
.39228
.39231
9.59587
.59591
.59595
.59599
.39434
.39437
.39441
.39444
9.59821
.59825
.59829
.59833
.39647
.39651
.39654
.39658
9.60054
.60058
.60062
.60066
.39861
.39864
.39868
.39871
9.60287
.60291
.60294
.60298
.40074
.40078
.40081
.40085
48
47
46
45
+ 4'
17
18
19
9.59367
.59371
.59375
.59379
.39235
.39238
.39242
.39245
9.59602
.59606
.59610
.59614
.39448
.39451
.39455
.39459
9.59837 .39661
,59841 .39665
.59845 .39668
.59848 .39672
9.60070
.60074
.60078
.60082
.39875
.39878
.39882
.39886
9.60302
.60306
.60310
.60314
.40089
.40092
.40096
.40099
44
4-3
42
41
+ $'
21
22
23
9.59383
.59387
.59391
:59395
.39249
.39253
.392o6
.39260
9.59618
.59622
.59626
.59630
.39462
.39460
.39469
.39473
9.59852 .39676
.59856 .39679
.59860 .39683
.59864 .39686
9.60085
.60089
.60093
.60097
.39889
.39893
.39898
.39900
9.60318
.60321
.60325
.60329
.40103
.40106
.40110
.40114
40
39
38
37
+ 6'
-25
26
27
9.59399
.59403
.59406
.59410
.39263
.39267
.39270
.39274
9.59634
.59638
.59642
.59646
.39476
.39480
.39484
.39487
9.59868 .39690
.59872 .39693
.59876 .39697
.59880 .39700
9.60101
.60105
.60109
.60113
.39903
.39907
.39910
.39914
9.60333
.60337
.60341
.60345
.40117
.40121
.40124
.40128
36
35
34
33
+ r
29
30
31
9.59414
.59418
.59422
.59426
.39277
.39281
.39285
.39288
9.59649
.59653
.59657
.59661
.39491
.39494
.39498
.39501
9.59883 .39704
.59887 .39708
.59891 .39711
.59895 .39715
9.60116
.60120
.60124
.60128
.39918
.39921
.39925
.39928
9.60348
.60352
.60356
.60360
.40131
.40135
.40139
.40142
32
31
30
29
+ 8/
S3
S4
35
9.59430
.59434
.59438
.59442
.39292
.39295
.39299
.39302
9.59665
.59669
.59673
.59677
.39505
.39508
.39512
.39516
9.59899
.59903
.59907
.59911
.39718
.39722
.39725
.39729
9.60132
.60136
.60140
.60144
.39932
.39935
.39939
.39943
9.60364
.60368
.60372
.60375
.40146
.40149
.40153
.40156
28
27
26
25
+ 9'
37
S8
S9
9.59446
.59450
.59454
.59458
.39306
.39309
.39313
.39317
9.59681
.59685
.59688
.59692
.39519
.39523
.39526
.39530
9.59915
.59918
.59922
.59926
.39732
.39738
.39739
.39743
9.60147
.60151
.60155
.60159
.39946
.39950
.39953
.39957
9.60379
.60383
.60387
.60391
.40160
.40163
.40167
.40171
24
23
22
ti
+ W
41
42
4-3
9.59461
.59465
.59469
.59473
.39320
.39324
.39327
.39331
9.59696
.59700
.59704
.59708
.39533
.39537
.39540
.39544
9.59.930
.59934
.59938
.59942
.39746
.39750
.39754
.39757
9.60163
.60167
• .60171
.60175
.39960
.39964
.39967
.39971
9.60395
.60399
.60402
.60406
.40174
.40178
.40181
.40185
20
19
18
17
+ 11'
45
46
47
9.59477
.59481
.59485
.59489
.39334
.39338
.39341
.39345
9.59712
.59716
.59720
.59724
.39548
.39551
.39555
.39558
9.59946
.59950
.59953
.59957
.39761
.39765
'39768
-.39772
9.60178
.60182
.60186
\60190
.39975
.39978
.39982
.39985
9.60410
.60414
.60418
.60422
.40188
.40192
.40196
.40199
16
15
14
IS
+ 12'
49
50
51
9.59493
.59497
.59501
.59505
.39348
.39352
.39356
.39359
9.59728
.59731
.59735
.59739
.39562
.39565
.39569
.39572
9.59961
.59965
.59969
.59973
.39775
.39779
.39782
.39786
9.60194
.60198
.60202
.60206
.39989
.39992
.39996
.40000
9.60426
.60429
.60433
.60437
.40203
.40206
.40210
.40213
12
11
10
9
+ 13'
5-5
54
55
9.59508
.59512
.59516
.59520
.39363
.39366
.39370
.39373
9.59743
.59747
.59751
.59755
.39576
.39580
.39583
.39587
9.59977
.59981
.59985
.59988
.39789
.39793
.39796
.39800
9.60209
.60213
.60217
.60221
.40003
.40007
.40010
.40014
9.60441
.60445
.60449
.60452
.40217
.40220
.40224
.40228
8
7
6
5
+ 14'
57
58
59
9.59524
.59528
.59532
.59536
.39377
.39380
.39384
.39388
9.59759
.59763
.59767
.59770
.39590
.39594
.39597
.39601
9.59992
.59996
.60000
.60004
.39803
.39807
.39811
.39814
9.60225
.60229
.60233
.60236
.40017
.40021
.40024
.40028
9.60456
.60460
.60464
.60468
.40231
.40235
.40238
.40242
4
S
2
1
+ 15'
9.59540
.39391
9.59774 .39604
9.60008 .39818
9.60240 .40032
9.60472 : .40245
0
18* 49™
18*48*
ISh 47m
18*46*
18*45™
61828°— 16 18
Page 874] TABLE 45.
Haversines.
s
5U I5m 78° 45'
5h 16m 79° 0'
5h 17m 79° 15'
5h igm 79° 30'
5h idm 790 45/
s
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.60472
.60476
.60479
.60483
.40245
.40249
.40253
.40256
9.60702
.60706
.60710
.60714
.40460
.40463
.40467
.40470
9.60931
.60935
.60939
.60943
.40674
.40677
.40681
.40685
9.61160
.61164
.61167
.61171
.40888
.40892
.40895
.40899
9.61387
.61391
.61395
.61399
.41103
.41106
.41110
.41114
60
59
58
57
+ 1'.
5
6
7
9.60487
.60491
.60495
.60499
.40260
.40263
.40267
.40270
9.60717
.60721
.60725
.60729
.40474
.40477
.40481
.40485
9.60947
.60951
.60954
.60958
.40688
.40692
.40695
.40699
9.61175
.61179
.61183
.61186
.40903
.40906
.40910
.40913
9.61402
.61406
.61410
.61414
.41117
.41121
.41124
.41128
56
55
54
53
+ %'
9
10
11
9.60502
.60506
.60510
.60514
.40274
.40277
.40281
.40285
9.60733
.60737
.60740
.60744
.40488
.40492
.40495
.40499
9.60962
.60966
.60970
.60973
.40702
.40706
.40710
.40713
9.61190
.61194
.61198
.61202
.40917
.40920
.40924
.40928
9.61417
.61421
.61425
.61429
.41131
.41135
.41139
.41142
52
51
50
49
+ *
IS
14
15
9.60518
.60522
.60526
.60529
.40288
.40292
.40295
.40299
9.60748
.60752
.60756
.60760
.40502
.40506
.40510
.40513
9.60977
.60981
.60985
.60989
.40717
.40720
.40724
.40727
9.61205
.61209
-.61213
.61217
.40931
.40935
.40938
.40942
9.61433
.61436
.61440
.61444
.41146
.41149
.41153
.41156
48
47
46
45
+ V
17
18
19
9.60533
.60537
.60541
.60545
.40303
.40306
.40310
.40313
9.60763
.60767
.60771
.60775
.40517
.40520
.40524
.40527
9.60992
.60996
.61000
.61004
.40731
.40735
.40738
.40742
9.61221
.61224
.61228
.61232
.40945
.40949
.40953
.40956
9.61448
.61451
.61455
.61459
.41160
.41164
.41167
.41171
44
43
42
41
+ &'
21
22
23
9.60549
.60552
.60556
.60560
.40317
.40320
.40324
.40328
9.60779
.60783
.60786
.60790
.40531
.40535
.40538
.40542
9.61008
.61012
.61015
.61019
.40745
.40749
'40752
.40756
9.61236
.61240
.61243
.61247
.40960
.40963
.40967
.40970
9.61463
.61467
.61470
.61474
.41174
.41178
.41182
.41185
40
39
38
37
+ 6'
25
26
27
9.60564
.60568
.60572
.60576
.40331
.40335
.40338
.40342
9.60794
.60798
.60802
.60805
.40545
.40549
.40552
.40556
9.61023
.61027
.61031
.61034
.40760
.40763
.40767
.40770
9.61251
.61255
.61258
.61262
.40974
.40978
.40981
.40985
9.61478
.61482
.61485
.61489
.41189
.41192
.41196
.41199
36
35
34
33
+ r
29
SO
SI
9.60579
.60583
.60587
.60591
.40345
.40349
.40352
.40356
9.60809
.60813
.60817
.60821
.40560
.40563
.40567
.40570
9.61038
.61042
.61046
.61050
.40774
.40777
.40781
.40785
9.61266
.61270
.61274
.61277
.40988
.40992
.40996
.40999
9.61493
.61497
.61500
.61504
.41203
.41207
.41210
.41214
32
31
30
29
+ &
33
34
35
9.60595
.60599
.60602
.60606
.40360
.40363
.40367
.40370
9.60825
.60828
.60832
.60836
.40574
.40577
.40581
.40585
9.61053
.61057
.61061
.61065
.40788
.40792
.40795
.40789
9.61281
.61285
.61289
.61293
.41003
.41006
.41010
.41013
9.61508
.61512
.61516
.61519
.41217
.41221
.41225
.41228
28
27
26
25
+ V
37
38
39
9.60610
.60614
.60618
.60622
.40374
.40377
.40381
.40385
9.G0840
.60844
.60847
.60851
.40588
.40592
.40595
.40599
9.61069
.61072
.61076
.61080
.40802
.40806
.40810
.40813
9.61296
.61300
.61304
.61308
.41017
.41021
.41024
.41028
9.61523
.61527
.61531
.61534
.41232
.41235
.41239
.41242
24
23
22
21
+ W
41
42
43
9.60625
.60629
.60633
.60637
.40388
.40392
.40395
.40399
9.60855
.60859
.60863
.60867
.40602
.40606
.40610
.40613
9.61084
.61088
.61091
.61095
.40817
.40820
.40824
.40827
9.61312
.61315
.61319
.61323
.41031
.41035
.41039
.41042
9.61538
.61542
.61546
.61549
.41246
.41250
.41253
.41257
20
19
18
17
+ 11'
45
46
47
9.60641
.60645
.60648
.60652
.40402
.40406
.40410
.40413
9.60870
.60874
.60878
.60882
.40617
.40620
.40624
.40627
9.61099
.61103
.61107
.61110
.40831
.40835
.40838
.40842
9.61327
.61330
.61334
.61338
.41046
.41049
.41053
.41056
9.61553
.61557
.61561
.61565
.41260
.41264
.41267
.41271
16
15
14
13
+ 12'
49
50
51
9.60656
.60660
.60664
.60668
.40417
.40420
.40424
.40427
9.60886
.60890
.60893
.60897
.40631
.40635
.40638
.40642
9.61114
.61118
.61122
.61126
.40845
.40849
.40852
.40856
9.61342
.61346
.61349
.61353
.41060
.41063
.41067
.41071
9.61568
.61572
.61576
.61580
.41275
.41278
.41282
.41285
12
11
10
9
+ 13'
53
54
55
9.60671
.60675
.60679
.60683
.40431
.40434
.40438
.40442
9.60901
.60905
.60909
.60912
.40645
.40649
.40652
.40656
9.61129
.61133
.61137
.61141
.40860
.40863
.40867
.40870
9.61357
.61361
.61364
.61368
.41074
.41078
.41082
.41085
9.61583
.61587
.61591
.61595
.41289
.41293
.41296
.41300
8
7
6
5
+ W
57
58
59
9.60687
.60691
.60694
.60698
.40445
.40449
.40452
.40456
9.60916
.60920
.60924
.60928
.40660
.40663
.40667
.40670
9.61145
.61148
.61152
.61156
.40874
.40878
.40881
.40885
9.61372
.61376
.61380
.61383
.41089
.41092
.41096
.41099
9.61598
.61602
.61606
.61610
.41303
.41307
.41310
.41314
4
3
2
1
+ 15'
9.60702
.40460
9.60931
.40674
9.61160
.40888
9.61387
.41103
9.61614
.41318
0
ISh 44m
18* 43™
IgTi 42m
Igh 4im
Igh 40™
TABLE 45. [Page 875
Haversines.
s
5* 20m 80° <K
5* 21^ 80° 15'
5* 22™ 80° 30/
5h 03™ 80° 45'
5h 24m 81° <K
s
Log.Hav. Nat.Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.61614
.61617
.61621
.61625
.41318
.41321
.41325
.41328
9.61839 .41533
.61843 .41536
.61846 i .41540
.61850 I .41543
9.62063
.62067
.62071
.62074
.41748
.41751
.41755
.41758
9.62287
.62290
.62294
.62298
.41963
.41966
.41970
.41974
9.62509
.62513
.62516
.62520
.42178
.42182
.42185
.42189
60
59
58
57
+ v
5
6
7
9.61629
.61632
.61636
.61640
.41332
.41335
.41339
.41343
9.61854 .41547
.61858 ! .41550
.61861 .41554
.61865 ! .41558
9.62078
.62082
.62086
.62089
.41762
.41766
.41769
.41773
9.62301
.62305
.62309
.62313
.41977
.41981
.41984
.41988
9.62524
.62527
.62531
.62535
.42193
.42196
.42200
.42203
56
55
54
53
+ *'
9
10
11
9.61644
.61647
.61651
.61655
.41346
.41350
.41353
.41357
9.61869 • .41561
.61873 ! .41565
.61876 : .41568
.61880 i .41572
9.62093
.62097
.62100
.62104
.41776
.41780
.41783
.41787
9.62316
.62320
.62324
.62327
.41992
.41995
.41999
.42002
9.62538
.62542
.62546
.62550
.42207
.42211
.42214
.42218
52
51
50
49
+ 3'
13
14
15
9.61659
.61662
.61666
.61670
.41361
.41364
.41368
.41371
9.61884 ! .41576
.61888 : .41579
.61891 i .41583
.61895 i .41586
9.62108
.62112
.62115
.62119
.41791
.41794
.41798
.41801
9.62331
.62335
.62338
.62342
.42006
.42010
.42013
.42017
9.62553
.62557
.62561
.62564
.42221
.42225
.42229
.42232
48
47
46
45
+ *'
17
18
19
9.61674
.61677
.61681
.61685
.41375
.41378
.41382
.41386
9.61899
.61903
.61906
.61910
.41590
.41593
.41597
.41601
9.62123
.62127
.62130
.62134
.41805
.41809
.41812
.41816
9.62346
.62350
.62353
.62357
.42020
.42024
.42027
.42031
9.62568
.62572
.62575
.62579
.42236
.42239
.42243
.42247
44
4-3
42
41
+ 5/
21
22
23
9.61689
.61692
.61696
.61700
.41389
.41393
.41396
.41400
9.61914
.61917
.61921
.61925
.41604
.41608
.41611
.41615
9.62138 .41819
.62141 .41823
.62145 .41827
.62149 .41830
9.62361
.62364
.62368
.62372
.42035
.42038
.42042
.42045
9.62583
.62586
.62590
.62594
.42250
.42254
.42257
.42261
40
39
38
37
+ v
25
26
27
9.61704
.61708
.61711
.61715
.41404
.41407
.41411
.41414
9.61929
.61932
.61936
.61940
.41619
.41622
.41626
.41629
9.62153 .41834
.62156 .41837
.62160 .41841
.62164 .41844
9.62376 • .42049
.62379 .42053
.62383 .42056
.62387 .42060
9.62598
.62601
.62605
.62609
.42264
.42268
.42272
.42275
36
35
34
33
+ v
29
30
31
9.61719
.61723
.61726
.61730
.41418
.41421
.41425
.41429
9.61944
.61947
.61951
.61955
.41633
.41636
.41640
.41644
9.62168 ; .41848
.62171 .41852
.62175 i .41855
.62179 .41859
9.62390 .42063
.62394 .42067
.62398 ! .42071
.62402 ! .42074
9.62612
.62616
.62620
.62623
.42279
.42282
.42286
.42290
32
31
30
29
+ 8'
33
34
35
9.61734 j .4143?
.61738 .41436
.61741 .41439
.61745 j .41443
9.61959
.61962
.61966
.61970
.41647
.41651
.41654
.41658
9.62182 .41862
.62186 > .41866
.62190! .41870
.62194 .41873
9.62405 .42078
.62409 .42081
.62413 .420S5
.62416 ' .42089
9.62627 ! .42293
.62631 .42297
.62634 .42300
.62638 .42304
28
27
26
25
+ v
37
38
39
9.61749 i .41447
.61753 .41450
.61756 .41454
.61760 .41457
9.61974
.61977
.61981
.61985
.41662
.41665
.41669
.41672
9.62197 , .41877
.62201 .41880
.62205 .41884
.62208 ! .41888
9.62420
.62424
.62427
.62431
.42092
.42096
.42099
.42103
9.62642 .42308
.62646 .42311
.62649 .42315
.62653 .42318
24
23
gg
"21
+ 1<K
41
42
43
9.61764
.61768
.61771
.61775
.41461
.41464
.41468
.41472
9.61989
.61992
.61996
.62000
.41676
.41679
.41683
.41687.
9.62212 .41891
.62216 .41895
.62220 .41898
.62223 .41902
9.62435
.62439
.62442
.62446
.42106
.42110
.42114
.42117
9.62657 .42322
.62660 .42326
.62664 .42329
.62668 .42333
20
19
18
17
+ 11'
45
46
47
9.61779
.61783
.61786
.61790
.41475
.41479
.41482
.4148.
9.62003
.62007
.62011
.62015
.41690
.41694
.41697
. '1701
9.62227 .41905
.62231 .41909
.62234 .41913
.62238 .41916
9.62450
.62453
.62457
.62461
.42121
.42124
.42128
.42132
9.62671
.62675
.62679
.62682
.42336
.42340
.42344
.42:347
16
15
14
13
+ 12'
49
50
51
9.61794
.61798
.61801
.61805
.41490
.41493
.41497
.41500
9.62018
.62022
.62026
.62030
.41705
.41708
.41712
.41715
9.62242
.62246
.62249
.62253
.41920
.41923
.41927
.41931
9.62464
.62468
.62472
.62476
.42135
.42139
.42142
.42146
9.62686
.62690
.62693
.62697
.42351
.42354
.42358
.42361
12
11
10
9
+ 13',
53
54
55
9.61809
.61813
.61816
.61820
.41504
.41507
.41511
.41515
9.62033
.62037
.62041
2045
.41719
.41722
.41726
.41730
9,. 62257
.62261
.62264
.62268
.41934
.41938
.41941
.41945
9.62479
.62483
.62487
.62490
.42150
.42153
.42157
.42160
9.62701
.62704
.62708
.62712
.42365
.42369
.42372
.42376
8
6
5
+ 14'
57
58
59
9.61824
.61828
.61831
.61835
.4^ 18
.41522
.41525
.41529
9.62048
.62052
.62056
.62059
.41733
.41737
.41740
.41744
9.62272
.62275
.62279
.62283
.41949
.41952
.41956
.41959
9.62494
.62498
.62501
.62505
.42164
.42168
.42171
.42175
9.62716
.62719
.62723
.62727
.42379
.42383
.42387
.42390
4
3
2
1
+ 15'
9.61839
.41533
9.62063
.41748
9.62287
.41963
9.62509
.42178
9.62730
.42394
0
18& 39™
18* 38m
18* 37^
18*361*
18* 3om
Page 876] TABLE 45.
Haversines.
s
5* 25™ 81° 15'
5h 26^ 81° 30'
$h 27^ 81° 45'
Sh 28m 82° 0'
5* 29^ 82° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav.
0
1
2
3
9.62730
.62734
.62738
.62741
.42394
.42397
.43401
.42405
9.62951
.62954
.62958
.62962
.42610
.42613
.42617
.42620
9.63170
.63174
.63177
.63181
.42825
.42829
.42833
.42836
9.63389
.63392
.63396
.63399
.43041
.43045
.43049
.43052
9.63606
.63610
.63613
.63617
.43257
.43261
.43265
.43268
60
59
58
57
+ V
5
6
7
9.62745
.62749
.62752
.62756
.42408
.42412
.42415
.42419
9.62965
.62969
.62973
.62976
.42624
.42628
.42631
.42635
9.63185
.63188
.63192
.63196
.42840
.42843
.42847
.42851
9.63403
.63407
.63410
.63414
.43056
.43059
.43063
.43067
9.63621
.63624
.63628
.63631
.43272
.43275
.43279
.43283
56
55
54
53
+ 2'
9
10
11
9.62760
.62763
.62767
.62771
.42423
.42426
.42430
.42433
9.62980
.62984
.62987
.62991
.42638
.42642
.42645
.42649
9.63199
.63203
.63207
.63210
.42854
.42858
.42861
.42865
9.63418
.63421
.63425
.63429
.43070
.43074
.43077
.43081
9.63635
.63639
.63642
.63646
.43286
.43290
.43293
.43297
52
51
50
49
+ &
13
14
15
9.62774
.62778
.62782
.62785
.42437
.42441
.42444
.42448
9.62995
.62998
.63002
.63006
.42653
.42656
.42660
.42663
9.63214
.63218
.63221
.63225
.42869
.42872
.42876
.42879
9.63432
.63436
.63439
.63443
.43085
.43088
.43092
.43095
9.63649
.63653
.63657
.63660
.43301
.43304
.43308
.43312
48
47
46
45
+ *'
17
18
19
9.62789
.62793
.62796
.62800
.42451
.42455
.42459
.42462
9.63009
.63013
.63017
.63020
.42667
.42671
.42674
.42678
9.63228
.63232
.63236
.63239
.42883
.42887
.42890
.42894
9.63447
.63450
.63454
.63458
.43099
.43103
.43106
.43110
9.63664
.63668
.63671
.63675
.43315
.43319
.43322
.43326
44
43
42
41
+ V
21
22
23
9.62804
.62808
.62811
.62815
.42466
.42469
.42473
.42477
9.63024
.63028
.63031
.63035
.42681
.42685
.42689
.42692
9.63243
.63247
.63250
.63254
.42897
.42901
.42905
.42908
9.63461
.63465
.63468
.63472
.43113
.43117
.43121
.43124
9.63678
.63682
.63686
.63689
.43330
.43333
.43337
.43340
40
39
38
37
+ 6'
25
26
27
9.62819
.62822
.62826
.62830
.42480
.42484
.42487
.42491
9.63039
.63042
.63046
.63050
.42696
.42699
.42703
.42707
9.63258
.63261
.63265
.63269
.42912
.42915
.42919
.42923
9.63476
.63479
.63483
.63487
.43128
.43131
.43135
.43139
9.63693,
.63693
.63700
.63704
.43344
.43348
.43351
.43355
36
35
34
33
+ V
29
30
31
9.62833
.62837
.62841
.62844
.42494
.42498
.42502
.42505
9.63063
.63057
.63061
.63064
.42710
.42714
.42717
.42721
9.63272
.63276
.63279
.63283
.42926
.42930
.42933
.42937
9.63490
.63494
.63497
.63501
.43142
.43146
.43149
.43153
9.63707
.63711
.63714
.63718
.43358
.43362
.43366
.43369
32
31
30
29
+ 8'
33
34
35
9.62848
.62852
.62855
.62859
.42509
.42512
.42516
.42520
9.63068
.63071
.63075
.63079
.42725
.42728
.42732
742735
9.63287
.63290
.63294
.63298
.42941
.42944
.42948
.42951
9.63505
.63508
.63512
.63516
.43157
.43160
.43164
.43167
9.63722
.63725
.63729
.63733
.43373
.43376
.43380
.43384
28
27
26
25
+ V
37
38
39
9.62863
.62866
.62870
.62874
.42523
.42527
.42530
.42534
9.63082
.63086
.63090
.63093
.42739
.42743
.42746
.42750
9.63301
.63305
.63309
.63312
.42955
.42959
.42962
.42966
9.63519
.63523
.63526
.63530
.43171
.43175
.43178
.43182
9.63736
.63740
.63743
.63747
.43387
.43391
.43394
.43398
24
23
22
21
+ 10'
41
42
43
9.62877
.62881
.62885
.62888
.42538
.42541
.42545
.42548
9.63097
.63101
.63104
.63108
.42753
.42757
.42761
.42764
9.63316
.63320
.63323
.63327
.42969
.42973
.42977
.42980
9.63534
.63537
.63541
.63545
.43185
.43189
.43193
.43196
9.63751
.63754
.63758
.63761
.43402
.43405
.43409
.43412
20
19
18
17
+ 11'
45
46
47
9.62892
.62896
.62899
.62903
.42552
.42556
.42559
.42563
9.63112
.63115
.63119
.63123
.42768
.42771
.42775
.42779
9.63330
.63334
.63338
.63341
.42984
.42987
.42991
.42995
9.63548
.63552
.63555
.63559
.43200
.43203
.43207
.43211
9.63765
.63769
.63772
.63776
.43416
.43420
.43423
.43427
16
15
14
13
+ 12'
49
50
51
9.62907
.62910
.62914
.62918
.42566
.42570
.42574
.42577
9.63126
.63130
.63134
.63137
.42782
.42786
.42789
.42793
9.63345
.63349
.63352
.63356
.42998
.43002
.43005
.43009
9.63563
.63566
.63570
.63574
.43214
.43218
.43221
.43225
9.63779
.63783
.63787
.63790
.43430
.43434
.43438
.43441
12
11
10
9
+ 13'
53
54
55
9.62921
.62925
.62929
.62932
.42581
.42584
.42588
.42592
9.63141
.63145
.63148
.63152
.42797
.42800
.42804
.42807
9.63360
.63363
.63367
.63370
.43013
.43016
.43020
.43023
9.63577
.63581
.63584
.63588
.43229
.43232
.43236
.43239
9.63794
.63797
.63801
.63805
.43445
.43448
.43452
.43456
8
7
6
5
+ 14'
57
58
59
9.62936
.62940
.62943
.62947
.42595
.42599
.42602
.42606
9.63156
.63159
.63163
.63166
.42811
.42815
.42818
.42822
9.63374
.63378
.63381
.63385
.43027
.43031
.43034
.43038
9.63592
.63595
.63599
.63602
.43243
.43247
.43250
.43254
9.63808
.63812
.63815
.63819
.43459
.43463
.43466
.43470
4
3
2
1
+ 15'
9.62951
.42610
9.63170
.42825
9.63389
.43041
9.63606
.43257
9.63823
.43474
0
isn $4m
l$h s$m
18*32™
18* Sim
18* 30m
TABLE 45. [Page 877
Haversines.
5ft ,50™ 82° SO7
5^ Sim 82° 45'
5ft 32™ 83° 0/
5ft 33™ 83° 15'
5ft 34m 83° 307
s
s
Log. Hav.j Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.! Nat. Hav
0
1
2
S
9.63823
.63826
.63830
.63833
.43474
.43477
.43481
.43485
9.64038
.64042
.64046
.64049
.43690
.43694
.43697
.43701
9.64253
.64256
.64260
.64264
.43907
.43910
.43914
.43917
9.64467
.64470
.64474
.64477
.44123
.44127
.44130
.44134
9.64679
.64683
.64686
.64690
.44340
.44343
.44347
.44351
60
59
58
57
-h V
5
6
7
9.63837
.63841
.63844
.63848
.43488
.4349?
.43495
.43499
9.64053
.64Q56
.64060
.64063
.43704
.43708
.43712
.43715
9.64267
.64271
.64274
.64278
.43921
.43925
.43928
.43932
9.64481
.64484
.64488
.64492
.44138
.44141
.44145
.44148
9.64694
.64697
.64701
.64704
.44354
.44358
.44362
.44365
56
55
54
53
+ v
9
10
11
9.63851
.63855
.63859
.63862
.43503
.43506
.43510
.43513
9.64067
.64071
.64074
.64078
.43719
.43723
.43726
.43730
9.64281
.64285
.64289
.64292
.43935
.43939
.43943
.43946
9.64495
.64499
.64502
.64506
.44152
.411.M,
.44159
.44163
9.64708
.64711
.64715
.64718
.44369
.44372
.44376
.44380
52
51
50
49
+ *'
IS
14
15
9.63866
.63869
.63873
.63877
.43517
.43521
.43524
.43528
9.64081
.64085
.64088
.64092
.43733
.43737
.43741
.43744
9.64296
.64299
.64303
.64306
.43950
.43953
.43957
.43961
9.64509
.64513
.64516
.64520
.44166
.44170
.44174
.44177
9.64722
.64725
.64729
.64732
.44383
.44387
.44390
.44394
48
47
46
45
+ *x
17
18
19
9.63880
.63884
.63887
.63891
.43531
.43535
.43539
.43542
9.64096
.64099
.64102
.64106
.43748
.43751
.43755
.43759
9.64310
.64314
.64317
.64321
.43964
.43968
.43972
.43975
9.64523
.64527
.64531
.64534
.44181
.44185
.44188
.44192
9.64736
.64740
.64743
.64747
.44398
.44401
.44405
.44408
44
43
42
41
+ 5'
gl
g%
23
9.63895
.63898
.63902
.63905
.43546
.43549
.43553
.43557
9.64110
.64113
.64117
.64121
.43762
.43766
.43769
.43773
9.64324
.64328
.64331
.64335
.43979
.43982
.43986
.43990
9.64538
.64541
.64545
.64548
.44195
.44199
.44203
.44206
9.64750
.64754
.64757
.64761
.44412
.44416
.44419
.44423
40
39
38
37
+ 8'
25
£6
27
9.63909
.63913
.63916
.63920
.43560
.43564
.43567
.43571
9.64124
.64128
.64131
.64135
.43777
.43780
.43784
.43787
9.64339
.64342
.64346
.64349
.43993
.43997
.44000
.44004
9.64552
.64555
.64559
.64563
.44210
.44213
.44217
.44221
9.64764
.64768
.64771
.64775
.44427
.44430
.44434
.44437
36
35
34
33
+ ?'
29
SO
SI
9.63923
.63927
.63931
.63934
.43575
.43578
.43582
.43585
9.64139
.64142
.64146
.64149
.43791
.43795
.43798
.43802
9.64353
.64356
.64360
.64363
.44008
.44011
.44015
.44018
9.64566
.64570
.64573
.64577
.44224
.44228
.44231
.44235
9.64778
.64782
.64785
.64789
.44441
.44445
.44448
.44452
32
31
30
29
+ 8'
S3
34
S5
9.63938
.63941
.63945
.63949
.43589
.43593
.43596
.43600
9.64153
.64156
.64160
.64164
.43805
.43809
.43813
.43816
9.64367
.64371
.64374
.64378
.44022
.44026
.44029
.44033
9.64580
.64584
.64587
.64591
.44239
.44242
.44246
.44250
9.64793
.64796
.64800
.64803
.44455
.44459
.44463
.44466
28
27
26
25
+ V
S7
S8
39
9.63952
.63956
.63959
.63963
.43603
.43607
.43611
.43614
9.64167
.64171
.64174
.64178
.43820
.43824
.43827
.43831
9.64381
.64385
.64388
.64392
.44036
.44040
.44044
.44047
9.64594
.64598
.64602
.64605
.44253
.44257
.44260
.44264
9.64807
.64810
.64814
.64817
.44470
.44474
.44477
.44481
24
23
22
21
+ W
41
42
43
9.63966
.63970
.63974
.63977
.43618
.43622
.43625
.43629
9.64181
.64185
.64189
.64192
.43834
.43838
.43842
.43845
9.64396
.64399
.64403
.64406
.44051
.44055
.44058
.44062
9.64609
.64612
.64616
.64619
.44268
.44271
.44275
.44278
9.64821
.64824
.64828
.64831
.44484
.44488
.44492
.44495
20
19
18
17
+ iix
45
46 •
47
9.63981
.63984
.63988
.63992
.43632
.43636
.43640
.43643
9.64196 ! .43849
.64199 .43852
.64203 • .43856
.64206 .43860
9.64410
.64413
.64417
.64420
.44065
.44069
.44073
.44076
9.64623 .44282
.64626 .44286
.64630 .44289
.64633 .44293
9.64835
.64838
.64842
.64845
.44499
.44502
.44506
.44510
16
15
14
13
+ 12'
49
50
51
9.63995
.63999
.64002
.64006
.43647
.43650
.43654
.43658
9.64210
.64214
.64217
.64221
.43863
.43867
.43870
.43874
9.64424
.64428
.64431
.64435
.44080
.44083
.44087
.44091
9.64637 .44296
.64640: .44300
.64644' .44304
.64648 •• .44307
9.64849
.64852
.64856
.64860
.44513
.44517
.44521
.44524
12
11
10
9
+ 13'
53
54
55
9.64010
.64013
.64017
.64020
.43661
.43665
.43668
.43672
9.64224
64228
.64231
.64235
.43878
.43881
.43885
.43888
9.64438
.64442
.64445
.64449
.44094
.44098
.44101
.44105
9.64651
.64655
.64658
.64662
.44311
.44315
.44318
.44322
9.64863
.64867
.64870
.64874
.44528
.44531
.44535
.44539
8
7
6
5
+ U7
57'
55
5S>
9.64024
.64028
.64031
.64035
.43676
.43679
.43683
.43686
9.64239 ! .43892
.64242 .43896
.64246 i .43899
.64249 ! .43903
9.64452
.64456
.64460
.64463
.44109
.44112
.44116
.44120
9.64665 .44325
.64669 ! .44329
.64672 .44333
.64676 .44336
9.64877
.64881
.64884
.64888
.44542
.44546
.44549
.44553
4
3
2
1
+ 15'
9.64038 .43690
9.64253 .43907
9.64467
.44123
9.64679 | .44340
9.64891
.44557
0
28* 29™
18* 2Sm
18* 27m
18*26™
18* 25^
Page 878] TABLE 45.
Haversines.
s
5h 35™ 83° 45'
5h 36m 84° 0'
5h 37m 84° 15'
5>> 38™ 84° 30'
5h 39™ 84° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.! Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.| Nat. Hav.
0
1
2
3
9.64891
.64895
.64898
.64902
.44557
.44560
.44564
.44568
9.65102
.65106
.65109
.65113
.44774
.44777
.44781
.44784
9.65312
.65316
.65319
.65323
.44991
.44994
.44998
.45001
9.65521
.65525
.65528
.65532
.45208
.45211
.45215
.45219
9.65729
.65733
.65736
.65740
.45425
.45429
.45432
.45436
60
59
58
57
+ 1'
5
6
7
9.64905
.64909
.64912
.64916
.44571
.44575
.44578
.44582
9.65116 I
.65120
.65123
.65127
.44788
.44792
.44795
.44799
9.65326
.65330
.65333
*. 65337
.45005
.45009
.45012
.45016
9.65535
.65539
.65542
.65546
.45222
.45226
.45229
.45233
9.65743
.65747
.65750
.65754
.45439
.45443
.45447
.45450
56
55
54
53
+ *
9
10
11
9.64919
.64923
.64926
.64930
.44586
.44589
.44593
.44596
9.65130
.65134
.65137
.65141
.44803
.44806
.44810
.44813
9.65340
.65344
.65347
.65351
.45020
.45023
.45027
.45030
9.65549
.65553
.65556
.65559
.45237
.45240
.45244
.45248
9.65757
.65761
.65764
.65767
.45454
.45458
.45461
.45465
52
51
50
49
+ *
13
14
15
9.64934
.64937
.64941
.64944
.44600
.44604
.44607
.44611
9.65144
.65148
.65151
.65155
.44817
.44821
.44824
.44828
9.65354
.65358
.65361
.65365
.45034
.45038
.45041
.45045
9.65563
.65566
.65570
.65573
.45251
.45235
.45258
.45262
9.65771
.65774
.65778
.65781
.45468
.45472
.45476
.45479
48
47
46
45
+ 4'
17
18
19
9.64948
.64951
.64955
.64958
.44614
.44618
.44623
.44625
9.65158
.65162
.65165
.65169
.44831
.44835
.44839
.44842
9.65368
.65372
.65375
.65378
.45048
.45052
.45056
.45059
9.65577
.65580
.65584
.65587
.45266
.45269
.45273
.45276
9.65785
.65788
.65792
.65795
.45483
.45486
.45490
.45494
44
43
42
41
+ V
21
22
23
9.64962
.64965
.64969
.64972
.44629
.44633
.44636
.44640
9.65172
.65176
.65179
.65183
.44846
.44850
.44853
.44857
9.65382
.65385
.65389
.65392
.45063
.45067
.45070
.45074
9.65591
.65594
.65598
.65601
.45280
.45284
.45287
.45291
9.65799
.65802
.65806
.65809
.45497
.45501
.45505
.45508
40
39
38
37
+ 6'
25
26
27
9.64976
.64979
.64983
.64986
.44643
.44647
.44651
.44654
9.65186
.65190
.65193
.65197
.44860
.44864
.44868
.44871
9.65396
.65399
.65403
.65406
.45077
.45081
.45085
.45088
9.65605
.65608
.65612
.65615
.45295
.45298
.45302
.45305
9.65812
.65816
.65819
.65823
.45512
.45515
.45519
.45523
36
35
34
33
+ ?'
29
30
31
9.64990
.64993
.64997
.65000
.44658
.44661
.44665
.44669
9.65200
.65204
.65207
.65211
.44875
.44878
.44882
.44886
9.65410
.65413
.65417
.65421
.45092
.45096
.45099
.45103
9.65619
.65622
.65625
.65629
.45309
.45313
.45316
.45320
9.65826
.65830
.65833
.65837
.45526
.45530
145534
.45537
32
31
30
29
+ 8'
33
34
35
9.65004
.65007
.65011
.65014
.44672
.44676
.44680
.44683
9.65214
.65218
.65221
.65225
.44889
.44893
.44897
.44909
9.65424
.65427
.65431
.65434
.45106
.45110
.45114
.45117
9.65632
.65636
.65639
.65643
.45324
.45327
.45331
.45334
9.65840
.65844
.65847
.65850
.45541
.45544
.45548
.45552
28
27
26
25
+ 9'
37
38
39
9.65018
.65021
.65025
.65028
.44687
.44690
.44694
.44698
9.65228
.65232
.65235
.65239
.44904
.44907
.44911
.44915
9.65438
.65441
.65445
.65448
.45121
.45124
.45128
.45132
9.65646
.65650
.65653
.65657
.45338
.45342
.45345
.45349
9.65854
.65857
.65861
.65864
.45555
.45559
.45563
.45566
24
23
22
21
+ W
41
42
43
9.65032
.65035
.65039
.65043
.44701
.44705
.44708
.44712
9.65242
.65246
.65249
.65253
.44918
.44922
.44925
.44929
9.65452
.65455
.65459
.65462
.45135
.45139
.45143
.45146
9.65660
.65664
.65667
.65671
.45353
.45356
.45360
.45363
9.65868
.65871
.65875
.65878
.45570
.45573
.45577
.45581
20
19
18
17
+ H'
45
46
• 47
9.65046
.65050
.65053
.65057
.44716
.44719
.44723
.44727
9.65256
.65260
.65263
.65267
.44933
.44936
.44940
.44944
9.65466
.65469
.65473
.65476
.45150
.45153
.45157
.45161
9.65674
.65677
.65681
.65684
.45367
.45371
.45374
.45378
9.65881
.65885
.65888
.65892
.45584
.45588
.45592
.45595
16
15
14
13
+ 12'
49
50
51
9.65060
.65064
.65067
.65071
.44730
.44734
.44737
.44741
9.65270
.65274
.65277
.65281
.44947
.44951
.44954
.44958
9.65480
.65483
.65486
.65490
.45164
.45168
.45172
.45175
9.65688
.65691
.65695
.65698
.45381
.45385
.45389
.45392
9.65895
.65899
.65902
.65906
.45599
.45602
.45606
.45610
12
11
10
9
+ 13'
53
54
55
9.65074
.65078
.65081
.65085
.44745
.44748
.44752
.44755
9.65284
.65288
.65291
.65295
.44962
.44965
.44969
.44973
9.65493
.65497
.65500
.65504
.45179
.45182
.45186
.45190
9.65702
.65705
.65709
.65712
.45396
.45400
.45403
.45407
9.65909
.65913
.65916
.65919
.45613
.45617
.45620
.45624
8
7
6
5
+ 14'
57
58
59
9.65088
.65092
.65095
.65099
.44759
.44763
.44766
.44770
9.65298
.65302
.65305
.65309
.44976
.44980
.44983
.44987
9.65507
.65511
.65514
.65518
.45193
.45197
.45200
.45204
9.65716 .45410
.65719 .45414
.65722 .45418
.65726 .45421
9.65923
.65926
.65930
.65933
.45628
.45631
.45635
.45639
4
3
2
1
+ 15'
9.65102
.44774
9.65312
.44991
9.65521
.45208
9.65729 ! .45425
9.65937
.45642
0
18*> 24™
18* 23™
18h 2%m
Igh 2im
18* 20™
TABLE 45. [Page 879
Haversines.
s
5& 40™ 85° O7
5h 4im 85° 15'
5h 42™ 85° 307
5h 43™ 85° 45'
5h 44m 86° V
s
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
0
1
2
• S
9.65937
.65940
.65944
.65947
.45643
.45646
.45649
.45653
9.66143
.66146
.66150
.66153
.45860
.45863
.45867
.45870
9.66348
.66352
.66355
.66359
.46077
.46081
.46084
.46088
9.66553
.66556
.66560
.66563
.46395
.46398
.46303
.46305
9.66757
.66760
.66763
.66767
.46513
.46516
.46519
.46533
60
59
58
57
+ 1'
5
6
7
9.65950
.65954
.65957
.65961
.45657
.45660
.45664
.45668
9.66157
.66160
.66164
.66167
.45874
.45878
.45881
.45885
9.66362
.66366
.66369
.66372
.46093
.46095
.46099
.46103
9.66567
.66570
.66573
.66577
.46309
.46313
.46316
.46330
9.66770
.66774
.66777
.66780
.46537
.46530
.46534
.46538
56
55
54
53
52
51
50
49
+ v
9
10
11
9.65964
.65968
.65971
.65975
.45671
.45675
.45678
.45683
9.66170
.66174
.66177
.66181
.45889
.45893
.45896
.45899
9.66376
.66379
.66383
.66386
.46106
.46110
.46113
.46117
9.66580
.66584
.66587
.66590
.46334
.46337
.46331
.46334
9.66784
.66787
.66791
.66794
.46541
.46545
.46548
.46553
+ 3'
13
14
15
9.65978
.65981
.65985
.65988
.45686
.45689
.45693
.45697
9.66184
.66188
.66191
.66194
.45903
.45907
.45910
.45914
9.66389
.66393
.66396
.66400
.46131
.46134
.46138
.46131
9.66594
.66597
.66601
.66604
.46338
.46343
.46345
.46349
9.66797
.66801
.66804
.66807
.46556
.46559
.46563
.46567
48
47
46
45
+ *'
17
18
19
9.65992
.65995
.65999
.66002
.45700
.45704
.45707
.45711
9.66198
.66201
.66205
.66208
.45918
.45931
.45935
.45938
9.66403
.66407
.66410
.66413
.46135
.46139
.46143
.46146
9.66607
.66611
.66614
.66618
.46353
.46356
.46360
.46363
9.66811
.66814
.66818
.66821
.46570
.46574
.46577
.46581
44
43
42
41
+ 5/
21
22
23
9.66006
.66009
.66012
.66016
.45715
.45718
.45733
.45736
9.66212
.66215
.66218
.66222
.45933
.45936
.45939
.45943
>9. 66417
.66420
.66424
.66427
.46150
.46153
.46157
.46161
9.66621
.66624
.66628
.66631
.46367
.46371
.46374
.46378
9.66824
.66828
.66831
.66835
.46585
.46588
.46593
.46596
40
39
38
37
+ v
25
26
27
9.66019
.66023
.66026
.66030
.45739
.45733
.45736
.45740
9.66225
.66229
.66232
.66236
.45947
.45950
.45954
.45957
9.66430
.66434
.66437
.66441
.46164
.46168
.46171
.46175
9.66635
.66638
.66641
.66645
.46383
.46385
.46389
.46393
9.66838
.66841
.66845
.66848
.46599
.46603
.46606
.46610
36
35
34
33
+ r
29
30
81
9.66033
.66037
.66040
.66043
.45744
.45747
.45751
.45755
9.66239
.66242
.66246
.66249
.45961
.45965
.45968
.45973
9.66444
.66447
.66451
.66454
.46179
.46183
.46186
.46189
9.66648
.66652
.66655
.66658
.46396
.46400
.46403
.46407
9.66851
.66855
.66858
.66862
.46614
.46617
.46631
.46635
32
31
30
29
+ 8'
S3
34
35
9.66047
.66050
.66054
.66057
.45758
.45763
.45765
.45769
9.66253
.66256
.66260
.66263
.45976
.45979
.45983
.45986
9.66458
.66461
.66464
.66468
.46193
.46197
.46300
.46304
9.66662
.66665
.66669
.66672
.46411
.46414
.46418
.46431
9.66865
.66868
.66872
.66875
.46638
.46633
.46636
.46639
28
27
26
25
+ 9'
37
38
39
9.66061
.66064
.66067
.66071
.45773
.45776
.45780
.45783
9.66266
.66270
.66273
.66277
.45990
.45994
.45997
.46001
9.66471
.66475
.66478
.66482
.46308
.46311
.46315
.46318
9.66675
.66679
.66682
.66685
.46435
.46439
.16433
.46436
9.66878
.66882
.66885
.66889
.46643
.46646
.46650
.46654
24
23
22
21
+ KK
41
42
43
9.66074
.66078
.66081
.66085
.45787
.45791
.45794
.45798
9.66280
.66284
.66287
.66290
.46005
.46008
.46013
.46015
9.66485
.66488
.66492
.66495
.46333
.46336
.46339
.46333
9.66689
.66692
.66696
.66699
.46440
.46443
.46447
.46451
9.66892
.66895
.66899
.66902
.46657
.46661
.46665
.46668
20
19
18
17
+ Hx
45
46
47
9.66088
.66092
.66095
.66098
.45803
.45805
.45809
.45813
9.66294
.66297
.66301
.66304
.46019
.46033
.46036
.46030
9.66499
.66502
.66505
.66509
.46337
.46340
.46344
.46347
9.66702
.66706
.66709
.66713
.46454
.46458
.46461
.46465
9.66905
.66909
.66912
.66916
.46673
.46675
.46679
.46683
16
15
14
13
+ 12'
49
50
51
9.66102
.66105
.66109
.66112
.45816
.45830
.45833
.45837
9.66307
.66311
.66314
.66318
.46034
.46037
.46041
.46044
9.66512
.66516
.66519
.66522
.46351
.46355
.46358
.46363
9.66716
.66719
.66723
.66726
.46469
.46473
.46476
.46480
9.66919
.66922
.66926
.66929
.46686
.46690
.46694
.46697
12
11
10
9
8
7
6
5
4
3
2
1
0
+ 13'
53
54
55
9.66116
.66119
.66122
.66126
.45831
.45834
.45838
.45841
9.66321
.66325
.66328
.66331
.46048
.46053
.46055
.46059
9.66526
.66529
.66533
.66536
.46366
.46369
.46373
.46376
9.66730
.66733
.66736
.66740
.46483
.46487
.46490
.46494
9.66932
.66936
.66939
.66943
.46701
.46704
.46708
.46713
+ 14'
57
58
59
9.66129
.66133
.66136
.66140
.45845
.45849
.45853
.45858
9.66335
.66338
.66342
.66345
.46063
.46066
.46070
.46073
9.66539
.66543
.66546
.66550
.46380
.46384
.46387
.46391
9.66743
.66747
.66750
.66753
.46498
.46501
.46505
.46509
9.66946
.66949
.66953
.66956
.46715
.46719
.46733
.46736
+ 15'
9.66143
.45860
9.66348
.46077
9.66553
.46395
9.66757
.46513
9.66959
.46730
ISh 19m
18^18™
Igh i7m
18* 16m
18* 15™
Page 880] TABLE 45.
Haversines.
s
5& -#™ 86° 15'
5h 46^ 86° 3<K
5*> 47™ 86° 45'
5& 42^87° 0/
5* 49™ 87° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.66959
.66963
.66966
.66970
.46730
.46733
.46737
.46741
9.67161
.67165
.67168
.67171
.46948
.46951
.46955
.46958
9.67362
.67366
.67369
.67372
.47165
.47169
.47173
.47176
9.67562
.67566
.67569
.67572
.47383
.47387
.47390
,47394
9.67762
.67765
.67768
.67772
.47601
.47605
.47608
.47612
60
59
58
57
+ 1'
5
6
7
9.66973
.66976
.66980
.66983
.46744
.46748
.46752
.46755
9.67175
.67178
.67181
' .67185
.46962
.46966
.46969
.46973
9.67376
.67379
.67382
.67386
.47180
.47184
.47187
.47191
9.67576
.67579
.67582
.67586
.47398
.47401
.47405
.47409
9.67775
.67778
.67782
.67785
.47616
.47619
.47623
.47627
56
55
54
53
+ 2'
9
10
11
9.66986
.66990
.66993
.66997
.46759
.46762
.46766
.46770
9.67188
.67192
.67195
.67198
.46977
.46980
.46984
.46987
9.67389
.67392
.67396
.67399
.47194
.47198
.47202
.47205
9.67589
.67592
.67596
.67599
.47412
.47416
.47420
.47423
9.67788
.67792
.67795
.67798
.47630
.47634
.47637
.47641
52
51
50
49
+ 3'
13
14
15
9.67000
.67003
.67007
.67010
.46773
.46777
.46781
.46784
9.67202
.67205
.67208
.67212
.46991
.46995
.46998
.47002
9.67402
.67406
.67409
.67412
.47209
.47213
.47216
.47220
9.67602
.67606
.67609
.67612
.47427
.47430
.47434
.47438
9.67801
.67805
.67808
.67811
.47645
.47648
.47652
.47656
48
47
46
45
+ *'
17
18
19
9.67013
.67017
.67020
.67023
.46788
.46792
.46795
.46799
9.67215
.67218
.67222
.67225
.47006
.47009
.47013
.47017
9.67416
.67419
.67422
.67426
.47223
.47227
.47231
.47234
9.67616
.67619
.67622
.67626
.47441
.47445
.47449
.47452
9.67815
.67818
.67821
.67825
.47659
.47663
.47666
.47670
44
43
42
41
+ &'
21
22
23
9.67027
.67030
.67034
.67037
.46802
.46806
.46810
.46813
9.67228
.67232
.67235
.67238
.47020
.47024
.47027
.47031
9.67429
.67432
.67436
.67439
.47238
.$7242
.47245
.47249
9.67629
.67632
.67636
.67639
.47456
.47459
.47463
.47467
9.67828
.67831
.67835
.67838
.47674
.47677
.47681
.47685
40
39
38
37
+ *'
25
26
27
9.67040
.67044
.67047
.67050
.46817
.46821
.46824
.46828
9.67242
.67245
.67249
.67252
.47035
.47038
.47042
.47046
9.67443
.67446
.67449
.67452
.47252
.47256
.47260
.47263
9.67642
.67646
.67649
.67652
.47470
.47474
.47478
.47481
9.67841
.67844
.67848
.67851
.47688
.47692
.47696
.47699
36
35
34
33
+ r
29
SO
31
9.67054
.67057
.67060
.67064
.46831
.46835
.46839
.46842
9.67255
.67259
.67262
.67265
.47049
.47053
.47056
.47060
9.67456
.67459
.67462
.67466
.47267
.47271
.47274
.47278
9.67656
.67659
.67662
.67666
.47485
.47489
.47492
.47496
9.67854
.67858
.67861
.67864
.47703
.47706
.47710
.47714
32
31
30
29
+ 8'
33
34
35
9.67067
.67071
,67074
.67077
.46846
.46850
.46853
.46857
9.67269
.67272
.67275
.67279
.47064
.47067
.47071
.47075
9.67469
.67472
.67476
.67479
.47282
.47285
.47289
.47292
9.67669
.67672
.67675
.67679
.47499
.47503
.47507
.47510
9.67868
.67871
.67874
.67878
.47717
.47721
.47725
.47728
28
27
26
25
+ 9'
37
38
39
9.67081
.67084
.67087
.67091
.46860
.46864
.46868
.46871
9.67282
.67285
.67289
.67292
.47078
.47082
.47086
.47089
9.67483
.67486
.67489
.67493
.47296
.47300
.47303
.47307
9.67682
.67685
.67689
.67692
.47514
.47518
.47521
.47525
9.67881
.67884
.67887
.67891
.47732
.47735
.47739
.47743
24
23
22
21
+ 1(K
41
42
43
9.67094
.67097
.67101
.67104
.46875
.46879
.46882
.46886
9.67295
.67299
.67302
.67305
.47093
.47096
.47100
.47104
9.67496
.67499
.67503
.67506
.47311
.47314
.47318
.47321
9.67695
.67699
.67702
.67705
.47528
.47532
.47536
.47539
9.67894
.67897
.67901
.67904
.47746
.47750
.47754
.47757
20
19
18
17
+ 11'
45
46
47
9.67108
.67111
.67114
.67118
.46890
.46893
.46897
.46900
9.67309
.67312
.67315
.67319
.47107
.47111
.47115
.47118
9.67509
.67512
.67516
.67519
.47325
.47329
.47332
.47336
9.67709
.67712
.67715
.67719
.47543
.47547
.47550
.47554
9.67907
.67911
.67914
.67917
.47761
.47765
.47768
.47772
16
15
14
13
+ 12'
49
50
£?
9.67121
.67124
.67128
.67131
.46904
.46908
.46911
.46915
9.67322
.67326
.67329
.67332
.47122
.47125
.47129
.47123
9.67522
.67526
.67529
.67532
.47340
.47343
.47347
.47351
9.67722
.67725
.67729
.67732
.47558
.47561
.47565
.47568
9.67920
.67924
.67927
.67930
.47775
.47779
.47783
.47786
'12
11
10
9
+ 13'
53
54
55
9.67134
.67138
.67141
.67145
.46919
.46922
.46926
.46929
9.67336
.67339
.67342
.67346
.47136
.47140
.47144
.47147
9.67536
.67539
.67542
.67546
.47354
.47358
.47361
.47365
9.67735
.67738
.67742
.67745
.47572
.47576
.47579
.47583
9.67934
.67937
.67940
.67944
.47790
.47794
.47797
.47801
8
7
6
5
+ 14'
57
58
59
9.67148
.67151
.67155
.67158
.46933
.46937
.46940
.46944
9.67349
.67352
.67356
.67359
.47151
.47155
.47158
.47162
9.67549
.67552
.67556
.67559
.47369
.47372
.47376
.47380
9.67748
.67752
.67755
.67758
.47587
.47590
.47594
.47597
9.67947
.67950
.67953
.67957
.47805
.47808
.47812
.47815
4
3
2
1
+ 15'
9.67161
.46948
9.67362
.47165
9.67562
.47383
9.67762
.47601
9.67960
.47819
0
l$h 14m
IS* 13m
18& 12**
ISh lim
18h iom
TABLE 45. [Page 881
Haversines.
,
5* oOm 87° SO7
5* Sim 87° 45'
5h 52m 88° O7
5* 53m 88° 15'
5h 54m 88° 307
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
s
0
9.67960
.67963
.67967
.67970
.47819
.47823
.47826
.47830
9.68158
.68161
.68164
.68167
.48037
.48041
.48044
.48048
9.68354
.68358
.68361
.68364
.48255
.48259
.48262
.48266
9.68550
.68553
.68557
.68560
.48473
.48477
.48480
.48484
9.68745
.68748
.68751
.68755
.48691
.48695
.48698
.48702
60
59
58
57
+ 1'
9.67973
.67977
.67980
.67983
.47834
.47837
.47841
.47844
9.68171
.68174
.68177
.68181
.48052
.48055
.48059
.48062
9.68367
.68371
.68374
.68377
.48269
.48273
.48277
.48280
9.68563
.68566
.68570
.68573
.48488
.48491
.48495
.48499
9.68758
.68761
.68764
.68768
.48706
.48709
.48713
.48717
56
55
54
53
+ v
Q
10
11
9.67986
.67990
.67993
.67996
.47848
.47852
.47855
.47859
9.68184
.68187
.68190
.68194
.48066
.48070
.48073
.48077
9.68380
.68384
.68387
.68390
.48284
.48288
.48291
.48295
9.68576
.68579
.68583
.68586
.48502
.48506
.48509
.48513
9.68771
.68774
.68777
.68781
.48720
.48724
.48728
.48731
52
51
50
49
+ 3'
13
14
15
9.68000
.68003
.68006
.68010
.47863
.47866
.47870
.47874
9.68197
.68200
.68204
.68207
.48081
.48084
.48088
.48092
9.68393
.68397
.68400
.68403
.48299
.48302
.48306
.48310
9.68589
.68592
.68596
.68599
.48517
.48520
.48524
.48528
9.68784
.68787
.68790
.68794
.48735
.48738
.48742
.48746
48
47
46
45
+ *'
17
18
19
9.68013
.68016
.68019
.68023
.47877
.47881
.47884
.47888
9.68210
.68213
.68217
.68220
.48095
.48099
.48102
.48106
9.68407
.68410
.68413
.68416
.48313
.48317
.48320
.48324
9.68602
.68605
.68609
.68612
.48531
.48535
.48538
.48542
9.68797
.68800
.68803
.68806
.48749
.48753
.48757
.48760
44
43
42
41
+ V
21
22
23
9.68026
.68029
.68033
.68036
.47892
.47895
.47899
.47903
9.68223
.68227
.68230
.68233
.48110
.48113
.48117
.48121
9.68420
.68423
.68426
.68429
.48328
.48331
.48335
.48339
9.68615
.68618
.68622
.68625
.48546
.48549
.48553
.48557
9.68810
.68813
.68816
.68820
.48764
.48767
.48771
.48775
40
39
38
37
+ 6'
25
26
27
+ r
29
SO
31
9.68039 .47906
.68042 j .47910
.68046 .47913
.68049 .47917
9.68236
.68240
.68243
.68246
.48124
.48128
.48131
.48135
9.68433
.68436
.68439
.68442
.48342
.48346
.48350
.48353
9.68628
.68631
.68635
.68638
.48560
.48564
.i8568
.48571
9.68823
.68826
.68829
.68832
.48778
.48782
.48786
.48789
36
35
34
33
9.68052
.68056
.68059
.68062
.47921
.47924
.47928
.47932
9.68249
.68253
.68256
.68259
.48139
.48142
.48146
.48150
9.68446
.68449
.68452
.68456
.48357
.48360
.48364
.48368
9.68641
.68644
.68648
.68651
.48575
.48578
.48582
.48586
9.68836
.68839
.68842
.68845
.48793
.48797
.48800
.48804
32
31
30
29
28
27
te
25
+ 8'
S3
34
35
9.68066
.68069
.68072
.68075
.47935
.47939
.47943
.47946
9.68263
.68266
.68269
.68272
.48153"
.48157
.48161
.48164
9.68459
.68462
.68465
.68469
.48371
.48375
.48379
.48382
9.68654
.68657
.68661
.68664
.48589
.48593
.48597
.48600
9.68849
.68852
.68855
.68858
.48807
.48811
.48815
.48818
+ 9/
37
38
39
9.68079
.68082
.68085
.68089
.47950
.47953
.47957
.47961
9.68276
.68279
.68282
.68286
.48168
.48171
.48175
.48179
9.68472
.68475
.68478
.68482
.48386
.48389
.48393
.48397
9.68667
.68670
.68674
.68677
.48604
.48608
.48611
.48615
9.68862
.68865
.68868
.68871
.48822
.48826
.48829
.48833
24
23
o-j
tl
-f 10'
41
42
43
9.68092 i .4796-4
.68095 .47968
.68098 .47972
.68102 ! .47975
9.68289
.68292
.68295
.68299
.48182
.48186
.48190
.48193
9.68485
.68488
.68491
.68495
.48400
.48404
.48408
.48411
9.68680
.68683
.68687
.68690
.48618
.48622
.48626
.48629
9.68875
.68878
.68881
.68884
.48837
.48840
.48844
.48847
20
19
18
17
+ H'
45
46
47
9.68105
.68108
.68112
.68115
.47979
.47983
.47986
.47990
9.68302
.68305
.68308
.68312
.48197
.48201
.48204
.48208
9.68498
.68501
.68504
.68508
.48415
.48419
.48422
.48426
9.68693
.68696
.68700
.68703
.48633
.48637
.48640
.48644
9.68887
.68891
.68894
.68897
.48851
.48855
.48858
.48862
16
15
14
13
+ 12'
49
50
51
9.68118
.68121
.68125
.68128
.47993
.47997
.48001
.48004
9.68315
.68318
.68322
.68325
.48211
.48215
.48219
.48222
9.68511
.68514
.68517
.68521
.48429
.48433
.48437
.48440
9.68706
.68709
.68713
.68716
.48648
.48651
.48655
.48658
9.68900
.68904
.68907
.68910
.48886
.48869
.48873
.48877
12
11
10
9
+ 13'
53
54
55
9.68131
.68135
.68138
.68141
.48008
.48012
.48015
.48019
9.68328
.68331
.68335
.68338
.48226
.48230
.48233
.48237
9.6S524
.68527
.68531
.68534
.48444
.48448
.48451
.48455
9.68719
.68722
.68726
.68729
.48662
.48666
.48669
.48673
9.68913
.68917
.68920
.68923
.48880
.48884
.48887
.48891
8
7
6
5
+ 14'
57
58
59
9.68144
.68148
.68151
.68154
.48022
.48026
.48030
.48033
9.68341
.68344
.68348
.68351
.48241
.48244
.48248
.48251
9.68537
.68540
.68544
.68547
.48459
.48462
.48466
.48469
9.68732
.68735
.68739
.68742
.48677
.48680
.48684
.46688
9.68926 1
.68929
.68933
.68936
.48895
.48898
.48902
.48906
4
3
2
1
+ 15'
9.68158
.48037
9.68354
.48255
9.68550
.48473
9.68745 | .48691
9.68939
.48909
0
18*9™
18*8™
18* 7m
*#*£•
18*5™
Page 882] TABLE 45.
Haversines.
s
5*> 55™ 88° 45'
5*> 56m 89° 0'
5*> 57™ 89° 15'
5h 58™ 89° 30'
5h 59m 89° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.68939
.68942
.68946
.68949
.48909
.48913
.48917
.48920
9.69132
.69136
.69139
.69142
.49127
.49131
.49135
.49138
9.69325
.69328
.69331
.69334
.49346
.49349
.49353
.49356
.49360
.49364
.49367
.49371
9.69516
.69520
.69523
.69526
.49564
.49567
.49571
.49575
9.69707
.69710
.69713
.69717
.49782
.49785
.49789
.49793
60
59
58
57
+ 1'
5
6
7
9.68952
.68955
.68958
.68962
.48924
.48927
.48931
.48935
9.69145
.69148
.69152
.69155
.49142
.49146
.49149
.49153
9.69338
.69341
.69344
.69347
9.69529
.69532
.69535
.69539
.49578
.49582
.49585
.49589
9.69720
.69723
.69726
.69729
.49796
.49800
.49804
.49807
56
55
54
53
+ 3'
9
10
11
9.68965
.68968
.68971
.68975
.48938
.48942
.48946
.48949
9.69158
.69161
.69164
.69168
.49156
.49160
.49164
.49167
9.69350
.69354
.69357
.69360
.49375
.49378
.49382
.49386
9.69542
.69545
.69548
.69551
.49593
.49596
.49600
.49604
9.69732
.69736
.69739
.69742
.49811
.49815
.49818
.49822
52
51
50
49
+ 3'
13
14
15
9.68978
.68981
.68984
.68988
.48953
.48957
.48960
.48964
9.69171
.69174
.69177
.69181
.49171
.49175
.49178
.49182
9.69363
.69366
.69370
.69373
.49389
.49393
.49396
.49400
9.69555
.69558
.69561
.69564
.49607
.49611
.49615
.49618
9.69745
.69748
.69751
.69755
.49825
.49829
.49833
.49836
48
47
46
45
+ *'
17
18
19
9.68991
.68994
.68997
.69000
.48967
.48971
.48975
.48978
9.69184
.69187
.69190
.69193
.49186
.49189
.49193
.49196
9.69376
.69379
.69382
.69386
.49404
.49407
.49411
.49415
9.69567
.69570
.69574
.69577
.49622
.49625
.49629
.49633
9.69758
.69761
.69764
.69767
.49840
.49844
.49847
.49851
44
43
42
41
+ 5'
21
22
9.69004
.69007
.69010
.69013
.48982
.48986
.48989
.48993
9.69197
.69200
.69203
.69206
.49200
.49204
.49207
.49211
9.69389
.69392
.69395
.69398
.49418
.49422
.49426
.49429
9.69580
.69583
.69586
.69590
.49636
.49640
.49644
.49647
9.69770
.69774
.69777
.69780
.49855
.49858
.49862
.49865
40
39
38
37
+ v
25
26
27
9.69017
.69020
.69023
.69026
.48997
.49000
.49004
.49007
9.69209
.69213
.69216
.69219
.49215
.49218
.49222
.49226
9.69402
.69405
.69408
.69411
.49433
.49436
.49440
.49444
9.69593
.69596
.69599
.69602
.49851
.49655
.49658
.49662
9.69783
.69786
.69789
.69793
.49869
.49873
.49876
.49880
36
35
34
33
+ V
.29
30
31
9.69029
.69033
.69036
.69039
.49011
.49015
.49018
.49022
9.69222
.69225
.69229
.69232
.49229
.49233
.49236
.49240
9.69414
.69417
.69421
.69424
.49447
.49451
.49455
.49458
9.69605
.69609
.69612
.69615
.49665
.49669
.49673
.49676
9.69796
.69799
.69802
.69805
.49884
.49887
.49891
.49895
32
31
30
29
+ 8/
33
34
35
9.69042
.69046
.69049
.69052
.49026
.49029
.49033
.49036
9.69235
.69238
.69242
.69245
.49244
.49247
.49251
.49255
9.69427
.69430
.69433
.69437
.49462
.49465
.49469
.49473
9.69618
.69621
.69625
.69628
.49680
.49684
.49687
.49691
9.69808
.69812
.69815
.69818
.49898
.49902
.49905
.49909
28
27
26
25
+ V
37
38
39
9.69055
.69058
.69062
.69065
.49040
.49044
.49047
.49051
9.69248
.69251
.69254
.69258
.49258
.49262
.49266
.49269
9.69440
.69443
.69446
.69449
.49476
.49480
.49484
.49487
9.69631
.69634
.69637
.69640
.49695
.49698
.49702
.49705
9.69821
.69824
.69827
.69831
.49913
.49916
.49920
.49924
24
23
22
21
.+ 10'
41
42
43
9.69068
.69071
.69074
.69078
.49055
.49058
.49062
.49066
9.69261
.69264
.69267
.69270
.49273
.49276
.49280
.49284
9.69453
.69456
.69459
.69462
.49491
.49495
.49498
.49502
9.69644
.69647
.69650
.69653
.49709
.49713
.49716
.49720
9.69834
.69837
.69840
.69843
.49927
.49931
.49935
.49938
20
19
18
17
+ 11'
45-
46
47
9.69081
.69084
.69087
.69091
.49069
.49073
.49076
.49080
9.69274
.69277
.69280
.69283
.49287
.49291
.49295
.49298
9.69465
.69469
.69472
.69475
.49506
.49509
.49513
.49516
9.69656
.69659
.69663
.69666
.49724
.49727
.49731
.49735
9.69846
.69850
.69853
.69856
.49942
.49945
.49949
.49953
16
15
14
13
+ 13'
49
50
51
9.69094
.69097
.69100
.69103
.49084
.49087
.49091
.49095
9.69286
.69290
.69293
.69296
.49302
.49306
.49309
.49313
9.69478
.69481
.69484
.69488
.49520
.49524
.49527
.49531
9.69669
.69672
.69675
.69678
.49738
.49742
.49745
.49749
9.69859
.69862
.69865
.69869
.49956
.49960
.49964
.49967
12
11
10
9
+ 13'
53
54
55
9.69107
.69110
.69113
.69116
.49098
.49102
.49106
.49109
9.69299
.69302
.69306
.69309
.49316
.49320
.49324
.49327
9.69491
.69494
.69497
.69500
.49535
.49538
.49542
.49545
9.69682
.69685
.69688
.69691
.49753
.49756
.49760
.49764
9.69872
.69875
.69878
.69881
.49971
.49975
.49978
.49982
8
7
6
5
+ 14'
57
58
59
9.69120
.69123
.69126
.69129
.49113
.49116
.49120
.49124
9.69312
.69315
.69318
.69322
.49331
.49335
.49338
.49342
9.69504
.69507
.69510
.69513
.49549
.49553
.49556
.49560
9.69694
.69698
.69701
.69704
.49767
.49771
.49775
.49778
9.69884
.69888
.69891
.69894
.49985
.49989
.49993
.49997
4
3
2
1
+ 15'
9.69132
.49127
9.69325
.49346
9.69516
.49564
9.69707
.49782
9.69897
.50000
0
18*4™
IShsm
18h 2m
18*1*
Igk Qm
TABLE 45. [Page 883
Haversines.
s
6h Q™ 90° 0'
6b im 90° 15'
6^ 2m 90° 30'
6h 3m 90° 45'
6h 4m 91° (K
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.69897
.69900
.69903
.69906
.50000
.50004
.50007
.50011
9.70086
.70089
.70092
.70096
.50218
.50222
.50225
.50229
9.70274
.70277
.70281
.70284
.50436
.50440
.50444
.50447
9.70462
.70465
.70468
.70471
.50654
.50658
.50662
.50665
9.70648
.70652
.70655
.70658
.50873
.50876
.50880
.50884
60
59
58
57
+ 1'
5
6
7
9.69910
.69913
.69916
.69919
.50015
.50018
.50022
.50025
9.70099
.70102
.70105
.70108
.50233
.50236
.50240
.50244
9.70287
.70290
.70293
.70296
.50451
.50455
.50458
.50462
9.70474
.70477
.70480
.70484
.50669
.50673
.50676
.50680
9.70661
.70664
.70667
.70670
.50887
.50891
.50894
.50898
56
55
54
53
+ V
9
10
11
9.69922
.69925
.69929
.69932
.50029
.50033
.50036
.50040
9.70111
.70114
.70118
.70121
.50247
.50251
.50255
.50258
9.70299
.70303
.70306
.70309
.50465
.50469
.50473
.50476
9.70487
.70490
.70493
.70496
.50684
.50687
.50691
.50694
9.70673
.70676
.70679
.70683
.50902
.50905
.50909
.50913
52
51
50
49
+ &
13
14
15
9.69935
.69938
.69941
.69944
.50044
.50047
.50051
.50055
9.70124
.70127
.70130
.70133
.50262
.50265
.50269
.50273
9.70312
.70315
.70318
.70321
.50480
.50484
.50487
.50491
9.70499
.70502
.70505
.70509
.50698
.50702
.50705
.50709
9.70686
.70689
.70692
.70695
.50916
.50920
.50924
.50927
48
47
46
45
+ *'
17
18
19
9.69948
.69951
.69954
.69957
.50058
.50062
.50065
.50069
9.70136
.70140
.70143
.70146
.50276
.50280
.50284
.50287
9.70324
.70328
.70331
.70334
.50495
.50498
.50502
.50505
9.70512
.70515
.70518
.70521
.50713
.50716
.50720
.50724
9.70698
.70701
.70704
.70707
.50931
.50934
.50938
.50942
44
43
42
41
+ *'
21
22
23
9.69960
.69963
.69966
.69970
.50073
.50076
.50080
.50034
9.70149
.70152
.70155
.70158
.50291
.50295
.50298
.50302
9.70337
.70340
.70343
.70346
.50509
.50513
.50516
.50520
9.70524
.70527
.70530
.70533
.50727
.50731
.50734
.50738
9.70710
.70714
.70717
.70720
.50945
.50949
.50953
.50956
40
39
38
37
+ v
25
26
27
9.69973
.69976
.69979
.69982
.50087
.50091
.50095
.50098
9.70161
.70165
.70168
.70171
.50305
.50309
.50313
.50316
9.70349
.70353
.70356
.70359
.50524
.50527
.50531
.50534
9.70537
.70540
.70543
.70546
.50742
.50745
.50749
.50753
9.70723
.70726
.70729
.70732
.50960
.50964
.50967
.50971
36
35
34
33
+ 1'
29
30
31
9.69985
.69988
.69992
.69995
.50102
.50105
.50109
.50113
9.70174
.70177
.70180
.70183
.50320
.50324
.50327
.50331
9.70362
.70365
.70368
.70371
.50538
.50542
.50545
.50549
9.70549
.70552
.70555
.70558
.50756
.50760
.50764
.50767
9.70735
.70738
.70741
.70745
.50974
.50978
.50982
.50985
32
31
30
29
+ 8'
33
34
35
9.69998
.70001
.70004
.70007
.50116
.50120
.50124
.50127
9.70187
.70190
.70193
.70196
.50335
.50338
.50342
.50345
9.70374
.70378
.70381
.70384
.50553
.50556
.50560
.50564
9.70561
.70565
.70568
.70571
.50771
.50774
.50778
.50782
9.70748
.70751
.70754
.70757
.50989
.50993
.50996
.51000
28
27
26
25
-f »x
37
38
39
9.70011
.70014
.70017
.70020
.50131
.50135
.50138
.50142
9.70199
.70202
.70205
.70209
.50349
.50353
.50356
.50360
9.70387
.70390
.70393
.70396
.50567
.50571
.50574
.50578
9.70574
.70577
.70580
.70583
.50785
.50789
.50793
.50796
9.70760
.70763
.70766
.70769
.51004
.51007
.51011
.51014
24
23
22
21
+ 10'
41
42
43
9.70023
.70026
.70029
.70033
.50145
.50149
.50153
.50156
9.70212
.70215
.70218
.70221
.50364
.50367
.50371
.50375
9.70399
.70402
.70406
.70409
.50582
.50585
.50589
.50593
9.70586
.70589
.70593
.70596
.50800
.50804
.50807
.50811
9.70772
.70775
.70779
.70782
.51018
.51022
.51025
.51029
20
19
18
17
+ 11'
45
46
47
9.70036
.70039
.70042
.70045
.50160
.50164
.50167
.50171
9.70224
.70227
.70230
.70234
.50378
.50382
.50355
.50389
9.70412
.70415
.70418
.70421
.50598
.50600
.50604
.50607
9.70599
.70602
.70605
.70608
.50814
.50818
.50822
.50825
9.70785
.70788
.70791
.70794
.51033
.51036
.51040
.51043
16
15
14
13
+ 12'
49
50
51
9.70048
.70051
.70055
.70058
.50175
.50178
.50182
.50185
9.70237
.70240
.70243
.70246
.50393
.50396
.50400
.50404
9.70424
.70427
.70431
.70434
.50611
.50614
.50618
.50622
9.70611
.70614
.70617
.70620
.50829
.50833
.50836
.50840
9.70797
.70800
.70803
.70806
.51047
.51051
.51054
.51058
12
11
10
9
+ 13'
55
54
55
9.70061
.70064
.70067
.70070
.50189
.50193
.50196
.50200
9.70249
.70252
.70256
.70259
.50407
.50411
.50415
.50418
9.70437
.70440
.70443
.70446
.50625
.50629
.50633
.50636
9.70624 j .50844
.70627 .50847
.70630 .50851
.70633 ! .50854
9.70809
.70813
.70816
.70819
.51062
.51065
.51069
.51073
8
7
6
5
+ 14'
•57
58
59
9.70074
.70077
.70080
.70083
.50204
.50207
.50211
.50215
9.70262
.70265
.70268
.70271
.50422
.50425
.50429
.50433
9.70449
.70452
.70456
.70459
.50640
.50644
.50647
.50651
9.70636
.70639
.70642
.70645
.50858
.50862
.50865
.50869
9.70822
.70825
.70828
.70831
.51076
.51080
.51083
.51087
4
3
2
1
+ 15'
9.70086
.50218
9.70274 .50436
9.70462
.50654
9.70648 .50873
9.70834
.51091
0
17* 59m
17* 53™
IJh 57™
Ijh 5(>m
17^ 55™
Page 884] TABLE 45.
Ilaversines.
s
6h sm 91° 15'
6h 6™ 91° 30'
6h 7m 91° 45'
Sh gm 92° (K
6h gm 93° 15'
r
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.70834
.70837
.70840
.70843
.51091
.51094
.51098
.51102
9.71019
.71022
.71025
.71028
.51309
.51312
.51316
.51320
9.71203
.71206
.71210
.71213
.51527
.51531
.51534
.51538
9.71387
.71390
.71393
.71396
.51745
.51749
.51752
.51756
9.71569
.71572
.71575
.71579
.51963
.51967
.51970
.51974
60
59
58
57
56
55
54
53
+ 1'
5
6
7
9.70847
.70850
.70853
.70856
.51105
.51109
.51113
.51116
9.71032
.71035
.71038
.71041
.51323
.51327
.51331
.51334
9.71216
.71219
.71222
.71225
.51541
.51545
.51549
.51552
9.71399
.71402
.71405
.71408
.51760
.51763
.51767
.51770
9.71582
.71585
.71588
.71591
.51978
.51981
.51985
.51988
+ v
9
10
11
9.70859
.70862
.70865
.70868
.51120
.51123
.51127
.51131
9.71044
.71047
.71050
.71053
.51338
.51342
.51345
.51349
9.71228
.71231
.71234
.71237
.51556
.51560
.51563
.51567
9.71411
.71414
.71417
.71420
.51774
.51778
.51781
.51785
9.71594
.71597
.71600
.71603
.51992
.51996
.51999
.52003
52
51
50
49
+ *
13
14
15
9.70871
.70874
.70877
.70881
.51134
.51138
.51142
.51145
9.71056
.71059
.71062
.71065
.51352
.51356
.51360
.51363
9.71240
.71243
.71246
.71249
.51571
.51574
.51578
.51581
9.71423
.71426
.71430
.71433
.51789
.51792
.51796
.51799
9.71606
.71609
.71612
.71615
.52007
.52010
.52014
.52018
48
47
46
45
+ *'
17
18
19
9.70884
.70887
.70890
.70893
.51149
.51153
.51156
.51160
9.71068
.71072
.71075
.71078
.51367
.51371
.51374
.51378
9.71252
.71255
.71259
.71262
.51585
.51589
.51592
.51596
9.71436
.71439
.71442
.71445
.51803
.51807
.51810
.51814
9.71618
.71621
.71624
.71627
.52021
.52025
.52028
.52032
44
43
42
41
+ 5'
21
22
23
9.70896
.70899
.70902
.70905
.51163
.51167
.51171
.51174
9.71081
.71084
.71087
.71090
.51382
.51385
.51389
.51392
9.71265
.71268
.71271
.71274
.51600
.51603
.51607
.51611
9.71448
.71451
.71454
.71457
.51818
.51821
.51825
.51829
9.71630
.71633
.71636
.71639
.52036
.52039
.52043
.52047
40
39
38
37
+ 6'
25
26
27
9.70908
.70911
.70914
.70918
.51178
.51182
.51185
.51189
9.71093
.71096
.71099
.71102
.51396
.51400
.51403
.51407
9.71277
.71280
.71283
.71286
.51614
.51618
.51621
.51625
9.71460
.71463
.71466
.71469
.51832
.51836
.51839
.51843
9.71642
.71645
.71648
.71651
.52050
.52054
.52057
.52061
36
35
34
33
+ 1'
29
SO
31
9.70921
.70924
.70927
.70930
.51193
.51196
.51200
.51203
9.71105
.71108
.71111
.71114
.51411
.51414
.51418
.51422
9.71289
.71292
.71295
.71298
.51629
.51632
.51636
.51640
9.71472
.71475
.71478
.71481
.51847
.51850
.51854
.51858
9.71654
.71657.
.71660
.71663
.52065
.52068
.52072
.52076
32
31
30
29
+ 8'
S3
34
35
9.70933
.70936
.70939
.70942
.51207
.51211
.51214
.51218
9.71118
.71121
.71124
.71127
.51425
.51429
.51432
.51436
9.71301
.71304
.71307
.71311
.51643
.51647
.51650
.51654
9.71484
.71487
.71490
.71493
.51861
.51865
.51869
.51872
9.71666
.71670
.71673
.71676
.52079
.52083
.52087
.52090
28
27
26
25
+ 9'
37
S8
39
9.70945
.70948
.70951
.70955
.51222
.51225
.51229
.51233
9.71130
.71133
.71136
.71139
.51440
.51443
.51447
.51451
9.71314
.71317
.71320
.71323
.51658
.51661
.51665
.51669
9.71496
.71500
.71503
.71506
.51876
.51879
.51883
.51887
9.71679
.71682
.71685
.71688
.52094
.52097
.52101
.52105
24
23
22
21
+ W
41
42
43
9.70958
.70961
.70964
.70967
.51236
.51240
.51243
.51247
9.71142
.71145
.71148
.71151
.51454
.51458
.51462
.51465
9.71326
.71329
.71332
.71335
.51672
.51676
.51680
.51683
9.71509
.71512
.71515
.71518
.51890
.51894
.51898
.51901
9.71691
.71694
.71697
.71700
.52108
.52112
.52116
.52119
20
19
18
17
+ 11'
45
46
47
9.70970
.70973
.70976
.70979
.51251
.51254
.51258
.51262
9.71154
.71157
.71161
.71164
.51469
.51472
.51476
.51480
9.71338
.71341
.71344
.71347
.51687
.51690
.51694
.51698
9.71521
.71524
.71527
.71530
.51905
.51908
.51912
.51916
9.71703
.71706
.71709
.71712
.52123
.52126
.52130
.52134
16
15
14
13
+ 12'
49
50
51
9.70982
.70985
.70988
.70992
.51265
.51269
.51273
.51276
9.71167
.71170
.71173
.71176
.51483
.51487
.51491
.51494
9.71350
.71353
.71356
.71359
.51701
.51705
.51709
.51712
9.71533
.71536
.71539
.71542
.51919
.51923
.51927
.51930
9.71715
.71718
.71721
.71724
.52137
i.52141
^.52145
.52148
12
11
10
9
+ 13'
53
54
55
9.70995
.70998
.71001
.71004
.51280
.51283
.51287
.51291
9.71179
.71182
.71185
.71188
.51498
.51501
.51505
.51508
9.71362
.71365
.71369
.71372
.51716
.51720
.51723
.51727
9.71545
.71548
.71551
.71554
.51934
.51938
.51941
.51945
9.71727
.71730
.71733
.71736
.52152
.52156
.52159
.52163
8
' 7
6
5
+ 14'
57
58
59
£.7 1007
.71010
.71013
.71016
.51294
.51298
.51302
.51305
9.71191
.71194
.71197
.71200
.51512
.51516
.51520
.51523
9.71375
.71378
.71381
.71384
.51730
.51734
.51738
.51741
9.71557
.71560
.71563
.71566
.51948
.51952
.51956
.51959
9.71739
.71742
.71745
.71748
.52166
.52170
.52174
.52177
4
3
2
1
0
A- 15'
9.71019
.51309
9.71203
.51527
9.71387
.51745
9.71569
.51963
9.71751
.52181
17h 54m
l?h 53m
17h 52m
• 17h Si™
17h 5Qm
TABLE 45. [Page 886
Haversines.
s
6h iom 93° 307
6* urn 92° 45'
6h !2m 93° tf
6* IS* 93° 15'
6* 14m 93° W
s
Log. nav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.71751
.71754
.71757
.71760
.52181
.52185
.52188
.52192
9.71932
.71935
.71938
.71941
.52399
.52403
.52406
.52410
9.72112
.72115
.72118
.72121
.52617
.52620
.52624
.52628
9.72292
.72295
.72298
.72301
.52835
.52838
.52842
.52846
9.72471
.72474
.72476
.72479
.53052
.53056
.53060
.53063
60
59
58
57
+ 1'
5
6
7
9.71763
.71766
.71769
.71772
.52196
.52199
.52203
.52206
9.71944
.71947
.71950
.71953
.52413
.52417
.52421
.52424
9.72124
.72127
.72130
.72133
.52631
.52635
.52639
.52642
9.72304
.72307
.72310
.72313
.52849
.52853
.52856
.52860
9.72482
.72485
.72488
.72491
.53067
.53071
.53074
.53078
56
55
54
53
+ V
9
10
11
9.71775
.71778
.71781
.71784
.52210
.52214
.52217
.52221
9.71956
.71959
.71962
.71965
.52428
.52432
.52435
.52439
9.72136
.72139
.72142
.72145
.52646
.52649
.52653
.52657
9.72316
.72319
.72322
.72325
.52864
.52867
.52871
.52875
9.72494
.72497
.72500
.72503
.53081
.53085
.53089
.53092
52
51
50
49
+ 3'
13
14
15
9.71787
.71791
.71794
.71797
.52225
.52228
.52232
.52235
9.71968
.71971
.71974
.71977
.52442
.52446
.52450
.52453
9.72148
.72151
.72154
.72157
.52660
.52664
.52668
.52671
9.72328
.72331
.72334
.72337
.52878
.52882
.52885
.52889
9.72506
.72509
.72512
.72515
.53096
.53100
.53103
.53107
48
47
46
45
+ *'
17
18
19
9.71800
.71803
.71806
.71809
.52239
.52243
.52246
.52250
9.71980
.71983
.71986
.71989
.52457
.52461
.52464
.52468
9.72160
.72163
.72166
.72169
.52675
.52679
.52682
.52686
9.72340
.72343
.72346
.72349
.52893
.52896
.52900
.52904
9.72518
.72521
.72524
.72527
.53110
.53114
.53118
.53121
44
43
42
41
+ V
21
22
23
9.71812
.71815
.71818
.71821
.52254
.52257
.52261
.52264
9 71992
.71995
.71998
.72001
.52472
.52475
.52479
.52482
9.72172
.72175
.72178
.72181
.52689
.52693
.52697
.52700
9.72352
.72354
.72357
.72360
.52907
.52911
.52915
.52918
9.72530
.72533
.72536
.72539
.53125
.53129
.53132
.53136
40
39
38
37
+ 6'
25
26
27
9.71824
.71827
.71830
.71833
.52268
.52272
.52275
.52279
9.72004
.72007
.72010
.72013
.524S6
.52490
.52493
.52497
9.72184
.72187
.72190
.72193
.52704
.52708
.52711
.52715
9.72363
.72366
.72369
.72372
.52922
.52925
.52929
.52933
9.72542
.72545
.72548
.72551
.53140
.53143
.53147
.53150
36
35
34
33
+ r
29
30
31
9.71836
.71839
.71842
.71845
.52283
.52286
.52290
.52294
9.72016
.72019
.72022
.72025
.52501
.52504
.52508
.52511
9.72196
.72199
.72202
.72205
.52718
.52722
.52726
.52729
9.72375
.72378
.72381
.72384
.52936
.52940
.52944
.52947
9.72554
.72557
.72560
.72563
.53154
.53158
.53161
.53165
32
81
SO
29
~28~
27
26
25
+ 8'
33
34
35
9.71848
.71851
.71854
.71857
.52297
.52301
.52304
.52308
9.72028
.72031
.72034
.72037
.52515
.52519
.52522
.52526
9.72208
.72211
.72214
.72217
.52733
.52737
.52740
.52744
9.72387
.72390
.72393
.72396
.52951
.52954
.52958
.52962
9.72565
.72568
.72571
.72574
.53169
.53172
.53176
.53179
+ V
37
38
39
9.71860
.71863
.71866
.71869
.52312
.52315
.52319
.52323
9.72040
.72043
.72046
.72049
.52530
.52533
.52537
.52541
9.72220
.72223
.72226
.72229
.52748
.52751
.52755
.52758
9.72399
.72402
.72405
.72408
.52965
.52969
.52973
.52976
9.72577
.72580
.72583
.72586
.53183
.53187
.53190
.53194
24
23
21
+ W
41
42
43
9.71872
.71875
.71878
.71881
.52326
.52330
.52334
.52337
9.72052
.72055
.72058
.72061
.52544
.52548
.52551
.52555
9.72232
.72235
.72238
.72241
.52762
.52766
.52769
.52773
9.72411
.72414
.72417
.72420
.52980
.52983
.52987
.52991
9.72589
.72592
.72595
.72598
.53198
.53201
.53205
.53208
20
19
18
17
16
15
U
13
+ 11'
45
46
47
9.71884
.71887
.71890
.71893
.52341
.52344
.52348
.52352
9.72064
.72067
.72070
.72073
.52559
.52562
.52566
.52570
9.72244
.72247
.72250
.72253
.52776
.52780
.52784
.52787
9.72423
.72426
.72429
.72432
.52994
.52998
.53002
.53005
9.72601
.72604
.72607
.72610
.53212
.53216
.53219
.53223
+ 12'
49
50
51
9.71896
.71899
.71902
.71905
.52355
.52359
.52363
.52366
9.72076
.72079
.72082
.72085
.52573
.52577
.52580
.52584
9.72256
.72259
.72262
.72265
.52791
.52795
.52798
.52802
9.72435
.72438
.72441
.72444
.53009
.53013
.53016
.53020
9.72613
.72616
.72619
.72622
.53227
.53230
.53234
.53238
12
11
10
9
+ 13'
5S
54
55
9.71908
.71911
.71914
.71917
.52370
.52373
.52377
.52381
9.72088
.72091
.T2094
.72097
.52588
.52591
.52595
.52599
9.72268
.72271
.72274
.72277
.52806
.52809
.52813
.52816
9.72447
.72450
.72453
.72456
.53023
.53027
.53031
.53034
9.72625
.72628
.72631
.72634
.53241
.53245
.53248
.53252
8
7
6
5
+ 147
57
58
59
9.71920
.71923
.71926
.71929
.52384
.52388
.52392
.52395
9.72100
.72103
.72106
.72119
.52602
.52606
.52610
.52613
9.72280
.72283
.72286
.72289
.52820
.52824
.52827
.52831
9.72459
.72462
.72465
.72468
.53038
.53042
.53045
.53049
9.72637
.72640
.72642
.72645
.5R256
.53259
.53263
.53267
4
S
2
1
+ 15'
9.71932
.52399
9.72112
.52617
9.72292
.52835
9.72471
.53052
9.72648
.53270
0
17*149™
17*48™
17* 47™
17*46™
17*45^
Page 886] TABLE 45.
Haversines.
s
6& J5™ 93° 45'
Qh iem 94° 0'
Qh nm 94° is/
eh ism 94° 30'
Qh 19m 94° 45
s
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.72648
.72651
.72654
.72657
.53270
.53274
.53277
.53281
9.72825
.72828
.72831
.72834
.53488
.53491
.53495
.53499
9.73002
.73005
.73008
.73011
.53705
.53709
.53713
.53716
9.73177
.73180
.73183
.73186
.53923
.53927
.53930
.53934
9.73352
.73355
.73358
.73361
.54140
.54144
.54148
.54151
60
59
58
57
56
55
54
53
+ v
5
6
7
9.72660
.72663
.72666
.72669
.53285
.53288
.53292
.53296
9.72837
.72840
.72843
.72846
.53502
.53506
.53510
.53513
9.73014
.73016
.73019
.73022
.53720
.53724
.53727
.53731
9.73189
.73192
.73195
.73198
.53937
.53941
.53945
.53948
9.73364
.73367
.73370
.73373
.54155
.54159
.54162
.54166
+ V
. 9
10
11
9.72672
.72675
.72678
.72681
.53299
.53303
.53306
.53310
9.72849
.72852
.72855
.72858
.53517
.53520
.53524
.53528
9.73025
.73028
.73031
.73034
.53734
.53738
.53742
.53745
9.73201
.73204
.73207
.73209
.53952
.53956
.53959
.53963
9.73375
.73378
.73381
.73384
.54169
.54173
.54177
.54180
52
51
50
49
+ &
13
14
15
9.72684
.72687
.72690
.72693
.53314
.53317
.53321
.53325
9.72861.
.72864
.72867
.72870
.53531
.53535
.53539
.53542
9.73037
.73040
.73043
.73046
.53749
.53753
.53756
.53760
9.73212
.73215
.73218
.73221
.53966
.53970
.53974
.53977
9.73387
.73390
.73393
.73396
.54184
.54188
.54191
.54195
48
47
46
45
+ *'
17
18
19
9.72696
.72699
.72702
.72705
.53328
.53332
.53335
.53339
9.72873
.72876
.72878
.72881
.53546
.53549
.53553
.53557
9.73049
.73052
.73055
.73057
.53763
.53767
.53771
.53774
9.73224
.73227
.73230
.73233
.53981
.53985
.53988
.53992
9.73399
.73402
.73404
.73407
.54198
.54202
.54206
.54209
44
43
42
41
+ v
21
22
23
9.72708
.72710
.72713
.72716
.53343
.53346
.53350
.53354
9.72884
.72887
.72890
.72893
.53560
.53564
.53568
.53571
9.73060
.73063
.73066
.73069
.53778
.53782
.53785
.53789
9.73236
.73239
.73242
.73244
.53995
.53999
.54003
.54006
9.73410
.73413
.73416
.73419
.54213
.54217
.54220
.54224
40
39
38
37
+ 6'
25
26
27
9.72719
.72722
.72725
.72728
.53357
.53361
.53364
.53368
9.72896
.72899
.72902
.72905.
.53575
.53579
.53582
.53586
9.73072
.73075
.75078
.73081
.53792
.53796
.53800
.53803
9.73247
.73250
.73253
.73256
.54010
.54014
.54017
.54021
9.73422
.73425
.73428
.73431
.54227
.54231
.54235
.54238
36
35
34
33
+ r
29
30
31
9.72731
.72734
.72737
.72740
.53372
.53375
..53379
.53383
9.72908
.72911
.72914
.72917
.53589
.53593
.53597
.53600
9.73084
.73087
.73090
.73093
.53807
.53811
.53814
.53818
9.73259
.73262
.73265
.73268
.54024
.54028
.54032
.54035
9.73433
.73436
.73439
.73442
.54242
.54245
.54249
.54253
32
31
30
29
+ 8'
33
34
35
9.72743
.72746
.72749
.72752
.53386
.53390
.53394
.53397
9.72920
.72923
.72926
.72928
.53604
.53608
.53611
.53615
9.73096
.73098
.73101
.73104
.53821
.53825
.53829
.53832
9.73271
.73274
.73277
.73280
.54039
.54043
.54046
.54050
9.73445
.73448
.73451
.73454
.54256
.54260
.54264
.54267
28
27
26
25
+ 9'
37
38
39
9.72755
.72758
.72761
.72764
.53401
.53404
.53408
.53412
9.72931
.72934
.72937
.72940
.53618
.53622
.53626
.53629
9.73107
.73110
.73113
.73116
.53836
.53840
.53843
.53847
9.73282
.73285
.73288
.73291
.54053
.54057
.54061
.54064
9.73457
.73460
.73462
.73465
.54271
.54274
.54278
.54282
24
23
22
21
+ 10'
41
42
43
9.72767
.72770
.72772
.72775
.53415
.53419
.53423
.53426
9.72943
.72946
.72949
.72952
.53633
.53637
.53640
.53644
9.73119
.73122
.73125
.73128
.53850
.53854
.53858
.53861
9.73294
.73297
.73300
.73303
.54068
.54072
.54075
.54079
9.73468
.73471
.73474
.73477
.54285
.54289
.54293
.54296
20
19
18
17
+ 11'
45
46
47
9.72778
.72781
.72784
.72787
.53430
.53433
.53437
.53441
9.72955
.72958
.72961
.72964
.53647
.53651
.53655
.53658
9.73131
.73134
.73136
.73139
.53865
.53869
.53872
.53876
9.73306
.73309
.73311
.73314
.54082
.54086
.54090
.54093
9.73480
.73483
.73486
.73489
.54300
.54303
.54307
.54311
16
15
14
13
+ 12'
49
50
51
9.72790
.72793
.72796
.72799
.53444
.53448
.53452
.53455
9.72967
.72970
.72972
.72975
.53662
.53666
.53669
.53673
9.73142
.73145
.73148
.73151
.53879
.53883
.53887
.53890
9.73317
.73320
.73323
.73326
.54097
.54101
.54104
.54108
9.73491
.73494
.73497
.73500
.54314
.54318
.54322
.54325
12
11
10
9
+ 13'
53
54
55
9.72802
.72805
.72808
.72811
.53459
.53462
.53466
.53470
9.72978
.72981
.72984
.72987
.53676
.53680
.53684
.53687
9.73154
.73157
.73160
.73163
.53894
.53898
.53901
.53905
9.73329
.73332
.73335
.73338
.54111
.54115
.54119
.54122
9.73503
.73506
.73509
.73512
.54329
.54332
.54336
.54340
8
7
6
5
+ 14'
57
55
59
9.72814
.72817
.72820
.72823
.53473
.53477
.53481
.53484
9.72990
.72993
.72996
.72999
.53691
.53695
.53698
.53702
9.73166
.73169
.73172
.73174
.53908
.53912
.53916
.53919
9.73341
.73343
.73346
.73349
.54126
.54130
.54133
.54137
9.73515
.73517
.73520
.73523
.54343
.54347
.54351
.54354
4
3
2
1
4- 15'
9.72825
.53488
9.73002
.53705
9.73177
.53923
9.73352
.54140
9.73526
.54358
0
llh 44m
17 h 43m
Ijh 42m
17h 41™
17h40m
TABLE 45. [Page 887
Haversinee.
s
6h 90m 95° 0'
6* 21™ 95° 15'
6h 22^ 95° 307
6* 23m 95° 45'
6h 24m 96° (K
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.73526
.73529
.73532
.73535
.54358
.54361
.54365
.54369
9.73699
.73702
.73705
.73708
.54575
.54579
.54582
.54586
9.73872
.73875
.73878
.73881
.54792
.54796
.54800
.54803
9.74044
.74047
.74049
.74052
.55009
.55013
.55017
.55020
9.74215
.74218
.74220
.74223
.55226
.55230
.55234
.55237
60
59
58
57
+ v
5
6
7
9.73538
.73541
.73544
.73546
.54372
.54376
.54380
.54383
9.73711
.73714
.73717
.73720
.54590
.54593
.54597
.54600
9.73883
.73886
.73889
.73892
.54807
.54810
.54814
.54818
9.74055
.74058
.74061
.74064
.55024
.55028
.55031
.55035
9.74226
.74229
.74232
.74235
.55241
.55245
.55248
.55252
56
55
54
53
+ y
9
10
11
9.73549
.73552
.73555
.73558
.54387
.54390
.54394
.54398
9.73722
.73725
.73728
.73731
.54604
.54608
.54611
.54615
9.73895
.73898
.73901
.73903
.54821
.54825
.54828
.54832
9.74067 j .55038
.74069 .55042
.74072 .55046
.74075 .55049
9.74237
.74240
.74243
.74246
.55255
.55259
.55263
.55266
52
51
50
49
+ 3/
IS
14
15
9.73561
.73564
.73567
.73570
.54401
.54405
.54409
.54412
9.73734
.73737
.73740
.73743
.54619
.54622
.54626
.54629
9.73906
.73909
.73912
.73915
.54836
.54839
.54843
.54847
9.74078
.74081
.74084
.74087
.55053
.55056
.55060
.55064
9.74249
.74252
.74254
.74257
.55270
.55273
.55277
.55281
48
47
46
45
+ *'
17
18
19
9.73572
.73575
.73578
.73581
.54416
.54419
.54423
.54427
9.73746
.73748
.73751
.73754
.54633
.54637
.54640
.54644
9.73918
.73921
.73924
.73926
.54850
.54854
.54857
.54861
9.74089
.74092
.74095
.74098
.55067
.55071
.55075
.55078
9.74260
.74263
.74266
.74269
.55284
.55288
.55292
.55295
44
43
42
41
40
39
38
37
+ V
21
22
Is
9.73584
.73587
.73590
.73593
.54430
.54434
.54437
.54441
9.73757
.73760
.73763
.73766
.54647
.54651
.54655
.54658
9.73929
.73932
.73935
.73938
.54865
.54868
.54872
.54876
9.74101
.74104
.74106
.74109
.55082
.55085
.55089
.55093
9.74272
.74274
.74277
.74280
.55299
.55302
.55306
.55310
+ 6/
25
26
27
9.73596
.73598
.73601
.73604
.54445
.54448
.54452
.54456
9.73769
.73771
.73774
.73777
.54662
.54666
.54669
.54673
9.73941
.73944
.73946
.73949
.54879
.54883
.54886
.54890
9.74112
.74115
.74118
.74121
.55096
.55100
.55103
.55107
9.74283
.74286
.74289
.74291
.55313
.55317
.55320
.55324
36
35
34
33
32
31
30
29
+ r
29
SO
31
9.73607
.73610
.73613
.73616
.54459
.54463
.54466
.54470
9.73780
.73783
.73786
.73789
.54676
.54680
.54684
.54687
9.73952
.73955
.73958
.73961
.54894
.54897
.54901
.54904
9.74124
.74126
.74129
.74132
.55111
.55114
.55118
.55122
9.74294
.74297
.74300
.74303
.55328
.55331
.55335
.55339
+ 8'
S3
34
35
9.73619
.73622
.73624
.73627
.54474
.54477
.54481
.54485
9.73792
.73794
.73797
.73800
.54691
.54695
.54698
.54702
9.73964
.73967
.73969
.73972
.54908
.54912
.54915
.54919
9.74135
.74138
.74141
.74144
.55125
.55129
.55132
.55136
9.74306
.74308
.74311
.74314
.55342
.55346
.55349
.55353
28
27
26
25
+ &
37
S8
39
9.73630
.73633
.73636
.73639
.54488
.54492
.54495
.54499
9.73803
.73806
.73809
.73812
.54705
.54709
.54713
.54716
9.73975
.73978
.73981
.73984
.54923
.54926
.5:930
.51933
9.74146
.74149
.71152
.74155
.55140
.55143
.55147
.55150
9.74317
.74320
.74323
.74325
.55357
.55360
.55364
.55367
24
23
22
21
+ W
41
42
43
9.73642
.73645
.73648
.73650
.54503
.54506
.54510
.54514
9.73815
.73817
.73820
.73823
.54720
.54724
.54727
.54731
9.73987
.73989
.73992
.73995
.54937
.54941
.54944
.54948
9.74158
.74161
.74163
.74166
.55154
.55158
.55161
.55165
9.74328
.74331
.74334
.74337
.55371
.55375
.55378
.55382
20
19
18
17
+ ii'
45
46
47
9.73653
.73656
.73659
.73662
.54517
.54521
.54524
.54528
9.73826
.73829
.73832
.73835
.54734
.54738
.54742
.54745
9.73998
.74001
.74004
.74007
.54952
.54955
.54959
.54963
9.74169
.74172
.74175
.74178
.55169
.55172
.55176
.55179
9.74340
.74342
.74345
.74348
.55386
.55389
.55393
.55396
16
15
14
13
+ 12'
49
50
51
9.73665
.73668
.73671
.73674
.54532
.54535
.54539
.54542
9.73838
.73840
.73843
.73846
.54749
.54752
.54756
.54760
9.74009
.74012
.74015
.74018
.54966
.54970
.54973
.54977
9.74181
.74183
.74186
.74189
.55183
.55187
.55190
.55194
9.74351
.74354
.74357
.74359
.55400
.55404
.55407
.55411
12
11
10
9
+ 13'
53
54
55
9.73676
.73679
.73682
.73685
.54546
.54550
.54553
.54557
9.73849
.73852
.73855
.73858
.54763
.54767
.54771
.54774
9.74021
.74024
.74027
.74029
.54980
.54984
.54988
.54991
9.74192
.74195
.74198
.74200
.55197
.55201
.55205
.55208
9.74362
.74365
.74368
.74371
.55414
.55418
.55422
.55425
8
7
6
r
+ 14'
57
58
59
9.73688
.73691
.73694
.73697
.54561
.54564
.54568
.54571
9.73860
.73863
.73866
.73869
.54778
.54781
.54785
.54789
9.74032
.74035
.74038
.74041
.54995
.54999
.55002
.55006
9.74203
.74206
.74209
.74212
.55212
.55216
.55219
.55223
9.74374
.74376
.74379
.74382
.55429
.55433
.55436
.55440
1
+ 15'
9.73699
.54575
9.73872
.54792
9.74044
.55009
9.74215
.55226
9.74385
.55443
0
IJh 39 ,n
17 h 38m
17h sjm
17*- 36™
17*- 35^
Page 888] TABLE 45.
Haversinea.
s
6h 25m 96° 15'
6* 26™ 96° 30'
6h wm 96° 45'
6h 28m 97° O7
6h 29m 97° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.74385
.74388
.74391
.74393
.55443
.55447
.55451
.55454
9.74554
.74557
.74560
.74563
.55660
.55664
.55667
.55671
9.74723
.74726
.74729
.74732
.55877
.55880
.55884
.55888
9.74891
.74894
.74897
.74900
.56093
.56097
.56101
.56104
9.75059
.75061
.75064
.75067
.56310
.56314
.56317
.56321
60
59
58
57
+ lx
5
6
7
9.74390
.74399
.74402
.74405
.55458
.55461
.55465
.55469
9.74566
.74569
.74571
.74574
.55675
.55678
.55682
.55685
9.74734
.74737
.74740
.74743
.55891
.55895
.55899
.55902
9.74902
.74905
.74908
.74911
.56108
.56112
.56115
.56119
9.75070
.75072
.75075
.75078
.56324
.56328
.56332
.56335
56
55
54
53
+ V
9
10
11
9.74408
.74410
.74413
.74416
.55473
.55476
.55479
.55483
9.74577
.74580
.74583
.74585
.55689
.55693
.55696
.55700
9.74746
.74748
.74751
.74754
.55906
.55909
.55913
.55917
9.74914
.74916
.74919
.74922
.56122
.56126
.56130
.56133
9.75081
.75084
.75086
.75089
.56339
.56342
.56346
.56350
52
51
50
49
+ 3'
13
14
15
9.74419
.74422
.74425
.74427
.55487
.55490
.55494
.55498
9.74588
.74591
.74594
.74597
.55704
.55707
.55711
.55714
9.74757
.74760
.74762
.74765
.55920
.55924
.55927
.55931
9.74925
.74928
.74930
.74933
.56137
.56140
.56144
.56147
9.75092
.75095
.75097
.75100
.56353
.56357
.56360
.56364
48
47
46
45
+ ¥
17
18
19
9.74430
.74433
.74436
.74439
.55501
.55505
.55508
.55512
9.74600
.74602
.74605
.74603
.55718
.55722
.55725
.55729
9.74768
.74771
.74774
.74776
.55935
.55938
.55942
.55945
9.74936
.74939
.74941
.74944
.56151
.56155
.56158
.56162
9.75103
.75106
.75109
.75111
.56368
.56371
.56375
.56378
44
43
42
41
+ 5'
n
22
23
9.74442
.74444
.74447
.74450
.55516
.55519
.55523
.55526
9.74611
.74614
.74616
.74619
.55732
.55736
.55740
.55743
9.74779
.74782
.74785
.74788
.55949
.55953
.55956
.55960
9.74947
.74950
.74953
.74955
.56166
.56169
.56173
.56176
9.75114
.75117
.75120
.75122
.56382
.56386
.56389
.56393
40
39
38
37
+ v
25
26
27
9.74453
.74456
.74458
.74461
.55530
.55534
.55537
.55541
9.74622
.74625
.74628
.74630
.55747
.55750
.55754
.55758
9.74791
.74793
.74796
.74799
.55964
.55967
.55971
.55974
9.74958
.74961
.74964
.74967
.56180
.56184
.56187
.56191
9.75125
.75128
.75131
.75134
.56397
.56400
.56404
.56407
36
35
34
S3
+ v
29
30
31
9.74464
.74467
.74470
.74473
.55545
.55548
.55552
.55555
9.74633
.74636
.74639
.74642
.55761
.55765
.55769
.55772
9.74802
.74805
.74807
.74810
.55978
.55982
.55985
.55989
9.74969
.74972
.74975
.74978
.56195
.56198
.56202
.56205
9.75136
.75139
.75142
.75145
.56411
.56415
.56418
.56422
32
31
30
29
+ 8'
33
34
35
9.74475
.74478
.74481
.74484
.55559
.55563
.55566
.55570
9.74645
.74647
.74650
.74653
.55776
.55779
.55783
.55787
9.74813
.74816
.74819
.74821
.55992
.55996
.56000
.56003
9.74981
.74983
.74986
.74989
.56209
.56213
.56216
.56220
9.75147
.75150
.75153
.75156
.56425
.56429
.56433
.56436
28
27
26
25
+ V
37
38
39
9.74487
.74490
.74492
.74495
.55573
.55577
.55581
.55584
9.74656
.74659
.74661
.74664
.55790
.55794
.55797
.55801
9.74824
.74827
.74830
.74833
.56007
.56010
.56014
.56018
9.74992
.74994
.74997
.75000
.56223
.56227
.56231
.56234
9.75159
.75161
.75164
.75167
.56440
.56443
.56447
.56451
24
23
21
+ 10'
41
42
43
9.74498
.74501
.74504
.74506
.55588
.55592
.55595
.55599
9.74667
.74670
.74673
.74675
.55805
.55808
.55812
.55815
9.74835
.74838
.74841
.74844
.56021
.56025
.56029
.56032
9.75003
.75006
.75008
.75011
.56238
.56241
.56245
.56249
9.75170
.75172
.75175
.75178
.56454
.56458
.56461
.56465
20
19
18
17
~16~
15
14
13
+ 11'
45
46
47
9.74509
.74512
.74515
.74518
.55602
.55606
.55610
.55613
9.74678
.74681
.74684
.74687
.55819
.55823
.55826
.55830
9.74846
.74849
.74852
.74855
.56036
.56039
.56043
.56047
9.75014
.75017
.75020
.75022
.56252
.56256
.56259
.56263
9.75181
.75183
.75186
.75189
.56469
.56472
.56476
.56479
+ 12'
49
50
51
9.74521
.74523
.74526
.74529
.55617
.55620
.55624
.55628
9.74690
.74692
.74695
.74698
.55834
.55837
.55841
.55844
9.74858
.74860
.74863
.74866
.56050
.56054
.56057
.56061
9.75025
.75028
.75031
.75033
.56267
.56270
.56274
.56277
9.75192
.75195
.75197
.75200
.56483
.56487
.56490
.56494
12
11
10
9
-f 13'
53
54
55
9.74532
.74535
.74538
.74540
.55631
.55635
.55638
.55642
9.74701
.74704
.74706
.74709
.55848
.55852
.55855
.55859
9.74869
.74872
.74874
.74877
.56065
.56068
.56072
.56075
9.75036
.75039
.75042
.75045
.56281
.56285
.56288
.56292
9.75203
.75206
.75208
.75211
.56497
.56501
.56505
.56508
8
7
6
5
' + Ux
57
58
59
9.74543
.74546
.74549
.74552
.55646
.55649
.55653
.55657
9.74712
.74715
.74718
.74720
.55862
.55866
.55870
.55873
9.74880
.74883
.74886
.74888
.56079
.56083
.56086
.56090
9.75047
.75050
.75053
.75056
.56296
.56299
.56303
.56306
9.75214
.75217
.75220
.75222
.56512
.56516
.56519
.56523
4
S
2
1
+ 15'
9.74554
.55660
9.74723
.55877
9.74891
.56093
9.75059
.56310
9.75225
.56526
0
17 h 34m
l?h ssm
17^32m
17* Sim
17h SOm
TABLE 45. [Page 889
Haversines.
s
tfA$0ro97°30/
6* Si™ 91° &
6h 32™ 98° <K
6* 33m 98° 15'
6* 34m 98° 307
Log. Hav
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
s
0
1
2
S
9.75225
.75228
.75231
.75233
.56526
.56530
.56534
.56537
9.75391
.75394
.75396
.75399
.56743
.56746
.56750
.56753
9.75556
.75559
.75561
.75564
.56959
.56962
.56966
.56969
9.75720
.75723
.75726
.75729
.57175
.57178
.57182
.57185
9.75884
.75887
.75889
.75892
.57390
.57394
.57398
.57401
60
59
58
57
+ 1'
5
6
7
9.75236
.75239
.75242
.75244
.56541
.56544
.56548
.56552
9.75402
.75405
.75407
.75410
.56757
.56761
.56764
.56768
9.75567
.75570
.75572
.75575
.56973
.56977
.56980
.56984
9.75731
.75734
.75737
.75739
.57189
.57193
.57196
.57200
9.75895
.75898
.75900
.75903
.57405
.57408
.57412
.57416
56
5$
54
53
+ y
9
10
11
9.75247
.75250
.75253
.75256
.56555
.56559
.56562
.56566
9.75413
.75416
.75418
.75421
.56771
.56775
.56779
.56782
9.75578
.75581
.75583
.75586
.56987
.56991
.56994
.56998
9.75742
.75745
.75748
.75750
.57203
.57207
.57211
.57214
9.75906
.75908
.75911
.75914
.57419
.57423
.57426
.57430
52
51
50
49
+ 3'
13
14
15
9.75258
.75261
.75264
.75267
.56570
.56573
.56577
.56580
9.75424
.75427
.75429
.75432
.56786
.56789
.56793
.56797
9.75589
.75592
.75594
.75597
.57002
.57005
.57009
.57012
9.75753
.75756
.75759
.75761
.57218
.57221
.57225
.57229
9.75917
.75919
.75922
.75925
.57434
.57437
.57441
.57444
48
47
46
45
+ *'
17
18
19
9.75269
.75272
.75275
.75278
.56584
.56588
.56591
.56595
9.75435
.75438
.75440
.75443
.56800
.56804
.56807
.56811
9.75600
.75603
.75605
.75608
.57016
.57020
.57023
.57027
9.75764
.75767
.75770
.75772
.57232
.57236
.57239
.57243
9.75927
.75930
.75933
.75936
.57448
.57452
.57455
.57459
44
43
42
41
+ 5'
21
22
23
9.75280
.75283
.75286
.75289
.56598
.56602
.56606
.56609
9.75446
.75449
.75452
.75454
.56815
.56818
.56822
.56825
9.75611
.75614
.75616
.75619
.57031
.57034
.57038
.57041
9.75775
.75778
.75780
.75783
.57247
.57250
.57254
.57257
9.75938
.75941
.75944
.75947
.57462
.57466
.57470
.57473
40
39
38
37
+ 6'
25
26
27
9.75291
.75294
.75297
.75300
.56613
.56616
.56620
.56624
9.75457
.75460
.75463
.75465
.56829
.56833
.56836
.56840
9.75622
.75625
.75627
.75630
.57045
.57049
.57052
.57056
9.75786
.75789
.75791
.75794
.57261
.57265
.57268
.57272
9.75949
.75952
.75955
.75957
.57477
.57480
.57484
.57488
36
36
34
33
+ r
29
SO
31
9.75303
.75305
.75308
.75311
.56627
.56631
.56634
.56638
9.75468
.75471
.75474
.75476
.56843
.56847
.56851
.56854
9.75633
.75636
.75638
.75641
.57059
.57063
.57067
.57070
9.75797
.75800
.75802
.75805
.57275
.57279
.57283
.57286
9.75960
.75963
.75966
.75968
.57491
.57495
.57498
.57502
32
31
30
29
+ &
33
34
35
9.75314
.75316
.75319
.75322
.56642
.56645
.56649
.56652
9.75479
.75482
.75485
.75487
.56858
.56861
.56865
.56869
9.75644
.75646
.75649
.75652
.57074
.57077
.57081
.57085
9.75808
.75810
.75813
.75816
.57290
.57293
.57297
.57301
9.75971
.75974
.75976
.75979
.57506
.57509
.57513
.57516
28
27
26
25
+ V
37
38
39
9.75325
.75327
.75330
.75333
.56656
.56660
.56663
.56667
9.75490
.75493
.75496
.75498
.56872
.56876
.56879
.56883
9.75655
.75657
.75660
.75663
.57088
.57092
.57095
.57099
9.75819
.75821
.75824
.75827
.57304
.57308
.57311
.57315
9.75982
.75985
.75987
.75990
.57520
.57524
.57527
.57531
24
23
22
21
+ W
41
4"2
43
9.75336
.75338
.75341
.75344
.56670
.56674
.56878
.56681
9.75501
.75504
.75507
.75509
.56887
.56890
.56894
.56897
9.75666
.75668
.75671
.75674
.57103
.57106
.57110
.57114
9.75830
.75832
.75835
.75838
.57318
.57322
.57326
.57329
9.75993
.75995
.75998
.76001
.57534
.57538
.57541
.57545
-20
19
18
17
+ 11'
45
46
47
9.75347
.75350
.75352
.75355
.56685
.56689
.56692
.56696
9.75512
.75515
.75518
.75520
.56901
.56905
.56908
.56912
9.75677
.75679
.75682
.75685
.57117
.57121
.57124
.57128
9.75840
.75843
.75846
.75849
.57333
.57337
.57340
.57344
9.76004
.76006
.76009
.76012
.57549
.57552
.57556
.57559
16
15
14
13
12
11
10
9
+ W
49
50
51
9.75358
.75361
.75363
.75366
.56699
.56703
.56707
.56710
9.75523
.75526
.75529
.75531
.56915
.56919
.56923
.56926
9.75688
.75690
.75693
.75696
.57131
.57135
.57139
.57142
9.75851
.75854
.75857
.75859
.57347
.57351
.57355
.57358
9.76014
.76017
.76020
.76023
.57563
.57567
.57570
.57574
+ 13/
53
54
55
9.75369
.75372'
.75374
.75377
.5G714
.56717
.56721
.56725
9.75534 : .56930
.75537 .56933
.75540 .56937
.75542 .56941
9.75698
.75701
.75704
.75707
.57146
.57149
.57153
.57157
9:75862
.75865
.75868
.75870
.57362
.57365
.57369
.57373
9.76025
.76028
.76031
.76033
.57577
.57581
.57585
.57588
8
7
6
5
+ 14'
57
58
59
9.75380
.75383
.75385
.75388
.56728
.56732
.56735
.56739
9.75545 .56944
.75548 .56948
.75550 .56951
.75553 .56955
9.75709
.75712
.75715
.75718
.57160
.57164
.57167
.57171
9.75873
.75876
.75879
.75881
.57376
.57380
.57383
.57387
9.76036
.76039
.76041
.76044
.57592
.57595
.57599
.57603
4
3
2
1
+ 15'
9.75391
.56743
9.75556 .56959
9.75720
.57175
9.75884
.57390
9.76047
.57606
0
17* 29™
17* 28^
17* 27m
17^26m
17* 25m
61828°— 16-
Page 890] TABLE 45.
Haversines.
s
6ft 35™ 98° 45'
6* 36^ 99° ox
6h 37m 99° 15'
6h ss™ 99° 30'
6h 39m 990 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.76047
.76050
.76052
.76055
.57606
.57610
.57613
.57617
9.76209
.76212
.76215
.76217
.57822
.57825
.57829
.57833
9.76371
.76373
.76376
.76379
.58037
.58041
.58044
.58048
9.76531
.76534
.76537
.76539
.58252
.58256
.58260
.58263
9.76691
.76694
.76697
.76699
.58467
.58471
.58475
.58478
60
59
58
57
+ 1'
5
6
7
9.76058
.76060
.76063
.76066
.57621
.57634
.57628
.57631
9.76220
.76223
.76225
.76228
.57836
.57840
.57843
.57847
9.76381
.76384
.76387
.76389
.58051
.58055
.58059
.58062
9.76542
.76545
.76547
.76550
.58267
.58270
.58274
.58277
9.76702
.76705
.76707
.76710
.58482
.58485
.58489
.58493
56
55
54
53
+ V
9
10
11
9.76069
.76071
.76074
.76077
.57635
.57639
.57642
.57646
9.76231
.76233
.76236
.76239
.57850
.57854
.57858
.57861
9.76392
.76395
.76397
.76400
.58066
.58069
.58073
.58077
9.76553
.76555
.76558
.76561
.58281
.58285
.58288
.58292
9.76713
.76715
.76718
.76721
.58496
.58500
.58503
.58507
52
51
50
49
+ V
13
14
15
9.76079
.76082
.76085
.76088
.57649
.57653
.57656
.57660
9.76241
.76244
.76247
.76250
.57865
.57868
.57872
.57876
9.76403
.76405
.76408
.76411
.58080
.58084
.58087
.58091
9.76563
.76566
.76569
.76571
.58295
.58299
.58303
.58306
9.76723
.76726
.76729
.76731
.58510
.58514
.58518
.58521
48
47
46
45
+ *'
17
18
19
9.76090
.76093
.76096
.76098
.57664
.57667
.57671
.57675
9.76252
.76255
.76258
.76260
.57879
.57883
.57886
.57890
9.76414
.76416
.76419
.76422
.58095
.58098
.58102
.58105
9.76574
.76577
.76579
.76582
.58310
.58313
.58317
.58321
9.76734
.76737
.76739
.76742
.58525
.58528
.58532
.58536
44
43
42
41
+ 5'
21 '
22
23
9.76101
.76104
.76106
.76109
.57678
.57682
.57685
.57689
9.76263
.76266
.76268
.76271
.57894
.57897
.57901
.57904
9.76424
.76427
.76430
.76432
.58109
.58112
.58116
.58120
9.76585
.76587
.76590
.76593
.58324
.58328
.58331
.58335
9.76745
.76747
.76750
.76753
.58539
.58543
.58546
.58550
40
39
38
37
+ V
25
26
27
9.76112
.76115
.76117
.76120
.57692
.57696
.57700
.57703
9.76274
.76276
.76279
.76282
.57908
.57911
.57915
.57919
9.76435
.76438
.76440
.76443
.58123
.58127
.58130
.58134
9.76595
.76598
.76601
.76603
.58338
.58342
.58346
.58349
9.76755
.76758
.76761
.76763
.58553
.58557
.58561
.58564
36
35
34
S3
+ 7'
29
30
31
9.76123
.76125
.76128
.76131
,577«7
.57710
.57714
.57718
9.76285
.76287
.76290
.76293
.57922
.57926
.57929
.57933
9.76446
.76448
.76451
.76454
.58138
.58141
.58145
.58148
9.76606
.76609
.76611
.76614
.58353
.58356
.58360
.58364
9.76766
.76769
.76771
.76774
.58568
.58571
.58575
.58579
32
31
30
29
+ &
S3
34
35
9.76134
.76136
.76139
.76142
.57721
.57725
.57728
.57732
9.76296
.76298
.76301
.76303
.57937
.57940
.57944
.57947
9.76456
.76459
.76462
.76464
.58152
.58156
.58159
.58163
9.76617
.76619
.76622
.76625
.58367
.58371
.58374
.58378
9.76777
.76779
.76782
.76784
.58582
.58586
.58589
.58593
28
27
26
25
+ V
37
38
39
9.76144
.76147
.76150
.76152
.57736
.57739
.57743
.57746
9.76306
.76309
.76311
.76314
.57951
.57955
.57958
.57962
9.76467
.76470
.76473
.76475
.58166
.58170
.58173
.58177
9.76627
.76630
.76633
.76635
.58381
.58385
.58389
.58392
9.76787
.76790
.76792
.76795
.58596
.58600
.58604
.58607
24
23
22
21
+ 10'
41
42
43
9.76155
.76158
.76161
.76163
.57750
.57753
.57757
.57761
9.76317
.76320
.76322
.76325
.57965
.57969
.57973
.57976
9.76478
.76481
.76483
.76486
.58181
.58184
.58188
.58191
9.76638
.76641
.76643
.76646
.58396
.58399
.58403
.58407
9.76798
.76800
.76803
.76806
.58611
. .58614
.58618
.58622
20
19
18
17
+ I*'
45
46
47
9.76166
.76169
.76171
.76174
.57764
.57768
.57771
.57775
9.76328
.76330
.76333
.76336
.57980
.57983
.57987
.57990
9.76489
.76491
.76494
.76497
.58195
.58199
.58202
.58206
9.76649
.76651
.76654
.76657
.58410
.58414
.58417
.58421
9.76808
.76811
.76814
.76816
.58625
.58629
.58632
.58636
16
15
14
13
4- 12'
49
50
51
9.76177
.76179
.76182
.76185
.57779
.57782
.57786
.57789
9.76338
.76341
.76344
.76346
.57994
.57998
.58001
.58005
9.76499
.76502
.76505
.76507
.58209
.58213
.58217
.58220
9.76659
.76662
.76665
.76667
.58424
.58428
.58432
.58435
9.76819
.76822
.76824
.76827
.58639
.58643
.58647
.58650
12
11
10
9
+ 13'
53
54
55
9.76188
.76190
.76193
.76196
.57793
.57797
.57800
.57804
9.76349
.76352
.76354
.76357
.58008
.58012
.58016
.58019
9.76510
.76513
.76515
.76518
.58224
.58227
.58231
.58234
9.76670
.76673
.76675
.76678
.58439
.58442
.58446
.58450
9.76830
.76832
.76835
.76838
.58654
.58657
.58661
.58665
8
7
6
5
+ 14'
57
'58
59
9.76198
.76201
.76204
.76206
.57807
.57811
.57815
.57818
9.76360
.76363
.76365
.76368
.58023
.58026
.58030
.58034
9.76521
.76523
.76526
.76529
.58238
.58242
.58245
.58249
9.76681
.76683
.76686
.76689
.58453
.58457
.58460
.58464
9.76840
.76843
.76845
.76848
.58668
.58671
.58675
.58679
4
3
2
1
+ 15'
9.76209
.57822
9.76371
.58037
9.76531
.58252
9.76691
.58467
9.76851
.58682
0
17*> 24m
17h 2$m
Uh 2%™
Ijh 2im
17 h 20m
TABLE 45. [Page 891
Haversines.
s
6& 40™ 100° O7
€»• 41™ 100° 15f
6h 42™ 100° 3<K
6* 43™ 100° 45'
6h 44m 101° <K
Log.Hav. Nat.Hav
Log. Hav
Nat. Hav
Log. Hav. Nat. Hav
Log.Hav. Nat.Ha\
Log. Hav
Nat. Ha\
s
0
1
2
S
9.76851 ! .58682
.76853 .58686
.76856 .58690
.76859 : .58693
9.77009
.77012
.77015
.77017
.58897
.58901
.58904
.58908
9.77167 .59112
.77170 .59115
.77173 i .59119
.77175 .59122
9.77325
.77327
.77330
.77333
.59326
.59330
.59333
.59337
9.77481
.77484
.77486
.77489
.59540
.59544
.59548
.59.551
60
59
58
57
+ 1'
5
6
7
9.76861 .58697
.76864 .58700
.76867 .58704
.76869 .58707
9.77020
.77023
.77025
.77028
.58911
.58915
.58919
.58922
9.77178
.77181
.77183
.77186
.59126
.59130
.59133
.59137
9.77335 ! .59340
.773381 .59344
.77340 .59348
.77343 1 .59351
9.77492
.77494
.77497
.77499
.59555
.59558
.59562
.59565
56
55
54
53
+ *'
9
10
11
9.76872 I .58711
.76875 .58714
.76877 1 .58718
.76880 1 .58733
9.77031
.77033
.77036
.77038
.58926
.58929
.58933
.58937
9.77188
.77191
.77194
.77196
.59140
.59144
.59148
.59151
9.77346; .59355
.77348 .59358
.77351 .59362
.77353 .59365
9.77502
.77505
.77507
.77510
.59569
.59573
.59576
.59580
52
51
50
49
+ v
IS
14
15
9.76883 ' .58735
.76885 .58729
.76888 .58733
.76891 .58736
9.77041
.77044
.77046
.77049
.58940
.58944
.58947
.58951
9.77199
.77202
.77204
.77207
.59155
.59158
.59162
.59165
9.77356 .59369
.77359 ; .59373
.77361 .59376
.77364 .59380
9.77512
.77515
.77518
.77520
.59583
.59587
.59590
.59594
48
47
46
45
+ *'
17
18
19
9.76893
.76896
.76898
.76901
.58740
.58743
.58747
.58750
9.77052
.77054
.77057
.77060
.58954
.58858
.58962
.58965
9.77209
.77212
.77215
.77217
.59169
.59173
.59176
.59180
9.77366 .59383
.77369 ! .59387
.77372 .59391
.77374 ! .59394
9.77523
.77525
.77528
.77531
.59598
.59601
.59605
.59608
44
43
42
41
+ 5'
tl
22
23
9.76904
.76906
.76909
.76912
.58754
.58758
.58761
.58765
9.77062
.77065
.77067
.77070
.58969
.58972
.58976
.58979
9.77220
.77223
.77225
.77228
.59183
.59187
.59190
.59194
9.77377
.77380
.77382
.77385
.59398
.59401
.59405
.59408
9.77533
.77536
.77538
.77541
.59612
.59615
.59619
.59623
40
39
38
37
+ 6'
25
te
27
9.76914
.76917
.76920
.76922
.58768
.58772
.58776
.58779
9.77073
.77075
.77078
.77081
.58983
.58987
.58990
.58994
9.77230
.77233
.77236
.77238
.59198
.59201
.59205
.59208
9.77387
.77390
1 .77393
.77395
.59412
.59416
.59419
.59423
9.77544
.77546
.77549
.77551
.59626
.59630
.59633
.59637
36
35
34
33
+ ?'
29
30
31
9.76925
.76928
.76930
.76933
.58783
.58786
.58790
.58793
9.77083
.77086
.77089
.77091
.58997
.59001
.59005
.59008
9.77241
.77243
.77246
.77249
.59212
.59215
.59219
.59223
9.77398
.77400
.77403
.77406
.59426
.59430
.59433
.59437
9.77554
.77557
.77559
.77562
.59640
.59644
.59648
.59651
32
31
30
29
+ 8'
SS
34
35
9.76936
.76938
.76941
.76943
.58797
.58801
.58804
.58808
9.77094
.77096
.77099
.77102
.59012
.59015
.59019
.59022
9.77251
.77254
.77257
.77259
.59226
.59230
.59233
.59237
9.77408
.77411
.77413
.77416
.59440
.59444
.59448
.59451
9.77564
.77567
.77570
.77572
.59655
.59658
.59662
.59665
28
27
26
25
+ 9'
37
38
39
9.76946
.76949
.76951
.76954
.58811
.58815
.58818
.58822
9.77104
.77107
.77110
.77112
.59026
.59030
.59033
.59037
9.77262
.77264
.77267
.77270
.59240
.59244
.59248
.59251
9.77419
.77421
.77424
.77427
.59455
.59458
.59462
.59465
9.77575
.77577
.77580
.77583
.59669
.59672
.59676
.59680
24
23
°2
tl
+ ir
41
42
43
9.76957
.76959
.76962
.76965
.58826
.58829
.58833
.58836
9.77115
.77117
.77120
.77123
.59040
.59044
.59047
.59051
9.77272
.77275
.77278
.77280
.59255
.59258
.59262
.59265
9.77429
.77432
.77434
.77437
.59469
.59473
.59476
.59480
9.77585
.77588
.77590
.77593
.59683
.59687
.59690
.59694
20
19
18
17
+ 11'
45
46
47
9.76967
.76970
.76972
.76975
.58840
.58843
.58847
.58851
9.77125
.77128
.77131
.77133
.59055
.59058
.59062
.59065
9.77283
.77285
.77288
.77291
.59269
.59273
.59276
.59280
9.77440
.77442
.77445
.77447
.59483
.59487
.59490
.59494
9.77596
.77598
.77601
.77603
.59697
.59701
.59705
.59708
16
15
14
13
+ 12'
49
50
51
9.76978
.76980
.76983
.76986
.58854
.58858
.58861
.58865
9.77136
.77139
.77141
.77144
.59069
.59072
.59076
.59080
9.77293 .59283
.77296 .59287
.77298 ! .59290
.77301 .59294
9.77450 .59498
.77453 .59501
.77455 .59505
.77458 ' .59508
9.77606
.77609
.77611
.77614 1
.59712
.59715
.59719
.59722
12
11
10
9
+ 13'
53
54
55
9.76988
.76991
.76994
.76996
.58869
.58872
.58876
.58879
9.77146
.77149
.77152
.77154
.59083
.59087
.59090
.59094
9.77304 .59298
.77306 .59301
.77309 .59305
.77312 .59308
9.77460 .59512
.77463 .59515
.77466 .59519
.77468 : .59523
9.77616 I
.77619 j
.77622
.77624
.59726
.59730
.59733
.59737
8
7
6
5
+ 14'
57
58
59
9.76999
.77002
.77004
.77007
.58883
.58886
.58890
.58894
9.77157
.77160
.77162
.77165
.59097
.59101
.59105
.59108
9.77314 .59312
.77317 .59315
.77319 .59319
.77322 .59323
9.77471 .59526
.77473 .59530
.77476 .59533
.77479 .59537
9.77627
.77629
.77632
.77634
.59740
.59744
.59747
.59751
4
3
2
1
+ 15'
9.77009
.58897
9.77167
.59112
9.77325 .59326
9.77481 .59540
9.77637 ; .59755
0
Ijh 19m
17hism
17*17*
17* 16™
17*15"
Page 892] - TABLE 45.
Ilaversines.
s
eh 45m 101° 15'
6h 46m 101° 30'
6h 47m 101° 45'
6h 48^ 102° Ox
6h 49m 102° 15'
s
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3 •
9.77637
.77640
.77642
.77645
.59755
.59758
.59763
.59765
9.77792
.77795
.77797
.77800
.59968
.59972
.59976
.59979
9.77947
.77949
.77952
.77954
.60182
.60185
.60189
.60193
9.78101
.78103
.78106
.78108
.60396
.60399
.60403
.60406
9.78254
.78256
.78259
.78261
.60609
.60612
.60616
.60620
60
59
58
57
+ 1'
5
6
7
9.77647
.77650
.77653
.77655
.59769
.59773
.59776
..59779
9.77803
.77805
.77808
.77810
.59983
.59986
.59990
.59993
9.77957
.77960
.77962
.77965
.60196
.60200
.60203
.60207
9.78111
.78113
.78116
.78118
.60410
.60414
.60417
.60420
9.78264
.78266
.78269
.78271
.60623
.60627
.60630
.60634
56
55
54
53
+ y
9
10
11
9.77658
.77660
.77663
.77666
.59783
.59787
.59790
.59794
9.77813
.77815
.77818
.77821
9.77823
.77826
.77828
.77831
.59997
.60000
.60004
.60008
9.77967
.77970
.77972
.77975
.60211
.60214
.60218
.60221
9.78121
.78124
.78126
.78129
.60424
.60428
.60431
.60435
9.78274
.78277
.78279
.78282
.60637
.60641
.60644
.60648
52
51
50
49
48
47
46
45
+ 3'
13
14
15
9.77668
.77671
.77673
.77676
.59797
.59801
.59804
.59808
.60011
.60015
.60018
.60022
9.77978
.77980
.77983
.77985
.60225
.60228
.60232
.60235
9.78131
.78134
.78136
.78139
.60438
.60442
.60445
.60449
9.78284
.78287
.78289
.78292
.60652
.60655
.60659
.60662
+ *'
17
18
19
9.77679
.77681
.77684
.77686
.59812
.59815
.59819
.59832
9.77834
.77836
.77839
.77841
.60025
.60029
.60033
.60036
9.77988
.77990
.77993
.77996
.60239
.60243
.60246
.60250
9.78141
.78144
.78147
.78149
.60452
.60456
.60460
.60463
9.78294
.78297
.78299
.78302
.60666
.60669
.60673
.60676
44
43
42
41
+ &
2.Z
22
23
9.77689
.77691
.77694
.77697
.59836
.59829
.59833
.59837
9.77844
.77846
.77849
.77852
.60040
.60043
.60047
.60950
9.77998
.78001
.78003
.78006
.60253
.60257
.60260
.60264
9.78152
.78154
.78157
.78159
.60467
.60470
.60474
.60477
9.78305
.78307
.78310
.78312
.60680
.60684
.60687
.60691
40
39
38
37
36
35
34
33
+ v
25
26
27
9.77699
.77702
.77704
.77707
.59840
.59844
.59847
.59851
9.77854
.77857
.77859
.77862
.60054
.60057
.60061
.60065
.60068
.60072
.60075
.60079
9.78008
.78011
.78013
.78016
.60268
.60271
.60275
.60278
9.78162
.78164
.78167
.78170
.60481
.60484
.60488
.60492
9.78315
.78317
.78320
.78322
.60694
.60698
.60701
.60705
+ r
29
30
31
9.77710
.77712
.77715
.77717
.59854
.59858
.59861
.59865
9.77864
.77867
.77870
.77872
9.78019
.78021
.78024
.78026
.60282
.60285
.60289
.60292
9.78172
.78175
.78177
.78180
.60495
.60499
.60502
.60506
9.78325
.78327
.78330
.78332
.60708
.60713
.60715
.60719
32
31
30
29
+ V
33
34
35
9.77720
.77723
.77725
.77728
.59869
.59872
.59876
.59879
9.77875
.77877
.77880
.77882
.60082
.60086
.60090
.60093
9.78029
.78031
.78034
.78037
.60296
.60300
.60303
.60307
9.78182
.78185
.78187
" .78190
.60509
.60513
.60516
.60520
9.78335
.78338
.78340
.78343
.60723
.60726
.60730
.60733
28
27
26
25
+ 9'
37
38
39
9.77730
.77733
.77735
.77738
.59883
.59886
.59890
.59894
9.77885
.77888
.77890
.77893
.60097
.60100
.69104
.60107
9.78039
.78042
.78044
.78047
.60310
.60314
.60317
.60321
9.78192
.78195
.78198
.78200
.60524
.60527
.60531
.60534
9.78345
.78348
.78350
.78353
.60737
.60740
.60744
.60747
24
23
22
21
+ 10'
41
42
43
9.77741
.77743
.77746
.77748
.59897
.59901
.59904
.59908
9.77895
.77898
.77900
.77903
.60111
.60114
.60118
.60122
9.78049
.78052
.78054
.78057
.60324
.60328
.60332
.60335
9.78203
.78205
.78208
.78210
.60538
.60541
.60545
.60548
9.78355
.78358
.78360
.78363
.60751
.60755
.60758
.60762
20
19
18
17
+ 11'
45
46
47
9.77751
.77754
.77756
.77759
.59911
.59915
.59919
.59932
9.77906
.77908
.77911
.77913
.60125
.60129
.60133
.60136
9.78060
.78062
.78065
.78067
.60339
.60342
.60346
.60349
9.78213
.78215
.78218
.78221
.60552
.60556
.60559
.60563
9.78365
.78368
.78371
.78373
.60765
.60769
.60772
.60776
16
15
14
13
+ 12'
49
50
51
9.77761
.77764
-.77766
.77769
.59926
.59929
.59933
.59936
9.77916
.77918
.77921
.77924
.60139
.60143
.60146
.60150
9.78070
.78072
.78075
.78077
.60353
.60356
.60360
.60364
9.78223
.78226
.78228
.78231
.60566
.60570
.60573
.60577
9.78376
.78378
.78381
.78383
.60779
.60783
.60786
.60790
12
11
10
9
+ 13'
53
54
55
9.77772
.77774
.77777
.77779
.59940
.59943
.59947
.59951
9.77926
.77929
.77931
.77934
.60154
.60157
.60161
.60164
9.78080
.78083
.78085
.78088
.60367
.60371
.60374
.60378
9.78233
.78236
.78238
.78241
.60580
.60584
.60588
.60591
9.78386
.78388
.78391
.78393
.60794
.60797
.60801
.60804
8
7
6
5
+ 14'
57
58
59
9.77782
.77785
.77787
.77790
.59954
.59958
.59961
.59965
9.77936
.77939
.77942
.77944
.60168
.60171
.60175
.60179
9.78090
.78093
.78095
.78098
.60381
.60385
.60388
.60392
9.78243
.78246
.78249
.78251
.60595
.60598
.60602
.60605
9.78396
.78398
.78401
.78404
.60808
.60811
.60815
.60818
4
3
2
1
+ 15'
9.77792
.59968
9.77947
.60182
9.78101 | .60396
9.78254
.60609
9.78406
.60833
0
17*> 14m
Ijh urn
1JU 12m
17h urn
l?h iom
TABLE 45. [Page 893
Haversines.
6ft 50m 10?° 30'
6 * 5 1™ 102° 45'
6* 52m 103° O7
6* 53™ 103° 15'
6h 54m 103° W
s
s
Log. Hav. Nat. Hav.
Hav.Log. j Nat. Hav.
Log. Hav.
Nat.,Hav.
!x>g. Hav.
Nat. Hav.
log. Hav. Nat. Hav.
0
1
2
S
9.78406
.78409
.78411
.78414
.60823
.60825
.60829
.60833
9.78558
.78560
.78563
.78565
.61035
.61038
.61042
.61046
9.78709
.78711
.78714
.78716
.61248
.61251
.61255
.61258
9.78859
.78862
.78864
.78867
.61460
.61464
.61467
.61471
9.79009
.79011
.79014
.79016 |
.61672
.61676
.61679
.61683
60
59
58
57
+ 1'
5
6
7
9.78416
.78419
.78421
.78424
.60836
.60840
.60843
.60847
9.78568
.78570
.78573
.78575
.61049
.61053
.61056
.61060
9.78719
.78721
.78724
.78726
.61262
.61265
.61269
.61272
9.78869
.78872
.78874
.78877
.61474
.61478
.61481
.61485
9.79019
.79021
.79024
.79026
.61686
.61690
.61693
.61697
56
55
54
53
+ V
9
10
11
9.78426
.78429
.78431
.78434
.60850
.60854
.60*57
.60861
9.78578
.78581
.78583
.78586
.61063
.61067
.61070
.61074
9.78729
.78731
.78734
.78737
.61276
.61279
.61283
.61287
9.78879
.78882
.78884
.78887
.61488
.61492
.61495
.61499
9.79029
.79031
.79034
.79036
.61701
.61704
.61708
.61711
5-2
51
50
49
+ v
13
14
15
9.78436
.78439
.78442
.78444
.60865
.60868
.60872
.60875
9.78588
.78591
.78593
.78596
.61077
.61081
.61085
.61088
9.78739
.78742
.78744
.78747
.61290
.61294
.61297
.61301
9.78889
.78892
.78894
.78897
.61502
.61506
.61510
.61513
9.79039
.79041
.79044
.79046
.61715
.61718
.61722
.61725
48
47
46
45
+ *'
.77
15
19
9.78447
.78449
.78452
.78454
.60879
.60882
.60886
.60889
9.78598
.78601
.78603
.78606
.61092
.61095
.61099
.61102
9.78749
.78752
.78754
.78757
.61304
.61308
.61311
.61315
9.78899
.78902
.78904
.78907
.61517
.61520
.61524
.61527
9.79049
.79051
.79054
.79056
.61729
.61732
.61736
.61739
44
43
42
41
+ $'
21
22
2.3
9.78457
.78459
.78462
.78464
.60893
.60897
.60900
.60904
9.78608
.78611
.78613
.78616
.61106
.61109
.61113
.61116
9.78759
.78762
.78764
.78767
.61318
.61322
.61325
.61329
9.78909
.78912
.78914
.78917
.61531
.61534
.61538
.61541
9.79059; .61743
.79061! .61747
.79064 .61750
.79066 .61754
40
39
38
37
+ 6'
25
26
27
9.78467
.78469
.78472
.78474
.60907
.60911
.60914
.60918
9.78618
.78621
.78623
.78626
.61120
.61124
.61127
.61131
9.78769
.78772
.78774
.78777
.61333
.61336
.61340
.61343
9.78919
.78922
.78924
.78927
.61545
.61548
.61552
.61556
9.79069
.79071
.79074
.79076
.61757
.61761
.61764
.61768
36
35
34
33
+ 7'
19
50
51
9.78477
.78479
.78482
.78485
.60921
.60925
.60928
.60932
9.78628
.78631
.78633
.78636
.61134
.61138
.61141
.61145
9.7S779
.78782
.78784
.78787
.61347
.61350
.61354
.61357
9.78929
.78932
.78934
.78937
.61559
.61563
.61566
.61570
9.79079
.79081
.79084
.79086
.61771
.61775
.61778
.61782
32
31
30
29
+ 8'
33
34
35
9.78487
.78490
.78492
.78495
.60936
.60939
.60943
.60946
9.78638
.78641
.78643
.78646
.61148
.61152
.61155
.61159
9.78789
.78792
.78794
.78797
.61361
.61364
.61368
.61372
9.78939
.78942
.78944
.78947
.61573
.61577
.61580
.61584
9.79089
.79091
.79094
.79096
.61785
.61789
.61792
.61796
28
27
26
25
4- 9'
.57
55
59
9.78497
.78500
.78502
.78505
.60950
.60953
.60957
.60960
9.78649
.78651
.78654
.78656
.61163
.61166
.61170
.61173
9.78799
.78802
.78804
.78807
.61375
.61379
.61382
.61386
9.78949
.78952
.78954
.78957
.61587
.61591
.61594
.61598
9.79099 .61800
.79101 .61803
.79103 | .61807
.79106 .61810
24
23
22
21
+ W
41
42
43
9.78507
.78510
.78512
.78515
.60964
.60967
.60971
.60975
9.78659
.78661
.78664
.78666
.61177
.61180
.61184
.61187
9.78809
.78812
.78814
- .78817
.61389
.61393
.61396
.61400
9.78959
.78962
.78964
.78967
.61602
.61605
.61609
.61612
9.79108
.79111
.79113
.79116
.61814
.61817
.61821
.61824
20
19
18
17
+ 11'
45
46
47
9.78517
.78520
.78522
.78525
.60978
.60982
.60985
.60989
9.78669
.78671
.78674
.78676
.61191
.61194
.61198
.61201
9.78819
.78822
.78824
.78827
.61403
.61407
.61410
.61414
9.78969
.78972
.78974
.78977
.61616
.61619
.61623
.61626
9.79118
.79121
.79123
.79126
.61828
.61831
.61835
.61838
16
15
14
13
+ 12'
49
50
51
9.7S52S
.78530
.78533
.78535
.60992
.60996
.60999
.61003
9.78679
.78681
.78684
.78686
.61205
.61209
.61212
.61216
9.78829
.78832
.78834
.78837
.61418
.61421
.61425
.61428
9.78979
.78982
.78984
.78987
.61630
.61633
.61637
.61640
9.79128
.79131
.79133
.79136
.61842
.61845
.61849
.61853
12
11
10
9
+ 13'
55
54
55
9.78538
.78540
.78543
.78545
.61007
.61010
.61014
.61017
9.78689
.78691
.78694
.78696
.61219
.61223
.61226
.61230
9.78839
.78842
.78844
.78847
.61432
.61435
.61439
.61442
9.78989
.78992
.78994
.78997
.61644
.61648
.61651
.61655
9.79138
.79141
.79143
.79146
.61856
.61860
.61863
.61867
8
r*f
/
6
5
+ 14'
57
55
59
9.78548
.78550
.78553
.78555
.61021
.61024
.61028
.61032
9.78699
.78701
.78704
.78706
.61233
.61237
.61240
.61244
9.78849
.78852
.78854
.78857
.61446
.61449
.61453
.61456
9.78999
.79002
.79004
.79007
.61658
.61662
.61665
.61669
9.79148
.79151
.79153
.79156
.61870
.61874
.61877
.61881
4
3
-•)
1
+ 15'
9.78558
.61035
9.78709 .61248
9.78859 .61460
9.79009 i .61672
9.79158
.61884
0
17h 9m
IJUgm
l?h 7™,
l?h 6m
Ijh 5m
Page 894] TABLE 45.
Haversines.
s
eh 55m 103° 45'
6h 56m 104° Ox
eh 5im 104° 15'
6h 58^ 104° 30'
6h 59™ 104° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.79158
.79161
.79163
.79165
.61884
.61888
.61891
.61895
9.79306
.79309
.79311
.79314
.62096
.62100
.62103
.62107
9.79454
.79457
.79459
.79462
.62308
.62311
.62315
.62318
9.79601
.79604
.79606
.79609
.62519
.62522
.62526
.62530
9.79748
.79750
.79752
.79755
.62730
.62734
.62737
.62741
60
59
58
57
+ 1'
5
6
7
9.79168
.79170
.79173
.79175
.61898
.61902
.61905
.61909
9.79316
.79319
.79321
.79324
.62110
.62114
.62117
.62121
9.79464
.79466
.79469
.79471
.62322
.62325
.62329
.62332
9.79611
.79613
.79616
.79618
.62533
.62537
.62540
.62544
9.79757
.79760
.79762
.79765
.62744
.62748
.62751
.62755
56
55
54
53
+ 2'
9
10
11
9.79178
.79180
.79183
.79185
.61913
.61916
.61920
.61923
9.79326
.79329
.79331
.79334
.62124
.62128
.62131
.62135
9.79474
.79476
.79479
.79481
.62336
.62339
.62343
.62346
9.79621
.79623
.79626
.79628
.62547
.62551
.62554
.62558
9.79767
.79770
.79772
.79774
.62758
.62762
.62765
.62769
52
51
50
49
+ 3'
13
14
15
9.79188
.79190
.79193
.79195
.61927
.61930
.61934
.61937
9.79336
.79339
.79341
.79343
.62138
.62142
.62145
.62149
9.79484
.79486
.79489
.79491
.62350
.62353
.62357
.62361
9.79631
.79633
.79635
.79638
.62561
.62565
.62568
.62572
9.79777
.79779
.79782
.79784
.62772
.62776
.62779
.62783
48
47
46
45
+ ±'
17
18
19
9.79198
.79200
.79203
.79205
.61941
.61944
.61948
.61951
9.79346
.79348
.79351
.79353
.62153
.62156
.62160
.62163
'9.79493
.79496
.79498
.79501
.62364
.62368
.62371
.62375
9.79640
.79643
.79645
.79648
.62575
.62579
.62582
.62586
9.79787
.79789
.79791
.79794
.62786
.62790
.62793
.62797
44
43
42
41
+ 5'
21
22
23
9.79208
.79210
.79213
.79215
.61955
.61958
.61962
.61966
9.79356
.79358
.79361
.79363
.62167
.62170
.62174
.62177
9.79503
.79506
.79508
.79511
.62378
.62382
.62385
.62389
9.79650
.79653
.79655
.79657
.62589
.62593
.62596
.62600
9.79796
.79799
.79801
.79804
.62800
.62804
.62807
.62811
40
39
38
37
36
35
34
33
+ 6'
25
26
27
9.79217
.79220
.79222
.79225
.61969
.61973
.61976
.61980
9.79366
.79368
.79371
.79373
.62181
.62184
.62188
.62191
9.79513
.79516
.79518
.79520
.62392
.62396
.62399
.62403
9.79660
.79662
.79665
.79667
.62603
.62607
.62611
.62614
9.79806
.79808
.79811
.79813
.62814
.62818
.62822
.62825
+ r
29
30
31
9.79227
.79230
.79232
.79235
.61983
.61987
.61990
.61994
9.79376
.79378
.79380
.79383
.62195
.62198
.62202
.62205
9.79523
.79525
.79528
.79530
.62406
.62410
.62413
.62417
9.79670
.79672
.79674
.79677
.62618
.62621
.62625
.62628
9.79816
.79818
.79821
.79823
.62829
.62832
.62836
.62839
32
31
30
29
+ V
33
34
35
9.79237
.79240
.79242
.79245
.61997
.62001
.62004
.62008
9.79385
.79388
.79390
.79393
.62209
.62213
.62216
.62220
9.79533
.79535
.79538
.79540
.62420
.62424
.62427
.62431
9.79679
.79682
.79684
.79687
.62632
.62635
.62639
.62642
9.79825
.79828
.79830
.79833
.62843
.62846
.62850
.62853
28
27
26
25
+ 9'
37
38
39
9.79247
.79250
.79252
.79255
.62011
.62015
.62018
.62022
9.79395
.79398
.79400
.79403
.62223
.62227
.62230
.62234
9.79542
.79545
.79547
.79550
.62434
.62438
.62442
.62445
9.79689
.79692
.79694
.79696
.62646
.62649
.62653
.62656
9.79835
.79838
.79840
.79842
.62857
.62860
.62864
.62867
24
23
22
21
20
19
18
17
+ 10'
41
42
43
9.79257
.79260
.79262
.79264
.62026
.62029
.62033
.62036
9.79405
.79407
.79410
.79412
.62237
.62241
.62244
.62248
9.79552
.79555
.79557
.79560
.62449
.62452
.62456
.62459
9.79699
.79701
.79704
.79706
.62660
.62663
.62667
.62670
9.79845
.79847
.79850
.79852
.62871
.62874
.62878
.62881
+ 11'
45
46
' 47
9.79267
.79269
.79272
.79274
.62040
.62043
.62047
.62050
9.79415
.79417
.79420
.79422
.62251
.62255
.62258
.62262
9.79562
.79565
.79567
.79569
.62463
.62466
.62470
.62473
9.79709
.79711
.79714
.79716
.62674
.62677
.62681
.62684
9.79855
.79857
.79859
.79862
.62885
.62,888
.62892
.62895
16
15
14
13
+ 12'
49
50
51
9.79277
.79279
.79282
.79284
.62054
.62057
.62061
.62064
9.79425
.79427
.79430
.79432
.62265
.62269
.62272
.62276
9.79572
.79574
.79577
.79579
.62477
.62480
.62484
.62487
9.79718
.79721
.79723
.79726
.62688
.62691
.62695
.62698
9.79864
.79867
.79869
.79872
.62899
.62902
.62906
.62909
12
11
10
9
+ 13'
53
54
55
9.79287
.79289
.79292
.79294
.62068
.62071
.62075
.62078
9.79434
.79437
.79439
.79442
.62279
.62283
.62287
.62290
9.79582
.79584
.79587
.79589
.62491
.62494
.62498
.62501
9.79728
.79731
.79733
.79735
.62702
.62706
.62709
.62713
9.79874
.79876
.79879
.79881
.62913
.62916
.62920
.62923
8
7
6
5
+ 14'
57
58
59
9.79297
.79299
.79301
.79304
.62082
.62086
.62089
.62093
9.79444
.79447
.79449
.79452
.62294
.62297
.62301
.62304
9.79591
.79594
.79596
.79599
.62505
.62508
.62512
.62515
9.79738
.79740
.79743
.79745
.62716
.62720
.62723
.62727
9.79884
.79886
.79888
.79891
.62927
.62930
.62934
.62937
4
3
2
1
+ 15'
9.79306
.62096
9.79454
.62308
9.79601
.62519
9.79748
.62730
9.79893
.62941
0
17h4m
17h3™
17*2™
Ijhim
17* G™
TABLE 45. [Page 895
Haversines.
s
7* On. 105° (K
7* im 105° 15'
7* ?m 105° 307
7* 3m 105° 45'
7* 4m 106° (K
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
Q
3
9.79893
.79896
.79898
.79901
.63941
.62944
.62948
.62951
9.80038
.80041
.80043
.80046
.63152
.63155
.63159
.63162
9.80183
.80185
.80188
.80190
.63362
.63365
.63369
.63372
9.80327
.80329
.80331
.80334
.63572
.63576
.63579
.63583
9.80470
.80472
.80474
.80477
.63782
.63785
.63789
.63792
60
59
58
57
+ 1'
5
6
7
9.79903
.79905
.79908
.79910
.62955
.62958
.62962
.62965
9.80048
.80050
.80053
.80055
.63166
.63169
.63173
.63176
9.80192
.80195
.80197
.80200
.63376
.63379
.63383
.63386
9.80336
.80339
.80341
.80343
.63586
.63590
.63593
.63597
9.80479
.80482
.80484
.80486
.63796
.63799
.63803
.63806
56
55
54
53
+ V
9
10
11
9.79913
.79915
.79918
.79920
.62969
.62973
.62976
.62980
9.80058
.80060
.80063
.80065
.63180
.63183
.63187
.63190
9.80202
.80204
.80207
.80209
.63390
.63393
.63397
.63400
9.80346
.80348
.80351
.80353
.63600
.63604
.63607
.63611
9.80489
.80491
.80494
.80496
.63810
.63813
.63817
.63820
52
51
50
49
+ 3'
13
14
15
9.79922
.79925
.79927
.79930
.62983
.62987
.62990
.62994
9.80067
.80070
.80072
.80075
.63194
.63197
.63201
.63204
9.80212
.80214
.80216
.80219
.63404
.63407
.63411
.63414
9.80355
.80358
.80360
.80362
.63614
.63618
.63621
.63625
9.80498
.80501
.80503
.80505
.63824
.63827
.63831
.63834
48
47
46
45
+ V
17
18
19
9.79932
.79935
.79937
.79939
.62997
.63001
.63004
.63008
9.80077
.80079
.80082
.80084
.63208
.63211
.63215
.63218
9.S0221
.80224
.80226
.80228
.63418
.63421
.63425
.63428
9.80365
.80367
.80370
.80372
.63628
.63632
.63635
.63639
9.80508
.80510
.80513
.80515
.638*3
.63841
.63845
.63843
44
43
42
41
40
39
38
37
+ &
21
22
23
9.79942
.79944
.79947
.79949
.63011
.63015
.63018
.63022
9.80087
.80089
.80091
.80094
.63222
.63225
.63229
.63232
9.80231
.80233
.80236
.80238
.63432
.63435
.63439
.63442
9.80374
.80377
.80379
.80382
.63642
.63646
.63649
.63653
9.80517
.80520
.80522
.80524
.63852
.63855
.63859
.63862
+ v
25
26
27
9.79951
.79954
.79956
.79959
.63025
.63029
.63032
.63036
9.80096
.80099
.80101
.80103
.63236
.63239
.63243
.63246
9.80240
.80243
.80245
.80248
.63446
.63450
.63453
.63457
9.80384
.80386
.80389
.80391
.63656
.63660
.63663
.63666
9.80527
.80529
.80532
.80534
.63866
.63869
.63873
.63876
36
35
34
33
+ r
29
30
31
9.79961
.79964
.79966
.79968
.63039
.63043
.63046
.63050
9.80106
.80108
.80111
.80113
.63250
.63253
.63257
.63260
9.80250
.80252
.80255
.80257
.63460
.63464
.63467
.63471
9.80393
.80396
.80398
.80401
.63670
.63673
.63677
.63680
9.80536
.80539
.80541
.80543
.63880
.63883
.63887
.63890
32
31
30
29
+ 8'
33
34
35
9.79971
.79973
.79976
.79978
.63053
.63057
.63060
.63064
9.80116
.80118
.80120
.80123
.63264
.63267
.63271
.63274
9.80260
80262
.80264
.80267
.63474
.63478
.63481
.63485
9.80403
.80405
.80408
.80410
.63684
.63687
.63691
.63694
9.80546
.80548
.80551
.80553
.63894
.63897
.63901
.63904
28
27
26
25
+ 9'
37
38
39
9.79980
.79983
.79985
.79988
.63067
.63071
.63074
.63078
9.80125
.80128
.80130
.80132
.63278
.63281
.63285
.63288
9.80269
.80272
.80274
.80276
.63488
.63492
.63495
.63499
9.80413
.80415
.80417
.80420
.63698
.63701
.63705
.63708
9.80555
.80558
.80560
.80562
.63908
.63911
.63915
.63918
24
23
22
21
+ W
41
42
43
9.79990
.79993
.79995
.79997
.63081
.63085
.63088
.63092
9.80135
.80137
.80140
.80142
.63292
.63295
.63299
.63302
9.80279
.80281
.80284
.80286
.63502
.63506
.63509
.63513
9.80422
.80424
.80427
.80429
.63712
.63715
.63719
.63722
9.80565
.80567
.80570
.80572
.63922
.63925
.63929
.63932
20
19
18
17
+ 11'
45
46
47
9.80000
.80002
.80005
.80007
.63095
.63099
.63102
.63106
9.80144
.80147
.80149
.80152
.63306
.63309
.63313
.63316
9.80288
.80291
.80293
.80296
.63516
.63520
.63523
.63527
9.80432
.80434
.80436
.80439
.63726
.63729
.63733
.63736
9.80574
.80577
.80579
.80581
.63936
.63939
.63943
.63946
16
15
14
13
+ 12'
49
50
51
9.80009
.80012
.80014
.80017
.63109
.63113
.63116
.63120
9.80154
.80156
.80159
.80161
.63320
.63323
.63327
.63330
9.80298
.80300
.80303
.80305
.63530
.63534
.63537
.63541
9.80441 | .63740
.80444 1 .63743
.80446 .63747
.80448 .63750
9.80584
.80586
.80589
.80591
.63950
.63953
.63957
.63960
12
11
10
9
+ 13'
53
54
55
9.80019
.80022
.80024
.80026
.63123
.63127
.63131
.63134
9.80164
.80166
.80168
.80171
.63334
.63337
.63341
.63344
9.80307
.80310
.80312
.80315
.63544
.63548
.63551
.63555
9.80451
.80453
.80455
.80458
.63754
.63757
.63761
.63764
9.80593
.80596
.80598
.80600
.63964
.63967
.63971
.63974
8
7
6
5
4
S
2
1
0
+ 14'
57
58
59
9.80029
.80031
.80034
.80036
.63138
.63142
.63145
.63148
9.80173
.80176
.80178
.80180
.63348
.63351
.63355
.63358
9.80317
.80319
.80322
.80324
.63558
.63562
.63565
.63569
9.80460
.80463
.80465
.80467
.63768
.63771
.63775
.63778
9.80603
.80605
.80607
.80610
.63977
.63981
.63984
.63988
+ 15'
9.80038
.63152
9.80183
.63362
9.80327
.63572
9.80470
.63782
9.80612
.63991
16* 59m
16*58™
16h 57m
16*56™
16* 55™
Page 896] TABLE 45.
Haversines.
7^ 5«» 106° 15'
7h em 106° 3<K
7h 7m 106° 45'
7M"*107°0'
7h 9m 107° 15'
i
Log. Hav
Nat. Hav.
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav.
Log. Hav
Nat. Hav.
Log. Hav
Nat. Hav
s
0
1
2
3
9.80612
.80615
.80617
.80619
.63991
.63995
.63998
.64002
9.80754
.80756
.80759
.80761
.64201
.64204
.64208
.64211
9.80895
.80898
.80900
.80902
.64410
.64413
.64417
.64420
9.81036
.81038
.81040
.81043
.64619
.64622
.64626
.64629
9.81176
.81178
.81180
.81183
.64827
.64831
.64834
.64838
60
59
58
57
+ 1'
5
6
7
9.80622
.80624
.80626
.80629
.64005
.64009
.64012
.64016
9.80763
.80766
.80768
.80771
.64215
.64218
.64222
.64225
9.80905
.80907
.80909
.80912
.64424
.64427
.64431
.64434
9.81045
.81047
.81050
.81052
.64632
.64636
.64639
.64643
9.81185
.81187
.81190
.81192
.64841
.64844
.64848
.64851
56
55
54
53
+ 2X
9
10
11
9.80631
.80634
.80636
.80638
.64019
.64023
.64026
.64030
9.80773
.80775
.80778
.80780
.64229
.64232
.64236
.64239
9.80914
.80916
.80919
.80921
.64438
.64441
.64445
.64448
9.81054
.81057
.81059
.81061
.64646
.64650
.64653
.64657
9.81194
.81197
.81199
.81201
.64855
.64858
.64862
.64865
52
51
50
49
+ 3/
13
14
15
9.80641
.80643
.80645
.80648
.64033
.64037
.64040
.64044
9.80782
.80785
.80787
.80789
.64243
.64246
.64250
.64253
9.80923
.80926
.80928
.80930
.64452
.64455
.64459
.64462
9.81064
.81066
.81068
.81071
.64660
.64664
.64667
.64671
9.81204
.81206
.81208
.81211
.64869
.64872
.64876
.64879
48
47
46
45
+ ¥
17
18
19
9.80650
.80652
.80655
.80657
.64047
.64051
.64054
.64058
9.80792
.80794
.807^0
.80799
.64257
.64260
.64264
.64267
9.80933
.80935
.80937
.80940
.64466
.64469
.64472
.64476
.81073
.81075
.81078
.81080
.64674
.64678
.64681
.64685
9.81213
.81215
.81217
.81220
.64883
.64886
.64890
.64893
44
43
42
41
+ &
21
22
23
9.80660
.80662
.80664
.80667
.64061
.64065
.64068
.64072
9.80801
.80804
.80806
.80808
.64270
.64274
.64277
.64281
9.80942
.80944
.80947
.80949
.64479
.64483
.64486
.64490
9.81082
.81085
.81087
. .81089
.64688
.64692
.64695
.64699
9.8J222
.81224
.81227
.81229
.64897
.64900
.64903
.64907
40
39
38
37
+ 6/
25
26
27
9.80669
.80671
.80674
.80676
.64075
.64079
.64082
.64086
9.80811
.80813
.80815
.80818
.64284
.64288
.64291
.64295
9.80952
.80954
.80956
.80959
.64493
.64497
.64500
.64504
9.81092
.81094
.81096
.81099
.64702
.64705
.64709
.64712
9.81231
.81234
.81236
.81238
.64910
.64914
.64917
.64921
36
35
34
33
32
31
30
29
+ r
29
30
31
9.80678
.80681
.80683
.80686
.64089
.64093
.64096
.64100
9.80820
.80822
.80825
.80827
.64298
.64302
.64305
.64309
9.80961
.80963
.80966
.80968
.64507
.64511
.64514
.64518
9.81101
.81103
.81106
.81108
.64716
.64719
.64723
.64726
9.81241
.81243
.81245
.81248
.64924
.64928
.64931
.64935
+ 8'
33
34
35
9.80688
.80690
.80693
.80695
.64103
.64107
.64110
.64114
9.80829
.80832
.80834
.80836
.64312
.64316
.64319
.64323
9.80970
.80973
.80975
.80977
.64521
.64525
.64528
.64532
9.81110
.81113
.81115
.81117
.64730
.64733
.64737
.64740
.64744
.64747
.64751
.64754
9.81250
.81252
.81255
.81257
.64938
.64942
.64945
.64949
28
27
26
25
+ 9'
37
38
39
9.80697
.80700
.80702
.80704
.64117
.64121
.64124
.64128
9.80839
.80841
.80844
.80846
.64326
.64330
.64333
.64337
9.80980
.80982
.80984
.80987
.64535
.64539
.64542
.64546
9.81120
.81122
.81124
.81127
9.81259
.81262
.81264
.81266
.64952
.64956
.64959
.64962
24
23
22
21
+ W
41
42
43
9.80707
.80709
.80712
.80714
.64131
.64135
.64138
.64142
9.80848
.80851
.80853
.80855
.64340
.64344
.64347
.64351
9.80989
.80991
.80994
.80996
.64549
.64552
.64556
.64559
9.81129
.81131
.81134
.81136
.64758
.64761
.64765
.64768
9.81269
.81271
.81273
.81276
.64966
.64969
.64973
.64976
20
19
18
17
+ 11'
45
46
47
9.80716
.80719
.80721
.80723
.64145
.64148
.64152
.64155
9.80858
.80860
.80862
.80865
.64354
.64358
.64361
.64365
9.80998
.81001
.81003
.81005
.64563
.64566
.64570
.64573
9.81138
.81141
.81143
.81145
.64772
.64775
.64778
.64782
9.81278
.81280
.81282
.81285
.64980
.64983
.64987
.64990
16
15
14
13
H- 12'
49
50
51
9.80726
.80728
.80730
.80733
.64159
.64162
.64166
.64169
9.80867
.80869
.80872
.80874
.64368
.64372
.64375
.64378
9.81008
.81010
.81012
.81015
.G4577
.64580
.64584
.64587
9.81148
.81150
.81152
.81155
.64785
.64789
.64792
.64796
9.81287
.81289
.81292
.81294
.64994
.64997
.65001
.65004
U
11
10
9
+ 13'
53
54
55
9.80735
.80738
.80740
.80742
.64173
.64176
.64180
.64183
9.80876
.80879
.80881
.80883
.64382
.64385
.64389
.64392
9.81017
.81019
.81022
.81024
.64591
.64594
.64598
.64601
9.81157
.81159
.81162
.81164
.64799
.64803
.64806
.64810
9.81296
.81299
.81301
.81303
.65008
.65011
.65014
.65018
8
7
6
5
+ 14'
57
58
59
9.80745
.80747
.80749
.80752
.64187
.64190
.64194
.64197
9.80886
.80888
.80891
.80893
.64396
.64399
.64403
.64406
9.81026
.81029
.81031
.81033
.64605
.64608
.64612
.64615
9.81166
.81169
.81171
.81173
.64813
.64817
.64820
.64824
9.81306
.81308
.81310
.81313
.65021
.65025
.65028
.65032
4
3
2
1
+ 15'
9.80754
.64201
9.80895
.64410
9.81036
.64619
9.81176
.64827
9.81315
.65035
0
l$h 54111
16h 53™
16h 52m
16^ 51**
16* 50™
TABLE 45. [Page 897
Haversines.
s
7* 10m 107° 3<K
7h nm 107° 45'
?h iom 108° V
7* 13m 108° 15'
7* 14m 108° 307
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.81315
.81317
.81320
.81322
.65035
.65039
.6504?
.65046
9.81454
.81456
.81458
.81460
.65243
.65247
.65250
.65254
9.81592
.81594
.81596
.81598
.65451
.65454
.6545S
.65461
9.81729
.81731
.81733
.81736
.65658
.65662
.65665
.65668
9.81866
.81868
.81870
.81872
.65865
.65869
.65872
.65876
60
59
58
57
+ lx
5
6
7
9.81324
.81326
.81329
.81331
.65049
.65053
.65056
.65060
9.81463
.81465
.81467
.81470
.65257
.65261
.65264
.65267
9.81601
.81603
.81605
.81608
.65465
.65468
.65472
.65475
9.81738
.81740
.81743
.81745
.65672
.65675
.65679
.65682
9.81875
.81877
.81879
.81882
.65879
.65882
' .65886
.65889
56
55
54
53
+ *'
9
10
11
9.81333
.81336
.81338
.81340
.65063
.65066
.65070
.65073
9.81472
.81474
.81477
.81479
.65271
.65274
.65278
.65281
9.81610
.81612
.81614
.81617
.65479
.65482
.65485
.65489
9.81747
.81749
.81752
.81754
.65686
.65689
.65693
.65696
9.81884
.81886
.81888
.81891
.65893
.65896
.65900
.65903
52
51
50
49
+ V
13
14
15
9.81343
.81345
.81347
.81350
.65077
.65080
.65084
.65087
9.81481
.81483
.81486
.81488
.65285
.65288
.65292
.65295
9.81619
.81621
.81624
.81626
.65492
.65496
.65499
.65503
9.81756
.81759
.81761
.81763
.65700
.65703
.65707
.65710
9.81893
.81895
.81897
.81900
.65907
.65910
.65911
.65917
48
47
46
45
+ *'
17
18
19
9.81352
.81354
.81357
.81359
.65091
.65094
.65098
.65101
9.81490
.81493
.81495
.81497
.65299
.65302
.65306
.65309
9.81628
.81631
.81633
.81635
.65506
.65510
.65513
.65516
9.81765
.81768
.81770
.81772
.65713
.65717
.65720
.65724
9.81902
.81904
.81907
.81909
.65920
.65924
.65927
.65931
44
43
42
41
40
39
38
37
+ $'
21
22
23
9.81361
.81364
.81366
.81368
.65105
.65108
.65112
.65115
9.81500
.81502
.81505
.81507
.65312
.65316
.65319
.65323
9.81637
.81640
.81642
.81644
.65520
.65523
.65527
.65530
9.81775
.81777
.81779
.81781
.65727
.65731
.65734
.65738
9.81911
.81913
.81916
.81918
.65934
.65938
.65941
.65944
+ *'
25
26
21
9.81370
.81373
.81375
.81377
.65118
.6513?
.65125
.65129
9.81509
.81511
.81513
.81516
.65326
.65330
.65333
.65337
9.81647
.81649
.81651
.81653
.65534
.65537
.65541
.65544
9.81784
.81786
.81788
.81791
.65741
.65744
.65748
.65751
9.81920
.81922
.81925
.81927
.65948
.65951
.65955
.65958
36
35
34
33
+ 1'
29
30
31
9.81380
.81382
.81384
.81387
.65132
.65136
.65139
.65143
9.81518
.81520
.81523
.81525
.65340
.65344
.65347
.65351
9.81656
.81658
.81660
.81663
.65548
.65551
.65555
.65558
9.81793
.81795
.81797
.81800
.65755
.65758
.65762
.65765
9.81929
.81931
.81934
.81936
.65962
.65965
.65969
.65972
32
31
30
29
+ 8'
33
34
35
9.81389
.81391
.81394
.81396
.65146
.65150
.65153
.65157
9.81527
.81530
.81532
.81534
.65354
.65357
.65361
.65364
9.81665
.81667
.81669
.81672
.65561
.65565
.65568
.65572
9.81802
.81804
.81806
.81809
.65769
.65772
.65776
.65779
9.81938
.81941
.81943
.81945
.65976
.65979
.65982
.65986
28
27
26
25
+ V
37
38
39
9.81398
.81400
.81403
.81405
.65160
.65164
.65167
.65171
9.81536
.81539
.81541
.81543
.65368
.65372
.65375
.65378
9.81674
.81676
.81679
'.81681
.65575
.65579
.65582
.65586
9.81811
.81813
.81816
.81818
.65782
.65786
.65789
.65793
9.81947
.81950
.81952
.81954
.65989
.65993
.65996
.66000
24
23
22
21
+ W
41
42
43
9.81407
.81410
.81412
.81414
.65174
.65177
.65181
.65184
9.81546
.81548
.81550
.81552
.65382
.65385
.65389
.65392
9.81683
.81685
.81688
.81690
.65589
.65593
.65596
.65599
9.81820
.81822
.81825
.81827
.65796
.65800
.65803
.65807
9.81956
.81959
.81961
.81963
.66003
.66006
.66010
.66013
20
19
18
17
+ 11'
45
46
47
9.81417
.81419
.81421
.81424
.65188
.65191
.65195
.65198
9.81555
.81557
.81559
.81562
.65396
.65399
.65402
.65406
9.81692
.81695
.81697
.81699
.65603
.65606
.65610
.65613
.81829
.81832
.81834
.81836
.65810
.65813
.65817
.65820
9.81965
.81968
.81970
.81972
.66017
.66020
.66024
.66027
16
15
14
13
+ 12'
49
50
51
9.81426
.81428
.81430
.81433
.65202
.65205
.65209
.65212
9.81564
.81566
.81569
.81571
.65409
.65413
.65416
.65420
9.81701
.81704
.81706
.81708
.65617
.65620
.65624
.65627
9.81838
.81841
.81843
.81845
.65824
.65827
.65831
.65834
9.81975
.81977
.81979
.81981
.66031
.66034
.66038
.66041
12
11
10
9
+ 13'
53
54
55
9.81435
.81437
.81440
.81442
.65216
.65219
.65222
.65226
9.81573
.81575
.81578
.81580
.65423
.65427
.65430
.65434
9.81711
.81713
.81715
.81717
.65630
.65634
.65637
.65641
9.81847
.81850
.81852
.81854
.65838
.65841
.65845
.65848
9.81984
.81986
.81988
.81990
.66044
.66048
.66051
.66055
8
7
6
5
+ 14'
57
58
59
9.81444
.81447
.81449
.81451
.65229
.65233
.65236
.65240
9.81582 1 .65437
.815851 .65440
.81587 i .65444
.81589 | .65447
9.81720
.81722
.81724
.81727
.65644
.55648
.65651
.65655
9.81857
.81859
.81861
.81863
.65851
.65855
.65858
.65862
9.81993
.81995
.81997
.81999
.66058
.66062
.66065
.66068
4
3
2
1
+ 15'
9.81454
.65243
9.81592 j .65451
9.81729
.65658
9.81866 .65865
9.82002 .66072
0
16* 49m
16*4S™>
16* 4jm
16*46™
16*45™
Page 898] TABLE 45.
Haversines.
s
7h 15m 108° 45'
7h ism 109° 0'
7ft 17m 109° 15'
7ft ism 109° 307
7h 19m 109° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.82002
.82004
.82006
.82009
.66072
.66075
.66079
.66082
9.82137
.82139
.82142
.82144
.66278
.66282
.66285
.66289
9.82272
.82274
.82277
.82279
.66485
.66488
.66491
.66495
9.82406
.82409
.82411
.82413
.66690
.66694
.66697
.66701
9.82540
.82542
.82544
.82547
.66896
.66899
.66903
.66906
60
59
58
57
+ v
5
6
7
9.82011
.82013
.82015
.82018
.66086
.66089
.68093
.66096
9.82146
.82148
.82151
.82153
.66292
.66296
.66299
.66302
9.82281
.82283
.82286
.82288
1T82290"
.82292
.82294
.82297
.66498
.66502
.66505
.66508
9.82415
.82417
.82420
.82422
.66704
.66707
.66711
.66714
9.82549
.82551
.82553
.82555
.66910
.66913
.66916
.66920
56
55
54
53
+ *
9
10
11
9.82020
.82022
.82024
.82027
.66100
.66103
.66106
.66110
9.82155
.82157
.82160
.82162
.66306
.66309
.66313
.66316
.66512
.66515
.66519
.66522
9.82424
.82426
.82429
.82431
.66718
.66721
.66725
.66728
9.82558
.82560
.82562
.82564
.66923
.66927
.66930
.66933
52
51
50
49
+ V
13
14
15
9.82029
.82031
.82033
.82036
.66113
.66117
.66120
.66124
9.82164
.82166
.82169
.82171
.66320
.66323
.66327
.66330
9.82299
.82301
.82303
.82306
.66526
.66529
.66533
.66536
9.82433
.82435
.82438
.82440
.66731
.66735
.66738
.66742
9.82567
.82569
.82571
.82573
.66937
.66940
.66944
.66947
48
47
46
45
44
43
42
41
+ *
17
18
19
9.82038
.82040
.82042
.82045
.66127
.66130
.66134
.66137
9.82173
.82175
.82178
.82180
.66333
.66337
.66340
.66344
9.82308
.82310
.82312
.82315
.66539
.66543
.66546
.66550
9.82442
.82444
.82446
.82449
.66745
.66749
.66752
.66755
9.82575
.82578
.82580
.82582
.66951
.66954
.66957
.66961
+ 5/
21
22
23
9.82047
.82049
.82051
.82054
.66141
.66144
.66148
.66151
9.82182
.82184
.82187
.82189
.66347
.66351
.66354
.66357
9.82317
.82319
.82321
.82324
.66553
.66557
.66560
.66563
9.82451
.82453
.82455
.82458
.66759
.66762
.66766
.66769
9.82584
.82587
.82589
.82591
.66964
.66968
.66971
.66975
40
39
38
37
+ v
25
26
27
9.82056
.82058
.82061
.82063
.66155
.66158
.66161
.66165
9.82191
.82193
.82196
.82198
.66361
' .66364
.66368
.66371
9.82326
.82328
.82330
.82333
.66567
.66570
.66574
.66577
9.82460
.82462
.82464
.82467
.66773
.66776
.66779
.66783
9.82593
.82595
.82598
.82600
.66978
.66981
.66985
.66988
36
35
34
33
+ 7'
29
30
31
9.82065
.82067
.82070
.82072
.66168
.66172
.66175
.66179
9.82200
.82202
.82205
.82207
.66375
.66378
.66382
.66385
9.82335
.82337
.82339
.82341
.66581
.66584
.66587
.66591
9.82469
.82471
.82473
.82475
.66786
.66790
.66793
.66797
9.82602
.82604
.82606
.82609
.66992
.66995
.66998
.67002
32
31
30
29
+ 8'
S3
34
35
9.82074
.82076
.82079
.82081
.66182
.66186
.66189
.66192
9.82209
.82211
.82214
.82216
.66388
.66392
.66395
.66399
9.82344
.82346
.82348
.82350
.66594
.66598
.66601
.66605
9.82478
.82480
.82482
.82484
.66800
.66803
.66807
.66810
9.82611
.82613
.82615
.82618
9.82620
.82622
.82624
.82627
.67005
.67009
.67012
.67016
28
27
26
25
+ *
37
38
39
9.82083
.82085
.82088
.82090
.66196
.66199
.66203
.66206
9.82218
.82220
.82223
.82225
.66402
.66406
.66409
.66412
9.82353
.82355
.82357
.82359
.66608
.66611
.66615
*.66618
9.82487
.82489
.82491
.82493
.66814
.66817
.66821
.66824
.67019
.67022
.67026
.67029
24
23
22
21
20"
19
18
17
+ NK
41
42
43
9.82092
.82094
.82097
.82099
.66210
.66213
.66217
.66220
9.82227
.82229
.82232
.82234
.66416
.66419
.66423
.66426
9.82362
.82364
.82366
.82368
.66622
.66625
.66629
.66632
9.82495
.82498
.82500
.82502
.66827
.66831
.66834
.66838
9.82629
.82631
.82633
.82635
.67033
.67036
.67039
.67043
+ 11'
45
46
47
9.82101
.82103
.82106
.82108
.66223
.66227
.66230
.66234
9.82236
.82238
.82241
.82243
.66430
.66433
.66436
.66440
9.82371
.82373
.82375
.82377
.66635
.66639
.66642
.66646
9.82504
.82507
.82509
.82511
.66841
.66844
.66848
.66851
9.82638
.82640
.82642
.82644
.67046
.67050
.67053
.67057
16
15
14
13
+ 12'
49
50
51
9.82110
.82112
.82115
.82117
.66237
.66241
.66244
.66247
9.82245
.82247
.82250
.82252
.66443
.66447
.66450
.66454
9.82380
.82382
.82384
.82386
.66649
.66653
.66656
.66659
9.82513
.82515
.82518
.82520
.66855
.66858
.66862
.66865
9.82646
.82649
.82651
.82653
.67060
.67063
.67067
.67070
12
11
10
9
+ 13'
53
54
55
9.82119
.82121
.82124
.82126
.66251
.66254
.66258
.66261
9.82254
.82256
.82259
.82261
.66457
.66460
.66464
.66467
9.82388
.82391
.82393
.82395
.66663
.66666
.66670
.66673
9.82522
.82524
.82527
.82529
.66868
.66872
.66875
.66879
9.82655
.82657
.82660
.82662
.67074
.67077
.67081
.67084
8
7
6
5
+ 14'
57
55
59
9.82128
.82130
.82133
.82135
.66265
.66268
.66272
.66275
9.82263
.82265
.82268
.82270
.66471
.66474
.66478
.66481
9.82397
.82400
.82402
.82404
.66677
.66680
.66683
.66687
9.82531
.82533
.82535
.82538
.66882
.66886
.66889
.66892
9.82664
.82666
.82668
.82671
.67087
.67091
.67094
.67098
4
3
1
~~0
+ 15'
9.82137
.66278
9.82272
.66485
9.82406
.66690
9.82540
.66896
9.82673
.67101
16^44™
16h43m
16h 42^
16k 41™
Jtfft 40m
TABLE 45. [Page 899
Haversines.
s
7ft 2#™ 110° <K
7ft 2im 110° 15'
7^ 22m HO0 307
7^ 23^ 110° 45'
7ft 24m 111° V
3
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.1 Nat. Hav.
0
1
2
3
9.82673
.82675
.82677
.82680
.67101
.67104
.67108
.67111
9.82805
.82807
.82810
.82812
.67306
.67309
.67313
.67316
9.82937
.82939
.82941
.82944
.67510
.67514
.67517
.67521
9.83068
.83070
.83073
.83075
.67715
.67718
.67721
.67725
9.83199! .67918
.832011 .67922
.83203 : .67925
.83205 .67929
60
59
58
57
+ 1'
5
6
7
9.82682
.82684
.82686
.82688
.67115
.67118
.67132
.67125
9.82814
.82816
.82818
.82821
.67320
.67323
.67326
.67330
9.82946
.82M8
.82950
.82952
.67524
.67527
.67531
.67534
9.83077
.83079
.83081
.83083
.67728
.67732
.67735
.67738
9.83207
.83210
.83212
.83214
.67932
.67935
.67939
.67942
56
55
54
53
+ *'
9
10
11
9.82691
.82693
.82695
.82697
.67128
.67132
.67135
.67139
9.82823
.82825
.82827
.82829
.67333
.67337
.67340
.67343
9.82955
.82957
.82959
.82961
.67538
.67541
.67544
.67548
9.83086
.83088
.83090
.83092
.67742
.67745
.67749
.67752
9.83216
.83218
.83220
.83223
.67946
.67949
.67952
.67956
52
51
50
49
+ 3'
IS
14
15
9.82699
.82702
.82704
.82706
.67142
.67145
.67149
.67152
9.82832
.82834
.82836
.82838
.67347
.67350
.67354
.67357
9.82963
.82966
.82968
.82970
.67551
.67555
.67558
.67561
9.83094
.83097
.83099
.83101
.67755
.67759
.67762
.67766
9.83225
.83227
.83229
.83231
.67959
.67963
.67966
.67969
48
47
46
45
+ *'
17
18
19
9.82708
.82710
.82713
.82715
.67156
.67159
.67163
.67166
9.82840
.82843
.82845
.82847
.67360
.67364
.67367
.67371
9.82972
.82974
.82976
.82979
.67565
.67568
.67572
.67575
9.83103
.83105
.83107
.83110
.67769
.67772
.67776
.67779
9.83233
.83236
.83238
.83240
.67973
.67976
.67979
.67983
44
43
42
41
H- 5'
21
22
23
9.82717
.82719
.82722
.82724
.67169
.67173
.67176
.67180
9.82849
.82851
.82854
.82856
.67374
.67377
.67381
.67384
9.82981
.82983
.82985
.82987
.67578
.67582
.67585
.67589
9.83112
.83114
.83116
.83118
.67783
.67786
.67789
.67793
9.83242
.83244
.83246
.83249
.67986
.67990
.67993
.67996
40
39
38
37
+ V
25
26
27
9.82726
.82728
.82730
.82733
.67183
.67186
.67190
.67193
9.82858
.82860
.82862
.82865
.67388
.67391
.67395
.67398
9.82990
.82992
.82994
.82996
.67592
.67595
.67599
.67602
9.83120
.83123
.83125
.83127
.67796
.67800
.67803
.67806
9.83251
.83253
.83255
.83257
.68000
.68003
.68007
.68010
36
35
34
33
+ r
29
SO
SI
9.82735
.82737
.82739
.82741
.67197
.67200
.67203
.67207
9.82867
.82869
.82871
.82873
.67401
.67405
.67408
.67412
9.82998
.83001
.83003
.83005
.67606
.67609
.67613
.67616
9.83129
.83131
.83134
.83136
.67810
.67813
.67817
.67820
9.83259
.83262
.83264
.83266
.68013
.68017
.68020
.68024
32
31
30
29
+ V
S3
S4
35
9.82744
.82746
.82748
.82750
.67210
.67214
.67217
.67221
9.82876
.82878
.82880
.82882
.67415
.67418
.67422
.67425
9.83007
.83009
.83011
.83014
.67619
.67623
.67626
.67630
9.83138
.83140
.83142
.83144
.67823
.67827
.67830
.67834
9.83268
.83270
.83272
.83275
.68027
.68030
.68034
.68037
28
27
26
25
+ «K
S7
S8
39
9.82752
.82755
.82757
.82759
.67224
.67227
.67231
.67234
9.82884
.82887
.82889
.82891
.67429
.67432
.67435
.67439
9.83016
.83018
.83020
.83022
.67633
.67636
.67640
.67643
9.83147
.83149
.83151
.83153
.67837
.67840
.67844
.67847
9.83277
.83279
.83281
.83283
.68041
.68044
.68047
.68051
24
23
22
21
+ W
41
42
43
9.82761
.82763
.82766
.82768
.67238
.67241
.67244
.67248
9.82893
.82895
.82898
.82900
.67442
.67446
.67449
.67452
9.83025
.83027
.83029
.83031
.67647
.67650
.67653
.67657
9.83155
.83157
.83160
.83162
.67850
.67854
.67857
.67861
9.83285
.83288
.83290
.83292
.68054
.68058
.68061
.68064
20
19
18
17
+ 11'
45
46
47
9.82770
.82772
.82774
.82777
.67251
.67255
.67258
.67261
9.82902
.82904
.82906
.82909
.67456
.67459
.67463
.67466
9.83033
.83035
.83038
.83040
.67660
.67664
.67667
.67670
9.83164
.83166
.83168
.83170
.67864
.67868
.67871
.67874
9.83294
.83296
.83298
.83301
.68068
.68071
.68074
.68078
16
15
14
13
+ 12'
49
50
51
9.82779
.82781
.82783
.82785
.67265
.67268
.67272
.67275
9.82911
.82913
.82915
.82917
.67469
.67473
.67476
.67480
9.83042
.83044
.83046
.83049
.67674
.67677
.67681
.67684
9.83173
.83175
.83177
.83179
.67878
.67881
.67884
.67888
9.83303
.83305
.83307
.83309
.68081
.68085
.68088
.68091
12
11
10
9
+ 13'
5S
54
55
9.82788
.82790
.82792
.82794
.67279
.67282
.67285
.67289
9.82920
.82922
.82924
.82926
.67483
.67487
.67490
.67493
9.83051
.83053
.83055
.83057
.67687
.67691
.67694
.67698
9.83181
.83184
.83186
.83188
.67891
.67895
.67898
.67901
9.83311
.83314
.83316
.83318
.68095
.68098
.68102
.68105
8
7
6
5
+ 14'
57
55
59
9.82796
.82799
.82801
.82803
.67292
.67296
.67299
.67302
9.82928
.82930
.82933
.82935
.67497
.67500
.67504
.67507
9.83059
.83062
.83064
.83066
.67701
.67704
.67708
.67711
9.83190
.83192
.83194
.83197
.67905
.67908
.67912
.67915
9.83320
.83322
.83324
.83327
.68108
.68112
.68115
.681^9
4
3
2
1
+ 15'
9.82805
.67306
9.82937
.67510
9.83068
.67715
9.83199
.67918
9.83329
.68122
0
16*39m
16*38™
16* 37m
16* 36m
16* 35m
Page 900] TABLE 45.
Haversines.
s
?h 25m Hl° 15'
?h 26m m° 30'
7A 27m m° 45'
7h 28m 113° o'
7h 29m 112° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.j Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.83329
.83331
.83333
.83335
.68133
.68125
.68139
.68133
9.83458
.83460
.83462
.83464
.68335
.68338
.68333
.68335
9.83587
.83589
.83591
.83593
.68538
.68531
.68535
.68538
9.83715
.83717
.83719
.83721
.68730
.68734
.68737
.68740
9.83842
.83844
.83847
.83849
.68933
.68936
.68939
.68943
60
59
58
57
+ I7
5
6
7
9.83337
.83339
.83342
.83344
.68135
.68139
.68143
.68146
9.83467
.83469
.83471
.83473
.68339
.68343
.68345
.68349
9.83595
.83597
.83600
.83602
.68541
.68545
.68548
.68553
9.83723
.83725
.83728
.83730
.68744
.68747
.68751
.68754
9.83851
.83853
.83855
.83857
.68946
.68949
.68953
.68956
56
55
54
53
+ *'
9
10
11
9.83346
.83348
.83350
.83352
.68149
.68153
.68156
.68159
9.83475
.83477
.83480
.83482
.68353
.68356
.68359
.68363
9.83604
.83606
.83608
.83610
.68555
.68558
.68563
.68565
9.83732
.83734
.83736
.83738
.68757
.68761
.68764
.68767
9.83859
.83861
.83864
.83866
.68959
.68963
.68966
.68969
52
51
50
49
+ &
IS
14
15
9.83355
.83357
.83359
.83361
.68163
.68166
.68169
.68173
9.83484
.83486
.83488
.83490
.68366
.68369
.68373
.68376
9.83612
.83615
.83617
.83619
.68568
.68573
.68575
.68579
9.83740
.83743
.83745
.83747
.68771
.68774
.68778
.68781
9.83868
.83870
.83872
.83874
.68973
.68976
.68980
.68983
48
47
46
45
+ *'
17
18
19
9.83363
.83365
.83368
.83370
.68176
.68180
.68183
.68186
9.83492
.83495
.83497
.83499
.68379
.68383
.68386
.68389
9.83621
.83623
.83625
.83627
.68583
.68585
.68589
.68593
9.83749
.83751
.83753
.83755
.68784
.68788
.68791
.68794
9.83876
.83878
.83881
.83883
.68986
.68990
.68993
.68996
44
43
42
41
40
39
38
37
+ V
21
22
23
9.83372
.83374
.83376
.83378
.68190
.68193
.68196
.68300
9.83501
.83503
.83505
.83507
.68393
.68396
.68399
.68403
9.83630
.83632
.83634
.83636
.68595
.68599
.68603
.68606
9.83757
.83760
.83762
.83764
.68798
.68801
.68804
.68808
9.83885
.83887
.83889
.83891
.69000
.69003
.69006
.69010
+ 6'
25
26
27
9.83380
.83383
.83385
.83387
.68303
.68307
.68310
.68313
9.83510
.83512
.83514
.83516
.68406
.68410
.68413
.68416
9.83638
.83640
.83642
.83644
.68609
.68613
.68616
.68619
9.83766
.83768
.83770
.83772
.68811
.68815
.68818
.68831
9.83893
.83895
.83897
.83900
.69013
.69017
.69030
.69033
36
35
34
33
+ 1'
29
SO
31
9.83389
.83391
.83393
.83396
.68317
.68330
.68334
.68337
9.83518
.83520
.83522
.83525
.68430
.68433
.68437
.68430
9.83647
.83649
.83651
.83653
.68633
.68636
.68639
.68633
9.83774
.83777
.83779
.83781
.68835
.68838
.68831
.68835
9.83902
.83904
.83906
.83908
.69037
.69030
.69Q33
.69037
32
31
30
29
+ 8'
33
34
35
9.83398
.83400
.83402
.83404
.68330
.68334
.68337
.68340
9.83527
.83529
.83531
.83533
.68433
.68437
.68440
.68443
9.83655
.83657
.83659
.83662
.68636
.68639
.68643
.68646
9.83783
.83785
.83787
.83789
.68838
.68843
.68845
.68848
9.8C910
.83912
.83914
.83916
.69040
.69044
.69047
.69050
28
27
26
25
+ 9'
37
38
39
9.83406
.83409
.83411
.83413
.68344
.68347
.68351
.68354
9.83535
.83537
.83540
.83542
.68447
.68450
.68454
.68457
9.83664
.83666
.83668
.83670
.68649
.68653
.68656
.68660
9.83791
.83794
.83796
.83798
.68853
.68855
.68858
.68863
9.83919
.83921
.83923
.83925
.69054
.69057
.69060
.69064
24
23
22
21
+ 10'
41
42
43
9.83415
.83417
.83419
.83421
.68357
.68361
.68364
.68368
9.83544
.83546
.83548
.83550
.68460
.68464
.68467
.68470
9.83672
.83674
.83676
.83679
.68663
.68666
.68670
.68673
9.83800
.83802
.83804
.83806
.68865
.68869
.68873
.68875
9.83927
.83929
.83931
.83933
.69067
.69070
.69074
.69077
20
19
18
17
+ 11'
* 45
46
47
9.83424
.83426
.83428
.83430
.68371
.68374
.68378
.68381
9.83552
.83555
.83557
.83559
.68474
.68477
.68481
.68484
9.83681
.83683
.83685
.83687
.68676
.68680
.68683
.68687
9.83808
.83811
.83813
.83815
.68879
.68883
.68885
.68889
9.83935
.83938
.83940
.83942
.69080
.69084
.69087
.69091
16
15
14
13
12
11
10
9
+ 13'
49
50
51
9.83432
.83434
.83436
.83439
.68384
.68388
.68391
.68395
9.83561
.83563
.83565
.83567
.68487
.68491
.68494
.68497
9.83689
.83691
.83694
.83696
.68690
.68693
.68697
.68700
9.83817
.83819
.83821
.83823
.68893
.68895
.68899
.68903
9.83944
.83946
.83948
.83950
.69094
.69097
.69101
.69104
+ 13'
53
54
55
9.83441
.83443
.83445
.83447
.68398
.68301
.68305
.68308
9.83570
.83572
.83574
.83576
.68501
.68504
.68508
.68511
9.83698
.83700
.83702
.83704
.68703
.68707
.68710
.68713
9.83825
.83828
.83830
.83832
.68906
.68909
.68913
.68916
9.83952
.83955
.83957
.83959
.69107
.69111
.69114
.69117
8
7
6
5
+ 14'
57
58
59
9.83449
.83452
.83454
.83456
.68313
.68315
.68318
.68333
9.83578
.83580
.83582
.83585
.68515
.68518
.68531
.68535
9.83706
.83708
.83711
.83713
.68717
.68730
.68734
.68737
9.83834
.83836
.83838
.83840
.68919
.68933
.68936
.68939
9.83961
.83963
.83965
.83967
.69131
.69134
.69137
.69131
4
3
2
1
0
+ 15'
9.83458
.68335
9.83587
.68538
9.83715
.68730
9.83842
.68933
9.83969
.69134
IQh S4m
l£h 33^
16h 32m
IQh sim
16* som
TABLE 45. [Page 901
Haversines.
s
7* 50n» 112° W
7h 3im 112° 45'
7h 32m H3° 0'
7^ 33^ 113^ 15'
7h 34m 113° 30'
s
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.' Nat. Hav.
Log. Hav.j Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
S
9.83969
.83971
.83974
.83976
.69134
.69138
.69141
.69144
9.84096
.84098
.84100
.84102
.69336
.69339
.69342
.69346
9.S4221 i .69537
.84223 i .69540
.84226 , .69543
.84228! .69547
9.84346
.84349
.84351
.84353
.69737
.69741
.69744
.69747
9.84471
.84473
.84475
.84477
.69937
.69941
.69944
.69947
60
59
58
57
56
55
54
53
52
51
50
49
+ 1'
5
6
7
9.83978
.83980
.83982
.83984
.69148
.69151
.69154
.69158
9.84104
.84106
.84108
.84110
.69349
.69352
.69356
.69359
9.84230 i .69550
.84232 .69553
.84234| .69557
.84236 j .69560
9.84355
.84357
.84359
.84361
.69751
.69754
.69757
.69761
9.84479
.84481
.84483
.84485
.69951
.69954
.69957
.69961
+ V
9
10
11
9.83986
.83988
.83990
.83992
.69161
.69164
.69168
.69171
9.84112
.84114
.84117
.84119
.69362
.69366
.69369
.69372
9.84238
.84240
.84242
.84244
.69563
.69567
.69570
.69573
9.84363
.84365
.84367
.84369
.69764
.69767
.69771
.69774
9.84488
.84490
.84492
.84494
.69964
.69967
.69971
.69974
+ 3'
M
14
15
9.83995
.83997
.83999
.84001
.69174
.69178
.69181
.69185
9.84121
.84123
.84125
.84127
.69376
.69379
.69382
.69386
9.84246 .69577
.84248 .69580
.84251 .69583
.84253 .69587
9.84371 i .69777
.843731 .69781
.84376! .69784
.84378 .69787
9.84496 | .69977
.84498 .69981
.84500 i .69984
.84502 .69987
48
47
46
45
+ *'
17
15
1.9
9.84003
.84005
.84007
.84009
.69188
.69191
.69195
.69198
9.84129
.84131
.84133
.84135
.69389
.69393
.69396
.69399
9.84255
.84257
.84259
.84261
.69590
.69593
.69597
.69600
9.84380
.84382
.84384
.84386
.69791
.69794
.69797
.69801
9.84504 .69991
.84506 .69994
.84508 j .69997
.84510 i .70001
44
43
42
41
+ 5'
£1
Jtt
23
9.84011
.84014
.84016
.84018
.69201
.69205
.69208
.69211
9.84138
.84140
.84142
.84144
.69403
.69406
.69409
.69413
9.84263 .69603
.84265 .69607
.84267 .69610
.84269 | .69614
9.84388
.84390
.84392
.84394
.69804
.69807
.69811
.69814
9.84512 .70004
.84514 .70007
.84517 .70011
.84519 .70014
40
39
38
37
+ 6'
25
26
27
9.84020
.84022
.84024
.84026
.69215
.69218
.69221
.69225
9.84146
.84148
.84150
.84152
.69416
.69419
.69423
.69426
9.84271 I .69617
.842741 .69620
.84276 I .09624
.84278 : .69627
9.84396
.84398
.84400
.84403
.69817
.69821
.69824
.69827
9.84521 .70017
.84523 .70021
.84525 .70024
.84527 .70027
36
35
34
33
+ 7X
29
JO
«?!
9.84028
.84030
.84033
.84035
.69228
.69232
.69235
.69238
9.84154
.84156
.84159
.84161
.69429
.69433
.69436
.69439
9.84280 i .69630
.84282 .69634
.84284 .69637
.84286 1 .69640
9.84405
.84407
.84409
.84411
.69831
.69834
.69837
.69841
9.84529
.84531
.84533
.84535
.70031
.70034
.70037
.70041
32
31
30
29
+ 8'
S3
34
35
9.84037
.84039
.84041
.84043
.69242
.69245
.69248
.69252
9.84163
.84165
.84167
.84169
.69443
.69446
.69450
.69453
9.84288
.84290
.84292
.84294
.69644
.69647
.G9650
.69654
9.84413
.84415
.84417
.84419
.69844
.69847
.69851
.69854
9.84537
.84539
.84541
.84543
.70044
.70047
.70051
.70054
28
27
26
25
+ V
37
38
39
9.84045
.84047
.84049
.84051
.69255
.69258
.69262
.69265
9.84171
.84173
.84175
.84177
.69456
.69460
.69463
.69466
9.84296
.84299
.84301
.84303
.69657
.69660
.69664
.69667
9.84421
.84423
.84425
.84427
.69857
.69861
.69864
.69867
9.84545
.84547
.84550
.84552
.70057
.70061
.70064
.70067
24
23
22
21
+ NK
41
42
43
9.84054
.84056
.84058
.840GO
.69268
.69272
.69275
.69279
9.84179
.84182
.84184
.84186
.69470
.69473
.69476
.69480
9.84305
.84307
.84309
.84311
.69670
.69674
.69677
.69680
9.84430
.84432
.84434
.84436
.69871
.69874
.69877
.69881
9.84554 .70071
.84556 .70074
.84558 .70077
.84560 : .70081
20
19
IS
17
+ 11'
45
46
47
9.84062
.84064
.84066
.84068
.69282
.69285
.69289
.69292
9.84188
.84190
.84192
.84194
.69483
.69486
.69490
.69493
9.84313
.84315
.84317
.84319
.69684
.69687
.69690
.69694
9.84438
.84440
.84442
.84444
.69884
.69887
.69891
.69894
9.84562
.84564
.84566
.84568
.70084
.70087
.70091
.70094
16
15
14
13
+ 12'
49
50
51
9.84070
.84072
.84075
.84077
.69295
.69299
.69302
.69305
9.84196
.84198
.84200
.84203
.69496
.69500
.69503
.69506
9.84321
.84324
.84326
.84328
.69697
.69700
.69704
.69707
9.84446
.84448
.84450
.84452
.69897
.69901
.69904
.69907
9.84570
.84572
.84574
.84576
.70097
.70101
.70104
.70107
12
11
10
9
+ 13'
53
54
55
9.84079
.84081
.84083
.84085
.69309
.69312
.69315
.69319
9.84205
.84207
.84209
.84211
.69510
.69513
.69516
.69520
9.84330
.84332
.84334
.84336
.69710
.69714
.69717
.69720
9.84454
.84456
.84459
.84461
.69911
.69914
.69917
.69921
9.84578
.84581
.84583
.84585
.70111
.70114
.70117
.70121
8
7
6
5
+ 14'
57
55
59
9.84087
.84089
.84091
.84093
.69322
.69326
.69329
.69332
9.84213
.84215
.84217
.84219
.69523
.69527
.69530
.69533
9.84338
.84340
.84342
.84344
.69724
.69727
.69731
.69734
9.84463
.84465
.84467
.84469
.69924
.69927
.69931
.69934
9.84587
.84589
.84591
.84593
.70124
.70127
.70131
.70134
4
3
2
1
+ I*'
9.84096
.69336
9.84221
.69537
9.84346 | .69737
9.84471
.69937
9.84595
.70137
0
16* 29m
16h 2Sm
16h 27m
16h 26^
16* 25m
Page 902] TABLE 45.
Haversines.
s
jh 35m 113° 45'
?h sem 114° 0'
7h sjm 114° is/
?h 38™ 114° 30'
7h sgm 114° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
3
9.84595
.84597
.84599
.84601
.70137
.70141
.70144
.70147
9.84718
.84720
.84722
.84724
.70337
.70340
.70343
.70347
9.84841
.84843
.84845
.84847
.70536
.70539
.70543
.70546
9.84963
.84965
.84967
.84969
.70735
.70738
.70741
.70745
9.85085
.85087
.85089
.85091
.70933
.70936
.70940
.70943
60
59
58
57
+ 1'
5
6
7
9.84603
.84605
.84607
.84609
.70151
.70154
.70157
.70161
9.84726
.84729
.84731
.84733
.70350
.70353
.70357
.70360
9.84849
.84851
.84853
.84855
.70549
.70553
.70556
.70559
9.84971
.84973
.84975
.84977
.70748
.70751
.70755
.70758
9.85093
.85095
.85097
.85099
.70946
.70950
.70953
.70956
56
55
54
53
+ v
9
10
11
9.84611
.84613
.84616
.84618
.70164
.70167
.70171
.70174
9.84735
.84737
.84739
.84741
.70363
.70367
.70370
.70373
9.84857
.84859
.84861
.84863
.70562
.70566
.70569
.70572
9.84979
.84982
.84984
.84986
.70761
.70764
.70768
.70771
9.85101
.85103
.85105
.85107
.70959
.70963
.70966
.70969
52
51
50
49
48
47
46
45
44
43
42
41
+ &
13
14
15
9.84620
.84622
.84624
.84626
.70177
.70181
.70184
.70187
9.84743
.84745
.84747
.84749
.70377
.70380
.70383
.70387
9.84866
.84868
.84870
.84872
.70576
.70579
.70582
.70586
9.84988
.84990
.84992
.84994
.70774
.70778
.70781
.70784
9.85109
.85111
.85113
.85115
.70973
.70976
.70979
.70983
+ *'
17
18
19
9.84628
.84630
.84632
.84634
.70191
.70194
.70197
.70301
9.84751
.84753
.84755
.84757
.70390
.70393
.70397
.70400
9.84874
.84876
.84878
.84880
.70589
.70592
.70596
.70599
9.84996
.84998
.85000
.85002
.70788
.70791
.70794
.70798
9.86117
.85119
.85121
.85123
.70986
.70989
.70992
.70996
+ *'
21
22
23
9.84636
.84638
.84640
.84642
.70204
.70207
.70211
.70214
9.84759
.84761
.84763
.84765
.70403
.70407
.70410
.70413
9.84882
.84884
.84886
.84888
.70602
.70606
.70609
.70612
9.85004
.85006
.85008
.85010
.70801
.70804
.70807
.70811
9.85125
.85127
.85129
.85131
.70999
.71002
.71006
.71009
40
39
38
37
+ v
25
26
27
9.84644
.84646
.84648
.84651
.70217
.70221
.70224
.70227
9.84767
.84770
.84772
.84774
.70417
.70420
.70423
.70426
9.84890
.84892
.84894
.84896
.70615
.70619
.70622
.70625
9.85012
.85014
.85016
.85018
.70814
.70817
.70821
.70824
9.85133
.85135
.85137
.85139
.71012
.71016
.71019
.71022
36
35
34
33
+ v
29
30
31
9.84653
.846*55
.84657
.84659
.70230
.70234
.70237
.70240
9.84776
.84778
.84780
.84782
.70430
.70433
.70436
.70440
9.84898
.84900
.84902
.84904
.70629
.70632
.70635
.70639
9.85020
.85022
.85024
.85026
.70827
.70831
.70834
.70837
9.85141
.85143
.85145
.85147
.71025
.71029
.71032
.71035
32
31
30
29
+ 8'
33
34
35
9.84661
.84663
.84665
.84667
.70244
.70247
.70250
.70254
9.84784
.84786
.84788
.84790
.70443
.70446
.70450
.70453
9.84906
.84908
.84910
.84912
.70642
.70645
.70649
.70652
9.85028
.85030
.85032
.85034
.70840
.70844
.70847
.70850
9.85149
.85151
.85153
.85155
.71039
.71042
.71045
.71049
28
27
26
25
+ V
37
38
39
9.84669
.84671
.84673
.84675
.70257
.70260
.70264
.70267
9.84792
.84794
.84796
.84798
.70456
.70460
.70463
.70466
9.84914
.84916
.84919
.84921
.70655
.70659
.70662
.70665
9.85036
.85038
.85040
.85042
.70854
.70857
.70860
.70864
9.85158
.85160
.85162
.85164
.71052
.71055
.71058
.71062
24
23
22
21
+ 10'
41
42
43
9.84677
.84679
.84681
.84683
.70270
.70274
.70277
.70280
9.84800
.84802
.84804
.84806
.70470
.70473
.70476
.70480
9.84923
.84925
.84927
.84929
.70668
.70672
.70675
.70678
9.85044
.85046
.85048
.85050
.70867
.70870
.70874
.70877
9.85166
.85168
.85170
.85172
.71065
.71068
.71072
.71075
20
19
18
17
+ 11'
45
46
47
9.84685
.84688
.84690
.84692
.70284
.70287
.70290
.70294
9.84808
.84810
.84812
.84815
.70^83
.70486
.70490
.70493
9.84931
.84933
.84935
.84937
.70682
.70685
.70688
.70692
9.85052
.85054
.85057
.85059
.70880
.70884
.70887
.70890
9.85174
.85176
.85178
.85180
.71078
.71082
.71085
.71088
16
15
14
13
+ 12'
49
50
51
9.84694
.84696
.84698
.84700
.70297
.70300
.70304
.70307
9.84817
.84819
.84821
.84823
.70496
.70499
.70503
.70506
9.84939
.84941
.84943
.84945
.70695
.70698
.70702
.70705
9.85061
.85063
.85065
.85067
.70893
.70897
.70900
.70903
9.85182
.85184
.85186
.85188
.71091
.71095
.71098
.71101
12
11
10
9
+ 13'
53
54
55
9.84702
.84704
.84706
.84708
.70310
.70314
.70317
.70320
9.84825
.84827
.84829
.84831
.70509
.70513
.70516
.70519
9.84947
.84949
.84951
.84953
.70708
.70712
.70715
.70718
9.85069
.85071
.85073
.85075
.70907
.70910
.70913
.70916
9.85190
.85192
.85, 94
.85196
.71105
.71108
.71111
.71114
8
7
6
5
+ 14'
57
58
59
9.84710
.84712
.84714
.84716
.70324
.70327
.70330
.70333
9.84833
.84835
.84837
.84839
.70523
.70526
.70529
.70533
9.84955
.84957
.84959
.84961
.70721
.70725
.70729
.70731
9.85077
.85079
.85081
.85083
.70920
.70923
.70926
.70930
9.85198
.85200
.85202
.85204
.71118
.71121
.71124
.71128
4
3
2
1
+ 15'
9.84718
.70337
9.84841
.70536
9.84963
.70735
9.85085
.70933
9.85206
.71131
0
16h 24m
16h 23m
16h ggm
16^ 2im
IQh 20™
TABLE 45. [Page 903
Haversines.
s
7h 4Qm H5° O7
7 A 4im H5° 15'
7 A 42m 115° 30'
7* 43™ 115° 45'
7h 44m 116° O7
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.85206
.85208
.85210
.85212
.71131
.71134
.71138
.71141
9.85326
.85328
.85330
.85332
.71328
.71332
.71335
.71338
9.85446
.85448
.85450
.85452
.71526
.71529
.71532
.71535
9.85565
.85567
.85569
.85571
.71722
.71726
.71729
.71732
9.85684
.85686
.85688
.85690
.71919
.71922
.71925
.7W28
60
59
58
57
+ 1'
0
6
7
9.85214
.85216
.85218
.85220
.71144
.71147
.71151
.71154
9.85334
.85336
.85338
.85340
.71342
.71345
.71348
.71351
9.85454
.85456
.85458
.85460
.71539
.71542
.71545
.71549
9.85573
.85575
.85577
.85579
.71735
.71739
.71742
.71745
9.85692
.85694
.85696
.85698
.71932
.71935
.71938
.71941
56
55
54
53
+ *'
9
10
11
9.85222
.85224
.85226
.85228
.71157
.71161
.71164
.71167
9.85342
.85344
.85346
.85348
.71355
.71358
.71361
.71365
9.85462
.85464
.85466
.85468
.71552
.71555
.71558
.71562
9.85581
.85583
.85585
.85587
.71748
.71752
.71755
.71758
9.85700
.85702
.85704
.85706
.71945
.71948
.71951
.71955
52
51
50
49
+ *'
13
14
15
9.85230
.85232
.85234
.85236
.71170
.71174
.71177
.71180
9.85350
.85352
.85354
.85356
.71368
.71371
.71374
.71378
9.85470
.85472
.85474
.85476
.71565
.71568
.71571
.71575
9.85589
.85591
.85593
.85595
.71762
.71765
.71768
.71771
9.85708
.85710
.85712
.85714
.71958
.71961
.71964
.71968
48
47
46
45
+ V
17
18
19
9.85238
.85240
.85242
.85244
.71184
.71187
.71190
.71194
9.85358
.85360
.85362
.85364
.71381
.71384
.71388
.71391
9.85478
.85480
.85482
.85484
.71578
.71581
.71585
.71588
9.85597
.85599
.85601
.85603
.71775
.71778
.71781
.71784
9.85716
.85718
.85720
.85722
.71971
.71974
.71977
.71981
44
43
42
41
+ 5'
21
22
is
9.85246
.85248
.85250
.85252
.71197
.71200
.71203
.71207
9.85366
.85368
.85370
.85372
.71394
.71397
.71401
.71404
9.85486
.85488
.85490
.85492
.71591
.71594
.71598
.71601
9.85605
.85607
.85609
.85611
.71788
.71791
.71794
.71798
9.85724
.85726
.85727
.85729
.71984
.71987
.71990
.71994
40
39
38
37
+ *'
25
26
27
9.85254
.85256
.85258
.85260
.71210
.71213
.71217
.71220
9.85374
.85376
.85378
.85380
.71407
.71411
.71414
.71417
9.85494
.85496
.85498
.85500
.71604
.71608
.71611
.71614
9.85613
.85615
.85617
.85619
.71801
.71804
.71807
.71811
9.85731
.85733
.85735
.85737
.71997
.72000
.72003
.72007
36
35
34
33
+ r
29
30
31
9.85262
.85264
.85266
.85268
.71223
.71226
.71230
.71233
9.85382
.85384
.85386
.85388
.71420
.71421
.71427
.71430
9.85502
.85504
.85506
.85508
.71617
.71621
.71624
.71627
9.85621
.85623
.85625
.85627
.71814
.71817
.71820
.71824
9.85739
.85741
.85743
.85745
.72010
.72013
.72017
.72020
32
31
30
29
+ 8'
S3
34
35
9.85270
.85272
.85274
.85276
.71236
.71240
.71243
.71246
9.85390
.85392
.85394
.85396
.71434
.71437
.71440
.71443
9.85510
.85512
.85514
.85516
.71631
.71634
.71637
.71640
9.85629
.85631
.85633
.85635
.71827
.71830
.71834
.71837
9.85747
.85749
.85751
.85753
.72023
.72026
.72030
.72033
28
t7
"26
25
+ 9X
37
38
39
9.85278
.85280
.85282
.85284
.71249
.71253
.71256
.71259
9.85398
.85400
.85402
.85404
.71447
.71450
.71453
.71^56
9.85518
.85520
.85522
.85524
.71644
.71647
.71650
.71653
9.85637
.85639
.85641
.85643
.71840
.71843
.71847
.71850
9.85755
.85757
.85759
.85761
.72036
.72039
.72043
.72046
24
23
22
21
+ W
41
42
43
9.85286
.85288
.85290
.85292
.71263
.71266
.71269
.71273
9.85406
.85408
.85410
.85412
.71460
.71463
.71466
.71470
9.85526
.85528
.85530
.85532
.71657
.71660
.71663
.71667
.71670
.71673
.71676
.71680
9.85645
.85647
.85649
.85651
.71853
.71856
.71860
.71863
9.85763
.85765
.85767
.85769
.72049
.72052
.72056
.72059
20
19
18
17
16
15
14
13
+ 11'
45
46
47
9.85294
.85296
.85298
.85300
.71276
.71279
.71282
.71286
9.85414
.85416
.85418
.85420
.71473
.71476
.71480
.71483
9.85534
.85536
.85538
.85540
9.85653 I .71866
.85654 .71870
.85656 .71873
.85658 1 .71876
9.85771
.85773
.85775
.85777
.72062
.72066
.72069
.72072
+ 12'
49
50
51
9.85302
.85304
.85306
.85308
.71289
.71292
.71296
.71299
9.85422
.85424
.85426
.85428
.71486
.71489
.71493
.71496
9.85542
.85544
.85546
.85548
.71683
.71686
.71690
.71693
9.85660
.85662
.85664
.85666
.71879
.71883
.71886
.71889
9.85779
.85781
.85783
.85785
.72075
.72079
.72082
.72085
12
11
10
9
+ 13'
53
54
55
9.85310
.85312
.85314
.85316
.71302
.71305
.71309
.71312
9.85430
.85432
.85434
.85436
.71499
.71503
.71506
.71509
9.85550
.85552
.85554
.85555
.71696
.71699
.71703
.71706
9.85668
.85670
.85672
.85674
.71892
.71896
.71899
.71902
9.85787
.85788
.85790
.85792
.72088
.72092
.72095
.72098
8
7
6
5
'+ 14'
57
58
59
9.85318
.85320
.85322
.85324
.71315
.71319
.71322
.71325
9.85438
.85440
.85442
.85444
.71512
.71516
.71519
.71522
9.85557
.85559
.85561
.85563
.71709
.71712
.71716
.71719
9.85676
.85678
.85680
.85682
.71905
.71909
.71912
.71915
9.85794
.85796
.85798
.85800
.72101
.72105
.72108
.72111
4
3
2
1
+ 15'
9.85326
.71328
9.85446
.71526
9.85565 .71722
9.85684
.71919
9.85802
.72114
0
Hjh igm
16* 18m
16h nm
16* 16*"
16h ism
Page 904] TABLE 45.
Haversines.
s
s
7& 45™ 116° 15'
7h 46™ 116° 30'
7h 47m 116° 45'
7h 48m 117° 0'
?h 49m 117° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.85802
.85804
.85806
.85808
.72114
.72118
.72121
.72124
9.85920
.85922
.85924
.85926
.72310
.72313
.72316
.72320
9.86037
.86039
.86041
.86043
.72505
.72508
.72511
.72515
9.86153
.86155
.86157
.86159
.72700
.72703
.72706
.72709
9.86269
.86271
.86273
.86275
.72894
.72897
.72900
.72903
60
59
58
57
56
55
54
53
52
51
50
49
+ V
5
6
7
9.85810
.85812
.85814
.85816
.72127
.72131
.72134
.72137
9.85928
.85930
.85931
.85933
.72323
.72326
.72329
.72333
9.86045
.86046
.86048
.86050
.72518
.72521
.72524
.72528
9.86161
.86163
.86165
.86167
.72712
.72716
.72719
.72722
9.86277
.86279
.86281
.86282
.72907
.72910
.72913
.72916
+ %'
9
10
11
9.85818
.85820
.85822
.85824
.72141
.72144
.72147
.72150
9.85935
.85937
.85939
.85941
.72336
.72339
.72342
.72346
9.86052
.86054
.86056
.86058
.72531
.72534
.72537
.72541
9.86169
.86171
.86173
.86174
.72725
.72729
.72732
.72735
9.86284
.86286
.86288
.86290
.72920
.72923
.72926
.72929
+ 3'
13
14
15
9.85826
.85828
.85830
.85832
.72154
.72157
.72160
.72163
9.85943
.85945
.85947
.85949
.72349
.72352
.72355
.72359
9.86060
.86062
.86064
.86066
.72544
.72547
.72550
.72554
9.86176
.86178
.86180
.86182
.72738
.72742
.72745
.72748
9.86292
.86294
.86296
.86298
.72932
.72936
.72939
.72942
48
47
46
45
+ *'
17
18
19
9.85834
.85836
.85838
.85840
.72167
.72170
.72173
.72176
9.85951
.85953
.85955
.85957
.72362
.72365
.72368
.72372
9.86068
.86070
.86072
.86074
.72557
.72560
.72563
.72567
9.86184
.86186
.86188
.86190
.72751
.72755
.72758
.72761
9.86300
.86302
.86304
.86306
.72945
.72949
.72953
.72955
44
43
42
41
+ v
21
22
23
9.85841
.85843
.85845
.85847
.72180
.72183
.72186
.72189
9.85959
.85961
.85963
.85965
.72375
.72378
.72381
.72385
9.86076
.86078
.86080
.86081
.72570
.72573
.72576
.72580
9.86192
.86194
.86196
.86198
.72764
.72768
.72771
.72774
9.86307
.86309
.86311
.86313
.72958
.72962
.72965
.72968
40
39
38
37
+ 6'
25
26
27
9.85849
.85851
.85853
.85855
.72193
.72196
.72199
.72202
9.85967
.85969
.85971
.85972
.72388
.72391
.72394
.72398
9.86083
.86085
.86087
.86089
.72583
.72586
.72589
.72593
9.86200
.86201
.86203
.86205
.72777
.72780
.72784
.72787
9.86315
.86317
.86319
.86321
.72971
.72974
.72978
.72981
36
35
34
33
+ 7'
29
30
31
9.85857
.85859
.85861
.85863
.72206
.72209
.72212
.72215
9.85974
.85976
.85978
.85980
.72401
.72404
.72407
.72411
9.86091
.86093
.86095
.86097
.72596
.72599
.72602
.72606
9.86207
.86209
.86211
.86213
.72790
.72793
.72797
.72800
9.86323
.86325
.86327
.86329
.72984
.72987
.72991
.72994
32
31
30
29
+ 8'
33
34
35
9.85865
.85867
.85869
.85871
.72219
.72222
.72225
.72229
9.85982
.85984
.85986
.85988
.72414
.72417
.72420
.72424
9.86099
.86101
.86103
.86105
.72609
.72612
.72615
.72618
9.86215
.86217
.86219
.86221
.72803
.72806
.72810
.72813
9.86331
.86332
.86334
.86336
.72997
.73000
.73004
.73007
28
27
26
25
24
23
22
21
+ 9'
37
38
39
9.85873
.85875
.85877
.85879
.72232
.72235
.72238
.72242
9.85990
.85992
.85994
.85996
.72427
.72430
.72433
.72437
9.86107
.86109
.86111
.86112
.72622
.72625
.72628
.72631
9.86223
.86225
.86227
.86229
.72816
.72819
.72823
.72826
9.86338
.86340
.86342
.86344
.73010
.73013
.73016
.73020
+ 10'
41
42
43
9.85881
.85883
.85885
.85887
.72245
.72248
.72251
.72255
9.85998
.86000
.86002
.86004
.72440
.72443
.72446
.72450
9.86114
.86116
.86118
.86120
.72635
.72638
.72641
.72644
9.86230
.86232
.86234
.86236
.72829
.72832
.72835
.72839
9.86346
.86348
.86350
.86352
.73023
.73026
.73029
73033
20
19
18
17
16
15
14
13
+ 11'
45
46
47
9.85888
.85890
.85892
.85894
.72258
.72261
.72264
.72268
9.86006
.86008
.86010
.86011
.72453
.72456
.72459
.72463
9.86122
.86124
.86126
.86128
.72648
.72651
.72654
.72657
9.86238
.86240
.86242
.86244
.72842
.72845
.72848
.72852
9.86354
.86355
.86357
.86359
.73036
.73039
.73042
.73046
+ 12'
49
50
51
9.85896
.85898
.85900
.85902
.72271
.72274
.72277
.72281
9.86013
.86015
.86017
.86019
.72466
.72469
.72472
72476
9.86130
.86132
.86134
.86136
.72661
.72664
.72667
.72670
9.86246
.86248
.86250
.86252
.72855
.72858
.72861
.72865
9.86361
.86363
.86365
.86367
.73049
.73052
.73055
.73058
n
11
10
9
+ 13'
55
54
55
9.85904
.85906
.85908
.85910
.72284
.72287
.72290
.72294
9.86021
.86023
.86025
.86027
.72479
.72482
.72485
.72489
9.86138
.86140
.86142
.86143
.72674
.72677
.72680
.72683
9.86254
.86256
.86257
.86259
.72868
.72871
.72874
.72878
9.86369
.86371
.86373
.86375
.73062
.73065
.73068
.73071
8
7
6
5
+ 14'
57
55
59
9.85912
.85914
.85916
.85918
.72297
.72300
.72303
72307
9.86029
.86031
.86033
.86035
.72492
.72495
.72498
.72502
9.86145
.86147
.86149
.86151
.72687
.72690
.72693
.72696
9.86261
.86263
.86265
.86267
.72881
.72884
.72887
.72890
9.86377
.86379
.86380
.86382
.73076
.73078
.73081
.73084
4
3
2
1
+ 15'
9.85920
.72310
9.86037
.72505
9.86153
.72700
9.86269
.72894
9.86384
.73087
0
16^ 14^
16h 13™
16h i2m
16* ll™
16h 10™
TABLE 45. [Page 905
Haversines.
s
7h 50™ 117° SO7
7h 5im 117° 45'
7h 52m H8° (K
7h 5sm 118° 15'
7h 54m 118° W
s
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.86384
.86386
.86388
.86390
.73087
.73091
.73094
.73097
9.86499
.86501
.86503
.86505
.73281
.73284
.73287
.73290
9.86613
.86615
.86617
.86619
.73474
.73477
.73480
73483
9.86727
.86729
.86730
.86732
.73666
.73669
.73672
.73676
9.86840
.86842
.86843
.86845
.73858
.73861
.73864
.73868
60
59
58
57
+ 1'
5
6
7
9.86392
.86394
.86396
.86398
.73100
.73104
.73107
.73110
9.86507 .73294
.86509 .73297
.86510 .73300
.86512 .73303
9.86621
.86623
.86625
.86626
.73486
.73490
.73493
.73496
9.86734
.86736
.86738
.86740
.73679
.73682
.73685
.73688
8.86847
.86849
.86851
.86853
.73871
.73874
.73877
.73880
56
55
54
53
52
51
50
49
+ 2'
9
10
11
9.86400
.86401
.86403
.86405
.73113
.73116
.73120
.73123
9.86514
.86516
.86518
.86520
.73306
.73310
.73313
.73316
9.86628
.86630
.86632
.86654
.73499
.73502
.73506
.73509
9.86742
.86744
.86746
.86747
.73692
.73695
.73698
.73701
9.86855
.86857
.86859
.86860
.73884
.73887
.73890
.73893
+ &
13
14
15
9.86407
.86409
.86411
.86413
.73126
.73129
.73133
.73136
9.86522
.86524
.86526
.86528
.73319
.73323
.73326
.73329
9.86636
.86638
.86640
.86642
.73513
.73515
.73519
.73523
9.86749
.86751
.86753
.86755
.73704
.73708
.73711
.73714
9.86862
.86864
.86866
.86868
.73896
.73899
.73903
.73906
48
47
46
45
+ 4'
17
18
19
9.86415
.86417
.86419
.86421
.73139
.73142
.73145
.73149
9.86529
.86531
.86533
.86535
.73332
.73335
.73339
.73342
9.86643
.86645
.86647
.86649
.73525
.73528
.73531
.73535
9.86757
.86759
.86761
.86763
.73717
.73730
.73724
.73737
9.86870
.86872
.86874
.86875
.73909
.73912
.73915
.73919
44
43
42
41
+ &'
21
22
23
9.86423
.86424
.86426
.86428
.73152
.73155
.73158
.73162
9.86537
.86539
.86541
.86543
.73345
.73348
.73351
.73355
9.86651
.86653
.86655
.86657
.73538
.73541
.73544
.73547
9.86764
.86766
.86768
.86770
.73730
.73733
.73736
.73740
9.86877
.86879
.86881
.86883
.73922
.73925
.73928
.73931
40
39
38
37
36
35
34
33
+ v
25
26
27
+ V
29
SO
31
9.86430
.86432
.86434
.86436
.73165
.73168
.73171
.73174
9.86545
.86547
.86569
.86550
.73358
.73361
.73364
.73368
9.86659
.86661
.86662
.86664
.73551
.73554
.73557
.73560
9.86772
.86774
.86776
.86778
.73743
.73746
.73749
.73753
9.86885
.86887
.86889
.86890
.73935
.73938
.73941
.73944
9.86438
.86440
.86442
.86444
.73178
.73181
.73184
.73187
9.86552
.86554
.86556
.86558
.73371
.73374
.73377
.73380
9.86666
.86668
.86670
.86672
.73563
.73567
.73570
.73573
9.86780
.86781
.86783
-.86785
.73756
.73759
73763
.73765
9.86892
.86894
.86896
.86898
.73947
.73951
.73954
.73957
32
31
30
29
+ 8'
33
34
35
9.86446
.86447
.86449
.86451
.73191
.73194
.73197
.73200
9.86560
.86562
.86564
.86566
.73384
.73387
.73390
.73393
9.86674
.86676
.86678
.86679
.73576
.73579
.73583
.73586
9.86787
.86789
.86791
.86793
.73768
.73772
.73775
.73778
9.86900
.86902
.86904
.86905
.73960
.73963
.73967
.73970
28
27
26
25
24
23
22
21
+ *
37
38
39
9.86453
.86455
.86457
.86459
.73203
.73207
.73210
.73213
9.86568
.86569
.86571
.86573
.73396
.73400
.73403
.73406
9.86681
.86683
.86685
.86687
.73589
.73593
.73595
.73599
9.86795
.86796
.86798
.86800
.73781
.73784
.73788
.73791
9.86907
.86909
.86911
.86913
.73973
.73976
.73979
.73982
+ W
41
42
43
+ ii'
45
4€
47
9.86461
.86463
.86465
.86467
.73216
.73220
.73223
.73226
9.86575
.86577
.86579
.86581
.73409
.73413
.73416
.73419
9.86689
.86691
.86693
.86695
.73602
.73605
.73608
.73611
9.86802
.86804
.86806
.86808
.73794
.73797
.73800
.73804
9.86915
.86917
.86919
.86920
.73986
.73989
.73992
.73995
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
9.86468
.86470
.86472
.86474
.73229
.73232
.73236
.73239
9.86583
.86585
.86587
.86588
.73422
.73425
.73429
.73432
9.86696
.86698
.86700
.86702
.73615
.73618
.73621
.73624
9.86810
.86812
.86813
.86815
.73807
.73810
.73813
.73816
9.86922
.86924
.86926
.86928
.73998
.74002
.74005
.74008
+ 13'
W
50
51
9.86476
.86478
.86480
.86482
.73242
.73245
.73249
.73252
9.86590
.86592
.86594
.86596
.73435
.73438
.73441
.73445
9.86704
.86706
.86708
.86710
.73628
.73631
.73634
.73637
9.86817
.86819
.86821
.86823
.73820
.73823
.73826
.73829
9.86930
.86932
.86933
.86935
.74011
.74014
.74018
.74021
+ 13'
53
54
55
9.86484
.86486
.86488
.86489
.73255
.73258
.73261
.73265
9.86598
.86600
.86602
.86604
.73448
.73451
.73454
.73458
9.86712
.86713
.86715
.86717
.73640
.73644
.73647
.73650
9.86825
.86827
.86828
.86830
.73832
.73836
.73839
.73842
9.86937
.86939
.86941
.86943
.74024
.74027
.74030
.74033
+ 14'
57
58
59
+ 15'
9.86491
.86493
.86495
.86497
.73268
.73271
.73274
.73278
9.86606
.86607
.86609
.86611
.73461
.73464
.73467
.73470
9.86719
.86721
.86723
.86725
.73653
.73656
.73660
.73663
9.86832
.86834
.86836
.86838
.73845
.73848
.73852
.73855
9.86945
.86947
.86948
.86950
.74037
.74040
.74043
.74046
4
3
2
1
0
9.86499
.73281
9.86613
.73474
9.86727
.73666
9.86840
.73858
9.86952
.74049
16* 9m
16*8™
IS* 7-n
16*6™
16* 5^
61828°—
Page 906] TABLE 45.
Haversines.
s
7* 55™ 118° 45'
7h 56m 119° 0'
7h 57m 119° 15'
7fc.5#»119°30/
jh 59m 1190 45'
s
jog. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0
1
2
3
9.86952
.86954
.86956
.86958
.74049
.74052
.74056
.74059
9.87064
.87066
.87068
.87070
.74240
.74244
.74247
.74250
9.87175
.87177
.87179
.87181
.74431
.74434
.74437
.74441
9.87286
.87288
.87290
.87292
.74621
.74624
.74628
.74631
9.87396
.87398
.87400
.87402
.74811
.74814
.74817
.74820
60
59
58
57
+ lx
5
6
7
9.86960
.86962
.86963
.86965
.74062
.74065
.74069
.74072
9.87072
.87073
.87075
.87077
.74253
.74256
.74260
.74263
9.87183
.87185
.87187
.87188
.74444
.74447
.74450
.74453
9.87294
.87295
.87297
.87299
.74634
.74637
.74640
.74643
9.87404
.87406
.87407
.87409
.74823
.74827
.74830
.74833
56
55
54
53
+ v
9
10
11
9.86967
.86989
.86971
.86973
.74075
.74078
.74081
.74084
9.87079
.87081
.87083
.87085
.74266
.74269
.74272
.74275
9.87190
.87192
.87194
.87196
.74456
.74460
.74463
.74466
9.87301
.87303
.87305
.87306
.74646
.74650
.74653
.74656
9.87411
.87413
.87415
.87417
.74836
.74839
.74842
.74846
52
51
.50
49
+ 3'
IS
14
15
9.86975
.86977
.86978
.86980
.74088
.74091
.74094
.74097
9.87086
.87088
.87090
.87092
.74279
.74282
.74285.
.74288
9.87198
.87199
.87201
.87203
.74469
.74472
.74475
.74479
9.87308
.87310
.87312
.87314
.74659
.74662
.74665
.74669
9.87418
.87420
.87422
.87424
.74849
.74852
.74855
.74858
48
47
46
45
+ ¥
17
18
19
9.86982
.86984
.86986
.86988
.74100
.74104
.74107
.74110
9.87094
.87096
.87098
.87100
.74291
.74294
.74298
.74301
9.87205
.87207
.87209
.87211
.74482
.74485
.74488
.74491
9.87316
.87318
.87319
.87321
.74672
.74675
.74678
.74681
9.87426
.87428
.87429
.87431
.74861
.74864
.74868
74871
44
43
42
41
+ v
21
22
23
9.86990
.86991
.86993
.86995
.74113
.74116
.74120
.74123
9.87101
.87103 '
.87105
.87107
.74304
.74307
.74310
.74314
9.87212
.87214
.87216
.87218
.74494
.74498
.74501
.74504
9.87323
.87325
.87327
.87329
.74684
.74688
.74691
.74694
9.87433
.87435
.87437
.87439
.74874
.74877
.74880
.74883
40
39
38
37
+ V
25
26
27
9.86997
.86999
.87001
.87003
.74126
.74129
.74132
.74135
9.87109
.87111
.87112
.87114
.74317
.74320
.74323
.74326
9.87220
.87222
.87224
.87225
.74507
.74510
.74514
.74517
9.87330
.87332
.87334
.87336
.74697
.74700
.74703
.74707
9.87440
.87442
.87444
.87446
.74887
.74890
.74893
.74896
36
35
34
33
+ 7'
29
30
31
9.87004
.87006
.87008
.87010
.74139
.74142
.74145
.74148
9.87116
.87118
.87120
.87122
.74329
.74333
.74336
.74339
9.87227
.87229
.87231
.87233
.74520
.74523
.74526
.74529
9.87338
.87340
.87341
.87343
.74710
.74713
.74716
.74719
9.87448
.87450
.87451
.87453
.74899
.74902
.74905
.74908
32
31
30
29
+ &
33
34
35
9.87012
.87014
.87016
.87018
.74151
.74155
.74158
.74161
9.87124
.87125
.87127
.87129
.74342
.74345
.74349
.74352
9.87235
.87236
.87238
.87240
.74533
.74536
.74539
.74542
9.87345
.87347
.87349
.87351
.74722
.74726
.74729
.74732
9.87455
.87457
.87459
.87460
.74912
.74915
.74918
.74921
28
27
26
25
+ 9/
37
38
39
9.87019
.87021
.87023
.87025
.74164
.74167
.74170
.74174
9.87131
.87133
.87135
.87137
.74355
.74358
.74361
.74364
9.87242
.87244
.87246
.87248
.74545
.74548
.74552
.74555
9.87352
.87354
.87356
.87358
.74735
.74738
.74741
.74744
9.87462
.87464
.87466
.87468
.74924
.74928
.74931
.74934
24
21
+ W
41
42
43
9.87027
.87029
.87031
.87032
.74177
.74180
.74183
.74186
9.87138
.87140
.87142
.87144
.74368
.74371
.74374
.74377
9.87249
.87251
.87253
.87255
.74558
.74561
.74564
.74567
9.87360
.87362
.87363
.87365
.74748
.74751
.74754
.74757
9.87470
.87471
.87473
.87475
.74937
.74940
.74943
.74946
20
19
18
17
+ w
45
46
47
9.87034
.87036
.87038
.87040
.74190
.74193
.74196
.74199
9.87146
.87148
.87149
.87151
.74380
.74383
.74387
.74390
9.87257
.87259
.87260
.87262
.74571
.74574
.74577
.74580
9.87367
.87369
.87371
.87373
.74760
.74763
.74767
.74770
9.87477
.87479
.87481
.87482
.74950
.74953
.74956
.74959
16
15
14
13
12
11
10
9
+ W
49
50
51
9.87042
.87044
.87045
.87047
.74202
.74205
.74209
.74212
9.87153
.87155
.87157
.87159
.74393
.74396
.74399
.74402
9.87264
.87266
.87268
.87270
.74583
.74586
.74590
.74593
9.87374
.87376
.87378
.87380
.74773
.74776
.74779
.74782
9.87484
.87486
.87488
.87490
.74962
.74965
.74969
.74972
+ 13'
53
54
55
9.87049
.87051
.87053
.87055
.74215
.74218
.74221
.74225
9.87161
.87162
.87164
.87166
.74406
.74409
.74412
.74415
9.87271
.87273
.87275
.87277
.74596
.74599
.74602
.74605
9.87382
.87384
.87385
.87387
.74786
.74789
.74792
.74795
9.87492
.87493
.87495
.87497
.74975
.74978
.74981
.74984
8
7
6
5
+ 14'
57
' 58
59
9.87057
.87059
.87060
.87062
.74228
.74231
.74234
.74237
9.87168
.87170
.87172
.87174
.74418
.74422
.74425
.74428
9.87279
.87281
.87283
.87284
.74609
.74612
.74615
.74618
9.87389
.87391
.87393
.87395
.74798
.74801
.74805
.74808
9.87499
.87501
.87502
.87504
.74987
.74891
.74994
.74997
4
4
2
1
+ 15'
9.87064
.74240
9.87175
.74431
9.87286
.74621
9.87396
.74811
9.87506
.75000
0
16h 4™
16h sm
16h 2m
16h im
16^ Om
TABLE 45. [Page 907
• Haversines.
s '
8* G™ 120° (K
8* 2m 120° 30X
8* 4m 121° r
8* 6m 121° 30'
8* 8m 122° O7
S
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.; Nat. Hav.
Log. Hav. Nat. Hav.
0 0
2
4+ 1
6
9.87506
.87510
.87513
.87517
0.75000
.75006
.75013
.75019
9.87724
.87727
.87731
.87735
0.75377
.75383
.75389
.75396
9.87939
.87943
.87947
.87950
0.75752
.75758
.75764
.75771
9.88153
.88156
.88160
.88163
0.76125
.76131
.76137
.76144
9.88364
.88367
.88371
.88374
0.76496
.76502
.76508
.76514
60
55
56
54
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
9.87521
.87524
.87528
.87532
9.87535
.87539
.87543
.87546
0.75025
.75032
.75038
.75044
0.75050
.75057
.75063
.75069
9,87738
.87742
.87745
• .87749
9.87753
.87756
.87760
.87764
0.75402
.75408
.75415
.75421
0.75427
.75433
.75440
.75446
9.87954
.87957
.87961
.87964
9.87968
.87971
.87975
.87979
0.75777
.75783
.75789
.75795
0.75802
.75808
.75814
.75820
9.88167
.88170
.88174
.88177
9.88181
.88185
.88188
.88192
0.76150
.76156
.76162
.76168
0.76175
.76181
.76187
.76193
9.88378
.88381
.88385
.88388
9.88392
.88395
.88399
.88402
0.76521
.76527
.76533
.76539
0.76545
.76551
.76558
.76564
52
50
48
46
44
42
JO
'38
24+ 6
26
28+ 7
SO
32+ 8
34
36+ 9
38
9.87550
.87553
.87557
.87561
9.87564
.87568
.87572
.87575
0.75075
.75082
.75088
.75094
0.75101
.75107
.75113
.75120
9.87767
.87771
.87774
Q_ — -rQ
.O/ / /O
9.87782
.87785
.87789
.87792
0.75452
.75458
.75465
.75471
0.75477
.75483
.75490
.75496
9.87982
.87986
.87989
.87993
9.87996
.88000
.88004
.88007
0.75827
.75833
.75839
.75845
0.75852
.75858
.75864
.75870
9.88195 0.76199
.88199 • .76205
.88202 i .76212
.88206 .76218
9.88209 0.76224
.88213 .76230
.88216 i .76236
.88220 i .76243
9.88406
.88409
.88413
.88416
9.88420
.88423
.88427
.88430
0.76570
.76576
.76582
.76588
0.76595
.76601
.76607
.76613
36
34
32
30
28
26
24
22
40+10
46
45+12
50
52+13
54
9.87579
.87583
.87586
.87590
9.87593
.87597
.87601
.87604
0.75126
.75132
.75138
.75145
0.75151
.75157
.75164
.75170
9.87796
.87800
.87803
.87807
9.87810
.87814
.87818
.87821
0.75502
.75508
.75515
.75521
0.75527
.75533
.75540
.75546
9.88011
.88014
.88018
.88021
9.88025
.88029
.88032
.88036
0.75876
.75883
.75889
.75895
0.75901
.75908
.75914
.75920
9.88223 0.76249
.88227 .76255
.88230 .76261
.88234 .76267
9.88237 0.76274
.88241 .76280
.88244 .76286
.88248 .76292
9.88434
.8S437
.88441
.88444
9.88448
.88451
.88455
.88458
0.76619
.76625
.76632
.76638
0.76644
.76650
.76656
.76662
SO
18
16
14
12
10
8
6
56+14
9.87608
9.87612
0.75176
0.75182
9.87825
9.87828
0.75552
0.75558
9.88039 0.75926
9.88043 0.75932
9.88252^ 0.76298
9.88255 0.76305
9.88462
9.88465
0.76668
0.76675
4
2
15* 59m
15* 57m
15* 55m
15* 53m
15* 5im
s '
0+15
o
4+16
8* im 120° O7
S* 3m 120° 30'
8* 5m 121° (K
8* 7m 121° 307
$h 9m 122° (K
s
60
55
56
54
9.87615
.87619
.87623
.87626
0.75189
.75195
.75201
.75208
9.87832
.87835
.87839
.87843
0.75565
.75571
.75577
.75583
9.88046 0.75939
.88050 .75945
.88053 .75951
.88057 .75957
9.88259 0.76311
.88262 .76317
.88266 .76323
.88269 .76329
9.88469 0.76681
.88472 i .76687
.88476 .76693
.88479 .76699
5+17
10
12+18
14
76+19
,20+20
22
9.87630
.87633
.87637
.87641
9.87644
.87648
.87652
.87655
0.75214
.75220
.75226
.75233
0.75239
.75245
.75251
.75258
9.87846
.87850
.87853
.87857
9.87861
.87864
.87868
. .87871
0.75590
.75596
.75602
.75608
0.75615
.75621
.75627
.75633
9.'88061
.88064
.88068
.88071
9.88075
.88078
.88082
.88085
0.75964
.75970
.75976
.75982
0.75988
.75995
.76001
.76007
9.88273
.-8276
.88280
.88283
9.88287
.88290
.88294
.88297
0.76335
.76342
.76348
.76354
0.76360
.76366
.76373
.76379
9.88483
.88486
.88490
.88493
9.88496
.88500
.88503
.88507
0.76705
.76711
.76718
.76724
0.76730
.76736
.76742
.76748
62
50
48
46
44
42
40
38
36
34
32
30
28
26
24
22
£4+21
£5+22
50
36+24
9.87659
.87662
.87666
.87670
9.87673
.87677
.87680
.87684
0.75264
.75270
.75277
.75283
0.75289
.75295
.75302
.75308
9.87875
.87879
.87882
^87886
9.87889
.87893
.87896
.87900
0.75640
.75646
.75652
.75G58
0.75665
.75671
.75677
.75683
9.88089
.88092
.88096
.88100
9.88103
.88107
.88110
.88114
0.76013
.76019
.76026
.76032
0.76038
.76044
.76050
.76057
9.88301
.88304
.88308
.88311
9.88315
.88318
88322
.88325
0.76385
.76391
.76397
.76403
0.76410
.76416
.76422
.76428
9.88510
.88514
.88517
.88521
9.88524
.88528
.88531
.88535
0.76754
.76761
.76767
.76773
0.76779
.76785
.70791
.76797
40+25
42
44+26
46
50
5£+28
54
9.87688
.87691
.87695
.87699
9.87702
.87706
.87709
.87713
0.75314
.75321
.75327
.75333
0.75339
.75346
.75352
.75358
9.87904
.87907
.87911
.87914
9.87918
.87921
.87925
.87929
0.75690
.75696
.75702
.75708
0.75714
.75721
.75727
.75733
9.88117
.88121
.88124
.88128
9.88131
.88135
.88139
.88142
0.76063
.76069
.76075
.76082
0.76088
.76094
.76100
.76106
9.88329
.88332
.88336
.88339
9.88343
.88346
.88350
.88353
0.76434
.76440
.76447
.76453
0.76459
.76465
.76471
.76477
9.88528
.88542
.88545
.88549
9.88552
.88556
.88559
.88562
0.76804
.76810
.76816
.76822
0.76828
.76834
.76840
.76847
20
18
16
14
12
10
8
6
56+29
60+30
9.87717
.87720
9.87724
0.75364
.75371
0.75377
9.87932
.87936
9.87939
0.75739
.75746
0.75752
9.88146
.88149
9.88153
0.76113
.76119
0.76125
9.88357
.88360
9.88364
0.76484
.76490
0.76496
9.88566
.88569
9.88573
0.76853
.76859
0.76865
4
2
0
J.3^ oS^
15* 56m
15* 54m
15* 52m
15*50m
Page 908] TABLE 45.
Haversines. .
s '
8h iQm 122° 30'
8h 12^ 123° 0'
8* 14™ 123° 30'
8h 16m 124° 0'
8h ism 1340 30'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0 0
2
4+ 1
6
9.88573
.88576
.88580
.88583
0.76865
.76871
.76877
.76883
9.88780
.88783
.88787
.88790
0.77232
.77238
.77244
.77250
9.88984
.88988
.88991
.88995
0.77597
.77603
.77609
.77615
9.89187
.89190
.89194
.89197
0.77960
.77966
.77972
.77978
9.89387
.89391
.89394
.89397
0.78320
.78326
.78332
.78338
60
58
56
54
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
9.88587
.88590
.88594
.88597
9.88600
.88604
.88607
.88611
0.76890
.76896
.76902
.76908
0.76914
.76920
.76926
.76932
9.88793
.88797
.88800
.88804
9.88807
.88811
.88814
.88817
0.77256
.77262
.77269
.77275
0.77281
.77287
.77293
.77299
9.88998
.89001
.89005
.89008
9.89012
.89015
.89018
.89022
0.77621
.77627
.77633
.77639
0.77645
.77651
.77657
.77664
9.89200
.89204
.89207
.89210
9.89214
.89217
.89221
.89224
0.77984
.77990
.77996
.76002
0.78008
.78014
.78020
.78026
9.89400
.89404
.89407
.89411
9.89414
.89417
.89421
.89424
0.78344
.78350
.78356
.78362
0.78368
.78374
.78380
.78386
52
50
48
46
44
42
40
38
24+ 6
.26
28+ 7
SO
32+ 8
34
36+ 9
38
9.88614
.88618
.88621
.88625
9.88628
.88632
.88635
.88639
.076939
.76945
.76951
.76957
0.76963
.76969
.76975
.76981
9.88821
.88824
.88828
.88831
9.88835
.88838
.88841
.88845
0.77305
.77311
.77317
.77323
0.77329
.77336
.77342
.77348
9.89025
.89028
.89032
.89035
9.89039
.89042
.89045
.89049
0.77670
.77676
.77682
.77688
0.77694
.77700
.77706
.77712
9.89227
.89231
.89234
.89237
9.89241
.89244
.89247
.89251
0.78032
.78038
.78044
.78050
0.78056
.78062
.78068
.78074
9.89427
.89431
.89434
.89437
9.89441
.89444
.89447
.89450
0.78392
.78398
.78404
.78410
0.78416
.78422
.78428
.78434
36
34
32
30
28
26
24
n
40+10
42
44+11
46
48+12
50
52+13
54
9.88642
.88645
.88649
.88652
9.88656
.88659
.88663
.88666
0.76988
.76994
.77000
.77006
0.77012
.77018
.77024
.77030
.9.88848
.88852
.88855
.88858
9.88862
.88865
.88869
.88872
0.77354
.77360
.77366
.77372
0.77378
.77384
.77390
.77396
9.89052
.89056
.89059
.89062
9.89066
.89069
.89072
.89076
0.77718
.77724
.77730
.77736
0.77742
.77748
.77754
.77760
9.89254
.89257
.89261
.89264
9.89267
.89271
.89274
.89277
0.78080
.78086
.78092
.78098
0.78104
.78110
.78116
.78122
9.89454
.89457
.89460
.89464
9.89467
.89470
.89474
.89477
0.78440
.78446
.78452
.78458
0.78464
.78470
.78476
.78482
20
18
16
14
12
10
8
6
56+14
58
9.88670
9.88673
0.77036
0.77043
9.88876
9.88879
0.77403
0.77409
9.89079
9.89083
0.77766
0.77772
9.89281
9.89284
0.78128
0.78134
9.89480
.9.89484
0.78488
0.78494
4
2
15h 49m
15h 4777*
15* 45™
15* 43m
15h 4im
8 '
0+15
£
4+16
<S
8h nm 122° 30'
8h ism 123° (K
8h 15™ 123° 30'
8h 17m 124° ox
8h i9m 124° 307
s
9.88677
.88680
.88683
.88687
0.77049
.77055
.77061
.77067
9.88882
.88886
.88889
.88893
0.77415
.77412
.77427
.77433
9.89086
.89089
.89093
.89096
0.77779
.77785
.77791
.77797
9.89287
.89291
.89294
.89298
0.78140
.78146
.78152
.78158
9.89487
.89490
.89493
.89497
0.78500
.78506
.78512
,78518
60
58
56
54
£+17
.70
^+18
J?4
.76+19
.?£
20+20
22
9.88690
.88694
.88697
.88701
9.88704
.88708
.88711
.88714
0.77073
.77079
.77085
.77092
0.77098
.77104
.77110
.77116
9.88896
.88899
.88903
.88906
9.88910
.88913
.88916
.88920
0.77439
.77445
.77451
.77457
0.77463
.77469
.77475
.77482
9.89099
.89102
.89106
.89110
9.89113
.89116
.89120
.89123
0.77803
.77809
.77815
.77821
0.77827
.77833
.77839
.77845
9.89301
.89304
.89308
.89311
9.89314
.89318
.89321
.89324
0.78164
.78170
.78176
.78182
0.78188
.78194
.78200
.78206
9.89500
.89503
.89507
.89510
9.89513
.89517
.89520
.89523
0.78524
.78530
.78536
.78542
0.78548
.78554
.78560
.78566
52
50
48
•46
44
42
40
38
24+21
26
28+22
30 .
32+23
34
36+21
38
9.88718
.88721
.88725
.88728
9.88732
.88735
.88739
.88742
0.77122
.77128
.77134
.77140
0.77147
.77153
.77159
.77165
0.77171
.77177
.77183
.77189
0.77195
.77201
.77208
.77214
9.88923
.88927
.88930
.88933
9.88937
.88940
.88944
.88947
0.77488
.77494
.77500
.77506
0.77512
.77518
.77524
.77530
9.89126
.89130
.89133
.89137
9.89140
.89143
.89147
.89150
0.77851
.77857
.77863
.77869
0.77875
.77881
.77887
.77893
9.89328
.89331
.89334
.89338
9.89341
.89344
.89348
.89351
0.78212
.78218
.78224
.78230
0.78236
.78242
.78248
.78254
9.89527
.89530
.89533
.89536
9.89540
.89543
.89546
.89550
0.78572
.78577
.78583
.78589
0.78595
.78601
.78607
.78613
36
34
32
30
28
26
24
40+25
42
44+26
46
48+27
50
52+28
54
9.88745
.88749
.88752
.88756
9.88759
.88763
.88766
.88769
9.88950
.88954
.88957
.88961
9.88964
.88967
.88971
.88974
0.77536
.77542
.77548
.77554
0.77560
.77567
.77573
.77579
9.89153
.89157
.89160
.89163
9.89167
.89170
.89174
.89177
0.77899
.77905
.77911
.77917
0.77923
.77929
.77936
.77942
9.89354
.89358
.89361
.89364
9.89368
.89371
.89374
.89378
0.78260
.78266
.78272
.78278
0.78284
.78290
.78296
.78302
9.89553
.89556
.89559
.89563
9.89566
.89569
.89573
.89576
0.78619
.78625
.78531
.78637
0.78643
.78649
.78655
.78661
20
18
16
14
12
10
8
6
56+29
58
60+30
9.88773
.88776
9.88780
0.77220
.77226
0.77232
9.88978
.88981
9.88984
0.77585
.77591
0.77597
9.89180
.89184
9.89187
0.77948
.77954
0.77960
9.89381
.89384
9.89387
0.78308
.78314
0.78320
9.89579
.89583
9.89586
0.78667
.78673
0.78679
4
0
15h 48m
15h 46™
15h 44m
15h 4%m
15h4Qm
TABLE 45. [Page 909
Havcr?ines.
s
gh 20m
125° r
gh 22m 125° 307
5ft 24m
126° V
5^ 26m 126° 30'
5ft 28m 127° O7
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
Log. Hav. Nat. Hav.
Log. Hav.J Nat. Hav
s
0 0
2
4+ 1
6
9.89586
.89589
.89592
.89596
0.78679
.78685
.78691
.78697
9.89782
.89785
.89789
.89792
0.79035
.79041
.79047
.79053
9.89976
.89979
.89983
.89986
0.79389
.79395
.79401
.79407
9.90168
.90171
.90175
.90178
0.79741
.79747
.79753
.79759
9.90358
.90361
.90365
.90368
0.80091
.80097
.80102
.80108
60
55
56
54
8+ 3
10
12+ 3
14
16+ 4
18
20+ 5
22
9.89599
.89602
.89606
.89609
9.89612
.89615
.89619
.89622
0.78703
.78709
.78715
.78721
0.78726
.78732
.78738
.78744
9.89795
.89798
.89802
.89805
9.89808
.89811
.89815
.89818
0.79059
.79065
.79071
.79077
0.79082
.79088
.79094
.79100
9.89989
.89992
.89995
.89999
9.90002
.90005
.90008
.90012
0.79413
.79419
.79425
.79430
0.79436
.79442
.79443
.79454
9.90181 ! 0.79765
.90184 .79770
.90187 .79776
.90191 .79782
9.90194 0.79788
.90197 ! .79794
.90200 j .78800
.90203 .79805
9.90371 i G.80114
.90374! .80120
.90377 .S0126
.90380 .80131
9.90383 0.80137
.90387 .80143
.90390 .80149
.90393 ; .80155
52
50
48
46
44
42
40
38
24+ 6
26
28+ 7
SO
32+ 8
34
36+ 9
38 »
9.89625
.89628
.89632
.89635
9.89638
.89642
.89645
.89648
0.78750
.78756
.78762
.78768
0.78774
.78780
.78786
.78792
9.89821
.89824
.89828
.89831
9.89834
.89837
.89840
.89844
0.79106
.79112
.79118
.79124
0.79130
.79136
.79142
.79148
9.90015
.90018
.90021
.90024
9.90028
.90031
.90034
.90037
0.79460
.79466
.79471
.79477
0.79483
.79489
.79495
.79501
9.90206
.90210
.90213
.90216
9.90219
.90222
.90225
.90229
0.79811
.79817
.79823
.79829
0.79835
.79840
.70846
.79852
9.90396
.90399
.90402
.90405
9.90409
.90412
.90415
.90418
0.80160
.80166
.80172
.80178
0.80184
.80189
.80195
.80201
36
34
3'2
30
28
26
24
ff
44+11
46
45+13
50
52+13
54
9.89651
.89655
.89658
.89661
9.89665
.89668
.89671
.89674
0.78798
.78804
.78810
.78816
0.78823
.78838
.78834
.78839
9.89847 0.79153
.89850 .79159
.89853 .79165
.89857 .79171
9.89860 ! 0.79177
.89863 .79183
.89866 .79189
.89870 .79195
9.90040
.90044
.90047
.90050
9.90053
.90056
.90060
.90063
0.79507
.79513
.79519
.79524
0.79530
.79536
.79542
.79548
9.90232 0.7985S
.90235 .79864
.90238 .79870
.90241 .79875
9.90244 0.79881
.90248 .79887
.90251 .79899
.90254 .79893
9.90421
.90425
.90428
.90431
9.90434
.90437
.90440
.90443
0.80207
.80213
.80218
.80224
0.80230
.80236
.80242
.80247
20
18
16
14
12
10
8
6
56+14
55
9.89678
9.89681
0.78845
0.78851
9.89873 0.79201
9.89876 0.79207
9.90066
9.90069
0.79554
0.79560
9.90257
9.90260
0.79905
0.79910
9.90446
.9.90449
0.80253
0.80259
4
2
IS*
39m
15*37*
.75ft Jjm
.75ft 33m
.75ft 31 m
8 '
0+15
2
4+16
6
gh 2im
135° 0'
gh 23m 125° «j0x
gh 25m
126° 0'
5ft 27m 126° 30'
5ft 29m 127° &
e
60
58
56
54
9.89684
.89687
.89691
.89694
0.78857
.78863
.78869
.78875
9.89879 0.79212
.89883 .79218
.89886 : .79224
.89889 .79230
.9.90072
.90076
.90079
.90082
0.79565
.79571
.79577
.79583
9.90264
.90267
.90270
.90273
0.79916
.79922
.79928
.79934
9.90452
.90456
.90459
.90462
0.80265
.80270
.80276
.80282
5+17
.70
.72+18
.74 '5
-76+19
20+30
9.89697
.89701
.89704
.89707
9.89-710
.89714
.89717
.89720
0.78881
.78887
.78893
.78899
0.78905
.78911
.78917
.78923
9.89892
.89896
.89899
.89902
9.89905
.89908
.89912
.89915
0.79236
.79242
.79248
.79254
0.79260
.79266
.79271
.79277
9.90085
.90088
.90092
.90095
9.90098
.90101
.90104
.90108 i
0.79589
.79595
.79601
.79607
0.79612
.79618
.79624
.79630
9.90276
.90279
.90282
.90286
9.90289
.90292
.90295
.90298
0.79940
.79945
.79951
.79957
0.79963
.79969
.79974
.79980
9.90465
.90468
.90471
.90475
9.90478
.90481
.90484
.90487
0.80288
.80294
.80299
.80305
0.80311
.80317
.80323
.80328
52
50
48
46
44
42
40
38
24+31
50
32+33
34
36+34
35
9.89723
.89727
.89730
.89733
9.89736
.89740
.89743
.89746
0.78928
.78934
.78940
.78946
0.78952
.78958
.78964
.78970
9.89918
.89921
.89925
.89928
9.89931
.89934
.89938
.89941
0.79283
.79289
.79295
.79301
0.79307
.79313
.79319
.79325
9.90111 ,
.90114
.90117
.90120
9.90124
.90127 !
.90130
.90133
0.79636
.79642
.79648
.79653
0.79659
.79665
.79671
.79677
9.90301
.90305
.90308
.90311
9.90314
.90317
.90320
.90324
0.79986
.79992
.79998
.80004
0.80009
.80015
.80021
.80027
9.90490
.90493
.90496
.90499
9.90503
.90506
.90509
.90512
0.80334
.80340
.80346
.80351
0.80357
.80363
.80369
.80375
36
34
32
30
28
26
u
40+15
44+36
46
45+37
50
52+38
54
9.89749
.89753
.89756
.89759
9.89763
.89766
.89769 '
.89772
0.78976
.78982
.78988
.78994
0.79000
.79006
.79011
.79017
9.89944
.89947
.89950
.89954
9.89957
.89960
.89963
.89966
0.79330
.79336
.79342
.79348
0.79354
.79360
.79366
.79372
9.90136
.90140
.90143 !
.90146 !
9.90149
.90152
.90356
.90159
0.79683
.79688
.79694
.79700
0.79706
.79712
.79718
.79724
9.90327
.90330
.90333
.90336
9.90339
.90342 !
.90346
.90349
0.80033
.80038
.80044
.80050
0.80056
.80062
.80068
.80073
9.90515 0.80380
.90518 .80386
.90521 ; .80392
.90524 .80398
9.90527 0.80403
.90531 .80409
.90534 .80415
.90537 .80421
20
18
16
14
12
10
8
6
56+39
55
60+30
9.89776
.89779
9.89782
0.79023
.79029
0.79035
9.89970
.89973
9.89976
0.79377
.79383
0.79389
9.90162
.90165
9.90168
0.79729
.79735
0.79741
9.90352
.90355
9.90358
0.80079
.80085
0.80091
9.90540 0.80427
.90543 .80432
9.90546 0.80438
4
2
0
.75^ 38m
.75ft 36~>n
.75ft 34m
.75ft 32m
15ft SO™
Page 910] TABLE 45.
Haversines.
s '
8h 30m 127° 30'
gh 32m 128° Ox
8^ 34m 128° 30'
8h 36^ 129° 0'
gh 38m 129° 3^
s
Log. Ilav.j Nat. Hav
i
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
0 0
2
4+ 1
6
9.90546
.90549
.90552
.90556
0.80438
.80444
.80450
.80455
9.90732
.90735
.90738
.90741
0.80783
.80789
.80795
.80800
9.90916
.90919
.90922
.90925
0.81126
.81131
.81137
.81143
9.91098
.91101
.91104
.91107
0.81466
.81472
.81477
.81483
9.91277
.91280
.91283
.91286
0.81804
.81810
.81815
.81821
60
58
56
54
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
9.90559
.90562
.90565
.90568
9.90571
.90574
.90577
.90580
0.80461
.80467
.80473
.80478
0.80484
.80490
.80496
.80502
9.90744
.90747
.90751
.90754
9.90757
.90760
.90763
.90766
0.80806
.80812
.80817
.80823
0.80829
.80835
.80840
.80846
9.90928
.90931
.90934
.90937
9.90940
.90943
.90946
.90949
0.81148
.81154
.81160
.81165
0.81171
.81177
.81183
.81188
9.91110
.91113
.91116
.91119
9.91122
.91125
.91128
.91131
081489
.81494
.81500
.81506
081511
.81517
.81523
.81528
9.91289
.91292
.91295
.91298
9.91301
.91304
.91307
.91310
0.81826
.81832
.81838
.81843
0.81849
.81854
.81860
.81866
52
50
48
46
44
42
40
38
24+ 6
26
28+ 1
30
32+ 8
34
36+ 9
38
9.90584
.90587
.90590
.90593
9.90596
.90599
.90602
.90605
0.80507
.80513
.80519
.80525
0.80530
.80536
.80542
.80548
9.90769
.90772
.90775
.90778
9.90781
.90784
.90787
.90790
0.80852
.80858
.80863
.80869
0.80875
.80880
.80886
.80892
9.90952
.90955
.90958
.90962
9.90965
.90968
.90971
.90974
0.81194
.81200
.81205
.81211
0.81217
.81222
.81228
.81234
0.81239
.81245
.81251
.81256
0.81262
.81268
.81273
.81279
9.91134
.91137
.91140
.91143
9.91146
.91149
.91152
.91155
0.81534
.81539
.81545
.81551
0.81556
.81562
.81568
.81573
9.91313
.91316
.91319
.91322
9.91325
.91328
.91331
.91334
0.81871
.81877
.81882
.81888
0.81894
.81899
.81905
.81910
36
34
32
30
28
26
22
40+10
42
44+11
46
4S+12
50
52+13
54
9.90608
.90611
.90615
.90618
9.90621
.90624
.90627
.90630
0.80553
.80559
.80565
.80571
0.80576
.80582
.80588
.80594
9.90794
.90797
.90800
.90803
9.90806
.90809
.90812
.90815
0.80898
.80903
.80909
.80915
0.80920
.80926
.80932
.80938
9.90977
.90980
.90983
.90986
9.90989
.90992
.90995
.90998
9.91158
.91161
.91164
.91167
9.91170
.91173
.91176
.91179
0.81579
.81585
.81590
.81596
0.81601
.81607
.81613
.81618
9.91337
.91340
.91343
' .91346
9.91349
.91352
.91355
.91358
0.81916
.81922
.81927
.81933
0.81938
.81944
.81950
.81955
20
18
16
14
12
10
8
6
4
S6+U
58
9.90633
9.90636
0.80599
0.80605
9.90818
9.90821
0.80943
0.80949
9.91001
9.91004
0.81285
0.81291
9.91182
9.91185
0.81624
0.81630
9.91361
9.91364
081961
0.81966
15h 29™
15h 27m
15* 25m
loh 23m
15h 2im
s '
0+15
4+16
6
8h sim 127° 30'
Sh 33m 128° 0/
8h 35^ 128° 30/
Sh 37m 129° ox
8h 39m 129° 3^
s
60
58
56
54
9.90639
.90642
,90646
.90646
0.80611
.80617
.80622
.80628
9.90824
.90827
.90830
.90833
0.80955
.80960
.80966
.80972
9.91007
.91010
.91013
.91016
0.81296
.81302
.81308
.81313
9.91188
.91191
.91194
.91197
0.81635
.81641
.81647
.81652
9.91367
.91369
.91372
.91375
0.81972
.81978
.81983
.81989
0.81994
.82000
.82005
.82011
0.82017
.82022
.82028
.82033
8+11
10
12+18
14
16+19
18
20+20
22
9.90652
.90655
.90658
.90661
9.90664
.90667
.90670
.90673
9.90676
.90680
.90683
.90686
9.90689
.90692
.90695
.90698
0.80634
.80640
.80645
.80651
0.80657
.80663
.80668
.80674
9.90836
.90840
.90843
.90846
9.90849
.90852
.90855
.90858
0.80978
.80983
.80989
.80995
0.81000
.81006
.81012
.81017
9.91019
.91022
.91025
.91028
9.91031
.91034
.91037
.91040
0.81319
.81325
.81330
.81336
0.81342
.81347
.81353
.81359
9.91200
.91203
.91206
.91209
9.91212
.91215
.91218
.91221
0.81658
.81663
.81669
.81675
0.81680
.81686
.81692
.81697
9.91378
.91381
.91384
.91387
9.91390-
.91393
.91396
.91399
9.91402
.91405
.91408
.91411
9.91414
.91417
.91420
.91423
52
50
48
46
44
42
40
38
24+21
26
28+22
30
32+23
34
36+24:
38
0.80680
.80686
.80691
.80697
0.80703
.80709
.80714
.80720
9.90861
.90864
.90867
.90870
9.90873
.90876
.90879
.90882
0.81023
.81029
.81035
.81040
0.81046
.81052
.81057
.81063
9.91043
.91046
.91049
.91052
9.91055
.91058
.91061
.91064
0.81364
.81370
.81376
.81381
0.81387
.81392
.81398
.81404
9.91224
.91227
.91230
.91233
9.91236
.91239
.91242
.91245
0.81703
.81708
.81714
.81720
0.81725
.81731
.81737
.81742
0.82039
.82045
.82050
.82056
0.82061
.82067
.82072
.82078
36
34
32
30
28
26
24
22
40+25
42
44+26
46
48+21
50
52+28
54
9.90701
.90704
.90707
.90710
9.90714
.90717
.90720
.90723
0.80726
.80731
.80737
.80743
0.80749
.80754
.80760
.80766
9.90885
.90888
.90892
.90895
9.90898
.90901
.90904
.90907
0.81068
.81074
.81080
.81086
0.81092
.81097
.81103
.81109
9.91067
.91071
.91074
.91077
9.91080
.91083
.91086
.91089
0.81409
.81415
.81421
.81426
0.81432
.81438
.81443
.81449
9.91248
.91251
.91254
.91257
9.91260
.91263
.91265
.91268
0.81748
.81753
.81759
.81765
0.81770
.81776
.81781
.81787
9.91426
.91429
.91432
.91435
9.91437
.91440
.91443
.91446
0.82084
.82089
.82095
.82100
0.82106
.82112
.82117
.82123
20
18
16
14
12
10
8
6
56+29
58
60+30
9.90726
.90729
9.90732
0.80772
.80777
0.80783
9.90910
.90913
9.90916
0.81114
.81120
0.81126
9.91092
.91095
9.91098
0.81455
.81460
0.81466
9.91271
.91274
9.91277
0.81793
.81798
0.81804
9.91449
.91452
9.91455
0.82128
.82134
0.82139
4
0
15h 28m
15h 26m
15h 24™
15h 22m
l$h 20m
TABLE 45.
Haversines.
[Page 911
s '
8* 40m 130° 9/
8* 42m 130° 30"
8* 44m 131° (K
8* 46m 131° 3<X
8* 4Sm 132° <K
s
Log. Hav.j Xat. Hav.
Log. Hav.
Xat. Hav.
Log. Hav. Xat. Hav.
Log. Hav.
Xat. Hav.
Log. Hav.
Xat. Hav.
0 9
4+ 1
6
9.91455
.91458
.91461
.91464
0.82139
.82145
.82151
.82156
9.91631
.91634
.91637
.91640
0.82472
.82478
.82483
.82489
9.91805
.91807
.91810
.91813
0.82803
.82808
.82814
.82819
9.91976
.91979
.91982
.91985
0.83131
.83136
.83142
.83147
9.92146
.92149
.92152
.92154
0.83457
.83462
.83467
.83473
60
58
56
54
8+ 2
to
14 '
16+ 4
18
20+ 5
22
9.91467
.91470
.91473
.91476
9.91479
.91482
.91485
.91488
0.82162
.82167
.82173
.82178
0.82184
.82189
.82195
.82200
9.91643
.91645
.91648
.91651
9.91654
.91657
.91660
.91663
0.82495
.82500
.82506
.82511
0.82517
.82522
.82528
.82533
9.91816
.91819
.91822
.91825
9.91828
.91830
.91833
.91836
O.v>v>5
.82830
.82836
.82841
0.82847
.82852
.82858
.82863
9.91988
.91991
.91993
.91996
9.91999
.92002
.92005
.92008
O.VU53
.83158
.83164
.83169
0.83175
.83180
.83185
.83191
9.92157
.92160
.92163
.92166
9.92169
.92171
.92174
.92177
0.83478
.83484
.83489
.83494
0.83500
.83505
.83511
.83516
52
50
48
46
44
42
40
38
36
34
32
30
28
26
t4
22
24+ 6
26
28+ 7
30
32+ 8
36+ 9
9.91490 0.82206
.91493 i .82212
.91496 i .82217
.91499 .82223
9.91502 0.82228
.91505 .82234
.91508! .82240
.91511 ; .82245
9.91666
.91669
.91672
.91674
9.91677
.91680
.91683
.91686
0.82539
.82544
.82550
.82555
0.82561
.82566
.82572
.82577
9.91839
.91842
.91845
.91848
9.91851
.91853
.91856
.91859
0.82369
.82874
.82880
.82885
0.82891
.82896
.82902
.82907
9.92010
.92013
.92016
.92019
9.92022
.92025
.92027
.92030
0.83196
.83202
.83207
.83213
0.83218
.83224
.83229
.83234
9.92180
.92183
.92185
.92188
9.92191
.92194
.92197
.92199
0.83531
.83527
.83532
.83538
0.83543
.83548
.83554
.83559
40+10
4-?
44+11
46
50
52+13
54
9.91514 0.82251
.91517 .82256
.91520 .82262
.91523 .82267
9.91526 0.82273
.91529 .82278
.91532 .82284
.91534 .82290
9.91689
.91692
.91695
.91698
9.91701
.91703
.91706
.91709
0.82583
.82588
.82594
.82599
0.82605
.82610
.82616
.82621
9.91862
.91865
.91868
.91871
9.91874
.91876
.91879
.91882
0.82913
.82918
.82924
.82929
0.82934
.82940
.82945
.82951
9.92033
.92036
.92039
.92042
9.92044
.92047
.92050
.92053
0.83240
.83245
.83251
.83256
0.83262
.83267
.83272
.83378
9.92202
.92205
.92208
.92211
9.92213
.92216
.92219
.92222
0.83564
.83570
.83575
.83581
0.83586
.83591
.83597
.83602
to
18
16
14
12
10
8
6
56+14
58
9.91537 0.82295
9.91540 0.82301
9.91712
9.91715
0.82627
0.82632
9.91885
9.91888
0.82956
0.82962
9.92056
9.92059
0.83283
0.83289
9.92225
9.92227
0.83608
0.83613
4
15* 19m
16*
17 m
15* 15m
16*
13m
16*
lim
s '
0+15
4+16
6
8* 41™ 130° 9/
Sh 4.3m 130° 39/
8* 45m 131° 0'
8* 47m 131° 30:
8* 49m
132° V
s
60
58
56
54
9.91543
.91546
.91549
.91552
0.82306
.82312
.82317
.82323
9.91718
.91721
.91724
.91727
0.82638
.82644
.82649
.82655
9.91891 0.82967
.91894 .82973
.91896 i .82978
.91899 I .82984
9.92061
.92064
.92067
.92070
0.83294
.83300
.83305
.83310
9.92230
.92233
.92236
.92239
0.83618
.83624
.83629
.83635
8+11
10
12+18
14
16+19
18
20+29
9.91555
.91558
.91561
.91564
9.91567
.91570
.91573
.91575
0.82328
.82334
.82339
.82345
0.82351
.82356
.82362
.82367
9.91730
.91732
.91735
.91738
9.91741
.91744
.91747
.91750
0.82660
.82666
.82671
.82677
0.82682
.82688
.82693
.82699
9.91902
.91905
.91908
.91911
9.91914
.91916
.91919
.91922
0.82989
.82995
.83000
.83006
0.83011
.83016
.83022
.83027
9.92073
.92076
.92078
.92081
9.92084
.92087
.92090
.92093
0.83316
.83321
.83327
.83332
0.83337
.83343
.83348
.83354
9.92241
.92244
.92247
.92250
9.92253
.92255
.92258
.92261
0.83640
.83645
.83651
.83656
0.83661
.83667
.83672
.83678
52
50
4S
46
44
42
40
38
24+21
26
32+23
34
.36+24
38
9.91578
.91581
.91584
.91587
9.91590
.91593
.91596
.91599
0.82373
.82378
.82384
.82389
0.82395
.82400
.82406
.82412
9.91753
.91756
.91758
.91761
9.91764
.91767
.91770
.91773
0.82704
.82710
.82715
.82721
0.82726
.82732
.82737
.82743
9.91925
.91928
.91931
.91934
9.91936
.91939
.91942
.91945
0.83033
.83038
.83044
.83049
0.83055
.83060
.83066
.83071
9.92095
.92098
.92101
.92104
9.92107
.92109
.92112
.92115
0.83359
.83365
.83370
.83375
0.83381
.83386
.83392
.83397
0.83402
.83408
.83413
.83419
0.83424
.83430
.83435
.83440
9.92264
.92266
.92269
.92272
9^92275
.92278
.92280
.92283
0.83683
.83688
.83694
.83699
0.83704
.83710
.83715
.83720
36
34
32
30
28
26
24
22
40+35
44+26
46
48+21
50
52+2$
54
9.91602
.91605
.91608
.91610
9.91613
.91616
.91619
.91622
0.82417
.82423
.82428
.82434
0.82439
.82445
.82450
.82456
9.91776
.91779
.91782
.91784
9.91787
.91790
.91793
.91796
0.82748
.82754
.82759
.82765
0.82770
.82776
.82781
.82786
9.91948
.91951
.91954
.91956
9.91959
.91962
.91965
.91968
0.83077
.83082
.83087
.83093
0.83098
.83104
.83109
.83115
9.92118
.92121
.92124
.92126
9.92129
.92132
.92135
.92138
9.92286
.92289
.92292
.92294
9.92297
.92300
.92303
.92305
0.83726
.83731
.83737
.83742
0.83747
.83753
.83758
.83763
20
18
16
14
10
8
6
56+29
58
60+30
9.91625
.91628
9.91631
0.82461
.82467
0.82472
9.91799
.91802
9.91805
0.82792
.82797
0.82803
9.91971
.91973
9.91976
O.S3130
.83126
0.83131
9.92140
.92143
9.92146
0.83446
.83451
0.83457
9.92308
.92311
9.92314
0.83769
.83774
0.83780
4
2
0
15* 18m
15* 16m
15* 14m
15* 12™
15* 10™
Page 912] TABLE 45.
Haversines.
s '
8* 50™ 132° 30X
8*> 52m 133° 0'
8h 54™ 133° 30'
8h 56™ 134° Ox
S*> 58m 1340 30'
s
60
58
56
54
Log. Hav.j Nat. Hav.
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
0 0
2
4+ 1
6
9.92314
.92317
.92319
.92322
0.83780
.83785
.83790
.83796
9.92480
.92482
.92485
.92488
0.84100
.84105
.84111
.84116
9.92643
.92646
.92649
.92652
0.84418
.84423
.84428
.84434
9.92805
.92808
.92811
.92813
0.84733
.84738
.84743
.84749
9.92965
.92968
.92970
.92973
0.85045
.85051
.85056
.85061
8+ 2
10
12+ 3
14
16+ 4
18
20+ 5
22
9.92325
.92328
.92330
.92333
9.92336
.92339
.92342
.92344
0.83801
.83806
.83813
.83817
0.83822
.83838
.83833
.83838
9.92491
.92493
.92496
.92499
9.92502
.92504
.92507
.92510
0.84121
.84127
.84132
.84137
0.84142
.84148
.84153
.84158
0.84164
.84169
.84174
.84180
0.84185
.84190
.84196
.84301
9.92654
.92657
.92660
.92662
9 92665
.92668
.92670
.92673
0.84439
.84444
.84449
.84455
0.84460
.84465
.84470
.84476
9.92816
.92819
.92821
.92824
9.92827
.92829
.92832
.92835
0.84754
.84759
.84764
.84770
0.84775
.84780
.84785
.84790
9.92975
.92978
.92981
.92984
9.92986
.92989
.92992
.92994
0.85066
.85071
.85077
.85082
0.85087
.85092
.85097
.85102
52
50
48
46
44
42
40
38
24+ 6
26
28+ 7
30
32+ 8
34
36+ 9
38
9.92347
.92350
.92353
.92355
9.92358
.92361
.92364
.92366
0.83844
.83849
.83855
.83860
0.83865
.83871
.83876
.83881
9.92512
.92515
.92518
.92521
9.92523
.92526
.92529
.92532
9.92676
.92679
.92681
.92684
9.92687
.92689
.92692
.92695
0.84481
.84486
.84492
.84497
0.84502
.84507
.84513
.84518
9.92837
.92840
.92843
.92845
9.92848
.92851
.92853
.92856
0.84796
.84801
.84806
.84811
0.84817
.84822
.84837
.84832
9.92997
.93001
.93002
.93005
9.93007
.93010
.93013
.93015
0.85108
.85113
.85118
.85123
0.85128
.85134
.85139
.85144
36
34
30
28
26
24
22
40 +10
42
44+11
46
48+12
50
52+13
54
9.92369
.92372
.92375
.92378
9.92380
.92383
.92386
.92389
0.83887
.83892
.83897
.83903
0.83908
.83913
.83919
.83924
9.92534
.92537
.92540
.92543
9.92545
.92548
.92551
.92554
0.84206
.84211
.84317
.84323
0.84227
.84233
.84238
.84243
9.92698
.92700
.92703
.92706
9.92708
.92711
.92714
.92716
0.84523
.84528
.84534
.84539
0.84544
.84549
.84555
.84560
9.92859
.92861
.92864
.92867
9.92869
.92872
.92875
.92877
0.84837
.84843
.84848
.84853
0.84858
.84863
.84869
.84874
9.93018
.93021
.93023
.93026
9.93029
.93031
.93034
.93036
0.85149
.85154
.85159
.85165
0.85170
.85175
.85180
.85185
20
18
16
U
12
10
8
6
56+U
58
9.92391
9.92394
0.83929
0.83935
9.92556
9.92559
6T84249
0.84254
9.92719
9.92722
0.84565
0.84570
9.92880
9.92883
0.84879
0.84884
9.93039
9.93042
0.85190
0.85196
4
2
15h gm
ISliym
15h5m
15h$m
15k im
& /
8h sim 133° 30'
8^ 53m 133° <K
8h 55™ 133° 30'
8h 57m 134° 0'
gh 59m 134° 30'
8
0+15
4+16
6
9.92397
.92400
.92402
.92405
0.83940
.83945
.83951
.83956
9.92562
.92564
.92567
.92570
0.84259
.84264
.84270
.84275
9.92725
.92727
.92730
.92733
0.84576
.84581
.84586
.84591
9.92885
.92888
.92891
.92893
0.84890
.84895
.84900
.84905
9.93044
.93047
.93050
.93052
0.85201
.85206
.85211
.85216
60
58
56
54
8+n
10
12+lS
14
16+19
18
20+20
22
9.92408
.92411
.92413
.92416
9.92419
.92422
.92425
.92427
0.83961
.83967
.83972
.83977
0.83983
.83988
.83993
.83999
9.92573
.92575
.92578
.92581
9.92584
.92586
.92589
.92592
0.84280
.84286
.84291
.84296
0.843P2
.84307
.84312
.84317
9.92735
.92738
.92741
.92743
9.92746
.92749
.92751
.92754
0.84597
.84602
.84607
.84612
0.84618
.84623
.84628
.84633
9.92896
.92899
.92901
.92904
9.92907
.92909
.92912
.92915
0.84910
.84916
.84921
.84936
0.84931
.84936
.84942
.84947
9.93055
.93057
.93060
.93063
9.93065
.93068
.93071
.93073
0.85221
.85227
.85232
.85237
0.85242
.85247
.85252
.85258
52
50
48
46
44
42
40
38
24+21
26
28+22
30
32+23
34
36+24
38
9.92430
.92433
.92436
.92438
9.92441
.92444
.92447
.92449
0.84004
.84009
.84015
.84020
0.84025
.84031
.84036
.84041
9.92594
.92597
.92600
.92603
9.92605
.92608
.92611
.92613
0.84323
.84328
.84333
.84339
0.84344
.84349
.84354
.84360
9.92757
.92760
.92762
.92765
9.92768
.92770
.92773
.92776
0.84639
.84644
.84649
.84654
0.84660
.84665
.84670
.84675
9.92917
.92920
.92923
.92925
9.92928
.92931
.92933
.92936
0.84952
.84957
.84962
.84968
0.84973
.84978
.84983
.84988
9.93076
.93079
.93081
.93084
9.93086
.93089
.93092
.93094
0.85263
.85268
.85273
.85278
0.85283
.85288
.85294
.85299
36
34
32
30
28
26
24
22
40+25
44+26
46
48+21
50
52+28
54
9.92452
.92455
.92458
.92460
9.92463
.92466
.92469
.92471
0.84047
.84052
.84057
.84063
0.84068
.84073
.84079
.84084
9.92616
.92619
.92622
.92624
9.92627
.92630
.92633
.92635
0.84365
.84370
.84376
.84381
0.84386
.84391
.84397
.84402
9.92778
.92781
.92784
.92786
9.92789
.92792
.92794
.92797
0.84681
.84686
.84691
.84696
0.84702
.84707
.84712
.84717
9.92939
.92941
.92944
.92947
9.92949
.92952
.92955
.92957
0.84994
.84999
.85004
.85009
0.85014
.85020
.85025
.85030
9.93097
.93100
.93102
.93105
9.93107
.93110
.93113
.93115
0.85304
.85309
.85314
.85319
0.85324
.85330
.85335
.85340
20
18
16
14
12
10
8
6
4
2
0
56+29
58
60+30
9.92474
.92477
9.92480
0.84089
.84095
0.84100
9.92638
.92641
9.92643
0.84407
.84412
0.84418
9.92800
.92802
9.92805
0.84722
.84728
0.84733
9.92960
.92962
9.92965
0.85035
.85040
0.85045
9.93118
.93120
9.93123
0.85345
.85350
0.85355
15h8m
15h 6m
15h 4m
Idhgm
IShQm
TABLE 45. [Page 913
Haversines.
9* Om 135°
9k 4m 136°
9k 8m 137°
9k 12m 138°
9k 16m 139°
s '
Log. Hav.. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.! Nat. Hav
Log. Hav.1 Nat. Hav
s
0 0
9.93123 0.85355
9.93433
0.85967
9.93736
0.86568
9.94030
0.87157
9.91:
0.87735
60
4 1
.93128
.85366
.93438
.85977
.93741
.86578
.94035
.87167
.94322
.87745
56
8- 2
.93134 .85376
.93443
.85987
.93746
.86588
.94040 .87177
.94327
.87755
52
12 3
.93139! .85386
.93448
.85997
.93751 .86597
.94045 .87186
.94332
.87764
48
16 4
9.93144 i 0.85396
9.93454
0.86007
9.93755 0.86607
9.94050
0.87196
9.94336
0.87774
44
20 5
.93149 ! .85407
.93459
.86017
.937601 .86617
.94055
.87206
.94341
.87783
40
t4 6
.93154 i .85417
.93464
.86028
.93765
.S6627
.94059
.87216
.94346
.87793
36
28 7
.93160 1 .85427
.93469
.86038
.93770
.86637
.94064
.87225
.94351
.87802
32
32 8
9.93165 j 0.85438
9.93474
0.86048
9.93775
0.86647
9.94069
0.87235
9.94355
0.87812
28
36 9
.93170, .85448
.93479
.86058
.93780
.86657
.94074
.87245
.94360
.87821
24
44 10
.93175 .85458
.93484
.86068
.93785
• ^OQO 4
.94079
.87254
.94365
.87831
20
44 11
.93181 .85468
.93489
.86078
.93790
.86677
.94084
.87264
.94369
.87840
16
48 12
9.93186
0.85479
9.93494
0.86088
9.93795
0.86686
9.94088
0.87274
9.94374
0.87850
12
52 13
.93191
.85489
.93499
.86098
.93800
.86696
.94093
.87283
.94379
.87859
8
56 14
9.93196 0.85499
9.93504 i 0.86108
9.93805 0.86706
9.94098 : 0.87293
9.94383
0.87869
4
14h 59m
14h 55^
Uh 5im
14h 47m
14k 4,3711 •
s '
9k im 135°
9k 5m 136°
9k 9m 137°
9k 13m 138°
9k 17m 139=
s
0 15
9.93201 0.855C9
9.93509 | 0.86118
9.93810
0.86716
9.94103 0.87303
9.94388 0.87878
60
4 16
.93207 .85520
.93515
.86128
.93815
.86726
.94108 ! .87313
.94393
.87888
56
* 17
.93212 ' .85530
.93520
.86138
.93820
.86736
.94112 i .87322
.94398
.87897
52
12 18
.93217 .85540
.93525 .86148
.93825
.88746
.94117 .87332
.94402
.87907
48
16 19
9.93222 0.85550
9.93530
0.86158
9.93830
0.86756
9.94122 0.87342
9.94407
0.87916
44
£0 20
.93227 | .85560
.93535
.86168
.93835
.86765
.94127 .87351
.94412
.87926
40
24 21
.93232 j .85571
.93540 .86178
.93840
.86775
.94132 .87361
.94416
.87935
36
2£ 22
.93238
.85581
.93545 .86189
.93845
.86785
.94137 ! .87371
.94421
.87945
32
32 23
9.93243
0.85591
9.93550 0.86199
9.93849
0.86795
9.94141 ' 0.87380
9.94426
0.87954
28
35 24
.93248
.85601
.93555 .86209
.93854
.86805
.94146 .87390
.94430
.87964
24
40 25
.93253
.85612
.93560 .86219
.93859
.86815
.94151 ! .87400
.94435
.87973
20
44 26
.93258
.85622
.93565 .86229
.93864
.86825
.94156 .87409
.94440
.87983
16
45 27
9.93264
0.85632
9.93570
0.86239
9.93869
0.86834
9.94161 ! 0.87419
9.94444
0.87992
12
52 28
.93269
.85642
.93575 .86249
.93874
.86844
.94165 .87428
.94449
.88001
8
56 29
9.93274
0.85652
9.9.3580 0.86259
9.93879
0.86854
9.94170 : 0.87438
9.94454
0.88011
4
14h 58™
14h 54™
14k o<jm
14h 46m
14k 42m
s '
gh -2m 135°
9k 6m 136°
9^ 10m 137°
9k 14™ 138°
9k 18m 139°
s
0 30
9.93279 0.85663
9.93585
0.86296
9.93884 i 0.86864
9.94175 0.87448
9.94458
0.88020
60
4 31
.93284 .85673
.93590
.86279
.93889 ! .86874
.94180 ; .87457
.94463
.88030
56
8 32
.93289
.85683
.93595
.86289
.93894 .86884
.94184 ! .87467
.94468
.88039
52
I;? 33
.93295 .85693
.93600
.86299
.93899 ! .86893
.94189 : .87477
.94472
.88049
48
16 34
9.93300 0.85703
9.93605
0.86309
9.93904 0.86903
9.94194
0.87486
9.94477
0.88058
44
20 35
.93305 .85713
.93611
.86319
.93908
.86913
.94199
.87496
.94482
.88068
40
24 36
.93310 .85724
.93616
.86329
.93913
.86923
.94204
.87505
.94486
.88077
36
28 37
.93315 .85734
.93621
.86339
.93918 [ .86933
.94208 : .87515
.94491
.88086
32
32 38
9.93320 0.85744
9.93626
0.86349
9.93923 0.86942
9.94213 0.87525
9.94496
0.88096
28
36 39
.93326 ; .85754
.93631
.86359
.93928 .86952
.94218 .87534
.94500
.88105
24
40 40
.93331 ! .85764
.93636
.86369
.93933 ! .86962
.94223 .87544
.94505
.88115
20
44 41
.93336 .85774
.93641
.86379
.93938 ! .86972
.94227 .87554
.94509
.88124
16
48 42
9.93341 0.85785
9.93646
0.86389
9.93943 0.86982
9.94232 0.87563
9.94514
0.88133
12
52 43
.93346 .85795
.93651
.86399
.93948 .86991
.94237 .87573
.94519
.88143
8
56 44
9.93351 0.85805
9.93656
0.86409
9.93952 i 0.87001
9.94242 0.87582
9.94523
0.88152
4
14h 57m
14h jjm
14h 49m
14h 45m
14h 41m
s '
9k 3m 135°
9k 7m 136°
9k lim 137°
9k 15m 138°
9k 19m 139°
s
0 45
9.93356
0.85815
9.93661
0.86419
9.93957
0.87011
9.94246
0.87592
9.94528
0.88162
60
4 46
.93362
.85825
.93666
.86429
.93962
.87021
.94251
.87602
.94533
.88171
56
5 47
.93367
.85835
.93671
.86438
.93967
.87030
.94256
.87611
.94537
.88180
52
^ 48
.93372
.85846
.93676
.86448
.93972
.87040
.94261
.87621
.94542
.88190
48
16 49
9.93377
0.85856
9.93681
0.86458
9.93977
0.87050
9.94265
0.87630
9.94546
0.88199
44
20 50
.93382
.85866
.93686
.86468
.93982
.87060
.94270
.87640
.94551
.88209
40
24 51
.93387
.85876
.93691
.86478
.93987
.87070
.94275
.87649
.94556
.88218
36
28 52
.93392
.85886
.93696
.86488
.93991
.87079
.94280
.87659
.94560
.88227
32
32 53
9.93397
0.85896
9.93701
0.86498
9.93996
0.87089
9.94284
0.87669
9.94565
0.88237
28
36 54
.93403
.85906
.93706
.86508
.94001
.87099
.94289
.87678
.94570
.88246
24
40 55
.93408
.85916
.03711
.86518
.94006
.87109
.94294
.87688
.94574
.88255
20
44 56
.93413
.85926
.93716
.86528
.94011
.87118
.94299
.87697
.94579
.88265
16
48 57
9.93418
0.85937
9.93721
0.86538
9.94016
0.87128
9.94303
0.87707
9.94583
0.88274
12
52 58
.93423
.85947
.93726
.86548
.94021
.87138
.94308
.87716
.94588
.88284
8
56 59
.93428
.85957
.93731
.86558
.94026
.87148
.94313
.87726
.94593
.88293
4
60 60
9.93433
0.85967
9.93736
0.86568
9.94030
0.87157
9.94318
0.87735
9.94597
0.88302
0
14h .56/;?
14h 52m
14h 4Sm
14h 44^
14* 4o'r-
Page 914] TABLE 45.
Haversines.
9h 20™ 140°
9h 24m 141°
9h 28m U2°
9h 32m 143°
9h 36m 1440
s '
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. I lav.
Log. Hav.
Nat. Hav.
s
0 0
9.94597
0.88302
9.94869
0.88857
9.95134
0.89401
9.95391
0.89932
9.95641
0.90451
60
4 1
.94602
.88312
.94874
.88866
.95138
.89409
.95396
.89941
.95645
.90459
56
8 2
.94606
.88321
.94878
.88876
.95143
.89418
.95400
.89949
.95649
.90468
52
12 3
.94611
.88330
.94883
.88885
.95147
.89427
.95404
.89958
.95654
.90476
48
16 4
9.94616
0.88340
9.94887
0.88894
9.95151
0.89436
9.95408
0.89967
9.95658
0.90485
44
20 5
.94620
.88349
.94892
.88903
.95156
.89445
.95412
.89976
.95662
.90494
40
24 6
.94625
.88358
.94896
.88912
.95160
.89454
.95417
.89984
.95666
.90502
36
28 7
.94629
.88368
.94901
.88921
.95164
.89463
.95421
.89993
.95670
.90511
32
32 8
9.94634
0.88377
9.94905
0.88930
9.95169
0.89472
9.95425
0.90002
9.95674
0.90519
28
36 9
.94638
.88386
.94909
.88940
.95173
.89481
.95429
.90010
.95678
.90528
24
40 10
.94643
.88396
.94914
.88949
.95177
.89490
.95433
.90019
.95682
.90537
20
44 H
.94648
.88405
.94918
.88958
.95182
.89499
.95438
.90028
.95686
.90545
16
45 13
9.94652
0.88414
9.94923
0.88967
9.95186
0.89508
9.95442
0.90037
9.95690
0.90553
12
52 13
.94657
.88423
.94927
.88976
.95190
.89517
.95446
.90045
.95694
.90582
8
56 U
9.94661
0.88433
9.94932
0.88985
9.95195
0.89526
9.95450
0.90054
9.95699
0.90570
4
14h 39™
14h 35m
14h Sim
14h 27m
14h 23m
s '
9h 2im 140°
9h 25m 141°
9h 29m 143°
9h 33m 143°
9h 37m 144°
s
0 15
9.94666
0.88442
9.94936
0.88994
9.95199
0.89534
9.95454
0.90063
9.95703
0.90579
60
4 16
.94670
.88451
.94941
.89003
.95203
.89543
.95459
.90071
.97507
.90588
56
5 17
.94675
.88461
.94945
.89012
.95208
.89552
.95463
.90080
.95711
.90596
52
12 18
.94680
.88470
.94950
.89022
.95212
.89561
.95467
.90089
.95715
.90604
48
J?6 19
9.94684
0.88479
9.94954
0.89031
9.95216
0.89570
9.95471
0.90097
9.95719
0.90613
44
20 20
.94689
.88489
.94958
.89040
.95221
.89579
.95475
.90106
.95723
.90621
40
24 21
.94693
.88498
.94963
.89049
.95225
.89588
.95480
.90115
.95727
.90630
36
25 22
.94698
.88507
.94967
.89058
.95229
o89597
.95484
.90124
.95731
.90638
32
32 23
9.94702
0.88516
9.94972
0.89067
0.95234
0.89606
9.95488
0.90132
9.95735
0.90647
28
56 24
.94707
.88526
.94976
.89076
.95238
.89614
.95492
.90141
.95739
.90655
24
40 25
.94711
.88535
.94981
.89085
.95242
.89623
.95496
.90150
.95743
.90664
20
44 26
.94716
.88544
.94985
.89094
.95246
.89632
.95501
.90158
.95747
.90672
16
45 27
9.94721
0.88553
9.94989
0.89103
9.95251
0.89611
9.95505
0.90167
9.95751
0.90680
12
52 28
.94725
.88563
.94994
.89112
.95255
.89650
.95509
.90176
.95755
.90689
8
5(5 29
9.94730
0.88572
9.94998
0.89121
9.95259
0.89659
9.95513
0.90184
9.95759
0.90697
4
14h38m .
14h 34m
'14* 30m
14h 26m
14h 22m
s '
9h $2™ 140°
9h 26m 141°
9h 3Qm 142°
9h 34m 1430
9h 3§m 144°
s
0 30
9.94734
0.88581
9.95003
0.89130
9.95264
0.89668
9.95517
0.90193
9.95763
0.90706
60
4 31
.94739
.88590
.95007
.89139
.95268
.89677
.95521
.90201
.95768
.90714
56
8 32
.94743
.88600
.95011
.89149
.95272
.89685
.95526
.90210
.95772
.90723
52
.72 33
.94748
.88609
.95016
.89158
.95276
.89694
.95530
.90219
.95776
.90731
48
J76 34
9.94752
0.88618
9.95020
0.89167
9.95281
0.89703
9.95534
0.90227
9.95780
0.90740
44
20 35
.94757
.88627
.95025
.89176
.95285
.89712
.95538
.90236
.95784
.90748
40
24 36
.94761.
.88637
.95029
.89185
.95289
.89721
.95542
.90245
.95788
.90756
36
28 37
.94766
.88646
.95033 .89194
.95294
.89730
.95546
.90253
.95792
.90765
32
32 38
9.94770
0.88655
9.95038
0.89203
9.95298
0.89738
9.95550
0.90262
9.95796
0.90773
28
,56 39
.94774
.88664
.95042
.89212
.95302
.89747
.95555
.90271
.95800
.90792
24
40 40
.94779
.88674
.95047 .89221
.95306
.8975G
.95559
.90279
.95804
.90790
20
44 41
.94784
.88683
.95051
.89230
.95311
.89765
.95563
.90288
.95808
.90798
16
48 42
9.94788
0.88692
9.95055
0.89239
9.95315 0.89774
9.95567
0.90296
9.95812
0.90807
12
52 43
.94793
.88701
.95060
.89248
.95319
.89783
.95571
.90305
.95816
.90815
8
56 44
9.94797
0.88710
9.95064
0.89257
9.95323
0.89791
9:95575
0.90314
9.95820
0.90824
4
14^ 37m
Uh 33m
14h 29m
14h 25m
14h 2im
s '
gh 23™ 140°
9h 27m 141°
9h sim 142°
9h 35m 143°
9h 39m 144°
s
0 45
9.94802 j 0.88720
9.95069
0.89266
9.95328 0.89800
9.95579
0.90322
9.95824
0.90832
60
4 46
.94806
.88729
.95073
.89275
.95332
.89809
.95584
.90331
.95828
.90840
56
5 47
.94811
.88738
.95077
.89284
.95336
.89818
.95588
.90339
.95832
.90849
52
J72 48
.94815
.88747
.95082
.89293
.95340
.89827
.95592
.90348
.95836
.90857
48
16 49
9.94820
0.88756
9.95086
0.89302
9.75345
0.89835
9.95596
0.90357
9.95840
0.90866
44
20 50
.94824
.88766
.95090
.89311
.95349
.89844
.95600
.90365
.95844
.90874
40
24 51
.94829
.88775
.95095
.89320
.95353
.89853
.95604
.90374
.95848
.90882
36
28 52
.94833
.88784
.95099
.89329
.95357
.89862
.95608
.90382
.95852
.90891
32
52 53
9.94838
0.88793
9.95104
0.89338
9.95362
0.89870
9.95613
0.90391
.9 95856
0.90899
28
36 54
.94842
.88802
.95108
.89347
.95366
.89879
.95617
.90399
.95860
.90907
24
40 55
.94847
.88811
.95112
.89356
.95370
.89888
.95621
.90408
.95864
.90916
20
44 56
.94851
.88821
.95117
.89365
.95374
.89897
.95625
.90417
.95868
.90924
16
48 57
9.94856
0.88830
9.95121
0.89374
9.95379
0.89906
9.95629
0.90425
9.95872
0.90933
12
52 58
.94860
.88839
.95125
.89383
.95383
.89914
.95633
.90434
.95876
.90941
8
56 59
.94865
.88848
.95130
.89392
.95387
.89923
.95637
.90442
.95880
.90949
4
60 60
9.94869
0.88857
9.95134
0.89401
9.95391
0.89932
9.95641
0.90451
9.95884
0.90958
0
14h 36m
141* 32m
14h 28m
14h 24m
14h 20m
TABLE
45. [Page 915
Haversines.
gh 4Qm 145°
gh 44" 146°
gh 4$m
147°
9 h 52"» 148°
9h 5&n 1490
s '
Log. Hav. Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.; Nat. Hav.
Log. Hav.
Nat. Hav.
s
0 0
9.95884
0.90958
9.96119 0.91452
9.96347
0.91934
9.96568 0.92402
9.96782
0.92858
60
4 1
.95888
.90966
.96123
.91469
.96351
.91941
.96572 .92410
.96786
.92866
56
8 2
.95892
.90974
.96127
.91468
.96355
.91949
.96576 .92418
.96789
.92873
.' .
12 3
.95896
.90983
.96131 .91476
.96359
.91957
.96579 .92426
.96793
.92881
48
16 4
9.95900
0.90991
9.96135 0.91484
9.96362
0.91965
9.96583 -0.92433
9.96796
0.92888
44
20 5
.95904
.90999
.96139; .91493
.96366
.91973
.96586 .92441
.96800
.92896
40
24 6
.95908
.91008
.96142 .91501
.96370
.91981
.96590 i .92449
.96803
.92903
36
^- (b i
.95912
.91016
.96146 ! .91509
.96374
.91989
.96594 ! .92456
.96807
.92011
32
52 8
9.95916
0.91024
9.96150 ! 0.91517
9.96377
0.91997
9.96597 0.92464
9.96810
0.92918
28
36 9
.95920
.91033
.96154 i .91525
.96381
.92005
.96601 ! .92472
.96814
.!)•„';»': t»
40 10
.95924
.91041
.96158! .91533
.96385
.92013
.96604 ; .92479
.96817
.92933
20
44 11
.95928
.91049
.96162 1 .91541
.96388
.92020
.9660S .92487
.96821
.92941
16
48 12
9.95932
0.91057
9.96165 0.91549
9.96392
0.92028
9.96612 0.9249.5
9.96824
0.92948
It
52 13
.95936
.91066
.96169 .91557
.96396
.92036
.96615 ! .92502
.96827
.929.5-5
8
56 14
9.95939
0.91074.
9.96173 0.91565
9.96400
0.92044
9.96619 0.92510
J31
0.92983
4
14*- 19m
14* 15m
14*
It*
14* 7m
14* 3™
s '
gh 4fm 145°
3* 4o"* 146°
gh 49m 147°
9* 55"» 148°
9* 57^ 149°
s
0 15
9.95943
0.91082
9.96177 0.91574
9.96403
0.92052
9.96622 0.92518
9.96834 0.92970
60
4 16
.95947
.91091
.96181 i .91582
.96407
.92060
.96626 , .92.52.5
.96837! .92978
56
S 17
.95951
.91099
.96185 .91590
.96411
.92068
.96630 .92.533
.96841 i .92985
52
12 18
.95955
.91107
.96188 .91598
.96412
.92076
.96633 .92541
.96845 i .92993
48
16 19
9.95959
0.91115
9.96192 0.9l&9«
9.96418
0.92083
9.96637 ! 0.92548
9.96848 ! 0.93000
44
20 20
.95963
.91124
.96196 .91611
.96422
.92091
.96640 .92.556
.96852
.93007
40
24 21
.95967
.91132
.96200 .91622
.96426
.92099
.96644 .92563
.96855
.93015
36
28 22
.95971
.91140
.96204 .91630
.96429
.92107
.96648 ! .92571
.96859
.93022
32
23
9.95975
0.91149
9.96208 0.91638
9.96433
0.92115
9.96651 1 0.92579
9.96862
0.93030
28
36 24
.95979
.91157
.96211 .91646
.96437
.92123
.96655 i .92586
.96866
.93037
24
40 25
.95983
.91165
.96215 .91654
.96440
.92130
.96658 .92594
.96869
.93045
20
44 26
.95987
.91173
.96219 ..91662
.96444
.92138
.96662 .92602
.96873
.93052
16
4$ 27
9.95991
0.91182
9.96223 0.91670
9.96448
0.92146
9.96665 ! 0.92609
9.96876
0.93059
12
52 28
.95995
.91190
.96227 .91678
.96451
.92154
.96669 i .92617
.96879
.93067
8
56 29
9.95999
0.91198
9.96230 0.91686
9.96455
0.92162
9.96673 0.92624
9.96883
0.93074
4
14* 18m
14h 14™
14*
10*
14h sm
14* 2™
s '
gh 42™
145°
gh 4Qm 146=
gh jQm
147°
9* 54m 148°
9h oSm 149°
s
0 30
9.96002
0.91206
9.96234
0.91694
9.96459
0.92170
9.96676 0.92632
9.96886 0.93081
60
4 31
.96006
.91215
.96238
.91702
.96462
.92177
.96680 ; .92640
.96890 .93089
56
8 32
.96010
.91223
.96242
.91710
.96466
.92185
.96683 .92647
.96894 .93096
52
12 33
.96014
.91231
.96246
.91718
.96470
.92193
.96687 : .92655
.96897 .93104
48
16 34
9.96018
0.91239
9.96249
0.91726
9.96473
0.92201
9.96690 0.92662
9.96900 0.93111
44
20 35
.96022
.91247
.96253
.91734
.96477
.92209
.96994 .92670
.96904 .93118
40
24 36
.96026
.91256
.96257
.91742
.96481
.92216
.96697 : .92678
.96907 .93126
36
28 37
.96030
.91264
.96261
.91750
.96484
.92224
.96701 .92685
.96910 .93133
32 38
9.96034
0.91272
9.96265
0.9175S
9.96488
0.92232
9.96705 0.92693
9.96914 0.93140
28
36 39
.96038
.91280
.96268
.91766
.96492
.92240
.96708 .92700
.96917 .93148
24
40 40
.96042
.91289
.96272
.91774
.96495
.92248
.96712 .92708
.96921 .93155
20
44 41
.96046
.91297
.96276
.91782
.96499
.92255
.96715 .92715
.96924 ! .93162
16
48 42
9.96049
0.91305
9.96280 0.91790
9.96503
0.92263
9.96719 0.92723
9.96928 0.93170
12
52 44
.96053
.91313
.96283 .91798
.96506
.92271
.96722 .92731
.96931
.93177
8
56 44
9.96057
0.91321
9.96287 0.91806
9.96510
0.92279
9.96726 0.92738
9.96934 0.93184
4
14*
17*
14* 15m
14*
gm
14* 5m
14* lm
s '
gh 4sm
145°
gh 47m 146°
Qh t5./^
147°
gh 55 m 148°
gh 59m 149°
s
0 45
9.96061
0.91329
9.96291 0.91814
9.96514
0.92286
9.96729 0.92746
9.96938 0.93192
60
4 46
.96065
.91338
.96295 .91822
.96517
.92294
.96733 .92753
.96941 .93199
56
5 47
.96069
.91346
.96299
.91830
.96521
.92302
.96736 .92761
.96945 .93206
52
12 48
.96073
.91354
.96302
.91838
.96525
.92310
.96740 .92768
.96948 .93214
48
16 49
9.96077
0.91362
9.96306 ! 0.91846
9.96528
0.92317
9.96743 0.92776
9.96951 0.93221
44
20 50
.96081
.91370
.96310
.91854
.96532
.92325
.96747 .92783
.969*5 .93228
40
24 51
.96084
.91379
.96314
.91862
.96536
.92333
.96750 .92791
.96958 .93236
36
28 52
.96088
.91387
.96317
.91870
.96539
.92341
.96754 .92798
.96962 .93243
32
52 53
9.96092
0.91395
9.96321
0.91878
9.96543
0.92348
9.96758 0.92S06
9.96965 0.93250
28
36 54
.96096
.91403
.96325
.91886
.96-547
.92356
.98761 .92813
.96968 .93258
24
40 55
.96100
.91411
.96329
.91894
.96550
.92364
.96765 .92821
.96972 .93265
to
44 56
.96104
.91419
.96332 .91902
.96554
.92372
.96768 .92S2S
.96975 .93272
16
48 57
9.96108
0.91427
9.96336
0.91910
9.96557
0.92379
9.96772 0.92836
9.96979 0.93279
12
52 58
.96112
.91436
.96340
.91918
.96561
.92387
.96775 .92843
.969*
.93287
8
50 59
.96115
.91444
.96344
.91926
.96565
.92394
.96779 .92,851
.96985
.93294
4
60 60
9.96119
0.91452
9.96347
0.91934
9.96568
0.92402
9.96782 0.92858
9.96989 0.93301
0
14h iQm
14* 12m
14* 8m
I4h4m
14*0">
Page 916] TABLE 45.
Haversines.
ion Om 150°
wn 4m 151°
10h 8m 153°
ion 12m 153°
ion ism 154°
s '
Log. Ilav.
Nat. Hav.
Los. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
s
0 0
9.96989
0.93301
9.97188
0.93731
9.97381
0.94147
9.97566
0.94550
9.97745
0.94940
60
4 1
.96992
.93309
.97192
.93738
.97384
.94154
.97569
.95557
.97748
.94946
56
8 2
.96996
.93316
.97195
.93745
.97387
.94161
.97572
.94564
.97751
.94953
52
12 3
.96999
.93333
.97198
.93753
.97390
.94168
.97575
.94570
.97754
.94959
48
16 4
9.97002
0.93330
9.97201
0.93759
9.97393
0.94175
9.97578
0.94577
9.97756
0.94965
44
20 5
.97006
.93338
.97205
.93766
.97397
.94181
.97581
.94583
.97759
.94973
40
24 6
.97009
.93345
.97208
.93773
.97400
.94188
.97584
.94590
.97762
.9.4978
36
28 7
.97012
.93353
.97211
.93780
.97403
.94195
.97587
.94596
.97765
.94984
32
82 8
9.97016
0.93359
9.97214
0.93787
9.97406
0.94303
9.97591
0.94603
9.97768
0.94991
28
36 9
.97019
.93367
.97218
.93794
.97409
.94309
.97594
.94610
.97771
.94997
24
40 10
.97022
.93374
.97221
.93801
.97412
.94315
.97597
.94616
.97774
.95003
20
44 11
.97026
.93381
.97224
.93808
.97415
.94333
.97600
.94633
.97777
.95010
16
45 13
9.97029
0.93388
9.97227
0.93815
9.97418
0.94339
9.97603
0.94639
9.97780
0.95016
12
52 13
.97033
.93395
.97231
.93833
.97422
.94336
.97606
.94636
.97783
.95033
8
56 14
9.97036
0.93403
9.97234
0.93839
9.97425
0.94343
9.97609
0.94643
9.97785
0.95039
4
13n 59m
13h 55m
13n sim
isn 47m
isn 4sm
s '
ion im 150°
ion 5m 151°
10h gm 152°
ion ism 153°
Wn 17m 154°
s
0 15
9.97039
0.93410
9.97237 i 0.93836
9.97428
0.94349
9.97612
0.94649
9.97788 0.95035
60
4 16
.97043
.93417
.97240
.93843
.97431
.94356
.97615
.94655
.97791
.95041
56
5 17
.97046
.93434
.97244
.93850
.97434
.94363
.97618
.94663
.97794
.95048
52
12 18
.97049
.93433
.97247
.93857
.97437
.94370
.97621
.94669
.97797
.95054
48
76 19
9.97052
093439
9.97250
0.93864
9.97440
0.94376
9.97624
0.94675
9.97800
0.950GO
44
20 30
.97056
.93446
.97253
.93871
.97443
.94383
.97627
.94683
.97803
.95066
40
24 31
.97059
.93453
.97257
.93878
.97447
.94390
.97630
.94688
.97806
.95073
36
25 33
.97063
.93460
.97260
.93885
.97450
.94397
.97633
.94695
.97808
.95079
32
32 33
9.97066
0.93468
9.97263
0.93893
9.97453
0.94303
9.97636
0.94701
9.97811
0.95085
28
36 34
.97069
.93475
.97266
.93899
.97456
.94310
.97639
.94708
.97814
.95093
24
40 35
.97073
.93483
.97269
.93906
.97459
.94317
.97642
.94714
.97817
.95098
20
44 36
.97076
.93489
.97273
.93913
.97462
.94334
.97645
.94731
.97820
.95104
16
4S 37
9.97079
0.93496
9.97276
0.93930
9.97465
0.94330
9.97647
0.94737
9.97823
0.95111
12
52 38
.97083
.93503
.97279
.93937
.97468
.94337
. .97650
.94734
.97826
.95117
8
56 39
9.97086
0.93511
9.97282
093934
9.97471 0.94344
9.97653
0.94740
9.97829
0.95133
4
13n ngm
13h 54m
13n 5Qm
isn 46^
isn 42m
s '
ion 2™ 150°
ion 6™ 151°
ion IQm 153°
ion um 153°
ion ism 154°
s
0 30
9.97089
0.93518
9.97285
0.93941
9.97474
0.94351
9.97656
0.94747
9.97831
0.95139
60
4 31
.97093
.93535
.97289
.93948
.97478
.94357
.97659
.94753
.97834
.95136
56
8 33
.97096
.93533
.97292
.93955
.97481
.94364
.97662
.94760
.97837
.95143
52
72 33
.97099
.93539
.97295
.93963
.97484
.94371
.97665
.94766
.97840
.95148
48
76 34
9.97103
0.93546
9.97298
0.93969
9.97487
0.94377
9.97668
0.94773
9.97843
0.95154
44
20 35
.97106
.93554
.97301
.93976
.97490
.94384
.97671
.94779
.97846
.95161
40
24 36
.97109
.93561
.97305
.93983
.97493
.94391
.97674
.94786
.97849
.95167
36
28 37
.97113
.93568
.97308
.93989
.97496
.94397
.97677
.94793
.97851
.95173
32
A? 38
9.97116
0.93575
9.97311
0.93996
9.97499
U»tf Trill*
9.97680
0.94799
9.97854
0.95179
28
36 39
.97119
.93583
.97314
.94003
.97502
.94411
.97683
.94805
.97857
.95185
24
40 40
.97123
.93589
.97317
.94010
.97505
.94418
.97686
.94811
.97860
.95193
20
44 41
.97126
.93596
.97321
.94017
.97508
.94434
.97689
.94818
.97863
.95198
16
48 43
9.97129
0.93603
9.97324
0.94034
9.97511
0.94431
9.97692
0.94834
9.97866
0.95304
12
52 43
.97132
.93611
.97327
.94031
.97514
.94438
.97695
.94831
.97868
.95310
8
56 44
9.97136
0.93618
9.97330
0.94038
9.97518
0.94444
9.97698
0.94837
9.97871
0.95317
4
13n 57m
13h 53m
13n 49™
l$n 45m
isn 4im
s '
ion B™ 150°
IQh 7m 151°
ion lim 153°
ion um 153°
10n 19m 1540
s
0 45
9.97139
0.93635
9.97333
0.94045
9.97521
0.94451
9.97701
0.94844
9.97874
0.95333
60
4 46
.97142
.93633
.97337
.94051
.97524
.94458
.97704
.94850
.97877
.95339
56
5 47
.97146
.93639
.97340
.94058
.97527
.94464
.97707
.94857
.97880
.95335
52
72 48
.97149
.93646
.97343
.94065
.97530
.94471
.97710
.94863
.97883
.95341
48
16 49
9.97152
0.93653
9.97346
0.94073
9.97533
0.94477
9.97713
0.94869
9.97885
0.95348
44
20 50
.97156
.93660
.97349
.94079
.97536
.94484
.97716
.94876
.97888
.95354
•40
24 51
.97159
.93667
.97352
.94086
.97539
.94491
.97718
.94883
.97891
.95360
36
28 53
.97162
.93674
.97356
.94093
.97542
.94497
.97721
.94889
.97894
.95366
32
52 53
9.97165
0.93683
9.97359
0.94099
9.97545
0.94504
9.97724
0.94895
9.97897
0.95373
28
36 54
.97169
.93689
.97362
.94106
.97548
.94511
.97727
.94901
.97899
.95378
24
40 55
.97172
.93696
.97365
.94113
.97551
.94517
.97730
.94908
.97902
.95385
20
44 56
.97175
.93703
.97368
.94130
.97554
.94534
.97733
.94914
.97905
.95391
16
48 57
9.97179
0.93710
9.97371
0.94137
9.97557
0.94531
9.97736
0.94931
9.97908
0.95397
12
52 58
.97182
.93717
.97575
.94134
.97560
.94537
.97739
.94937
.97911
.95303
8
56 59
.97185
.93734
.97378
.94141
.97563
.94544
.97742
.94933
.97914
.95309
4
60 60
9.97188
0.93731
9.97381
0.94147
9.97566
0.94550
9.97745
0.94940
9.97916
0.95315
0
13n 56m
13U 52m
isn 48m
13n 44m
isn 4om
TABLE 45. [Page 917
Haversines.
10^ 20"» 155°
10* 24m 156°-
10* 2Sm 157°
10* 32m 158°
10* 36m 159°
s
Log. Ilav. Nat. Hav
Log. Hav. Nat. Hav
Log. Hav
Nat. llo\
Log. Hav.
Log. Hav. Nat. Hav
s
o a
9.97916
0.95315
9.98081 0.95677
9.98239
0.96025
9.98389
0.96359
9.98533 0.96679
60
4 1
.97919
.95322
.98084 .95683
.98241
.96031
.98392
.96365
.98536 .96684
56
8 2
.97922
.95328
.98086 .95689
.98244
.96037
.98394
.96370
.98538 .96689
52
12 3
.97925
.95334
.98089 .95695
.98246
.96042
.98397
.96376
.98540 .96695
48
16 4
9.97927
0.95340
9.98092 0.95701
9.98249
0.96048
9.98399
0.96381
9.98543 0.96700
44
20 5
.97930
.95346
.98094 ; .95707
.98251
.96054
.98402
.96386
.98545 | .96705
40
24 6
.97933 .95352
.98097 .95713
.98254
.96059
.98404
.96392
.98547 1 .96710
36
23 7
.97936 .95358
.98100! .95719
.98256
.96065
.98406
.96397
.98550
.96715
..'.'
32 8
9.97939 0.95364
9.98102 0.95724
9.9S259
0.96071
9.98409
0.96403
9.98552
0.96721
28
J6 9
.97941 .95371
.98105 .95730
.98262
.96076
.98411
.96408
.98554
.96726
24
40 10
.97944 .95377
.98108 .95736
.98264
.96082
.98414
.96413
.98557
.96731
20
44 11
.97947 .95383
.98110
.95742
.98267
.96088
.98416
.96419
.98559
.96736
16
48 12
9.97950 0.95389
9.98113
0.95748
9.98269
0.96093
9.98419
0.96424
9.98561
0.96741
12
52 13
.97953 .95395
.98116
.95754
.98272
.96099
.98421
.96430
.98564
.96746
S
56 14
9.97955 0.95401
9.98118
0.95760
9.98274
0.96104
9.98424
0.96435
9.98566
0.96752
4
IS* 39™
13* 35m
13*
3im
13* 27m
13* 23m
s '
10* 2im 155°
10* 25m I5(j°
10* 29m 157°
10* 33m 158°
10* 37m 159°
s
0 15
9.97958
0.95407
9.98121
0.95766
9.98277
0.96110
9.98426
0.96440
9.98568
0.96757
60
4 16
.97961
.95413
.98124
.95771
.98279
.96116
.98428
.96446
.98570
.96762
56
£ 17
.97964
.95419
.98126
.95777
.98282
.96121
.98431
.96451
.98573
.96767
52
1? 18
.97966
.95425
.98129
.95783
.98285
.96127
.98433
.96457
.98575
.96772
48
16 19
9.97969
0.95431
9.98132
0.95789
9.98287
0.96133
9.98436
0.96462
9.98577
0.96777
44
20 20
.97972
.95438
.98134
.95795
.98290
.96138
.98438
.96467
.98580
.96782
40
24 21
.97975
.95444
.98137
.95801
.98292
.96144
.98440
.96473
.98582
.96788
36
2S 22
.97977
.95450
.98139
.95806
.98295
.96149
.98443
.96478
.98584
.96793
32
52 23
9.97980
0.95456
9.98142
0.95812
9.98297
0.96155
9.98455
0.96483
9.98587
0.96798
28
36 24
.97983
.95462
.98145
.95818
.98300
.96161
.98448
.96489
.98589
.96803
24
40 25
.97986
.95468
.98147
.95824
.98302
.96166
.98450
.96494
.98591
.96808
20
44 26
.97988
.95474
.98150
.95830
.98305
.96172
.98453
.96500
.98593
.96813
16
48 27
9.97991
0.95480
9.98153
0.95836
9.98307
0.96177
9.98455
0.96505
9.98596
0.96818
12
52 28
.97994
.95486
.98155
.95841
.98310
.96183
.98457
.96510
.98598
.96823
8
56 29
9.97997
0.95492
9.98158
0.95847
9.98312
0.96188
9.98460
0.96516
9.98600
0.96829
4
IS* 38m
13* 34m
13* SOW-
13* 26m
13* 22™
S '
10* 22^ 155°
10* 26m 156°
10* 30m 157°
10* 34m 158°
10* 3Sm 159°
s
0 30
9.97999 i 0.95498
9.98161
0.95853
9.98315
0.96194
9.98462
0.96521
9.98603
0.96834
60
4 31
.98002 ! .95504
.98163
.95859
.98317
.96200
.98465
.96526
.98605
.96839
56
5 32
.98005 ; .95510
.98166
.95865
.98320
.96205
.98467
.96532
.98607
.96844
52
12 33
.980081 .95516
.98168
.95870
.98322
.96211
.98469
.96537
.98609
.96849
48
16 34
9.9801*0 ; 0.95522
9.98171
0.95876
9.98325
0.96216
9.98472
0.96542
9.98612
0.96854
44
20 35
.98013 ! .95528
.98174
.95882
.98327
.96222
.98474
.96547
.98614
.96859
40
24 36
.98016 ! .95534
.98176
.95888
.98330
.96227
.98476
.96553
.98616
.96864
36
£S 37
.98019 ! .95540
.98179
.95894
.98332
.96223
.98479 ! .96558
.98619
.96869
32
32 38
9.98021 0.95546
9.98182
0.95899
9.98335
0.96238
9.98481 1 0.96563
9.98621 0.96874
28
56 39
.98024' .95552
.98184 ! .95905
.98337
.96244
.98484 ; .96569
.98623 .96879
24
40 40
.98027 .95558
.98187 .95911
.98340
.96249
.98486 i .96574
.98625
.96884
20
44 41
.98030 .95564
.98189 .95917
.98342
.96255
.98488 : .96579
.98628
.96889
16
45 42
9.98032 0.95570
9.98192 0.95922
9.98345
0.96260
9.98491 0.96585
9.98630
0.96894
It
52 43
.98035 ' .95576
.981951 .95928
.98347
.96266
.98493 .96590
.98632
.96899
8
56 44
9.98038 ; 0.95582
9.98197 , 0.95934
9.98350
0.96272
9.98496 0.96595
9.98634
0.96905
4
13* 37m
13* 33m
13*
29m
13* 25m
IS* 2im
s '
10h23™> 155°
10* 27m 156°
10* Sim - 157°
10* 35m 158°
10* 39m 159°
s
0 45
9.98040
0.95588
9.98200 0.95940
9.98352
0.96277
9.98498
0.96600
9.98637 0.96910
60
4 46
.98043
.95594
.98202 .95945
.98355
.96283
.98500
.96606
.98639
.96915
56
8 47
.98046
.95600
.98205 .95951
.98357
.96288
.98503
.96611
.98641
.96920
52
15 48
.98049
.95606
.98208 .95957
.98360
.96294
.98505
.96616
.98643
.96925
48
16 49
9.98051
0.9561?
9.98210 0.95962
9.98362
0.96299
9.98507
0.96621
9.98646
0.96930
44
20 50
.98054
.95618
.98213 .95968
.98365
.96305
.98510
.96627
.98648 .96935
40
24 51
.98057
.95624
.98215 .95974
.98367
.96310
.98512
.96632
.98650
.96940
36
28 52
.98059
.95630
.98218 .95980
.98370
.96315
.98514
.96637
.98652
.96945
32
&? 53
9.98062
0.95636
9.98221 0.95985
9.98372
0.96321
9.98517
0.96642
9.98655
0.96950
28
36 54
.98065
.95642
.98223 .95991
.98375
.96376
.98519 .96648
.98657
.96955
24
4<5 55
.98067
.95648
.98226 .95997
.98377
.96332
.98521
.96653
.98659
.96960
20
44 56
.98070
.95654
.98228 .96002
.98379
.96337
.98524 .96658
.98661
.96965
16
48 57
9.98073
0.95660
9.98231 - 0.96008
9.98382
0.96343
9.98526 0.96663
9.98664
0.96970
12
52 58
.98076
.95665
.98233 .96014
.98384
.96348
.98529 .96669
.98666
.96975
8
56 59
.98078
.95671
.98236 .96020
.98387
.96354
.98531 .96674
.98668
.96980
4
60 60
9.98081
0.95677
9.98239 0.96025
9.98389
0.96359
9.98533 0.96679
9.98670
0.96985
0
13 * S&n
13* 32m
13*
28m
13* 24™
13*20m
Page 918] TABLE 45.
Haversines.
10ft 40« 160°
10ft 44™ 161°
10ft 45>« 162°
10ft 52m 163°
10ft 56m 164°
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. ITav.
Log. Ilav. Nat. Hav.
Log. Hav. i Nat. Hav.
Log. Hav.
Nat. Hav.
8
0 0
9.98670
0.96985
9.98801
0.97276
9.98924 0.97553
9.99041
0.97815
9.99151
0.98063
60
4 1
.98673
.96990
.98803
.97281
.98926 .97557
.99043
.97819
.99152
.98067
56
8 2
.98675
.96995
.98805
.97285
.98928 1 .97562
.99044
.97824
.99154
.98071
52
12 3
.98677
.97000
.98807
.97290
.98930
.97566
.99046
.97828
.99156
.98075
48
16 4:
9.98679
0.97005
9.98809
0.97295
9.98932
0.97571
9.99048
0.97832
9.99158
0.98079
44
20 5
.98681
.97009
.98811
.97300
.98934
.97575
.99050
.97836
.99159
.98083
40
24 6
.98684
.97014
.98813
.97304
.98936
.97580
.99052
.97841
.99161
.98087
36
28 7
.98686
.97019
.98815
.97309
.98938
.97584
.99054
.97845
.99163
.98091
32
32 8
9.98688
0.97024
9.98817
0.97314
9.98940
0.97589
9.99056
0.97849
9.99165
0.98095
28
36 9
.98690
.97029
.98819
.97318
.98942
.97593
.99058
.97853
.99166
.98099
24
40 10
.98692
.97034
.98822
.97323
.98944
.97598
.99059
.97858
.99168
.98103
20
-44 11
.98695
.97039
.98824
.97328
.98946
.97602
.99061
.97862
.99170
.98107
16
48 12
9.98697
0.97044
9.98826
0.97332
9.98948
0.97606
9.99063
0.97866
9.99172
0.98111
12
52 13
.98699
.97049
.98828
.97337
.98950
.97611
.99065
.97870
.99173
.98115
8
5<5 14
9.98701
0.97054
9.98830
0.97342
9.98952
0.97615
9.99067
0.97874
9.99175
0.98119
4
13h wm
13h i,jm
15ft 11™
IShym
13ft 3m
s '
10^ 41™ 1GO°
10^ 4,5m !Gl°
10ft 49m 1G2°
10h 53m 1G3°
10h 5jm 184°
s
0 15
9.98703
0.97059
9.98832
0.97347
9.98954
0.97620
9.99069
0.97879
9.99177
0.98123
60
4 16
.98706
.97064
.98834
.97351
.98956
.97624
.99071
.97883
.99179
.98127
56
£ 17
.98708
.97069
.98836
.97356
.98958
.97629
.99072
.97887
.99180
.98131
52
12 18
.98710
.97074
.98838
.97361
.98960
.97633
.99074
.97891
.99182
.98135
48
16 19
9.98712
0.97078
9.98840
0.97365
9.98962
0.97637
9.99076
0.97895
9.99184
0.98139
44
20 20
.98714
.97083
.98842
.97370
.98964
.97642
.99078
.97899
.99186
.98142
40
24 21
.98717
.97088
.98845
.97374
.98966
.97646
.99080
.97904
.99187
.98146
36
25 22
.98719
.97093
.98847
.97379
.98968
.97651
.99082
.97908
.99189
.98150
32
32 23
9.98721
0.97098
9.98849
0.97384
9.98970
0.97655
9.99084
0.97912
9.99191
0.98154
28
36 24
.98723
.97103
.98851
.97388
.98971
.97660
.99085
.97916
.99193
.98158
24
40 25
.98725
.97108
.98853
.97393
.98973
.97664
.99087
.97920
.99194
.98162
20
44 26
.98728
.97113
.98855
.97398
.98975
.97668
.99089
.97924
.99196
.98166
16
45 27
9.98730
0.97117
9.98857
0.97402
9.98977
0.97673
9.99091
0.97929
9.99198
0.98170
12
52 28
.98732
.97122
.98859
.97407
.98979
.97677
.99093
.97933
.99200
.98174
8
56 29
9.98734
0.97127
9.98861
0.97412
9.98981
0.97681
9.99095
0.97937
9.99201
0.98178
4
13h igm
13h 14m
15ft 10"*
13 ft 6m
13h %m
s '
10ft 42™ 160°
10^ 46m 161°
10^ 50m 162°
10^ 54™ 163°
10ft 58m 164°
s
0 30
9.98736 0.97132
9.98863
0.97416
9.98983
0.97686
9.99096
0.97941
9.99203
0.98182
60
4 31
.98738 .97137
.98865
.97421
.98985
.97690
.99098
.97945
.99205
.98185
56
5 32
.98741 .97142
.98867
.97425
.98987
.97695
.99100
.97949
.99206
.98189
52
12 33
.98743 .97147
.98869
.97430
.98989
.97699
.99102
.97953
.99208
.98193
48
16 34
9.98745 0.97151
9.98871
0.97435
9.98991
0.97703
9.99104
0.97957
9.99210
0.98197
44
20 35
.98747 .97156
.98873
.97439
.98993
.97708
.99106
.97962
.99212
.98201
40
24 36
.98749 .97161
.98875
.97444
.98995
.97712
.99107
.97966
.99213
.98205
36
25 37
.98751 .97166
.98877
.97448
.98997
.97716
.99109
.97970
.99215
.98209
32
32 38
9.98754 0.97171
9.98880
0.97453
9.98999
0.97721
9.99111
0.97974
9.99217
0.98212
28
56 39
.98756 .97176
.98882
.97458
.99001
.97725
.99113
.97978
.99218
.98216
24
40 40
.98758 .97180
.98884
.97462
.99003
.97729
.99115
.97982
.99220
.98220
20
44 41
.98760 .97185
.98886
.97467
.99004
.97734
.99116
.97986
.99222
.98224
16
45 42
9.98762 0.97190
9.98888
0.97471
9.99006
0.97738
9.99118
0.97990
9.99223
0.98228
12
52 43
.98764 .97195
.98890
.97476
.99008
.97742
.99120
.97994
.99225
.98232
8
,56 44
9.98766 0.97200
9.98892
0.97480
9.99010
0.97747
9.99122
0.97998
9.99227
0.98236
4
13h ijm
15ft 13m
15ft 9m
15ft 5m
15ft lm
s '
10ft 43m 160°
10ft 47m 161°
10ft 5im 162°
10h 55m 163°
10ft 59m 104°
s
0 45
9.98769
0.97204
9.98894
0.97485
9.99012
0.97751
9.99124
0.98002
9.99229
0.98239
60
4 46
.98771
.97209
.98896
.97490
.99014
.97755
.99126
.98007
.99230
.98243
56
5 47
.98773
.97214
.98898
.97494
.99016
.97760
.99127
.98011
.99232
.98247
52
12 48
.98775
.97219
.98900 .97499
.99018
.97764
.99129
.98015
.99234
.98251
48
16 49
9.98777
0.97224
9.98902 0.97503
9.99020
0.97768
9.99131
0.98019
9.99235
0.98255
44
20 50
98779
.97228
.98904 .97508
.99022
.97773
.99133
.98023
.99237
.98258
40
24 51
.98781
.97233
.98906 .97512
.99024
.97777
.99135
.98027
.99239
.98262
36
25 52
.98784
.97238
.98908
.97517
.99026
.97781
.99136
.98031
.99240
.98266
32
32 53
9.98786
0.97243
9.98910
0.97521
9.99027
0.97785
9.99138
0.98035
9.99242
0.98270
28
36 54
.98788
.97247
.98912
.97526
.99029
.97790
.99140
.98039
.99244
.98274
24
40 55
.98790
.97252
.98914
.97530
.99031
.97794
.99142
.98043
.99245
.98277
20
44 56
.98792
.97257
.98916
.97535
.99033
.97798
.99143
.98047
.99247
.98281
16
45 57
9.98794
0.97262
9.98918
0.97539
9.99035
0.97802
9.99145
0.98051
9.99249
0.98285
12
52 58
.98796
.97266
.98920
.97544
.99037
.97807
.99147
.98055
.99250
.98289
8
56 59
.98798
.97271
.98922
.97548
.99039
.97811
.99149
.98059
.99252
.98293
4
(50 60
9.98801
0.97276
9.98924
0.97553
9.99041
0.97815
9.99151
0.98063
9.99254
0.98296
0
ISh iem
13~h 12m
IShgrn
15ft 4m
15ft Om
TABLE
45.
[Page 919
Haversines.
Hh Qm 165°
llh 4m 166°
llh gm 167°
Hh 12m 168°
11 h 16m 169°
S
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
Log. H;;v.
Nat. Hav.
s
0 0
9.99254
0.98296
9.99350
0.98515
9.99440
0.98719
9.99523
0.98907
9.99599
0.99081
60
4 1
.99255
.98300
.99352
.98518
.99441
.98722
.99524
.98910
.99600
.99084
56
8 2
.99257
.98304
.99353
.98522
.99443
.98725
.99526
.98913
.99602
.99087
.52
12 3
.99259
.98308
.99355
.98525
.99444
.98728
.99527
.98916
.99603
.99090
48
16 4
9.99260
0.98311
9.99356
0.98529
9.99446
0.98732
9.99528
0.98919
9.99604
0.99092
44
20 5
.99262
.98315
.99358
.98532
.99447
.98735
.99529
.98922
.99605
.99095
40
24 6
.99264
.98319
.99359
.98536
.99448
.98738
.99531
.98925
.99606
.99098
36
2S 7
.99265
.98323
.99361
.98539
.99450
.98741
.99532
.98928
.99608
.99101
32
#0 Q
Ox/ O
9.99267
0.98326
9.99362
0.98543
9.99451
0.98745
9.99533
0.98931
9.99609
0.99103
28
56 9
.99269
.98330
.99364
.98546
.99453
.98748
.99535
.98934
.99610
.99106
24
40 10
.99270
.98334
.99366
.98550
.99454
.98751
.99536
.98937
.99611
.99109
20
44 11
.99272
.98337
.99367
.98553
.99456
.98754
.99537
.98940
.99612
.99112
16
48 12
9.99274
0.98341
9.99369
0.98557
9.99457
0.98757
9.99539
0.98943
9.99614
0.99114
12
52 13
.99275
.98345
.99370
.98560
.99458
.98761
.99540
.98946
.99615
.99117
8
56 14
9.99277
0.98349
9.99372
0.98564
9.99460
0.98764
9.99541
0.98949
9.99616
0.99120
4
12h
59 m
12h 55m
12h Qim
12* 47m
12h 4jm
s '
llh im
165°
llh 5m
166°
llh 9m 167°
llhljm 1C8°
llh 17m 169°
s
0 15
9.99278
0.98352
9.99373
0.98567
9.99461
0.98767
9.99543
0.98952
9.99617
0.99123
60
4 16
.99280
.98356
.99375
.98571
.99463
.98770
.99544
.98955
.99618
.99125
56
8 17
.99282
.98360
.99376
.98574
.99464
.98774
.99545
.98958
.99620
.99128
52
12 18
.99283
.98363
.99378
.98577
.99465
.98777
.99546
.98961
.99621
.99131
48
16 19
9.99285
0.98367
9.99379
0.98581
9.99467
0.98780
9.99548
0.98964
9.99622
0.99133
44
20 20
.99287
.98371
.99381
.98584
.99468
.98783
.99549
.98967
.99623
.99136
40
24 21
.99288
.98374
.99382
.98588
.99470
.98786
.99550
.98970
.99624
.99139
36
28 22
.99290
.98378
.99384
.98591
.99471
.98789
.99552
.98973
.99626
.99141
32
52 23
9.99291
0.98382
9.993S5
0.98595
9.99472
0.98793
9.99553
0.98976
9.99627
0.99144
28
56 24
.99293
.98385
.99387
.98598
.99474
.98796
.99554
.98979
.99628
.99147
24
40 25
.99295
.98389
.99388
.98601
.99475
.98799
.99555
.98982
.99629
.99149
20
44 26
.99296
.98393
.99390
.98605
.99477
.98802
.99557
.98985
.99630
.99152
16
48 27
9.99298
0.98396
9.99391
0.98608
9.99478
0.98805
9.99558
0.98987
9.99631
0.99155
12
52 28
.99300
.98400
.99393
.98811
.99479
.98809
.99559
.98990
.99633
.99157
8
56 29
9.99301
0.98404
9.99394
0.98615
9.99481
0.98812
9.99561
0.989C3
9.99634
0.99160
4
12h 5Sm
l-2h
54m
12h join
12 h 4Qm
12h
42m
s '
llh 2m
165°
llh Qm 166°
llh iom 167°
Hh 14m 168°
llh ism 169°
s
0 30
9.99303
0.98407
9.99396
0.98619
9.99482
0.98815
9.99562
0.98996
9.99635
0.99163
60
4 31
.99304
.98411
.99397
.98622
.99484
.98818
.99563
.98999
.99636
.99165
56
8 32
.99306
.98415
.99399
.98625
.99485
.98821
.99564
.99002
.99637
.99168
52
12 33
.99308
.98418
.99400
.98629
.99486
.98824
.99566
.99005
.99638
.99171
48
16 34
9.99309
0.98422
9.99402
0.98632
9.99488
0.98827
9.99567 0.99008
9.99639
0.99173
44
20 35
.99311
.98426
.99403
.98635
.99489
.98830
.99568
.99011
.99641
.99176
40
24 36
.99312
.98429
.99405
.98639
.99490
.98834
.99569
.99014
.99642
.99179
36
28 37
.99314
.98433
.99406
.98642
.99492
.98837
.99571
.99016
.99643
.99181
32
52 38
9.99316
0.98436
9.99408
0.98646
9.99493
0.98840
9.99572
0.99019
9.99644
0.99184
28
56 39
.99317
.98440
.99409
.98649
.99495
.98843
.99573 .99022
.99645
.99186
U
40 40
.99319
.98444
.99411
.98652
.99496
.98846
.99575
.99025
.99646
.99189
20
44 41
.99320
.98447
.99412
.98656
.99497
.98849
.99576 .99028
.99648
.99192
16
48 42
9.99322
0.98451
9.99414
0.98659
9.99499
0.98852
9.99577 0.99031
9.99649
0.99194
12
52 43
.99324
.98454
.99415
.98662
.99500
.98855
.99578
.99034
.99650
.99197
8
56 44
9.99325
0.98458
9.99417
0.98666
9.99501
0.98858
9.99580
0.99036
9.99651
0.99199
4
12h 5Jm
12*
53 m
12h 49m
12 h 4o>»
12h 4im
s '
llh gm 165°
llh 7m
166°
llh nm 167°
llh 15m 168°
llh 19m 1G9°
s
0 45
9.99327
0.98462
9.99418
0.98669
9.99503
0.98862
9.99581 0.99039
9.99652
0.99202
60
4 46
.99328
.98465
.99420
.98672
.99504
.98865
.99582 .99042
.99653
.99205
56
5 47
.99330
.98469
.99421
.98676
.99505
.98868
.99583 .99045
.99654
.99207
52
12 48
.99331
.98472
.99422
.98679
.99507
.98871
.99584 .99048
.99655
.99210
48
16 49
9.99333
0.98476
9.99424
0.98682
9.99508
0.98874
9.995S6 0.99051
9.99657
0.99212
44
20 50
.99335
.98479
.99425
.98686
.99510
.98877
.99587 .99053
99658
.99215
40
24 51
.99336
.98483
.99427
.98689
.99511
.98880
.99588 .99056
.99659
.99217
36
2<? 52
.99338
.98487
.99429
.98692
.99512
.98883
.99589 .99059
.99660
.99220
32
52 53
9.99339
0.98490
9.99430
0.98696
9.99514
0.98886
9.99591 0.99062
9.99661 '
0.99223
28
56 54
.99341
.98494
.99431
.98699
.99515
.98889
.99592 .99065
.99662
.99225
24
40 55
.99342
.98497
.99433
.98702
.99516
.98892
.99593 .990G7
.99663
.99228
20
44 56
.99344
.98501
.99434
.98705
.99518
.98895
.99594 .99070
.99664
.99230
16
48 57
9.99345
0.98504
9.99436
0.98709
9.99519
0.98898
9.99596 0.99073
9.99666
0.99233
12
52 58
.99347
.98508
.99437
.98712
.99520
.98901
.99597 .99076
.99667
.99235
8
56 59
.99349
.98511
.99438
.98715
.99522
.98904
.99598 .99079
.99668 i
.99238
4
60 60
9.99350
0.98515
9.99440
0.98719
9.99523
0.98907
9.99599 0.99081
9.99669
0.99240
0
l-2h 56m
12 h 52m
12h 4gm
12h 44m
12h 40m
Page 920] TABLE 45.
Haversines.
llhzom 170°
11*24™ 171°
11*28™ 172°
11*32™ 173°
11*36™ 174°
s '
Log. Hav.
Nat. Hav.
Log. Hav.i Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
s
0 0
9.99669
0.99240
9.99732
0.99384
9.99788
0.99513
9.99838
0.99627
9.99881
0.99726
60
4 1
.99670
.99243
.99733
.99387
.99789
.99515
.99839
.99629
.99882
.99728
56
8 2
.99671
.99245
.99734
.99389
.99790
.99517
.99839
.99631
.99882
.99729
52
12 3
.99672
.99248
.99735
.99391
.99791
.99519
.99840
.99633
.99883
.99731
48
16 4
9.99673
0.99250
9.99736
0.99393
9.99792
0.99521
9.99841
0.99634
9.99884
0.99732
44
20 5
.99674
.99253
.99737
.99396
.99793
.99523
.99842
.99636
.99884
.99734
40
24 6
.99675
.99255
.99738
.99398
.99793
.99525
.99842
.99638
.99885
.99735
36
28 7
.99677
.99258
.99739
.99400
.99794
.99527
.99843
.99640
.99885
.99737
32
32 8
9.99678
0.99260
9.99740
0.99402
9.99795
0.99529
9.99844
0.99641
9.99886
0.99738
28
86 9
.99679
.99263
.99741
.99405
.99796
.99531
.99845
.99643
.99887
.99740
24
40 10
.99680
.99265
.99742
.99407
.99797
.99533
.99845
.99645
.99887
.99741
20
44 11
.99681
.99268
.99743
.99409
.99798
.99535
.99846
.99647
.99888
.99743
16
48 12
9.99682
0.99270
9.99744
0.99411
9,99799
0.99537
9.99847
0.99648
9.99889
0.99744
12
52 13
.99683
.99273
.99745
.99414
.99800
.99539
.99848
.99650
.99889
.99746
8
56 14
9.99684
0,99275
9.99746
0.99416
9.99800
0.99541
9.99848
0.99652
9.99890
0.99747
4
12 * 39^
12* 35™
12* Si™
12* 27™
12* 23™
s '
llkgim 170°
11*25™ 171°
11*29™ 172°
11*33™ 173°
11*37™ 174°
s
0 15
9.99685
0.99278
9.99747
0.99418
9.99801
0.99543
9.99849
0.99653
9.99891
0.99748
60
4 16
.99686
.99280
.99748
.99420
.99802
.99545
.99850
.99655
.99891
.99750
56
5 17
.99687
.99283
.99748
.99422
.99803
.99547
.99851
.99657
.99892
.99751
52
12 18
.99688
.99285
.99749
.99425
.99804
.99549
.99851
.99659
.99893
.99753
*48
^6 19
9.99690
0.99288
9.99750
0.99427
9.99805
0.99551
9.99852
0.99660
9.99893
0.99754
44
20 20
.99691
.99290
.99751
.99429
.99805
.99553
.99853
.99662
.99894
.99756
40
24 21
.99692
.99293
.99752
.99431
.99806
.99555
.99854
.99664
.99894
.99757
36
25 '22
.99693
.99295
.99753
.99433
.99807
.99557
.99854
.99665
.99895
.99759
32
32 23
9.99694
0.99297
9.99754
0.99436
9.99808
0.99559
9.99855
0.99667
9.99896
0.99760
28
56 24
.99695
.99300
.99755
.99438
.99809
.99561
.99856
.99669
.99896
.99761
24
40 25
.99696
.99302
.99756
.99440
.99810
.99563
.99857
.99670
.99897
.99763
20
44 26
.99697
.99305
.99757
.99442
.99811
.99565
.99857
.99672
.99897
.99674
16
45 27
9.99698
0.99307
9.99758
0.99444
9.99811
0.99567
9.99858
0.99674
9.99898
0.99766
12
52 28
.99699
.99309
.99759
.99446
.99812
.99568
.99859
.99675
.99899
.99767
8
56 29
9.99700
0.99312
9.99760
0.99449
9.99813
0.99570
9.99859
0.99677
9.99899
0.99768
4
12 n 33™
12* 34™ •*•
- 12* SO™ •-"
12* 26™
12* 22™
s '
11*22™ 170°
11* 26™ 171°
11* SO™ > 172°
ll*.34m 173°
11*38™ 174°
s
0 30
9.99701
0.99314
9.99761
0.99451
9.99814
0.99572
9.99860
0.99679
9.99900
0.99770
60
4 31
.99702
.99317
.99762
.99453
.99815
.99574
.99861
.99680
.99901
.99771
56
8 32
.99703
.99319
.99763
.99455
.99815
.99576
.99862
.99682
.99901
.99773
52
J2 33
.99704
.99321
.99764
.99457
.99816
.99578
.99862
.99684
.99902
.99774
48
:76 34
9.99705
0.99324
9.99765
0.99459
9.99817
0.99580
9.99863
0.99685
9.99902
0.99775
44
20 35
.99706
.99326
.99766
.99461
.99818
.99582
.99864
.99687
.99903
.99777
40
24 36
.99707
.99329
.99766
.99464
.99819
.99584
.99864
.99688
.99904
.99778
36
28 37
.99708
.99331
.99767
.99466
.99820
.99585
.99865
.99690
.99904
.99780
32
32 38
9.99710
0.99333
9.99768
0.99468
9.99820
0.99587
9.99866
0.99692
9.99905
0.99781
28
36 39
.99711
.99336
.99769
.99470
.99821
.99589
.99867
.99693
.99905
.99782
24
40 40
.99712
.99338
.99770
.99472
.99822
.99591
.99867
.99695
.99906
.99784
20
44 41
.99713
.99340
.99771
.99474
.99823
.99593
.99868
.99696
.99906
.99785
16
48 42
9.99714
0.99343
9.99772
0.99476
9.99824
0.99595
9.99869
0.99698
9.99907
0.99786
12
52 43
.99715
.99345
.99773
.99478
.99824
.99597
.99869
.99700
.99908
.99788
8
56 44
9.99716
0.99347
9.99774
0.99480
9.99825
0.99598
9.99870
0.99701
9.99908
0.99789
4
12* 37m
12* 33™
12* 29™
12* 25™
12* 21™
s '
11* 23m no0
11*27™ 171°
11* Si™ 172°
11*35™ 173°
11* 39™ 174°
s
0 45
9.99717
0.99350
9.99774
0.99483
9.99826
0.99600
9.99871
0.99703
9.99909
0.99790
60
4 46
.99718
.99352
.99775
.99485
.99827
.99602
.99871
.99704
.99909
.99792
56
5 47
.99719
.99354
.99776
.99487
.99828
.99604
.99872
.99706
.99910
.99793
52
.72 48
.99720
.99357
.99777
.99489
.99828
.99606
.99873
.99708
.99911
.99794
48
16 49
9.99721
0.99359
9.99778
0.99491
9.99829
0.99608
9.99874
0.99709
9.99911
0.99796
44
20 50
.99722
.99361
.99779
.99493
.99830
.99609
.99874
.99711
.99912
.99797
40
24 51
.99723
.99364
.99780
.99495
.99831
.99611
.99875
.99712
.99912
.99798
36
28 52
.99724
.99366
.99781
.99497
.99832
.99613
.99876
.99714
.99913
.99799
32
32 53
9.99725
0.99368
9.99782
0.99499
9.99832
0.99615
9.99876
0.99715
9.99913
0.99801
28
36 54
.99726
.99371
.99783
.99501
.99833
.99617
.99877
.99717
.99914
.99802
24
40 55
.99727
.99373
.99784
.99503
.99834
.99618
.99878
.99719
.99915
.99803
20
44 56
.99728
.99375
.99785
.99505
.99835
.99620
.99878
.99720
.99915
.99805
16
48 57
9.99729
0.99378
9.99786
0.99507
9.99836
0.99622
9.99879
0.99722
9.99916
0.99806
12
52 58
.99730
.99380
.99786
.99509
.99836
.99624
.99880
.99723
.99916
.99807
8
56 59
.99731
.99382
.99787
.99511
.99837
.99626
.99880
.99725
.99917
.99808
4
60 60
9.99732
0.99384
9.99788
0.99513
9.99838
0.99627
9.99881
0.99726
9.99917
0.99810
0
12* 36™
12* 32™
12* 28™
12* 24™
12* 20™
TABLE 45.
[Page 921
Haversines.
ll*40m 175°
Hh 44m 176°
11*48™ 177°
11*52™
178°
11* 56™ 179°
s '
Log. Hav.i Nat. Hav
Log. Hav.: Nat. Hav
Log. Hav. Nat. Hav
Log. Hav
1 Nat. Hav
Log. Hav.' Nat. Hav
s
0 0
9.99917
0.99810
9.99947 0.99878
9.99970 0.99931
9.99987
0.99970
9.99997 0.99992
60
4 1
.99918
.99811
.99948 .99879
.99971 .99932
.99987
.99971
.99997 .99993
56
S 2
.99918
.99812
.99948 .99880
.99971 .99933
.99987
.99971
.99997
.99993
52
12 3
.99919
.99814
.99948
.99881
.99971
.99934
.99987
.99971
.99997
.99993
48
16 4
9.99919
0.99815
9.99949 0.99882
9.99972
0.99934
9.999S8
0.99972
9.99997
0.99994
44
20 5
.99920
.99816
.99949 .99883
.99972
.99935
.99988
.99972
.99997
.99994
40
24 6
.99921
.99817
.99950 .99884
.99972
.99936
.99988
.99973
.99997
.99994
36
28 7
.99921
.99819
.99950
.99885
.99973
.99937
.99988
.99973
.99997
.99994
32
32 8
9.99922
0.99820
9.99951 0.99886
9.99973
0.99937
9.9998S
0.99973
9.99998
0.99994
28
36 9
.99922
.99821
.99951! .99887
.99973
.99938
.99989
.99974
.99998
.99995
24
40 10
.99923
.99822
.99951 .99888
.99973
.99939
.99989
.99974
.99998
.99995
20
44' H
.99923
.99823
.99952 i .99889
.99974
.99940
.99989
.99975
.99998
.99995
16
4$ 12
9.99924
0.99825
9.99952 : 0.99890
9.99974
0.99940
9.99989
0.99975
9.99998
0.99995
12
5;? 13
.99924
.99826
.99953 i .99891
.99974
- .99941
.99989
.99976
.99998
.99995
8
56 U
9.99925
0.99827
9.99953 0.99892
9.99975
0.99942
9.99990
0.99976
9.99998
0.99996
4
•12h 19m
12* 15m
12* 11™
12* 7m
12* 31™
s '
llh 4im 175°
11*45™ 176°
11*49™ 177
11 n ojm
178°
11*57™ 179°
s
0 15
9.99925 0.99828
9.99953
0.99893
9.99975 0.99942
9.99990
0.99977
9.99998
0.99996
60
4 16
.99926; .99829
.99954
.99894
.99975 : .99943
.99990
.99977
.99998
.99996
56
8 17
.99926 .99831
.99954
.99895
.99976 ; .99944
.99990
.99978
.99998
.99996
52
1,? 18
.99927 i .99832
.99954
.99896
.99976 .99944
.99990
.99978
.99998
.99996
48
16 19
9.99927 0.99833
9.99955
0.99S97
9.99976 0.99945
9.99991
0.99978
9.99998
0.99996
44
26> 20
.99928 .99834
.99955
.99898
.99976 .99946
.99991
.99979
.99999
.99997
40
34 21
.99928 .99835
.99956
.99899
.99977 .99947
.99991
.99979
.99999
.99997
36
2S 22
.99929 .99837
.99956
.99900
.99977 .99947
.99991
.99980
.99999
.99997
32
32 23
9.99929 0.99838
9.99957
0.99900
9.99977 0.99948
9.99991
0.99980
9.99999
0.99997
28
36 24
.999301 .99839
.99957
.99901
.99978 .99949
.99992
! .99981
.99999
.99997
24
4<? 25
.99931
.99840
.99958
.99902
.99978 .99949
.99992
.99981
.99999
.99997
20
44 26
.99931
.99841
.99958
.99903
.99978 .99950
.99992
.99981
.99999
.99998
16
48 27
9.99932
0.99842
9.99958
0.99904
9.99978 0.99950
9.99992
0.99982
9.99999
0.99998
12
52 28
.99932
.99844
.99959
.99905
.99979 i .99951
.99992
.99982
.99999
.99998
8
56 29
9.99933
0.99845
9.99959
0.99906
9.99979 1 0.99952
9.99992
0.999S2
9.99999
0.99998
4
12h is™
12* i4m
12* 10™
12* 6™
12* 2m
s '
llh 42m 175°
llh 46m 176°
11* 50™ 177°
11* 54m
178°
11* 58™ 179°
s
0 30
9.99933
0.99846
9.99959 0.99907
9.99979 0.99952
9.99993
0.99983
9.99999 0.99998
60
4 31
.99934
.99847
.99960 .99908
.99980 .99953
.99993
.99983
.99999
.99998
56
* 32
.99934
.99848
.99960 .99909
.99980 .99954
.99993
.99984
.99999
.99998
52
12 33
.99935
.99849
.99961 .99909
.99980
.99954
.99993
.99984
.99999
.99998
48
26 34
9.99935
0.99850
9.99961 0.99910
9.99980
0.99955
9.99993
0.99984
9.99999
0.99999
44
£0 35
.99935
.99851
.99961 .99911
.99981
.99956
.99993
.99985
.99999
.99999
40
24 36
.99936
.99853
.99962 .99912
.99981
.99956
.99994
.99985
9.99999
.99999
36
£«? 37
.99936
.99854
.99962 .99913
.99981
.99957
.99994
.99985
0.00000
.99999
32
32 38
9.99937
0.99855
9.99963 0.99914
9.99981
0.99957
9.99994
0.99986
0.00000
0.99999
28
36 39
.99937
.99856
.99963 .99915
.99982 .99958
.99994
.99986
.00000
.99999
24
40 40
.99938
.99857
.99963 .99915
.99982! .99959
.99994
.99986
.00000
.99999
20
44 41
.99938
.99858
.99964 .99916
.99982; .99959
.99994
.99987
.00000
.99999
16
48 42
9.99939
0.99859
9.99964 0.99917
9.99983 0.99960
9.99994
0.99987
0.00000
0.99999
12
52 43
.99939
.99860
.99964 .99918
.99983 .99960
.99995
.99987
.00000
.99999
8
56 44
9.99940
0.99861
9.99965 0.99919
9.99983
0.99961
9.99995
0.99988
0.00000
0.99999
4
12* 17™
12h 13™
12* 9™
12* 5m
12* 1™
s '
llh 43m 175°
llh 47m 176°
llh sim 177°
11*55™
178°
11*59™ 179°
s
0 45
9.99940
0.99863
9.99965
0.99920
9.99983 0.99961
9.99995
0.99988
0.00000 I 1.00000
60
4 46
.99941
.99864
.99965
.99920
.99983 .99962
.99995
.99988
.00000 .00000
56
S 47
.99941
.99865
.99966
.99921
.99984
.99963
.99995
.99989
.00000 .00000
52
12 48
.99942
.99866
.99966
.99922
.99984
.99963
.99995
.99989
.00000
.00000
48
16 49
9.99942
0.99867
9.99966
0.99923
9.99984 0.99964
9.99995
0.99989
0.00000
1.00000
44
20 50
.99943
.99868
.99967
.99924
.99984
.99964
.99996
.99990
.00000
.00000
40
?4 51
.99943 .99869
.99967
.99924
.99985
.99965
.99996
.99990
.00000
.00000
36
98 52
.99943 .99870
.99968
.99925
.99985 .99965
.99996
.99990
.00000
.00000
32
«?;? 53
9.99944
0.99871
9.99968
0.99926
9.999S5 0.99966
9.99996
0.99991
0.00000
1.00000
2S
06 54
.99944 .99872
.99968
.99927
.99985
.99960
.99996
.99991
.00000 ! .00000
24
40 55
.99945 .99873
.99969
.99928
.99986
.99967
.99996
.99991
.00000 ! .00000
20
44 56
.99945 .99874
.99969
.99928
.99986
.99967
.99996
.99991
.00000 ! .00000
16
43 57
9.99946 0.99875
9.99969
0.99929
9.99986
0.99968
9.99996
0.99992
0.00000 i 1.00000
12
52 58
.99946 .99876
.99970
.99930
.99986
.99969
.99996
.99992
.00000
.00000
8
56 59
.99947
.99877
.99970
.99931
.99987
.99969
.99997
.99992
.00000 .00000
4
60 60
9.99947 0.99878
9.99970
0.99931
9.99987 i 0.99970
9.99997
0.99992
0.00000 1.00000
0
12h 16™
j£h 12m
12* Sm
12*
4m
12*0™
61828°— 16 51
Page 922] TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude.
HEIGHT OF THE EYE.
8 Feet.
9 Feet.
10 Feet.
11 Feet.
12 Feet.
13 Feet.
OBS. ALT.
O
*
O
*
O
*
O
*
O
*
O
*
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
o t
6 30
5 29
10 40
5 19
10 50
5 09
11 00
5 00
11 09
4 51
11 18
4 43
11 26
40
5 39
10 30
5 29
10 40
5 19
10 50
5 10
10 59
5 01
11 08
4 53
11 16
50
5 49
10 20
5 39
10 30
5 29
10 40
5 20
10 49
5 11
10 58
5 03
11 06
7 00
5 59
10 10
5 49
10 20
5 39
10 30
5 30
10 39
5 21
10 48
5 13
10 56
10
6 08
10 01
5 58
10 11
5 48
10 21
5 39
10 30
5 30
10 39
5 22
10 47
20
6 17
9 52
6 07
10 02
5 57
10 12
5 48
10 21
5 39
10 30
5 31
10 38
7 30
6 26
9 43
6 16
9 53
6 06
10 03
5 57
10 12
5 48
10 21
5 40
10 29
40
6 34
9 35
6 24
9 45
6 14
9 55
6 05
10 04
5 56
10 13
5 48
10 21
50
6 42
9 27
6 32
9 37
6 22
9 47
6 13
9 56
6 04
10 05
5 56
10 13
8 00
6 50
9 19
6 40
9 29
6 30
9 39
6 21
9 48
6 12
9 57
6 04
10 05
10
6 57
9 12
6 47
9 22
6 37
9 32
6 28
9 41
6 19
9 50
6 11
9 58
20
7 04
9 05
6 54
9 15
6 44
9 25
6 35
9 34
6 26
9 43
6 18
9 51
8 30
7 11
8 58
7 01
9 08
6 51
9 18
6 42
9 27
6 33
9 36
6 25
9 44
40
7 18
8 51
7 08
9 01
6 58
9 11
6 49
9 20
6 40
9 29
6 32
9 37
50
7 24
8 45
7 14
8 55
7 04
9 05
6 55
9 14
6 46
9 23
6 38
9 31
9 00
7 30
8 39
7 20
8 49
7 10
8 59
7 01
9 08
6 52-
9 17
6 44
9 25
20
7 42
8 27
7 32
8 37
7 22
8 47
7 13
8 56
7 04
9 05
6 56
9 13
40
7 53
8 16
7 43
8 26
7 33
8 36
7 24
8 45
7 15
8 54
7 07
9 02
10 00
8 04
8 05
7 54
8 15
7 44
8 /"^
7 35
8 34
7 26
8 43
7 18
8 51
20
8 14
7 55
8 04
8 05
7 54
8 15
7 45
8 24
7 36
8 33
7 28
8 41
40
8 23
7 46
8 13
7 56
8 03
8 06
7 54
8 15
7 45
8 24
7 37
8 32
11 00
8 32
7 37
8 22
7 47
8 12
7 57
8 03
8 06
7 54
8 15
7 46
8 23
30
8 44
7 25
8 34
7 35
8 24
7 45
8 15
7 54
8 06
8 03
7 58
8 11
12 00
8 55
7 14
' 8 45
7 24
8 35
7 34
8 26
7 43
8 17
7 52
8 09
8 00
30
9 06
7 03
8 56
7 13
8 46
7 23
8 37
7 32
8 28
7 41
8 20
7 49
13 00
9 16
6 53
9 06
7 03
8 56
7 13
8 47
7 22
8 38
7 31
8 30
7 39
30
9 25
6 44
9 15
6 54
9 05
7 04
8 56
7 13
8 47
7 22
8 39
7 30
14 00
9 33
6 36
9 23
6 46
9,13
6 56
9 04
7 05
8 55
7 14
8 47
7 22
15 00
9 49
6 20
9 39
6 30
9 29
6 40
9 20
6 49
9 11
6 58
9 03
7 06
16 00
10 02
6 07
9 52
6 17
9 42
6 27
9 33
6 36
9 24
6 45
9 16
6 53
17 00
10 15
5 54
10 05
6 04
9 55
6 14
9 46
6 23
9 37
6 32
9 29
6 40
18 00
10 25
5 44
10 15
5 54
10 05
6 04
9 56
6 13
9 47
6 22
9 39
6 30
19 00
10 35
5 34
10 25
5 44
10 15
5 54
10 06
6 03
9 57
6 12
9 49
6 20
20 00
10 43
5 25
10 33
5 35
10 23
5 45
10 14
5 54
10 05
6 03
9 57
6 11
22 00
10 59
5 09
10 49
5 19
10 39
5 29
10 30
5 38
10 21
5 47
10 13
5 55
24 00
11 12
4 56
11 02
5 06
10 52
5 16
10 43
5 25
10 34
5 34
10 26
5 42
26 00
11 23
4 45
11 13
4 55
11 03
5 05
10 54
5 14
10 45
5 23
10 37
5 31
28 00
11 33
4 35
11 23
4 45
11 13
4 55
11 04
5 04
10 55
5 13
10 47
5 21
30 00
11 41
4 27
11 31
4 37
11 21
4 47
11 12
4 56
11 03
5 05
10 55
5 13
32 00
11 49
4 19
11 39
4 29
11 29
4 39
11 20
4 48
11 11
4 57
11 03
5 05
34 00
11 56
4 12
11 46
4 22
11 36
4 32
11 27
4 41
11 18
4 50
11 10
4 58
36 00
12 02
4 06
11 52
4 16
11 42
4 26
11 33
4 35
11 24
4 44
11 16
4 52
38 00-
12 07
4 01
11 57
4 11
11 47
4 21
11 38
4 30
11 29
4 39
11 21
4 47
40 00
12 12
3 55
12 02
4 05
11 52
4 15
11 43
4 24
11 34
4 33
11 26
4 41
45 00
12 23
3 44
12 13
3 54
12 03
4 04
11 54
4 13
11 45
4 22
11 37
4 30
50 00
12 31
3 35
12 21
3 45
12 11
3 55
12 02
4 04
11 53
4 13
11 45
4 21
55 00
12 38
3 27
12 28
3 37
12 18
3 47
12 09
3 56
12 00
4 05
11 52
4 13
60 00
12 44
3 20
12 34
3 30
12 24
3 40
12 15
3 49
12 06
3 58
11 58
4 06
65 00
12 51
3 13
12 41
3 23
12 31
3 33
12 22
3 42
12 13
3 51
12 05
3 59
70 00
12 56
3 07
12 46
3 17
12 36
3 27
12 27
3 36
12 18
3 45
12 10
3 53
75 00
13 00
3 02
12 50
3 12
12 40
3 22
12 31
3 31
12 22
3 40
12 14
3 48
80 00
13 06
2 56
12 56
3 06
12 46
3 16
12 37
3 25
12 28
3 34
12 20
3 42
85 00
13 10
2 51
13 00
3 01
12 50
3 11
12 41
3 20
12 32
3 29
12 24
3 37
90 00
13 14
2 46
13 04
2 56
12 54
3 06
12 45
3 15
12 36
3 24
12 28
3 32
Day of Month. Jan.
Feb. Mar. Apr
May.
June. July. Aug.
Sept. Oct. Nov. Dec.
ADDITIONAL CORR. "
FOR SUN'S ALT. lst to 15th- . . . +18
+15 +8 0
~ 8
-13 -14 -11
_5 +3 +11 +16
16th to 31st... +17
+12 +4 -4
-11
-14 -13 - 9
-1^+7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
taking account of the variation of the Sun's semidiameter in th, different months of the year is given at the foot of the main table
TABLE 46.
[Page 923
Corrections to be Applied to the Observed Altitude of a Star or of
the Sun's
Lower Limb, to Find
the True Altitude— Continued.
HEIGHT OF THE EYE.
14 Feet.
15 Feet.
16 Feet.
17 Feet.
18 Feet.
19 Feet.
OBS. ALT.
O *
O
*
0
*
O
*
*
O
*
Sun's ; Star's
Sun's !
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr. Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
(+) (-)
(+)
(-)
(+
)
(
)
(+)
(~
}
HO
(-)
(-
h)
(-)
6 30
4 35 11 34
4 27
11 42
4 20
11 49
4 13
11
56
4 06
12 03
3
59
12 10
40
4 45 i 11 24
4 37
11 32
4 30
11 39
4 23
11
46
4 16
11 53
4
09
12 00
50
4 55 i 11 14
4 47
11 22
4 40
11 29
4 33
11
36
4 26
11 43
4
19
11 50
7 00
5 05 11 04
4 57
11 12
4 50
11 19
4 43
11
26
4 36
11 33
4
29
11 40
10
5 14 i 10 55
5 06
11 03
4 59
11 10
4 52
11
17
4 45
11 24
4
38
11 31
20
5 23 10 46
5 15
10 54
5 C
)8
11 01
5 01
11 08
4 54
11 15
4
47
11 22
7 30
5 32 10 37
5 24
10 45
5 17
10 52
5 10
10
59
5 03
11 06
4
56
11 13
40
5 40 10 29
5 32
10 37
5 25
10 44
5 18
10
51
5 11
10 58
5
04
11 05
50
5 48 10 21
5 40
10 29
5 33
10 36
5 26
10
43
5 19
10 50
5
12
10 57
8 00
5 56 10 13
5 48
10 21
5 41 10 28
5 34
10 35
5 27
10 42
5
20
10 49
10
6 03 10 06
5 55
10 14
5 48 10 21
5 41
10 28
5 34
10 35
5
27
10 42
20
6 10 9 59
6 02
10 07
5 55 10 14
5 48
10 21
5 41
10 28
5
34
10 35
8 30
6 17 9 52
6 09
10 00
6 02 10 07
5 55
10
14
5 48
10 21
5
41
10 28
40
6 24 9 45
6 16
9 53
6 09 10 00
6 02
10 07
5 55
10 14
5
4S
10 21
50
6 30 9 39
6 22
9 47
6 15 9 54
6 08
10 01
6 01
10 08
5
54
10 15
9 00
6 36 ! 9 33
6 28
9 41
6 21 9 48
6 14
9 55
6 07
10 02
6
00
10 09
20
6 48
9 21
6 40
9 29
6 33 9 36
6 26
9 43
6 19
9 50
6
12
9 57
40
6 59
9 10
6 51 !
9 18
6 44
9 25
6 37
9 32
6 30
9 39
6
23
9 46
10 00
7 10
8 59
7 02
9 07
6 55
9 14
6 48 1 9 21
6 41
9 28
6
34
9 35
20
7 20
8 49
7 12 i
8 57
7 05
9 04
6 58
9
11
6 51
9 18
6
44
9 25
40
7 29
8 40
7 21
8 48
7 14
8 55
7 07
9 02
7 00
9 09
6
53
9 16
11 00
7 38
8 31
7 30
8 39
7 23
8 46
7 16
8 53
7 09
9 00
7
02
9 07
30
7 50
8 19
7 42 i
8 27
7 35
8 34
7 28
8 41
7 21
8 48
7
14
8 55
12 00
8 01
8 08
7 53 ;
8 16
7 46
8 23
7 39
8 30
7 32
8 37
7
25
8 44
30
8 12 7 57
8 04
8 05
7 57
8 12
7 30
8
L9
7 43
8 26
7
36
8 33
13 00
8 22
7 47
8 14
7 55
8 07
8
02
8 00 8 09
7 53
8 16
,
46
8 23
30
8 31
7 38
8 23
7 46
8 1
6
7
53
8 09 8 00
8 02
8 07
-7
55
8 14
14 00
8 39
7 30
8 31 |
7 38
8 24
7
45
8jl7 7 52
3 10
7 59
8
03
8 06
15 00
8 55
7 14
847
7 22
8 40
7
29
8 33 i 7 36
8 26
7 43
8
19
7 50
16 00
9 08
7 01
9 00 |
7 09
8 53
7
16
8 46 7 23
3 39
7 30
8
32
7 37
17 00
9 21
6 48
9 13 1
6 56
9 06
7
03
8 59 | 7 10
3 52
7 17
8
45
7 24
18 00
9 31
6 38
9 23 i
6 46
9 16
6
53
9 09 7 00
9 02
7 07
8
55
7 14
19 00
9 41
6 28
9 33 !
6 36
9 26
6
43
9 19 6 50
9 12
6 57
9
05
7 04
20 00
9 49
6 19
9 41 1
6 27
9 34
6
34
9 27 6 41
I
) 20
6 48
9
13
6 55
22 00
10 05
6 03
9 57 i
6-11
9 50
6
18
9 43 | 6 25
) 36
6 32
9
29
6 39
24 00
10 18
5 50
10 10 I
5 58
10 03
6
05
9 56 6 12
9 49
6 19
9
42
6 26
26 00
10 29
5 39
10 21
5 47
10 14
5
54
10 07 6 01
10 00 i
6 08
9
53
6 15
28 00
10 39
5 29
10 31
5 37
10 24
5
44
10 17 i 5 51
10 10 i
5 58
10
03 f
6 05
30 00
10 47
5 21
10 39
5 29
10 32
5
36
10 25 i 5 43
10 18 j
5 50
10
11
5 57
32 00
10 55
5 13
10 47
5 21
10 40
5
28
10 33 ! 5 35
10 26 i
5 42
10
19
5 49
34 00
11 02
5 06
10 54
5 14
10 47
5
21
10 40 5 28
10 33 i
5 35
10
26 1
5 42
36 00
11 08
5 00
11 00
5 08
10 53
5
15
10 46 5 22
10 39
5 29
10
32
5 36
38 00
11 13
4 55
11 05
5 03
10 58
5
10
10 51 i 5
17
10 44
5 24
10
37
5 31
40 00
11 18
4 49
11 10
4 57
11 03
5
04
10 56 5 11
10 49
5 18
10
42
5 25
45 00
11 29
4 38
11 21
4 46
11 14
4
53
11 07 5 00
11 00
5 07
10
53
5 14
50 00
11 37
4 29
11 29
4 37
11 22
4
44
11 15 1 4 51
11 08
4 58
11
01
5 05
55 00
11 44
4 21
11 36
4 29
11 29
4
36
11 22 4 43
11 15 !
4 50
11
03
4 57
60 00
11 50
4 14
11 42 !
4 22
11 35
4
29
11 28 4 36
11 21
4 43
11
14
4 50
65 00
11 57
4 07
11 49 i
4 15
11 42
4
22
11 35 i 4 29
11 28 i
4 36
11
21
4 43
70 00
12 02
4 01
11 54
4 09
11 47
4
16
11 40 4 23
11 33 i
4 30
11
26
4 37
• 75 00
12 06
3 56
11 58 '•
4 04
11 51
4
11
11 44 i 4 IS
11 37 i
4 25
11
30
4 32
80 00
12 12
3 50
12 04
3 58
11 57
4
05
11 50 i 4 12
11 43 !
4 19
11
36
4 26
85 00
12 16 3 45
12 08
3 53
12 01
4
00
11 54 j 4 07
11 47 j
4 14
11
40
4 21
90 00
12 20 3 40
12 12 !
3 48
12 05
3
55
11 58 4 02
11 51 i
4 09
11
44
4 16
Day of Month.
Jan. Feb.
Mar.
Apr. May. June.
July.
Aug.
Sept. Oct.
Nov
. Dec.
ADDITIONAL CORR.
FOB SUN'S ALT. lst to 15tn . . .
. +18 +15
+8
0
-8 -
-13
-14
-11
-5 +3
+11
+16
16th fo 31st..
.+17 +12
+4
-4 -11 -14
-13
- 9
-1 +7
+14
+18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed aWtude
of the Sirn^lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as lb'. A supplementary correction
^mg account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
Page 924] TABLE 46.
Corrections to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
20 Feet.
21 Feet.
22 Feet.
23 Feet.
24 Feet.
25 Feet.
OBS. ALT.
O
*
0
*
O
*
0
*
0
*
0
*
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
6 30
3 52
12 17
3 46
12 23
3 39
12 30
3 33
12 36
3 27
12 42
3 21
12 48
40
4 .2
12 07
3 56
12 13
3 49
12 20
3 43
12 26
3 37
12 32
3 31
12 38
50
4 12
11 57
4 06
12 03
3 59
12 10
3 53
12 16
3 47
12 22
3 41
12 28
7 00
4 22
11 47
4 16
11 53
4 09
12 00
4 03
12 06
3 57
12 12
3 51
12 18
10
4 31
11 38
4 25
11 44
4 18
11 51
4 12
11 57
4 06
12 03
4 00
12 09
20
4 40
11 29
4 34
11 35
4 27
11 42
4 21
11 48
4 15
11 54
4 09
12 00
7 30
4 49
11 20
4 43
11 26
4 36
11 33
4 30
11 39
4 24
11 45
4 18
11 Si
40
4 57
11 12
4 51
11 18
4 44
11 25
4 38
11 31
4 32
11 37
4 26
ll 43
50
5 05
11 04
4 59
11 10
4 52
11 17
4 46
11 23
4 40
11 29
4 34
11 35
8 00
5 13
10 56
5 07
11 02
5 00
11 09
4 54
11 15
4 48
11 214
4 42
11 27
10
5 20
10 49
5 14
10 55
5 07
11 02
5 01 1 11 08
4 55
11 14
4 49
11 20
20
5 27
10 42
5 21
10 48
5 14
10 55
5 08
11 01
5 02
11 07
4 56
11 13
8 30
5 34
10 35
5 28
10 41
5 21
10 48
5 15
10 54
5 09
11 00
5 03
11 06
40
5 41
10 28
5 35
10 34
5 28
10 41
5 22
10 47
5 16
10 53
5 10
10 59
50
5 47
10 22
5 41
10 28
5 34
10 35
5 28
10 41
5 22
10 47
5 16
10 53
9 00
5 53
10 16
5 47
10 22
5 40
10 29
5 34
10 35
5 28
10 41
5 22
10 47
20
6 05
10 04
5 59
10 10
5 52
10 17
5 46
10 23
5 40
10 29
5 34
10 35
40
6 16
9 53
6 10
9 59
6 03
10 06
5 57
10 12
5 51
10 18
5 45
10 24
10 00
6 27
9 42
6 21
9 48
6 14
9 55
6 08
10 01
6 02
10 07
5 56
10 13
20
6 37
9 32
6 31
9 38
6 24
9 45
6 18
9 51
6 12
9 57
6 06
10 03
40
6 46
9 23
6 40
9 29
6 33
9 36
6 27
9 42
6 21
9 48
6 15
9 54
11 00
6 55
9 14
6 49
9 20
6 42
9 27
6 36
9 33
6 30
9 39
6 24
9 45
30
7 07
9 02
7 01
9 08
6 54
9 15
6 48
9 21
6 42
9 27
6 36
9 33
12 00
7 18
8 51
7 12
8 57
7 05
9 04
6 59
9 10
6 53
9 16
6 47
9 22
30
7 29
8 40
7 23
8 46
7 16
8 53
7 10
8 59
7 04
9 05
6 58
9 11
13 00
7 39
8 30
7 33
8 36
7 26
8 43
7 20
8 49
7 14
8 55
7 08
9 01
30
7 48
8 21
7 42
8 27
' 7 35
8 34
7 29
8 40
7 23
8 46
7 17
8 52
14 00
7 56
8 13
7 50
8 19
7 43
8 26
7 37
8 32
7 31
8 38
7 25
8 44
15 00
8 12
7 57
8 06
8 03
7 59
8 10
7 53
8 16
7 47
8 22
7 41
8 28
16 00
8 25
7 44
8 19
7 50
8 12
7 57
8 06
8 03
8 00
8 09
7 54
8 15
17 00
8 38
7 31
8 32
7 37
8 25
7 44
8 19
7 50
8 13
7 56
8 07
8 02
18 00
8 48
7 21
8 42
7 27
8 35
7 34
8 29
7 40
8 23
7 46
8 17
7 52
19 00
8 58
7 11
8 52
7 17
8 45
7 24
8 39
7 30
8 33
7 36
8 27
7 42
20 00
9 06
7 02
9 00
7 08
8 53
7 15
8 47
7 21
8 41
7 27
8 35
7 33
22 00
9 22
6 46
9 16
6 52
9 09
6 59
9 03
7 05
8 57
7 11
8 51
7 17
24 00
9 35
6 33
9 29
6 39
9 22
6 46
9 16
6 52
9 10
6 58
9 04
7 04
•26 00
9 46
6 22
9 40
6 28
9 33
6 35
9 27
6 41
9 21
6 47
9 15
6 53
28 00
9 56
6 12
9 50
6 18
9 43
6 25
9 37
6 31
9 31
6 37
9 25
6 43
30 00
10 04
6 04
9 58
6 10
9 51
6 17
9 45
6 23
9 39
6 29
9 33
6 35
32 00
10 12
5 56
10 06
6 02
9 59
6 09
9 53
6 15
9 47
6 21
9 41
6 27
34 00
10 19
5 49
10 13
5 55
10 06
6 02
10 00
6 08
9 54
6 14
9 48
6 20
36 00
10 25
5 43
10 19
5 49
10 12
5 56
10 06
6 02
10 00
6 08
9 54
6 14
38 00
10 30
5 38
10 24
5 44
10 17
5 51
10 11
5 57
10 05
6 03
9 59
6 09
40 00
10 35
5 32
10 29
5 38
10 22
5 45
10 16
5 51
10 10
5 57
10 04
6 03
45 00
10 46
5 21
10 40
5 27
10 33
5 34
10 27
5 40
10 21
5 46
10 15
5 52
50 00
10 54
5 12
10 48
5 18
10 41
5 25
10 35
5 31
10 29
5 37
10 23
5 43
55 00
11 01
5 04
10 55
5 10
10 48
5 17
10 42
5 23
10 36
5 29
10 30
5 35
60 00
11 07
4 57
11 01
5 03
10 54
5 10
10 48
5 16
10 42
5 22
10 36
5 28
65 00
11 14
4 50
11 08
4 56
11 01
5 03
10 55
5 09
1.0 49
5 15
10 43
5 21
70 00
11 19
4 44
11 13
4 50
11 06
4 57
11 00
5 03
10 54
5 09
10 48
5 15
75 00
11 23
4 39
11 17
4 45
11 10
4 52
11 04
4 58
10 58
5 04
10 52
5 10
80 00
11 29
4 33
11 23
4 39
11 16
4 46
11 10
4 52
11 04
4 58
10 58
5 04
85 00
11 33
4 28
11 27
4 34
11 20
4 41
11 14
4 47
11 08
4 53
11 02
4 59
90 00
11 37
4 23
11 31
4 29
11 24 4 36
11 18
4 42
11 12
4 48
11 06
4 54
Day of Month. Jan.
Feb. Mar. Apr. May.
June. July. Aug.
Sept.
Dot. Nov. Dec.
ADDITIONAL CORR. "
FOR SUN'S ALT. lst to 15th_ _ _ +18
+15 +8 0 -8
-13 -14 -11
-5
+3 +11 +16
16th to 31st... +17
+12 +4 -4 -11
-14 -13 -' 9
-1
+7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
taking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
TABLE 46. [Page 925
Corrections* to be Applied to the Observed
Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
26 Feet.
27 Feet.
28 Feet.
29 Feet.
30 Feet.
OBS. ALT.
0
*
O
*
O *
O
*
O
*
Sun's
Star's
Sun's
Star's
Sun's i Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
6 30
3 15
12 54
3 09
13
00
3 04
13 05
2 58
13 11
2 53
13 16
40
3 25
12 44
3 19
12
50
3 14
12 55
3 08
13 01
3 03
13 06
50
3 35
12 34
3 29
12
40
3 24
12 45
3 18
12 51
3 13
12 56
7 00
3 45
12 24
3 39
12
30
3 34
12 35
3 28
12 41
3 23
12 46
10
3 54
12 15
3 48
12
21
3 43
12 26
3 37
12 32
3 32
12 37
20
4 03
12 06
3 57
12
12
3 52
12 17
3 46
12 23
3 41
12 28
7 30
4 12
11 57
4 06
12
03
4 01
12 08
3 55
12 14
3 50
12 19
40
4 20
11 49
4 14
11
55
4 09
12 00
4 03
12 06
3 58
12 11
50
4 28
11 41
4 22
11
47
4 17
11 52
4 11
11 58
4 06
12 03
8 00
4 36
11 33
4 30
11
39
4 25 ! 11 44
4 19
11 50
4 14
11 55
10
4 43
11 26
4 37 11
32
4 32
11 37
4 26
11 43
4 21
11 48
20
4 50
11 19
4 44
11
25
4 39
11 30
4 33
11 36
4 28
11 41
8 30
4 57
11 12
4 51
11
18
4 46
11 23
4 40
11 29
4 35
11 34
40
5 04
11 05
4 58
11
11
4 53
11 16
4 47
11 22
4 42
11 27
50
5 10
10 59
5 04
11
05
4 59-
11 10
4 53
11 16
4 48
11 21
9 00
5 16
10 53
5 10
10
59
5 05
11 04
4 59
11 10
4 54
11 15
20
5 28
10 41
5 22
10
47
5 17
10 52
5 11
10 58
5 06
11 03
40
5 39
10 30
5 33
10
36
5 28
10 41
5 22
10 47
5 17
10 52
10 00
5 50
10 19
5 44
10
25
5 39
10 30
5 33
10 36
5 28
10 41
20
6 00
10 09
5 54
10
15
5 49
10 20
5 43-
10 26
5 38
10 31
40
6 09
10 00
6 03
10
06
5 58
10 11
5 52
10 17
5 47
10 22
11 00
6 18
9 51
6 12
9
57
6 07
10 02
6 01
-10 08
5 56
10 13
30
6 30
9 39
6 24
9
45
6 19
9 50
6 13
9 56
6 08
10 01
12 00
6 41
9 28
6 35
9
34
6 30
9 39
6 24
9 45
6 19
9 50
30
6 52
9 17
6 46
9
23
6 41
9 28
6 35
9 34
6 30
9 39
13 00
7 02
9 07
6 56
9
13
6 51
9 18
6 45
9 24
6 40
9 29
30
7 11
8 58
7 05
9
04
7 00
9 09
6 54
9 15
6 49
9 20
14 00
7 19
8 50
7 13
8
56
7 08
9 01
7 02
9 07
6 57
9 12
15 00
7 35
8 34
7 29
8
40
7 24
8 45
7 18
8 51
7 13
8 56
16 00
7 48
8 21
7 42
8
27
7 37
8 32
7 31
8 38
7 26
8 43
17 00
8 01
8 08
7 55
8
14
7 50
8 19
7 44
8 25
7 39
8 30
18 00
8 11
7 58
8 05
8
04
8 00
8 09
7 54
8 15
7 49
8 20
19 00
8 21
7 48
8 15
7
54
8 10
7 59
8 04
8 05
7 59
8 10
20 00
8 29
7 39
8 23
7
45
8 18
7 50
8 12
7 56
8 07
8 01
22 00
8 45
7 23
8 39
7
29
8 34
7 34
8 28
7 40
8 23
7 45
too
8 58
7 10
8 52
7
16
8 47
7 21
8 41
7 27
8 36
7 32
00
9 09
6 59
9 03
7
05
8 58
7 10
8 52
7 16
-T47
7 21
w 00
9 19
6 49
9 13
6
55
9 08
7 00
9 02
7 06
8*57
7 H<r
30 00
9 27
' 6 41
9 21
6
47
9 16
6 52
9 10
6 58
9 05
7 03
32 00
9 35
6 33
9 29
6
39
9 24
6 44
9 18
6 50
9 13
6 55
34 00
9 42
6 26
9 36
6
32
9 31
6 37
9 25
6 43
9 20
6 48
36 00
9 48
6 20
9 42
6
26
9 37
6 31
9 31
6 37
9 26
6 42
38 00
9 53
6 15
9 47
6
21
9 42
6 26
9 36
6 32
9 31
6 37
40 00
9 58
6 09
9 52
6
15
9 47
6 20
9 41
6 26
9 36
6 31
45 00
10 09
5 58
10 03
6
04
9 58
6 09
9 52
6 15
9 47
6 20
50 00
10 17
5 49
10 11
5
55
10 06
6 00
10 00
6 06
9 55
6 11
55 00
10 24
5 41
10 18
5
47
10 13
5 52
10 07
5 58
10 02
6 03 x
60 00
10 30
5 34
10 24
5
40
10 19
5 45
10 13
5 51
10 08
5 56
65 00
10 37
5 27
10 31
5
33
10 26
5 38
10 20
5 44
10 15
5 49
70 00
10 42
5 21
10 36
5
27
10 31
5 32
10 25
5 38
10 20
5 43
75 00
10 46
5 16
10 40
5
22
10 35
5 27
10 29
5 33
10 24
5 38
80 00
10 52
5 10
10 46
5
16
10 41
5 21
10 35
5 27
10 30 5 32
85 00
10 56
5 05
10 50 5
11
10 45
5 16
10 39
5 22
10 34
5 27
90 00
11 00 5 00
10 54 5
06
10 49
5 11
10 43
5 17
10 38
5 22
Day of Month. Jan.
Feb.
Mar. Apr.
May. June
. July. | Aug. Sept.
Oct. Nov. Dec.
ADDITIONAL CORR.
FOR SUN'S ALT. lgt to ^fo .... +18
16th to 31st... +17
+15
+12
+8 0 -
+4 -4 -
- 8 -13
-11 -14
„
-14 -11 -5
-13 -9-1
+3 +11 +16
+7 +14 +18
onS^W^^^^
taking account of the variation of the Sun's semidiameter in the different months of the year is given at the fo
Page 926]
TABLE 46.
Corrrectiona to be
Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude— Continued.
HEIGHT OF THE EYE.
31 Feet.
32 Feet.
33 Feet.
34 Feet. •
35 Feet.
OBS. ALT.
©
*
©
*
O
*
0
*
O
#
Sur
I'S
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
6 30
2
48
13 21
2 42
13 27
2 37
13 32
2 32
13 37
2 27
13 42
40
2
58
13 11
2 52
13 17
2 47
13 22
2 42
13 27
2 37
13 32
50
3
08
13 01
3 02
13 07
2 57
13 12
2 52
13 17
2 47
13 22
7 00
3
18
12 51
3 12
12 57
3 07
13 02
3 02
13 07
2 57
13 12
10
3
27
12 42
3 21
12 48
3 16
12 53
3 11
12 58
3 06
13 03
20
3
36
12 33
3 30
12 39
3 25
12 44
3 20
12 49
3 15
12 54
7 30
3
45
12 24
3 39
12 30
3 34
12 35
3 29
12 40
3 24
12 45
40
3
53
12 16
3 47
12 22
3 42
12 27
3 37
12 32
3 32
12 37
50
4
01
12 08
3 55
12 14
3 50
12 19
3 45
12 24
3 40
12 29
8 00
4
09
12 00
4 03
12 06
3 58
12 11
3 53
12 16
3 48
12 21
10
4
16
11 53
4 10
11 59
4 05
12 04
4 00
12 09
3 55
12 14
20
4
23
11 46
4 17
11 52
4 12
11 57
4 07
12 02
4 02
12 07 .
8 30
4
30
11 39
4 24
11 45
4 19
11 50
4 14
11 55
4 09
12 00
40
4
37
11 32
4 31
11 38
4 26
11 43
4 21
11 48
4 16
11 53
50
4
43
11 26
4 37
11 32
4 32
11 37
4 27
11 42
4 22
11 47
9 00
4
49
11 20
4 43
11 26
4 38
11 31
4 33
11 36
4 28
11 41
20
5
01
11 08
4 55
11 14
4 50
11 19
4 45
11 24
4 40
11 29
40
5
12
10 57
5 06
11 03
5 01
11 08
4 56
11 13
4 51
11 18
10 00
5
23
10 46
5 17
10 52
5 12
10 57
5 07
11 02
5 02
11 07
20
5
33
10 36
5 27
10 42
5 22
10 47
5 17
10 52
5 12
10 57
40
5
42
10 27
5 36
10 33
5 31
10 38
5 26
10 43
5 21
10 48
11 00
5
51
10 18
5 45
10 24
5 40
10 29
5 35
10 34
5 30
10 39
30
6
03
10 06
5 57
10 12
5 52
10 17
5 47
10 22
5 42
10 27
12 00
6
14
9 55
6 08
10 01
6 03
10 06
5 58
10 11
5 53
10 16
30
6
25
9 44
6 19
9 50
6 14
9 55
6 09
10 00
6 04
10 05
13 00
6
35
9 34
6 29
9 40
6 24
9 45
6 19
9 50
6 14
9 55
30
6
44
9 25
6 38
9 31
6 33
9 36
6 28
9 41
6 23
9 46
14 00
6
52
9 17
6 46
9 23
6 41
9 28
6 36
9 33
6 31
9 38
15 00
7
08
9 01
7 02
9 07
6 57
9 12
6 52
9 17
6 47
9 22
16 00
7
21
8 48
7 15
8 54
7 10
8 59
7 05
9 04
7 00
9 09
17 00
7
34
8 35
7 28
8 41
7 23
8 46
7 18
8 51
7 13
8 56
18 00
7
44
8 25
7 38
8 31
7 33
8 36
7 28
8 41
7 23
8 46
19 00
7
54
8 15
7 48
8 21
7 43
8 26
7 38
8 31
7 33
8 36
20 00
8
02
8 06
7 56
8 12
7 51
8 17
7 46
8 22
7 41
8 27
22 00
8
18
7 50
8 12
7 56
8 07
8 01
8 02
8 06
7 57
8 11
24 00
8
31
7 37
8 25
7 43
8 20
7 48
8 15
•7 53
8 10
7 58
26 00
8
42
7 26
8 36
7 32
8 31
7 37
8 26
7 42
8 21
7 47
28 00
8
52
7 16
8 46
7 22
8 41
7 27
8 36
7 32
8 31
7 37
30 00
9
00
7 08
8 54
7 14
8 49
7 19
8 44
7 24
8 39
7 29
32 00
9
08
7 00
9 02
7 06
8 57
7 11
8 52
7 16
8 47
7 21
34 00
9
15
6 53
9 09
6 59
9 04
7 04
8 59
7 09
8 54
7 14
36 00
9
21
6 47
9 15
6 53
9 10
6 58
9 05
7 03
9 00
7 08
38 00
9
26
6 42
9 20
6 48
9 15
6 53
9 10
6 58
9 05
7 03
40 00
9
31
6 36
9 25
6 42
9 20
6 47
9 15
6 52
9 10
6 57
45 00
9
42
6 25
9 36
6 31
9 31
6 36
9 26
6 41
9 21
6 46
50 00
9
50
6 16
9 44
6 22
9 39
6 27
9 34
$ 32
9 29
6 37
55 00
9
57
6 08
9 51
6 14
9 46
6 19
9 41
6 24
9 36
6 29
60 00
10
03
6 01
9 57
6 07
9 52
6 12
9 47
6 17
9 42
6 22
65 00
10
10
5 54
10 04
6 00
9 59
6 05
9 54
6 10
9 49
6 15
70 00
10
15
5 48
10 09
5 54
10 04
5 59
9 59
6 04
9 54
6 09
75 00
10
19
5 43
10 13
5 49
10 08
5 54
10 03
5 59
9 58
6 04
80 00
10
25
5 37
10 19
5 43
10 14
5 48
10 09
5 53
10 04
5 58
85 00
10
29
5 32
10 23
5 38
10 18
5 43
10 13
5 48
10 08
5 53
90 00
10
33
5 27
10 27
5 33
10 22
5 38
10 17
5 43
10 ]2
5 48
Day of Month. Jan.
Feb. Mar. Apr. ]
Vfay. June
July. Aug. Sept.
Oct. Nov. Dec.
/-*
ADDITIONAL CORR.
FOR SUN'S ALT.
1st to 15th +18
+15 +8 0 -
- 8 -13
-14 -11 -5
+3 +11 +16
16th to 31st... +17
+12 +4 -4 -
-11 -14
-13 -9-1
+7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
;aking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
TABLE 46.
[Page 927
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE
EYE.
36 Feet.
37 Feet.
38 Fctn.
39 Feet.*
40 Feet.
OBJ». ALT.
O
*
O
*
O
*
O
*
O
*
Sun's
Star's
Sun's
Star's
Sun-'s
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr
Corr.
Corr.
Corr.
Corr.
Corr.
Coir.
0 /
6 3t)
2 22
13 47
2 17
13 52
2 13
13
56
2 08
14
01
2 03
14
06
40
2 32
13 37
2 27
13 42
2 23
13
46
2 18
13
51
2 13
13
56
50
2 42
13 27
2 37
13 32
2 33
13
36
2 28
13
41
2 23
13
46
7 00
2 52
13 17
2 47
13 22
2 43
13
26
2 38
13
31
2 33
13
36
10
3 01
13 08
2 56
13 13
2 52
13
17
2 47
13
22
2 42
13
27
20
3 10
12 59
3 05
13 04
3 01
13
08
2 56
13 13
2 51
13
18
7 30
3 19
12 50
3 14
12 55
3 10
12
59
3 05
13 04
3 00
13
09
40
3 27
12 42
3 22
12 47
3 18
12
51
3 13
12 56
3 08
13
01
50
3 35
12 34
3 30
12 39
3 26
12
43
3 21
12 48
3 16
12
53
8 00
3 43 I 12 26
3 38
12 31
3 34
12
35
3 29
12 40
3 24
12
45
10
3 50 i 12 19
3 45
12 24
3 41
12
28
3 36
12 33
3 31
12
38
20
3 57 12 12
3 52
12 17
3 48
12
21
3 43
12 26
3 38
12
31
8 30
4 04
12 05
3 59
12 10
3 55
12
14
3 50
12 19
3 45
12
24
40
4 11
11 58
4 06
12 03
4 02
12
07
3 57
12 12
3 52
12
17
50
4 17
11 52
4 12
11 57
4 08
12
01
4 03
12 06
3 58
12
11
9 00
4 23
11 46
4 18
11 51
4 14
11
55
4 09
12 00
4 04
12
05
20
4 35
11 34
4 30
11 39
4 26
11
43
4 21
11 48
4 16
11
53
40
4 46
11 23
4 41
11 28
4 37
11
32
4 32
11 37
4 2
7
11
42
10 00
4 57
11 12
4 52
11 17
4 48
11
21
4 43
11 26
4 38
11
31
20
5 07
11 02
5 02
11 07
4 58
11
11
4 53
11 16
4 48
11
21
40
5 16
10 53
5 11
10 58
5 07
11
02
5 02
11 07
4 57
11
12
11 00
5 25
10 44
5 20
10 49
5 16
*10
53
5 11
10 58
5 06
11
03
30
5 37
10 32
5 32
10 37
5 28
10
41
5 23
10 46
5 18
10
51
12 00
5 48
10 21
5 43
10 26
5 39
10
30
5 34
10 35
5 29
10 40
30
5 59
10 10
5 54
10
15
5 50
10
19
5 45
10 24
5 40
10
29
13 00
6 09
10 00
6 04
10 05
6 00
10
09
5 55
10 14
5 50
10
19
30
6 18
9 51
6 13
9 56
6 09
10
00
6 04 10 05
5 59
10 10
14 00
6 26
9 43
6 21
9 48
6 17
9
52
6 12
9 57
6 07
10 02
15 00
6 42
9 27
6 37
9 32
6 33
9
36
6 28
9 41
6 23
9
46
16 00
6 55
9 14
6 50
9
19
6 46
9
23
6 41
9 28
6 36
9 33
17 00
7 08
9 01
7 03
9 06
6 59
9
10
6 54
9 15
6 49
9 20
18 00
7 18
8 51
7 13
8 56
" 09
9
00
04
9 05
6 59
9 10
19 00
7 28
8 41
7 23
8
46
" 19
8
50
14
*
5 55
7 09 9 00
20 00
7 36
8 32
7 31
8
37
" 27
8
41
22
8 46
7 17 I 8 51
22 00
7 52
8 16
7 47
8
21
" 43
8
25
38
£
* 30
7 33 8 35
24 00
8 05
8 03
8 00
8
08
- 56
8
12
51
8 17
7 4
J> . 0 ZZ
26 00
8 16
7 52
8 11
7
57
8 07
8
01
8 02
8 06
7 57 t 8 11
28 00
8 26
7 42
8 21
7
47
8 17
7
51
8 12
7 56
8 07
8 01
30 00
8 34
7 34
8 29
7
39
8 25
7
43
8 20
7 48
8 15
7 53
32 00
8 42
7 26
8 37
7
31
8 33
7
35
8 28
'
7 40
8 23
7 45
34 00
8 49
7 19
8 44
7
24
8 40
7
28
8 35
7 33
8 30
7 38
36 00
8 55
7 13
8 50
7
18
8 46
7
22
8 41
'
r 27
8 36
7 32
38 00
9 00
7 08
8 55
7
13
8 51
7
17
8 46
7 22
8 41
7 27
40 00
9 05
7 02
9 00
7
07
8 56
7
11
8 51
7 16
8 46
7 21
45 00
9
18
6 51
9 11
6
56
9 07
7
00
9 02
7 05
8 57
7 10
50 00
9 24
6 42
9 19
6
47
9 15
6
51
9 10
6 56
9 05
7
01
55 00
9 31
6 34
9 26
6
39
9 22
6
43
9 17
6 48
9 12
6 56
60 00
9 37
6 27
9 32
6
32
9 28
6
36
9 23
6 41
9 18
6 46
65 00
70 00
75 00
80 00
85 00
90 00
9 44
9 49
9 53
9 59
10 03
10 07
6 20
6 14
6 09
6 03
5 58
5 53
9 39
9 44
9 48
9 54
9 58
10 02
6
6
6
6
6
5
25
19
14
OS
03
OS
9 35
9" 40
9 44
9 50
9 54
9 58
6
6
6
6
6
6
29
23
18
12
07
02
9 30
9 35
9 39
9 45
9 49
9 53
6 34
6 28
6 23
6 17
6 12
6 07
9 25 i 6 39
9 30 i 6 33
9 34 6 28
9 40 j 6 22
9 44 6 17
9 48 6 12
Day of Month. Jan.
Feb.
Mar.
Apr.
May.
June. July.
Aug.
Sept
Oct.
Nov.
Dec.
ADDITIONAL CORK.
FOE SUN'S ALT.
1st to 15th.... +18
16th to 31st... +17
+15
+12
4-8
+4
0
-4
- 8
-11
-13 -14
-14 j-13
-11
- 9
-5
-1
+3 +11
. +7 +14
+16
+18
Page 928] TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
OBS. ALT.
41 Feet.
42 Feet.
43 Feet.
44 Feet.
•^45 Feet.
46 Feet,
O
*
O
*
O
*
O
*
O
*
O
*''
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
0 /
6 30
/ //
1 58
1 44
14 25
1 39
14 30
/ n
1 35
/ //
14 34
14 11
1 54
14 15
1 49
14 20
40
2 08
14 01
2 04
14 05
1 59
14 10
1 54
14 15
1 49
14 20
1 45
14 24
50
2 18
13 51
2 14
13 55
2 09
14 00
2 04
14 05
1 59
14 10
1 55
14 14
7 00
2 28
13 41
2 24
13 45
2 19
13 50
2 14
13 55
2 09
14 00
2 05
14 04
10
2 37
33 32
2 33
13 36
2 28
13 41
2 23
13 46
2 18
13 51
2 14
13 55
20
2 46
13 23
2 42
13 27
2 37
13 32
2 32
13 37
2 27
13 42
2 23
13 46
7 30
2 55
13 14
2 51
13 18
2 46
13 23
2 41
13 28
2 36
13 33
2 32
13 37
40
3 03
13 06
2 59
13 10
2 54
13 15
2 49
13 20
2 44
13 25
2 40
13 29
50
3 11
12 58
3 07
13 02
3 02
13 07
2 57
13 12
2 52
13 17
2 48
13 21
8 00
3 19
12 50
3 15
12 54
3 10
12 59
3 05
13 04
3 00
13 09
2 56
13 13
10
3 26
12 43
3 22
12 47
3 17
12 52
3 12
12 57
3 07
13 02
3 03
13 06
20
3 33
12 36
3 29
12 40
3 24
12 45
3 19
12 50
3 14
]2 55
3 10
12 59
8 30
3 40
12 29
3 36
12 33
3 31
12 38
3 26
12 43
3 21
12 48
3 17
12 52
40
3 47
12 22
3 43
12 26
3 38
12 31
3 33
12 36
3 28
12 41
•3 24
12 45
50
3 53
12 16
3 49
12 20
3 44
12 25
3 39
12 30
3 34
12 35
3 30
12 39
9 00
3 59
12 10
3 55
12 14
3 50
12 19
3 45
12 24
3 40
12 29
3 36
12 33
20
4 11
11 58
4 07
12 02
4 02
12 07
3 57
14 12
3 52
]2 17
3 48
12 21
40
4 22
11 47
4 18
11 51
4 13
11 56
4 08
12 01
4 03
12 06
3 59
12 10
10 00
4 33
11 36
4 29
11 40
4 24
11 45
4 19
11 50
4 14
11 55
4 10
11 59
20
4 43
11 26
4 39
11 30
4 34
11 35
4 29
11 40
4 24
11 45
4 20
11 49
40
4 52
11 17
4 48
11 21
4 43
11 26
4 38
11 31
4 33
11 36
4 29
11 40
11 00
5 01
11 08
4 57
11 12
4 52
11 17
4 47
11 22
4 42
11 27
4 38
11 31
30
5 13
10 56
5 09
11 00
5 04
11 05
4 59
11 10
4 54
]1 15
4 50
11 19
12 00
5 24
10 45
5 20
10 49
5 15
10 54
5 10
10 59
5 05
11 04
5 01
11 08
30
5 35
10 34
5 31
10 38
5 26
10 43
5 21
10 48
5 16
10 53
5 12
10 57
13 00
5 45
10 24
5 41
10 28
5 36
10 33
5 31
10 38
5 26
10 43
5 22
10 47
30
5 54
10 15
5 50
10 19
5 45
10 24
5 40
10 29
5 35
10 34
5 31
10 38
14 00
6 02
10 07
5 58
10 11
5 53
10 16
5 48
10 21
5 43
10 26
5 39
10 30
15 00
6 18
9 51
6 14
9 55
6 09
10 00
6 04
10 05
5 59
10 10
5 55
10 14
16 00
6 31
9 38
6 27
9 42
6 22
9 47
6 17
9 52
6 12
9 57
6 08
10 01
17 00
6 44
9 25
6 40
9 29
6 35
9 34
6 30
9 39
6 25
9 44
6 21
9 48
18 00
6 54
9 15
6 50
9 19
6 45
9 24
6 40
9 29
6 35
9 34
6 31
9 38
19 00
7 04
9 05
7 00
9 09
6 55
9 14
6 50
9 19
6 45
9 24
6 41
9 28
20 00
7 12
8 56
7 08
9 00
7 03
9 05
6 58
9 10
6 53
9 15
6 49
9 19
22 00
7 28
8 40
7 24
8 44
7 19
8 49
7 14
8 54
7 09 8 59
7 05
9 03
24 00
7 41
8 27
7 37
8 31
7 32
8 36
7 27
8 41
7 22 8 46
7 18
8 50
26 00
7 52
8 16
7 48
820.
7 43
8 25
7 38
8 30
7 33 i 8 35
7 29
8 39
28 00
8 02
8 06
7 58
irnr
7 53
8 15
7 48
8 20
7 43 8 25
7 39
8 29
30 00
8 10
7 58
8 06
8 02
8 01
8 07
7 56
8 12
7 51
8 17
7 47
8 21
32 00
8 18
7 50
8 14
7 54
8 09
7 59
8 04
8 04
7 59
8 09
7 55
8 13
34 00
8 25
7 43
8 21
7 47
8 16
7 52
8 11
7 57
8 06
8 02
8 02
8 06
36 00
8 31
7 37
8 27
7 41
8 22
7 46
8 17
7 51
8 12
7 56
8 08
8 00
38 00
8 36
7 32
8 32
7 36
8 27
7 41
8 22
7 46
8 17
7 51
8 13
7 55
40 00
8 41
7 26
8 37
7 30
8 32
7 35
8 27
7 40
8 22
Si 45
8 18
7 49
45 00
8 52
7 15
8 48
7 19
8 43
7 24
8 38
7 29
8 33"
7 34.
8 29
7 38
50 00
9 00
7 06
8.56
7 10
8 51
7 15
8 46
7 20
8 41"
' 7 25
8 37
7 29
55 00
9 07
6 58
9 03
7 02
8 58
7 07
8 53
7 12
8 48
7 17
8 44
7 21
60 00
9 13
6 51
9 09
6 55
9 04
7 00
8 59
7 05
8 54
7 10
8 50
7 14
65 00
9 20
6 44
9 16
6 48
9 11
. 6 53
9 06
6 58
9 01
7 03
8 57
7 07
70 00
9 25
6 38
9 21
6 42
9 16
6 47
9 11
6 52
9 06
6 57
9 02
7 01
75 00
9 29
6 33
9 25
6 37
9 20
6 42
9 15
6 47
9 10
6 52
9 06
6 56
80 00
9 35
6 27
9 31
6 31
9. 26
6 36
9 21
6 41
9 16
6 46
9 12
6 50
85 00
9 39
6 22
9 35
6 26
9 30
6 31
9 25
6 36
9 20
6 41
9 16
6 45
90 00
9 43
6 17
9 39
6 21
9 34
6 26
9 29
6 31
9 24
6 36
9 20
6 40
Day of Month. Jan.
Feb. Mar. Apr
. May.
June. July. Aug.
Sept.
Oct. Nov. Dec.
ADDITIONAL CORE. //
FOR SUN'S ALT. lgt to 15ih.... +18
+15 +8 C
- 8
-13 -14 -11-
-5
+3 +11 +16
16th to 31st... +17
+12 +4 -4
-11
-14 -13 - 9
-1
+7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
taking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
TABLE 46. [Page 929
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude— Continued.
HEIGHT OF THE EYE.
47 Feet,
48 Feet.
49 Feet.
50 Feet.
51 Feet.
52 Feet.
OBS. ALT,
O
*
O
*
O
*
O
*
O
*
0
*
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun?s
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
6 30
1 31
14 38"
1 27
14 42
1 23
14 46
1 19
14 50
1 15
14 54
1 11
14 58
40
1 41
14 28
1 37
14 32
1 33
14 36
1 29
14 40
1 25
14 44
1 21
14 48
50
1 51
14 18
1 47
14 22
1 43
14 26
1 39
14 30
1 35
14 34
1 31
14 38
7 00
2 01
14 08
1 57
14 12
1 53
14 16
1 49
14 20
1 45
14 24
1 41
14 28
10
2 10
13 59
2 06
14 03
2 02
14 07
1 58
14 11
1 54
14 15
1 50
14 19
20
2 19
13 50
2 15
13 54
2 11
13 58
2 07
14 02
2 03
14 06
1 59
14 10
7 30
2 28
13 41
2 24
13 45
2 20
13 49
2 16
13 53
2 12
13 57
2 03
14 01
40
2 36
13 33
2 32
13 37
2 28
13 41
2 24
13 45
2 20
13 49
2 16
13 53
50
2 44
13 25
2 40
13 29
2 36
13 33
2 32
13 37
2 28
13 41
2 24
13 45
8 00
2 52
13 17
2 48
13 21
2 44
13 25
2 40
13 29
2 36
13 33
2 32
13 37
10
2 59
13 10
2 55
13 14
2 51
13 18
2 47
13 22
2 43
13 26
2 39
13 30
20
3 06
13 03
3 02
13 07
2 53
13 11
2 54
13 15
2 50
13 19
2 46
13 23
8 30
3 13
12 56
3 09
13 00
3 05
13 04
3 01
13 08
2 57
13 12
2 53
13 16
40
3 20
12 49
3 16
12 53
3 12
12 57
3 03
13 01
3 04
13 05
3 00
13 09
50
3 26
12 43
3 22
12 47
3 13
12 51
3 14
12 55
3 10
12 59
3 06
13 03
9 00
3 32
12 37
3 28
12 41
3 24
12 45
3 20
12 49
3 16
12 53
3 12
12 57
20
3 44
12 25
3 40
12 29
3 36
12 33
3 32
12 37
3 28
12 41
3 24
12 45
40
3 55
12 14
3 51
12 18
3 47
12 22
3 43
12 26
3 39
12 30
3 35
12 34
10 00
4 06
12 03
4 02
12 07
3 53
12 11
3 54
12 15
3 50
12 19
3 46
12 23
20
4 16
11 53
4 12
11 57
4 03
12 01
4 04
12 05
4 00
12 09
3 56
12 13
40
4 25
11 44
4 21
11 48
4 17
11 52
4 13
11 56
4 09
12 00
4 05
12 04
11 00
4 34
11 35
4 30
11 39
4 26
11 43
4 22
11 47
4 18
11 51
4 14
11 55
30
4 46
11 23
4 42
11 27
4 33
11 31
4 34
11 35
4 30
11 39
4 26
11 43
12 00
4 57
11 12
4 53
11 16
4 49
11 20
4 45
11 24
4 41
11 28
4 37
11 32
30
5 08
11 01
5 01
11 05
5 00
11 09
4 56
11 13
4 52
11 17
4 48
11 21
13 00
5 18
10 51
5 14
10 55
5 10
10 59
5 06
11 03
5 02
11 07
4 58
11 11
30
5 27
10 42
5 23
10 46
5 19
10 50
5 15
10 54
5 11
10 58
5 07
11 02
14 00
5 35
10 34
5 31
10 38
5 27
10 42
5 23
10 46
5 19
10 50
5 15
10 54
15 00
5 51
10 18
5 47
10 22
5 43
10 26
5 39
10 30
5 35
10 34
5 31
10 38
16 00
6 04
10 05
6 00
10 09
5 56
10 13
5 52
10 17
5 48
10 21
5 44
10 25
17 00
6 17
9 52
6 13
9 56
6 09
10 00
6 05
10 04
6 01
10 08
5 57
10 12
18 00
6 27
9 42
6 23
9 46
6 19
9 50
6 15
9 54
6 11
9 58
6 07
10 02
19 00
6 37
9 32
6 33
9 36
6 29
9 40
6 25
9 44
6 21
9 43
6 17
9 52
20 00
6 45
9 23
6 41
9 27
6 37
9 31
6 33
9 35
6 29
9 39
6 25
9 43
22 00
7 01
9 07
6 57
9 11
6 53
9 15
6 49
9 19
6 45
9 23
6 41
9 27
24 00
7 14
8 54
7 10
8 58
7 06
9 02
7 02
9 06
6 58
9 10
6 54
9 14
26 00
7 25
8 43
7 21
8 47
7 17
8 51
7 13
8 55
7 09
8 59
7 05
9 03
28 00
7 35
8 33
7 31
8 37
7 27
8 41
7 23
8 45-
7 19
8 49
7 15
8 53
30 00
7 43
8 25
7 39
8 29
7 35
8 33
7 31
8 37
7 27
8 41
7 23
8 45
32 00
7 51
8 17
7 47
8 21
7 43
8 25
7 39
8 29
7 35
8 33
7 31
8 37
34 00
7 58
8 10
754
8 14
7 50
8 18
7 46
8 22
7 42
8 26
7 38
8 30
36 00
8 04
8 04
8 00
8 08
7 56
8 12
7 52
8 16
7 48
8 20
7 44
8 24
38 00
8 09
7 59
8 05
8 03
8 01
8 07
7 57
8 11
7 53
8 15
7 49
8 19
40 00
8 14
7 53
8 10
7 57
8 06
8 01
8 02
8 05
7 58
8 09
7 54
8 13
45 00
8 25
7 42
8 21
7 46
8 17
7 50
8 13
7 54
8 09
7 58
8 05
8 02
50 00
8 33
7 33
8 29
7 37
8 25
7 41
8 21
7 45
8 17
7 49
8 13
7 53
55 00
8 40
7 25
8 36
7 29
8 32
7 33
8 28
7 37
8 24
7 41
8 20
7 45
60 00
8 46
7 18
8 42
7 92
8 38
7 26
8 34
7 30
8 30
7 34
8 26
7 38
65 00
8 53
7 11
8 49
7 15
8 45
7 19
8 41
7 23
8 37
7 27
8 33
7 31
70 00
8 58
7 05
8 54
7 09
8 50
7 13
8 46
7 17
8 42
7 21
8 38
7 25
75 00
9 02
7 00
8 58
7 04
8 54
7 08
8 50
7 12
8 46
7 16
8 42
7 20
80 00
9 08
6 54
9 04
6 58
9 00
7 02
8 56
7 06
8 52
7 10
8 48
7 14
85 00
9 12
6 49
9 08
6 53
9 04
6 57
9 00
7 01
8 56
7 05
8 52
7 09
90 00
9 16
6 44
9 12
6 48
9 OS 6 52
9 04 6 56
9 00
7 00
8 56
7 04
Day of Month. Jan.
Feb. Mar. Apr. May.
June. July. Aug.
Sept. Oct. Nov. Dec.
ADDITIONAL CORE. "
FOB SUN'S ALT. lgt to I5th....< + 18
+ 15 +8 0-8
-13 -14 -11
-5 +3 +11 +16
16th to 31st.. .j+17
+12 +4 -4 -11
-14 -13 - 9
-1 +'7 +14 +18
* The coarections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as .16'. A supplementary correction
Skin* account of the variation of the Sun's semidiameter in the dtferent months of the year is given at the foot ol
Page 930] TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
53 Feet.
54 Feet.
55 Feet.
56 Feet.
57 Feet.
58 Feet.
OBS. ALT.
0
*
O
*
O
*
O
*
O
*
O
*
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
0 /
6 30
1 07
15 02
1 03
15 06
0 59
15 10
0 55
15 14
0 51-
15 18
0 48
15 21
40
1 17
14 52
1 13
14 56
1 09
15 00
1 05
15 04
1 01
15 08
0 58
15 11
50
1 27
14 42
1 23
14 46
1 19
14 50
1 15
14 54
1 11
14 58
1 08
15 01
7 00
1 37
14 32
1 33
14 36
1 29
14 40
1 25
14 44
1 21
14 48
1 18
14 51
10
1 46
14 23
1 42
14 27
1 38
14 31
1 34
14 35
1 30
14 39
1 27
14 42
20
1 55
14 14
1 51
14 18
1 47
14 22
1 43
14 26
1 39
14 30
1 36
14 33
7 30
2 04
14 05
2 00
14 09
1 56
14 13
1 52
14 17
1 48
14 21
1 45
14 24
40
2 12
13 57
2 08
14 01
2 04
14 05
2 00
14 09
1 56
14 13
1 53
14 16
50
2 20
13 49
2 16
13 53
2 12
13 57
2 08
14 01
2 04
14 05
2 01
14 08
8 00
2 28
13 41
2 24
13 45
2 20
13 49
2 16
13 53
2 12
13 57
2 09
14 00
10
2 35
13 34
2 31
13 38
2 27
13 42
2 23
13 46
2 19
13 50
2 16
13 53
20
2 42
13 27
2 38
13 31
2 34
13 35
2 30
13 39
2 26
13 43
2 23
13 46
8 30
2 49
13 20
2 45
13 24
2 41
13 28
2 37
13 32
2 33
13 36
2 30
13 39
40
2 56
13 13
2 52
13 17
2 48
13 21
2 44
13 25
2 40
13 29
2 37
13 32
50
3 02
13 07
2 58
13 11
2 54
13 15
2 50
13 19
2 46
13 23
2 43
13 26
9 00
3 08
13 01
3 04
13 05
3 00
13 09
2 56
13 13
2 52
13 17
2 49
13 20
20
3 20
12 49
3 16
12 53
3 12
12 57
3 08
13 01
3 04
13 05
3 01
13 08
40
3 31
12 38
3 27
12 42
3 23
12 46
3 19
12 50
3 15
12 54
3 12
12 57
10 00
3 42
12 27
3 38
12 31
3 34
12 35
3 30
12 39
3 26
12 43
3 23
12 46
20
3 52
12 17
3 48
12 21
3 44
12 25
3 40
12 29
3 36
12 33
3 33
12 36
40
4 01
12 08
3 57
12 12
3 53
12 16
3 49
12 20
3 45
12 24
3 42
12 27
11 00
4 10
11 59
4 06
12 03
4 02
12 07
3 58
12 11
3 54
12 15
3 51
12 18
30
4 22
11 47
4 18
11 51
4 14
11 55
4 10
11 59
4 06
12 03
4 03
12 06
12 00
4 33
11 36
4 29
11 40
4 25
11 44
4 21
11 48
4 17
11 52
4 14
11 55
30
4 44
11 25
4 40
11 29
4 36
11 33
4 32
11 37
4 28
11 41
4 25
11 44
13 00
4 54
11 15
4 50
11 19
4 46
11 23
4 42
11 27
4 38
11 31
4 35
11 34
30
5 03
11 06
4 59
11 10
4 55
11 14
4 51
11 18
4 47
11 22
4 44
11 25
14 00
5 11
10 58
5 07
11 02
5 03
11 06
4 59
11 10
4 55
11 14
4 52
11 17
15 00
5 27
10 42
5 23
10 46
5 19
10 50
5 15
10 54
5 11
10 58
5 08
11 01
16 00
5 40
10 29
5 36
10 33
5 32
10 37
5 28
10 41
5 24
10 45
5 21
10 48
17 00
5 53
10 16
5 49
10 20
5 45
10 24
5 41
10 28
5 37
10 32
5 34
10 35
18 00
6 03
10 06
5 59
10 10
5 55
10 14
5 51
10 18
5 47
10 22
5 44
10 25
19 00
6 13
9 56
6 09
10 00
6 05
10 04
6 01
10 08
•5 57
10 12
5 54
10 15
20 00
6 21
9 47
6 17
9 51
6 13
9 55
6 09
9 59
6 05
10 03
6 02
10 06
22 00
6 37
9 31
6 33
9 35
6 29
9 39
6 25
9 43
6 21
9 47
6 18
9 50
24 00
6 50
9 18
6 46
9 22
6 42
9 26
6 38
9 30
6 34
9 34
6 31
9 37
26 00
7 01
9 07
6 57
9 11
6 53
9 15
6 49
9 19
6 45
9 23
6 42
9 26
28 00
7 11
8 57
7 07
9 01
7 03
9 05
6 59
9 09
6 55
9 13
6 52
9 16
30 00
7 19
8 49
7 15
8 53
7 11
8 57
7 07
9 01
7 03
9 05
7 00
9 08
32 00
7 27
8 41
7 23
8 45
7 19
8 49
7 15
8 53
7 11
8 57
7 08
9 00
34 00
7 34
8 34
7 30
8 38
7 26
8 42
7 22
8 46
7 18
8 50
7 15
8 53
36 00
7 40
8 28
7 36
8 32
7 32
8 36
7 28
8 40
7 24
8 44
7 21
8 47
38 00
7 45
8 23
7 41
8 27
7 37
8 31
7 33
8 35
7 29
8 39
7 26
8 42
40 00
7 50
8 17
7 46
8 21
7 42
8 25
7 38
8 29
7 34
8 33
7 31
8 36
45 00
8 01
8 06
7 57
8 10
7 53
8 14
7 49
8 13
7 45
8 22
7 42
8 25
50 00
8 09
7 57
8 05
8 01
8 01
8 05
7 57
8 09
7 53
8 13
7 50
8 16
55 00
8 16
7 49
8 12
^53
8 08
7 57
8 04
8 01
8 00
8 05
7 57
8 08
60 00
8 22
7 42
8 18
7 46
8 14
7 50
8 10
7 54
8 06
7 58
8 03
8 01
65 00
8 29
7 35
8 25
7 39
8 21
7 43
8 17
7 47
8 13
7 51
8 10
7 54
70 00
8 34
7 29
8 30
7 33
8 26
7 37
8 22
7 41
8 18
7 45
8 15
7 48
75 00
8 38
7 24
8 34
7 28
8 30
7 32
8 26
7 36
8 22
7 40
8 19
7 43
80 00
8 44
7 18
8 40
7 22
8 36
7 26
8 32
7 30
8 28
7 34
8 25
7 37
85 00
8 48
7 13
8 44
7 17
8 40
7 21
8 36
7 25
8 32
7 29
8 29
7 32
90 00
8 52
7 08
8 48
7 12
8 44
7 16
8 40
7 20
8 36
7 24
8 33
7 27
Day of Month. Jan.
Feb. Mar. Apr
May.
June. July. Aug.
Sept.
Oct. Nov. Dec.
ADDITIONAL CORR
TO» BTTN'S ALT. Isttol5th_.+18
+15 +8 0
- 8
-13 -14 -11
-5
+3 +11 +16
16th to 31st... +17
+12 +4 -4
-11
-14 -13 - 9
-1
+7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction ; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
taking account of the variation of the Sun's semidiameter in the different months of the year is given at the Toot of the main table.
TABLE 46.
[Page 931
Corrections* to be Applied to the Observed
Altitude of a Star or of the Sun's Lower Limb, to Find
the True
Altitude — Continued .
. HEIGHT OF THE EYE.
59 Feet,
60 Feet.
Gi Feet.
62 Feet.
63 Feet.
64 Feet.
O.BS. ALT
O
*
G
*
O
*
O
*
O *
0
*
Sun's
£
Star's
Sun's
Star's
Sun
3
S
tar's
Sun's
Sta
r's
Sun's
Star'
3
Su
n's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
(+)
Corr.
Corr.
Corr.
6 30
0 44
15 25
0 40
15 29
0 36
15 33
0 32
15
37
0 29
, „
15 40
0
25
15 44
40
0 54
15 15
0 50 i 15 19
0 46
15 23
0 42
15
27
0 39
15 30
0
35
15 34
50
1 04
15 05
1 00 15 09
0 56
15 13
0 52
15
17
0 49
15 20
0
45
15 24
7 00
1 14
14 55
1 10 14 59
1 06
15 03
1 02
15
07
0 59
15 10
0
55
15 14
10
1 23 14 46
1 19 14 50
1 15
14 54
1 11
14
53
1 08
15 01
1
04
15 05
20
1 32 14 37
1 28 i 14 41
1 24
14 45
1 20
14
49
1 17
14 52
1
13
14 56
7 30
1 41 | 14 28
1 37 14 32
1 33 14 36
1 29
14
40
1 26
14 43
1
22
14 47
40
1 49
14 20
1 45 14 24
1 41
14 28
1 37
14
32
1 34
14 35
1
30
14 39
50
1 57
14 12
1 53 14 16
1 49
14 20
1 45
14
24
1 42
14 27
1
38
14 31
8 00
2 05
14 04
2 01 I 14 08
1 57
14 12
1 53
14
16
1 50
14 19
1
46
14 23
10
2 12
13 57
2 08 | 14 01
2 04
14 05
2 00
14
09
1 57
14 12
1
53
14 16
20
2 19
13 50
2 15 13 54
2 11
13 58
2 07
14
02
2 04
14 05
2
00
14 09
8 30
2 26
13 43
2 22
13 47
2 18
13 51
2 14
13
55
2 11
13 58
2
07
14 02
40
2 33
13 36
2 29 13 40
2 25
13 44
2 21
13
48
2 18 13 51
2
14
13 55
50
2 39
13 30
2 35 ! 13 34
2 31
13 38
2 27
13
42
2 24 13 45
2
20
13 49
9 00
2 45
13 24
2 41 i 13 28
2 37
13 32
2 33
13
36
2 30
13 39
2
26
13 43
20
2 57
13 12
2 53 ' 13 16
2 49
13 20
2 45
13
24
2 42
13 27
2
38
13 31
40
3 08
13 01
3 04 ^ 13 05
3 00
13 09
2 56
13
13
2 53
13 16
2
49
13 20
10 00
3 19
12 50
3 15 12 54
3 11
12 58
3 07
13
02
3 04
13 05
3
00
13 09
20
3 29
12 40
3 25 i 12 44
3 21
12 48
3 17
12
52
3 14
12 55
3
10
12 59
40
3 38
12 31
3 34 i 12 35
3 30
12 39
3 26
12
43
3 23
12 46
3
19
12 50
11 00
3 47
12 22
3 43 12 26
3 39
12 30
3 35
12
34
3 32
12 37
3
28
12 41
30
3 59
12 10
3 55 12 14
3 51
12 18
3 47
12
22
3 44
12 25
3
40
12 29
12 00
4 10
11 59
4 06 ! 12 03
4 02
12 07
3 58
12
11
3 55
12 14
3
51
12 18
30
4 21
11 48
4 17 ! 11 52
4 13
11 56
4 09
12
00
4 06
12 03
4
02
12 07
13 00
4 31
11 38
4 27 11 42
4 23
11 46
4 19
11
50
4 16
11 53
4
12
11 57
30
4 40
11 29
4 36
11 33
4 32
11 37
4 28
11
41
4 25
11 44
4
21
11 48
14 00
4 48
11 21
4 44
11 25
4 40
11 29
4 36
11
33
4 33
11 36
4
29
11 40
15 00
5 04
11 05
5 00
11 09
4 56
11 13
4 52
11
17
4 49
11 20
4
45
11 24
16 00
5 17
10 52
5 13
10 56
5 09
11 00
5 05
11
04
5 02
11 07
4
58
11 11
17 00
5 30
10 39
5 26
10 43
5 22
10 47
5 18
10
51
5 15
10 54
5
11
10 58
18 00
5 40
10 29
5 36
10 33
5 32
10 37
5 28
10
41
5 25
10 44
5
21
10 48
19 00
5 50
10 19
5 46
10 23
5 42
10 27
5 38
10
31
5 35 10 34
5
31
10 38
20 00
5 58
10 10
5 54
10 14
5 50
10 18
5 46
10
22
5 43
10 25
5
39
10 29
22 00
6 14
9 54
6 10
9 58
6 06
10 02
6 02
10
06
5 59
10 09
5
55
10 13
24 00
6 27
9 41
6 23 j 9 45
6 19
9 49
6 15
9
53
6 12 9 56
6
08
10 00
26 00
6 38
9 30
6 34 9 34
6 30
9 38
6 26
9
42
6 23 9 45
6
19
9 49
28 00
6 48
9 20
6 44 9 24
6 40
9 28
6 36
9
32
6 33 9 35
6
29
9 39
30 00
6 56
9 12
6 52 9 16
6 48
9 20
6 44
9
24
6 41 9 27
6
37
9 31
32 00
7 04
9 04
7 00 j 9 08
6 56
9 12
6 52
9
16
6 49 9 19
6
45
9 23
34 00
7 11 8 57
7 07
9 01
7 03
9 05
6 59
9J)9
6 56 9 12
6
52
9 16
36 00
7 17 8 51
7 13
8 55
7 09
8 59
7 Q5
9 03
7 02 9 06
6
58
9 10
38 00
7 22
8 46
7 18
8 50
7 14
8 54
7 10
8 58
7 07 9 01
7
03
9 05
40 00
7 27
3 40
7 23
8 44
7 19
8 48
7 15
8 52
7 12
8 55
7
08
8 59
45 00
7 38 8 29
7 34
8 33
7 30
•8 37
7 26
8 41
7 23
8 44
7
19
8 48
50 00
7 46
3 20
7 42
8 24
7 38
8 28
7 34
8 32
7 31
8 35
7
27
8 39
55 00
7 53 8 12
7 49
8 16
7 45
8
20
7 41
8 24
7 38
8 27
7
34
8 31
60 00
7 59 8 05
7 55
8 09
7 51
8
13
7 47
8 17
7 44 8 20
7
40
8 24
65 00
8 06 7 58
8 02
8 02
7 58
8
06
7 54
8 10
7 51 8 13
7
47
8 17
70 00
8 11 7 52
8 07
7 56
8 03
8
00
7 59
8 04
7 56 i 8 07
7
52
8 11
75 00
8 15 7 47
8 11
7 51
8 07
7
55
8 03
7 59
8 00 8 02
7
56
8 06
80 00
8 21
7 41
8 17
745
8 13
7
49
8 09
7 53
8 06 7 56
8
02
8 00
85 00
8 25 !
7 36
8 21
7 40
8 17
7
44
8 13
7 48
8 10
7 51
8
06
7 55
90 00
8 29 7 31
8 25 1 7 35
8 21
7
39
8 17
7 43
8 14 7 46
8
10
7 50
I
Day of Month. Jan.
Feb.
Mar.
Apr.
May.
Fune.
July, j Aug.
Sept.
Oct.
Nov. Dec.
ADDITIONAL CORR.
FOR SUN'S ALT.
1st to 15th.... +18
+15
+8
0
- 8 -
-13
"i "
-14 -11
-5
+3
+11 +16
16th to 31st... +17
+12
+4
-4
-11 -
-14
-13 - 9
-1
+7
+14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
aking account of the variation of the Sun's semidiameter in the duTerent months of the year is given at the foot of the main table.
Page 932] TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
65 Feet.
66 Feet.
67 Feet.
68 Feet.
69 Feet.
70 Feet.
OBS. ALT.
O
*
O
*
O
*
0
*
O
*
o
* -
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
0 /
6 30
i a
0 21
15 48
0 18
15 51
0 14
i a
15 55
/ //
0 10
15 59
0 07
16 02
0 03
16 06
40
0 31
15 38
0 28
15 41
0 24
15 45
0 20
15 49
0 17
15 52
0 13
15 56
50
0 41
15 28
0 38
15 31
0 34
15 35
0 30
15 39
0 27
15 42
0 23
15 46
7 00
0 51
15 18
0 48
15 21
0 44
15 25
0 40
15 29
0 37
15 32
0 33
15 36
10
1 00
15 09
0 57
15 12
0 53
15 16
0 49
15 20
0 46
15 23
0 42
15 27
20
1 09
15 00
1 06
15 03
1 02
15 07
0 58
15 11
0 55
15 14
0 51
15 18
7 30
1 18
14 51
1 15
14 54
1 11
14 58
1 07
15 02
1 04
15 05
1 00
15 09
40
1 26
14 43
1 23
14 46
1 19
14 50
1 15
14 54
1 12
14 57
1 08
15 01
50
1 34
14 35
1 31
14 38
1 27
14 42
1 23
14 46
1 20
14 49
1 16
14 53
8 00
1 42
14 27
1 39
14 30
1 35
14 34
1 31
14 38
1 28
14 41
1 24
14 45
10
1 49
14 20
1 46
14 23
1 42
14 27
1 38
14 31
1 35
14 34
1 31
14 38
20
1 56
14 13
1 53
14 16
1 49
14 20
1 45
14 24
1 42
14 27
1 38
14 31
8 30
2 03
14 06
2 00
14 09
1 56
14 13
1 52
14 17
1 49
14 20
1 45
14 24
40
2 10
13 59
2 07
14 02
2 03
14 06
1 59
14 10
1 56
14 13
1 52
14 17
50
2 16
13 53
2 13
13 56
2 09
14 00
2 05
14 04
2 02
14 07
1 58
14 11
9 00
2 22
13 47
2 19
13 50
2 15
13 54
2 11
13 58
2 08
14 01
2 04
14 05
20
2 34
13 35
2 31
13 38
2 27
13 42
2 23
13 46
2 20
13 49
2 16
13 53
40
2 45
13 24
2 42
13 27
2 38
13 31
2 34
13 35
2 31
13 38
2 27
13 42
10 00
2 56
13 13
2 53
13 16
2 49
13 20
2 45
13 24
2 42
13 27
2 38
13 31
20
3 06
13 03
3 03
13 06
2 59
13 10
2 55
13 14
2 52
13 17
2 48
13 21
40
3 15
12 54
3 12
12 57
3 08
13 01
3 04
13 05
3 01
13 08
2 57
13 12
11 00
3 24
12 45
3 21
12 48
3 17
12 52
3 13
12 56
3 10
12 59
3 06
13 03
30
3 36
12 33
3 33
12 36
3 29
12 40
3 25
12 44
3 22
12 47
3 18
12 51
12 00
3 47
12 22
3 44
12 25
3 40
12 29
3 36
12 33
3 33
12 36
3 29
12 40
30
3 58
12 11
3 55
12 14
3 51
12 18
3 47
12 22
3 44
12 25
3 40
12 29
13 00
4 08
12 01
4 05
12 04
4 01
12 08
3 57
12 12
3 54
12 15
3 50
12 19
30
4 17
11 52
4 14
11 55
4 10
11 59
4 06
12 03
4 03
12 06
3 59
12 10
14 00
4 25
11 44
4 22
11 47
4 18
11 51
4 14
11 55
4 11
11 58
4 07
12 02
15 00
4 41
11 28
4 38
11 31
4 34
11 35
4 30
11 39
4 27
11 42
4 23
11 46
16 00
4 54
11 15
4 51
11 18
4 47
11 22
4 43
11 26
4 40
11 29
4 36
11 33
17 00
5 07
11 02
5 04
11 05
5 00
11 09
4 56
11 13
4 53
11 16
4 49
11 20
18 00
5 17
10 52
5 14
10 55
5 10
10 59
5 06
11 03
5 03
11 06
4 59
11 10
19 00
5 27
10 42
5 24
10 45
5 20
10 49
5 16
10 53
5 13
10 56
5 09
11 00
20 00
5 35
10 33
5 32
10 36
5 28
10 40
5 24
10 44
5 21
10 47
5 17
10 51
22 00
5 51
10 17
5 48
10 20
5 44
10 24
5 40
10 28
5 37
10 31
5 33
10 35
24 00
6 04
10 04
6 01
10 07
5 57
10 11
5 53
10 15
5 50
10 18
5 46
10 22
26 00
6 15
9 53
6 12
9 56
6 08
10 00
6 04
10 04
6 01
10 07
5 57
10 11
28 00
6 25
9 43
6 22
9 46
6 18
9 50
6 14
9 54
6 11
9 57
6 07
10 01
30 00
6 33
9 35
6 30
9 38
6 26
9 42
6 22
9 46
6 19
9 49
6 15
9 53
32 00
6 41
9 27
6 38
9 30
6 34
9 34
6 30
9 38
6 27
9 41
6 23
9 45
34 00
6 48
9 20
6 45
9 23
6 41
9 27
6 37
9 31
6 34
9 34
6 30
9 38
36 00
6 54
9 14
6 51
9 17
6 47
9 21
6 43
9 25
6 40
9 28
6 36
9 32
38 00
6 59
9 09
6 56
9 12
6 52
9 16
6 48
9 20
6 45
9 23
6 41
9 27
40 00
7 04
9 03
7 01
9 06
6 57
9 10
6 53
9 14
6 50
9 17
6 46
9 21
45 00
7 15
8 52
7 12
8 55
7 08
8 "59
7 04
9 03
7 01
9 06
6 57
9 10
50 00
7 23
8 43
7 20
8 46
7 16
8 50
7 12
8 54
7 09
8 57
7 05
9 01
55 00
7 30
8 35
7 27
8 38
7 23
8 42
7 19
8 46
7 16
8 49
7 12
8 53
60 00
7 36
8 28
7 33
8 31
7 29
8 35
7 25
8 39
7 22
8 42
7 18
8 46
65 00
7 43
8 21
7 40
8 24
7 36
8 28
7 32
8 32
7 29
8 35
7 25
8 39
70 00
7 48
8 15
7 45
8 18
7 41
8 22
7 37
8 26
7 34
8 29
7 30
8 33
75 00
7 52
8 10
7 49
8 13
7 45
8 17
7 41
8 21
7 38
8 24
7 34
8 28
80 00
7 58
8 04
7 55
8 07
7 51
8 11
7 47
8 15
7 44
8 18
7 40
8 22
85 00
8 02
7 59
7 59
8 02
7 55
8 06
7 51
8 10
7 48
8 13
7 44
8 17
90 00
8 06
7 54
8 03
7 57
7 59
8 01
7 55
8 05
7 52
8 08
7 48
8 12
Day of Month. Jan.
Feb. Mar. Apr. May.
June. July. Aug.
Sept. Oct. Nov. Dec.
ADDITIONAL CORR. „
FOR SUN'S ALT. lst to 15th.... +18
+ 15 +8 0-8
-13 -14 -11
-5 +3 +11 +16
16th to 31st... +17
+12 +4 -4 -11
-14 -13 - 9
-1 +7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction ; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
taking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
TABLE 46.
[Page 933
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb to Find
the True Altitude— Continued .
HEIGHT OF THE EYE.
71 Feet.
72 Feet.
73
Feet.
74 Feet.
75 Feet.
76 Feet.
OBS. ALT
/T)
*
Star's
Corr.
*
*
W
Sun's
Corr.
O
Sun's
Corr.
Star's
Corr.
O
Sun's
Corr.
Star's
Corr.
O
Sun's
Corr.
Star's
Corr.
Sun's
Corr.
7
Star's
Corr.
(— )
Sun's Star's
Corr. ~°™-
6 30
0 00
16 09
-0 04
16 13
-0 08
16 17
-0 11
16
20
-0 14 16 23
-0
17 16 26
40
0 10
15 59
+0 06
16 03
+0 02
16 07
-0 01
16
10
-0 04 16 13
-0
or 16 16
50
0 20
15 49
0 16
15 53
0 12
15 57
+0 09
16
00
+0 06 16 03
+0
03 16 06
7 00
0 30
15 39
0 26
15 43
0 22
15 47
1 19
15
50
0 16 15 53
0
13 15 56
10
0 39
15 30
0 35
15 34
0 31
15 38
1 28
15
41
0 25 15 44
o
22 In 47
20
0 48
15 21
0 44
15 25
0 40
15 29
1 37
15
32
0 34 15 35
0 31 In 38
7 30
0 57
15 12
0 53
15 16
0 49
15 20
1 46
15
23
0 43 15 26
0
40 15 29
40
1 05
15 04
1 01
15 08
0 57
15 12
1 54
15
15
0 51 15 18
0
48 15 21
50
1 13
14 56
1 09
15 00
1 05
15 04
1 02
15
07
0 59 15 10
0 5fi
15 13
8 00
1 21 | 14 48
1 17
14 52
1 13
14 56
1 10
14
59
1 07 15 02
1
04
15 On
10
1 28 14 41
1 24
14 45
1 20
14 49
1 17
14
52
1 14 14 55
1
11 14 58
20
1 35 14 34
1 31
14 38
1 27
! 14 42
1 24
14
45
1 21 j 14 48
1
18 14 51
8 30
1 42 14 27
1 38
14 31
1 34
14 35
1 31
14
38
1 28 i 14 41
1
25 14 44
40
1 49
14 20
1 45
14 24
1 41
14 28
1 38
14
31
1 35 ! 14 34
1
32
14 37
50
1 55
14 14
1 51
14 18
1 47
14 22
1 44
14
25
1 41 14 28
1
38
14 31
9 00
2 01
14 08
1 57
14 12
1 53
14 16
1 50
14
19
1 47 14 22
1
44
14 25
20
2 13
13-56
2 09
14 00
2 05
14 04
2 02
14
07
1 59 14 10
1
56
14 13
40
2 24
13 45
2 20
13 49
2 16
13 53
2 13
13
56
2 10 ! 13 59
2
07
14 02
10 00
2 35
13 34
2 31
13 38
2 27
13 42
2 24
13
45
2 21
13 48
2
18
13 51
20
2 45 13 24
2 41
13 28
2 37
1 13 32
2 34
13
35
2 31
13 38
2
28
13 41
40
2 54 1 13 15
2 50
13 19
2 46
13 23
2 43
13
26
2 40
13 29
2
37
13 32
11 00
3 03
13 06
2 59
13 10
2 55
13 14
2 52
13
17
2 49
13 20
2
46
13 23
30
3 15
12 54
3 11
12 58
3 07
13 02
3 04
13
05
3 01 ! 13 08
2
58
13 11
12 00
3 26
12 43
3 22
12 47
3 18
12 51
3 15
12
54
3 12
12 57
3
09
13 00
30
3 37
12 32
3 33
12 36
3 29
12 40
3 26
12
43
3 23
12 46
3
20
12 49
13 00
3 47
12 22
3 43 i
12 26
3 39
12 30
3 36
12
33
3 33
12 36
3
30
12 39
30
3 56
12 13
3 52
12 17
3 A
S
12 21
3 45 12
24
3 42
12 27
3
39
12 30
14 00
4 04
12 05
4 00 i
12 09
3 56
12 13
3 53
12
16
3 50
12 19
3
47
12 22
15 00
4 20
11 49
4 16 ;
11 53
4 12
11 57
4 09
12 00
4 06
12 03
4
03
12 06
16 00
4 33
11 36
4 29
11 40
4 25
11 44
4 22
11
47
4 19
11 50
4
16
11 53
17 00
4 46
11 23
4 42 '
11 27
4 38
11 31
4 35
11 34
4 32
11 37
4
29
11 40
18 00
4 56
11 13
4 52
11 17
4 48
11 21
4 45
11 24
4 42
11 27
4
39
11 30
19 00
5 06
11 03
5 02
11 07
4 58
11 11
4 55
11
14
4 52
11 17
4
49
11 20
20 00
5 14
10 54
5 10
10 58
5 06
11 02
5 03
11 05
5 00
11 08
4
57
11 11
22 00
5 30
10 38
5 26
10 42
5 22
10 46
5 19
10 49
5 16
10 52
5
13
10 55
24 00
5 43
10 25
5 39
10 29
5 35
10 33
5 32
10 36
5 29
10 39
5
26
10 42
26 00
5 54
10 14
5 50
10 18
5 46
10 22
5 43
10 25
5 40
10 28
5
37
10 31
28 00
6 04
10 04
6 00 :
10 08
5 56
10 12
5 53 i 10 15
5 50
10 18
5
47
10 21
30 00
6 12
9 56
6 08 !
10 00
6 04
10 04
6 01 10 07
5 58
10 10
5
55
10 13
32 00
6 20
9 48
6 16
9 52
6 12
9 56
6 09 ! 9 59
6 06
10 02
6
03
10 05
34 00
6 27
9 41
6 23
9 45
6 19
9 49
6 16 9 52
6 13
9 55
6
10
9 58
36 00
6 33
9 35
6 29
9 39
6 25
9 43
6 22
9 46
6 19
9 49
6
16
9 52
38 00
6 38
9 30
6 34 i
9 34
6 30
9 38
6 27
9 41
6 24
9 44
6
21
9 47
40 00
6 43
9 24
6 39
9 28
6 35
9 32
6 32 ; 9 35
6 29
9 38
6
26
9 41
45 00
6 54
9 13
6 50
9 17
6 46
9
21
6 43 9 24
6 40
9 21
6
37
9 30
50 00
7 02 9 04
6 58 :
9 08
6 54
9
12
6 51 9 15
6 48
9 18
6
45
9 21
55 00
7 09
S 56
7 05
9 00
7 01
9
-04
6 58 9 07
6 55
9 10
6
52
9 13
60 00
7 15
3 49
7 11 !
8 53
7 07
8
57
7 04 ! 9 00
7 01
9 03
6
58
9 06
65 00
7 22
8 42
7 18
8 46
7 14
S
50
7 11 8 53
7 08
8 56
7
05
8 59
70 00
7 27
3 36
7 23.
8 40
7 19
S
44
7 16
8 47
7 13
8 50
7
10
8 53
75 00
7 31
8 31
7 27
8 35
7 23
8
39
7 20
8 42
7 17
8 45
7
14
8 48
80 00
7 37
3 25
7 33
8 29
7 29
8
33
7 26 8 36
7 23
8 39
7
20
8 42
85 00
7 41
•
3 20
7 37
8 24
7 33
8
28
7 30 8 31
7 27
8 34
7
24
8 37
90 00
7 45
<
3 15
-L-7 41
8 19
+7 37
S
23
+7 34
8 26
-r7 31
8 29
+7
28
8 32
Day of Month.
Jan.
Feb.
Mar.
Apr.
May. .
Fune.
July. Aug.
Sept.
Oct.
Nov
. Dec.
ADDITIONAL CORK.
FOE SUN'S ALT.
1st to loth...
.+18
+ 15
+8
0
- 8 -
-13
-14 -11
-5
+3
+ 11
+16
16th to 31st... +17 +12
+4
-4
-11 -
-14
-13 - 9
-1
+7
+ 1-4
+18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction ; and for the observed altitude
f the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as It'. A supplementary correction
aking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
Page 934] TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
77 Feet.
78 Feet.
79 Feet.
80 Feet.
81 Feet,
82 Feet.
OBS. ALT
0
Sun's
Corr.
*
Star's
Corr.
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
Star's
Corr.
0 I
6 30
-0 21
16.30
-0 24
16 33
-0 28
16 37
-0 31
16 40
-0 34
16 43
-0 37
16 46
40
-0 11
16 20
-0 14
16 23
-0 18
16 27
-0 21
16 30
-0 24
16 33
-0 27
16 36
50
-0 01
16 10
-0 04
16 13
-0 08
16 17
-0 11
16 20
-0 14
16 23
-0 17
16 26'
7 00
+Q 09
16 00
+0 06
16 03
+0 02
16 07
-O'Ol
16 10
-0 04
16 13
-0 07
16 16
10
0 18
15 51
0 15
15 54
0 11
15 58
+0 08
16 01
+0 05
16 04
+0 02
16 07
20
0 27
15 42
0 24
15 45
0 20
15 49
0 17
15 52
0 14
15 55
0 11
15 58
7 30
0 36
15 33
0 33
15 36
0 29
15 40
0 26
15 43
0 23
15 46
0 20
15 49
40
0 44
15 25
0 41
15 28
0 37
15 32
0 34
15 35
0 31
15 38
0 28
15 41
50
0 52
15 17
0 49
15 20
0 45
15 24
0 42
15 27
0 39
15 30
0 36
15 33
8 00
1 00
15 09
0 57
15 12
0 53
15 16
0 50
15 19
0 47
15 22
0 44
15 25
10
1 07
15 02
1 04
15 05
1 00
15 09
0 57
15 12
0 54
15 15
0 51
15 18
20
1 14
14 55
1 11
14 58
1 07
15 02
1 04
15 05
1 01
15 08
0 58
15 11
8 30
1 21
14 48
1 18
14 51
1 14
14 55
1 11
14 58
1 08
15 01
1 05
15 04
40
1 28
14 41
1 25
14 44
1 21
14 48
1 18
14 51
1 15
14 54
1 12
14 57
50
1 34
14 35
1 31
14 38
1 27
14 42
1 24
14 45
1 21
14 48
1 18
14 51
9 00
1 40
14 29
1 37
14 32
1 33
14 36
1 30
14 39
1 27
14 42
1 24
14 45
20
1 52
14 17
1 49
14 20
1 45
14 24
1 42
14 27
1 39
14 30
1 36
14 33
40
2 03
14 06
2 00
14 09
1 56
14 13
1 53
14 16
1 50
14 19
1 47
14 22
10 00
2 14
13 55
2 11
13 58
2 07
14 02
2 04
14 05
2 01
14 08
1 58
14 11
20
2 24
13 45
2 21
13 48
2 17
13 52
2 M
13 55
2 11
13 58
2 08
14 01
40
2 33
13 36
2 30
13 39
2 26
13 43
2 23
13 46
2 20
13 49
2 17
13 52
11 00
2 42
13 27
2 39
13 30
2 35
13 34
2 32
13 37
2 29
13 40
2 26
13 43
30
2 54
13 15
2 51
13 18
2 47
13 22
2 44
13 25
2 41
13 28
2 38
13 31
12 00
3 05
13 04
3 02
13 07
2 58
13 11
2 55
13 14
2 52
13 17
2 49
13 20
30
3 16
12 53
3 13
12 56
3 09
13 00
3 06
13 03
3 03
13 06
3 00
13 09
13 00
3 26
12 43
3 23
12 46
3 19
12 50
3 16
12 53
3 13
12 56
3 10
12 59
30
3 35
12 34
3 32
12 37
3 28
12 41
3 25
12 44
3 22
12 47
3 19
12 50
14 00
3 43
12 26
3 40
12 29
3 36
12 33
3 33
12 36
3 30
12 39
3 27
12 42
15 00
3 59
'12 10
3 56
12 13
3 52
12 17
3 49
12 20
3 46
12 23
3 43
12 26
16 00
4 12
11 57
4 09
12 00
4 05
12 04
4 02
12 07
3 59
12 10
3 56
12 13
17 00
4 25
11 44
4 22
11 47
4 18
11 51
4 15
11 54
4 12
11 57
4 09
12 00
18 00
4 35
11 34
4 32
11 37
4 28
11 41
4 25
11 44
4 22
11 47
4 19
11 50
19 00
4 45
11 24
4 42
11 27
4 38
11 31
4 35
11 34
4 32
11 37
4 29
11 40
20 00
4 53
11 15
4 50
11 18
4 46
11 22
4 43
11 25
4 40
11 28
4 37
11 31
22 00
5 09
10 59
5 06
11 02
5 02
11 06
4 59
11 09
4 56
11 12
4 53
11 15
24 00
5 22
10 46
5 19
10 49
5 15
10 53
5 12
10 56
5 09
10 59
5 06
11 02
26 00
5 33
10 35
5 30
10 38
5 26
10 42
5 23
10 45
5 20
10 48
5 17
10 51
28 00
5 43
10 25
5 40
10 28
5 36
10 32
5 33
10 35
5 30
10 38
5 27
10 41
30 00
5 51
10 17
5 48
10 20
5 44
10 24
5 41
10 27
5 38
10 30
5 35
10 33
32 00
5 59
10 09
5 56
10 12
5 52
10 16
5 49
10 19
5 46
10 22
5 43
10 25
34 00
6 06
10 02
6 03
10 05
5 59
10 09
5 56
10 12
5 53
10 15
5 50
10 18
36 00
6 12
9 56
6 09
9 59
6 05
10 03
6 02
10 06
5 59
10 09
5 56
10 12
38 00
6 17
9 51
6 14
9 54
6 10
9 58
6 07
10 01
6 04
10 04
6 01
10 07
40 00
6 22
9 45
6 19
9 48
6 15
9 52
6 12
9 55
6 09
9 58
6 06
10 01
45 00
6 33
9 34
6 30
9 37
6 26
9 41
6 23
9 44
6 20
9 47
6 17
9 50
50 00
6 41
9 25
6 38
9 28
6 34
9 32
6 31
9 35
6 28
9 38
6 25
9 41
55 00
6 48
9 17
6 45
9 20
6 41
9 24
6 38
9 27
6 35
9 30
6 32
9 33
60 00
6 54
9 10
6 51
9 13
6 47
9 17
6 44
9 20
6 41
9 23
6 38
9'26
65 00
7 01
9 03
6 58
9 06
6 54
9 10
6 51
9 13
6 48
9 16
6 45
9 19
70 00
7 06
8 57
7 03
9 00
6 59
9 04
6 56
9 07
6 53
9 10
6 50
9 13
75 00
7 10
8 52
7 07
8 55
7 03
8 59
7 00
9 02
6 57
9 05
6 54
9 08
80 00
7 16
8 46
7 13
8 49
7 09
8 53
7 06
8 56
7 03
8 59
7 00
9 02
85 00
7 20
8 41
7 17
8 44
7 13
8 48
7 10
8 51
7 07
8 54
7 04
8 57
90 00
+7 24
8 36
+7 21
8 39
+7 17
8 43
+7 14
8 46
+7 11
8 49
+7 08
8 52
Day of Month. Jan.
Feb. Mar. Apr.
May.
June. July. Aug.
Sept. Oct. Nov. Dec.
A r*
ADDITIONAL L'ORR. ff
FOB SUN'S ALT. lgt to 15th___ _ +18
+ 15 +8 0
- 8
-13 -14 -11
-5 +3 +11 +16
16th to 31st... +17
+12 +4 -4
-11
-14 -13 - 9
-1 +7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction ; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
laking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table.
TABLE 46. [Pare 935
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
83 Feet.
84 Feet.
85 Feet.
86 Feet.
87 Feet.
88 Feet.
OBS. ALT.
Sun's
Corr.
Star's
Corr.
Sun's
Corr.
Star's
Corr.
Sun's
Corr.
Star's
Corr.
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
*
Star's
Conr.
6 30
-0 41
16 50
-0 44
16 53
-0 47 | 16 56
-0 50
16 59
/ u
-0 53
17 02
-0 57
17 06
40
-0 31
16 40
-0 34
16 43
-0 37 i 16 46
-0 40
16 49-
-0 43
16 52
-0 47
16 56
50
-0 21
16 30
-0 24
16 33
-0 27
16 36
-0 30
16 39
-0 33
16 42
-0 37
16 46
7 00
-0 11
16 20
-0 14
16 23
-0 17
16 26
-0 20
16 29
-0 23
16 32
-0 27
16 36
10
-0 02
16 11
-0 05
16 14
-0 08
16 17
-0 11
16 20
-0 14
16 23
-0 18
16 27
20
+0 07
16 02
+0 04
16 05
+0 01
16 08
-0 02
16 11
-0 05
16 14
-0 09
16 18
7 30
0 16
15 53
0 13
15 56
0 10
15 59
+0 07
16 02
+0 04
16 05
0 00
16 09
40
0 24
15 45
0 21
15 48
0 18
15 51
0 15
15 54
0 12
15 57
+0 08
16 01
50
0 32
15 37
0 29
15 40
0 26
15 43
0 23
15 46
0 20
15 49
0 16
15 53
8 00
0 40
15 29
0 37
15 32
0 34
15 35
0 31
15 38
0 28
15 41
0 24
15 45
10
0 47
15 22
0 44
15 25
0 41
15 28
0 38
15 31
0 35
15 34
0 31
15 38
20
0 54
15 15
0 51
15 18
0 43
15 21
0 45
15 24
0 42
15 27
0 38
15 31
8 30
1 01
15 08
0 58
15 11
0 55
15 14
0 52
15 17
0 49
15 20
0 45
15 24
40
1 08
15 01
1 05
15 04
1 02
15 07
0 59
15 10
0 56
15 13
0 52
15 17
50
1 14
14 55
1 11
14 58
1 08
15 01
1 05
15 04
1 02
15 07
0 58
15 11
9 00
1 20
14 49
1 17
14 52
1 14
14 55
1 11
14 58
1 08
15 01
1 04
15 05
20
1 32
14 37
1 29
14 40
1 26
14 43
1 23
14 46
1 20
14 49
1 16
14 53
40
1 43
14 26
1 40
14 29
1 37
14 32
1 34
14 35
1 31
14 38
1 27
14 42
10 00
1 54
14 15
1 51
14 18
1 48
14 21
1 45
14 24
1 42
14 27
1 38
14 31
20
2 04
14 05
2 01
14 08
1 58
14 11
1 55
14 14
1 52
14 17
1 48
14 21
40
2 13
13 56
2 10
13 59
2 07
14 02
2 04
14 05
2 01
14 08
1 57
14 12
11 00
2 22
13 47
2 19
13 50
2 16
13 53
2 13
13 56
2 10
13 59
2 06
14 03
30
2 34
13 35
2 31
13 38
2 28
13 41
2 25
13 44
2 22
13 47
2 18
13 51
12 00
2 45
13 24
2 42
13 27
2 39
13 30
2 36
13 33
2 33
13 36
2 29
13 40
30
2 56
13 13
2 53
13 16
2 50
13 19
2 47
13 22
2 44
13 25
2 40
13 29
13 00
3 06
13 03
3 03
13 06
3 00
13 09
2 57
13 12
2 54
13 15
2 50
13 19
30
3 15
12 54
3 12
12 57
3 09
1300
306
1303
3 03
13 06
2 59
13 10
14 00
3 23
12 46
3 20
12 49
3 17
12 52
3 14
12 55
3 11
12 58
3 07
13 02
15 00
3 39
12 30
3 36
12 33
3 33
12 36
3 30
12 39
3 27
12 42
3 23
12 46
16 00
3 52
12 17
3 49
12 20
3 46
12 23
3 43
12 26
3 40
12 29
3 36
12 33
17 00
4 05
12 04
4 02
12 07
3 59
12 10
3 56
12 13
3 53
12 16
3 49
12 20
18 00
4 15
11 54
4 12
11 57
4 09
12 00
4 06
12 03
4 03
12 06
3 59
12 10
19 00
4 25
11 44
4 22
11 47
4 19
11 50
4 16
11 53
4 13
11 56
4 09
12 00
20 00
4 33
11 35
4 30
11 38
4 27
11 41
4 24
11 44
4 21
11 47
4 17
11 51
22 00
4 49
11 19
4 46
11 22
4 43
11 25
4 40
11 28
4 37
11 31
4 33
11 35
24 00
5 02
11 06
4 59
11 09
4 56
11 12
4 53
11 15
4 50
11 18
4 46
11 22
26 00
5 13
10 55
5 10
10 58
5 07
11 01
5 04
11 04
5 01
11 07
4 57
11 11
28 00
5 23
10 45
5 20
10 48
5 17
10 51
5 14
10 54
5 11 10 57
5 07
11 01
30 00
5 31
10 37
5 28
10 40
5 25
10 43
5 22
10 46
5 19 10 49
5 15
10 53
32 00
5 39
10 29
5 36
10 32
5 33
10 35
5 30
10 38
5 27
10 41
5 23
10 45
34 00
5 46
10 22
5 43
10 25
5 40 j 10 28
5 37
10 31
5 34
10 34
5 30 10 38
36 00
6 52
10 16
5 49
10 19
5 46 i 10 22
5 43
10 25
5 40
10 28
5 36 I 10 32
38 00
5 57
10 11
5 54
10 14
5 51
10 17
5 48
10 20
5 45
10 23
5 41
10 27
40 00
6 02
10 05
5 59
10 08
5 56
10 11
5 53
10 14
5 50
10 17
5 46
10 21
45 00
6 13
9 54
6 10
9 57
6 07
10 00
6 04
10 03
6 01
10 06
5 57
10 10
50 00
6 21
9 45
6 18
9 48
6 15
9 51
6 12 9 54
6 09
9 57
6 05
10 01
55 00
6 28
9 37
6 25
9 40
6 22 9 43
6 19 9 46
6 16 9 49
6 12
9 53
60 00
6 34
9 30
6 31
9 33
6 28 9 36
6 25 9 39
6 22
9 42
6 18
9 46
65 00
6 41
9 23
6 38
9 26
6 35
9 29
6 32
9 32
6 29
9 35
6 25
9 39
70 00
6 46
9 17
6 43
9 20
6 40
9 23
6 37
9 26
6 34
9 29
6 30
9 33
75 00
6 50
9 12
6 47
9 15
6 44
9 18
6 41
9 21
6 38
9 24
6 34
9 28
80 00
6 56
9 06
6 53
9 09
6 50
9 12
6 47
9 15
6 44
9 18
6 40
9 22
85 00
7 00
9 01
6 57
9 04
6 54
9 07
6 51 9 10
6 48
9 13
6 44
9 17
90 00
+7 04
8 56
+7 01
8 59
+6 58
9 02
+6 55 9 05
+6 52
9 08
+6 48
9 12
' Day of Month. Jan.
Feb. Mar. Apr. May.
June. July. Aug.
Sept.
Oct. Nov. Dec.
ADDITIONAL CORR.
FOR SUN'S ALT. ist to 15th +18
+15 +8 0-8
-13 -14 -11
-5
+3 +11 +16
16th to 31st... +17
+12 +4 -4 -11
-14 -13 - 9
-1
+7 +14 +18
* Thecorrections for theobserved altitude of a Star or Planet involves the dip and the refraction: an^^^st!^™^
y^^s^^^^^^^^^^^^^^^^^
Page 936] TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
89 Feet.
90 Feet.
91 Feet.
92 Feet.
93 Feet.
94 Feet.
OBS. ALT.
O
Sun's
Corr.
Star's
Corr.
O
Sun's
Corr.
*
Star's
Corr.
O
Sun's
Corr.
Star's
Corr.
O
Sun's
Corr.
Star's
Corr.
O
Sun's
Corr.
Star's
Corr.
Sun's
Corr.
Star's
Corr.
0 /
6 30
/ //
-1 00
-1 06
17 15
-1 09
17 18
-1 12
17 21
-1 15
17 24
17 09
-1 03
17 12
^O
-0 50
16 59
-0 53
17 02
-0 56
17 05
-0 59
17 08
-1 02
17 11
-1 05
17 14
50
-0 40
16 49
-0 43
16 52
-0 46
16 55
-0 49
16 58
-0 52
17 01
-0 55
17 04
7 00
-0 30
16 39
-0 33
16 42
-0 36
16 45
-0 39
16 48
-0 42
16 51
-0 45
16 54
10
-0 21
16 30
-0 24
16 33
-0 27
16 36
-0 30
16 39
-0 33
16 42
-0 36
16 45
20
-0 12
16 21
-0 15
16 24
-0 18
16 27
-0 21
16 30
-0 24
16 33
-0 27
16 36
7 30
-0 03
16 12
-0 06
16 15
-0 09
16 18
-0 12
16 21
-0 15
16 24
-0 18
16 27
40
+0 05
16 04
+0 02
16 07
-0 01
16 10
-0 04
16 13
-0 07
16 16
-0 10
16 19
50
0 13
15 56
0 10
15 59
+0 07
16 02
+0 04
16 05
+0 01
16 08
-0 02
16 11
8 00
0 21
15 48
0 18
15 51
0 15
15 54
0 12
15 57
0 09
16 00
+0 06
16 03
10
0 28
15 41
0 25
15 44
0 22
15 47
0 19
15 50
0 16
15 53
0 13
15 56
20
0 35
15 34
0 32
15 37
0 29
15 40
0 26
15 43
0 23
15 46
0 20
15 49
8 30
0 42
15 27
0 39
15 30
0 36
15 33
0 33
15 36
0 30
15 39
0 27
15 42
40
0 49
15 20
0 46
15 23
0 43
15 26
0 40
15 29
0 37
15 32
0 34
15 35
50
0 55
15 14
0 52
15 17
0 49
15 20
0 46
15 23
0 43
15 26
0 40
15 29
9 00
1 01
15 08
0 58
15 11
0 55
15 14
0 52
15 17
0 49
15 20
0 46
15 23
20
1 13
14 56
1 10
14 59
1 07
15 02
1 04
15 05
1 01
15 08
0 58
15 11
40
1 24
14 45
1 21
14 48
1 18
14 51
1 15
14 54
1 12
14 57
1 09
15 00
10 00
1 35
14 34
1 32
14 37
1 29
14 40
1 26
14 43
1 23
14 46
1 20
14 49
20
1 45
14 24
1 42
14 27
1 39
14 30
1 36
14 33
1 33
14 36
1 30
14 39
40
1 54
14 15
1 51
14 18
1 48
14 21
1 45
14 24
1 42
14 27
1 39
14 30
11 00
2 03
14 06
2 00
14 09
1 57
14 12
1 54
14 15
1 51
14 18
1 48
14 21
30
2 15
13 54
2 12
13 57
2 09
14 00
2 06
14 03
2 03
14 06
2 00
14 09
12 00
2 26
13 43
2 23
13 46
2 20
13 49
2 17
13 52
2 14
13 55
2 11
13 58
30
2 37
13 32
2 34
13 35
2 31
13 38
2 28
13 41
2 25
13 44
2 22
13 47
13 00
2 47
13 22
2 44
13 25
2 41
13 28
2 38
13 31
2 35
13 34
2 32
13 37
30
2 56
13 13
2 53
13 16
2 50
13 19
2 47
13 22
2 44
13 25
2 41
13 28
14 00
3 04
13 05
3 01
13 08
2 58
13 11
2 55
13 14
2 52
13 17
2 49
13 20
15 00
3 20
12 49
3 17
12 52
3 14
12 55
3 11
12 58
3 08
13 01
3 05
13 04
16 00
3 33
12 36
3 30
12 39
3 27
12 42
3 24
12 45
3 21
12 48
3 18
12 51
17 00
3 46
12 23
3 43
12 26
3 40
12 29
3 37
12 32
3 34
12 35
3 31
12 38
18 00
3 56
12 13
3 53
12 16
3 50
12 19
3 47
12 22
3 44
12 25
3 41
12 28
19 00
4 06
12 03
4 03
12 06
4 00
12 09
3 57
12 12
3 54
12 15
3 51
12 18
20 00
4 14
11 54
4 11
11 57
4 08
12 00
4 05
12 03
4 02
12 06
3 59
12 09
22 00
4 30
11 38
4 27
11 41
4 24
11 44
4 21
11 47
4 18
11 50
4 15
11 53
24 00
4 43
11 25
4 40
11 28
4 37
11 31
4 34
11 34
4 31
11 37
4 28
11 40
26 00
4 54
11 14
4 51
11 17
4 48
11 20
4 45
11 23
4 42
11 26
4 39
11 29
28 00
5 04
11 04
5 01
11 07
4 58
11 10
4 55
11 13
4 52
11 16
4 49
11 19
30 00
5 12
10 56
5 09
10 59
5 06
11 02
5 03
11 05
5 00
11 08
4 57
11 11
32 00
5 20
10 48
5 17
10 51
5 14
10 54
5 11
10 57
5 08
11 00
5 05
11 03
34 00
5 27
10 41
5 24
10 44
5 21
10 47
5 18
10 50
5 15
10 53
5 12
10 56
36 00
5 33
10 35
5 30
10 38
5 27
10 41
5 24
10 44
5 21
10 47
5 18
10 50
38 00
5 38
10 30
5 35
10 33
5 32
10 36
5 29
10 39
5 26
10 42
5 23
10 45
40 00
5 43
10 24
5 40
10 27
5 37
10 30
5 34
10 33
5 31
10 36
5 28
10 39
45 00
5 54
10 13
5 51
10 16
5 48
10 19
5 45
10 22
5 42
10 25
5 39
10 28
50 00
6 02
10 04
5 59
10 07
5 56
10 10
5 53
10 13
5 50
10 16
5 47
10 19
55 00
6 09
9 56
6 06
9 59
6 03
10 02
6 00
10 05
5 57
10 08
5 54
10 11
60 00
6 15
9 49
6 12
9 52
6 09
9 55
6 06
9 58
6 03
10 01
6 00
10 04
65 00
6 22
9 42
6 19
9 45
6 16
9 48
6 13
9 51
6 10
9 54
6 07
9 57
70 00
6 27
9 36
6 24
9 39
6 21
9 42
6 18
9 45
6 15
9 48
6 12
9 51
75 00
6 31
9 31
6 28
9 34
6 25
9 37
6 22
9 40
6 19
9 43
6 16
9 46
80 00
6 37
9 25
6 34
9 28
6 31
9 31
6 28
9 34
6 25
9 37
6 22
9 40
85 00
6 41
9 20
6 38
9 23
6 35
9 26
6 32
9 29
6 29
9 32
6 26
9 35
90 00
+6 45
9 15
+6 42
9 18
+6 39
9 21
+6 36
9 24
+6 33
9 27
+6 30
9 30
Day of Month. Jan.
Feb. Mar. Apr
May.
Tune. July. Aug.
Sept. j Oct. Nov. Dec.
ADDITIONAL COKE. "
FOB SUN'S ALT. lgt to 15th_, +18
+15 +8 0
- 8
-13 -14 -11
-5 +3 +11 +16
16th to 31st.. +17
+12 +4 -4
-11
-14 -13 - 9
-1 +7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude
of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 10'. A supplementary correction
taking account of thev ariation of the Sun's semidiameter in the different months of the year is given at the loot of the mam table.
TABLE 46. [Page 937
Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find
the True Altitude — Continued.
HEIGHT OF THE EYE.
OBS. ALT
95 Feet.
96 Feet.
97 Feet.
98 Feet.
99 Feet.
100 Feet.
0
Sun's
Corr.
*
Star's
Corr.
(-)
Sun's
Corr.
*
Star's
Corr.
(-)
O
Sun's
Corr.
*
Star's
Corr.
(-)
sS-s
Corr.
*
Star's
Corr.
(-)
O
Sun's
Corr.
*
Star's
Corr.
(-)
Sun's
Corr.
*
Star's
Corr.
(-)
6 30
-1 18
17 27
-1 21
17 30
-1 24
17 33
-1 27
17 36
-1 30
17 39
-1 33
i n
17 42
40
-1 08
17 17
-1 11
17 20
-1 14
17 23
-1 17
17 26
-1 20
17 29
-1 23
17 32
50
-0 58
17 07
-1 01
17 10
-1 04
17 13
-1 07
17 16
-1 10
17 19
-1 13
17 22
7 00
-0 48
16 57
-0 51
17 00
-0 54
17 03
-0 57
17 06
-1 00
17 09
-1 03
17 12
10
-0 39
16 48
-0 42
16 51
-0 45
16 54
-0 48
16 57
-0 51
17 00
-0 54
17 03
20
-0 30
16 39
-0 33
16 42
-0 36
16 45
-0 39
16 48
-0 42
16 51
-0 45
16 54
7 30
-0 21
16 30
-0 24
16 33
-0 27
16 36
-0 30
16 39
-0 33
16 42
-0 36
16 45
40
-0 13
16 22
-0 16
16 25
-0 19
16 28
-0 22
16 31
-0 25
16 34
-0 28
16 37
50
-0 05
16 14
-0 08
16 17
-0 11
16 20
-0 14
16 23
-0 17
16 26
-0 20
16 29
8 00
+0 03
16 06
0 00
16 09
-0 03
16 12
-0 06
16 15
-0 09
16 18
-0 12
16 21
10
0 10
15 59
+0 07
16 02
+0 04
16 05
+0 01
16 08
-0 02
16 11
-0 05
16 14
20
0 17
15 52
0 14
15 55
0 11
15 58
0 08
16 01
+0 05
16 04
+0 02
16 07
8 30
0 24
15 45
0 21
15 48
0 18
15 51
0 15
15 54
0 12
15 57
0 09
16 00
40
0 31
15 38
0 28
15 41
0 25
15 44
0 22
15 47
0 19
15 50
0 16
15 53
50
0 37
15 32
0 34
15 35
0 31
15 38
0 28
15 41
0 25
15 44
0 22
15 47
9 00
0 43
15 26
0 40
15 29
0 37
15 32
0'34
15 35
0 31
15 38
0 28
15 41
20
0 55
15 14
0 52
15 17
0 49
15 20
0 46
15 23
0 43
15 26
0 40
15 29
40
1 06
15 03
1 03
15 06
1 00
15 09
0 57
15 12
0 54
15 15
0 51
15 18
10 00
1 17
14 52
1 14
14 55
1 11
14 58
1 08
15 01
05
15 04
1 02
15 07
20
1 27
14 42
1 24
14 45
1 21
14 48
1 18
14 51
15
14 54
1 12
14 57
40
1 36
14 33
1 33
14 36
1 30
14 39
1 27
14 42
24
14 45
1 21
14 48
11 00
1 45
14 24
1 42
14 27
1 39
14 30
1 36
14 33
33
14 36
1 30
14 39
30
1 57
14 12
1 54
14 15
1 51
14 18
1 48
14 21
45
14 24
1 42
14 27
12 00
2 08
14 01
2 05
14 04
2 02
14 07
1 59
14 10
1 56
14 13
1 53
14 16
30
2 19
13 50
2 16
13 53
2 13
13 56
2 10
13 59
2 07
14 02
2 04
14 05
13 00
2 29
13 40
2 26
13 43
2 23
13 46
2 20
13 49
2 17
13 52
2 14
13 55
30
2 38
13 31
2 35
13 34
2 32
13 37
2 29
13 40
2 26
13 43
2 23
13 46
14 00
2 46
13 23
2 43
13 26
2 40
13 29
2 37
13 32
2 34
13 35
2 31
13 38
15 00
3 02
13 07
2 59
13 10
2 56
13 13
2 53
13 16
2 50
13 19
2 47
13 22
16 00
3 15
12 54
3 12
12 57
3 09
13 00
3 06
13 03
3 03
13 06
3 00
13 09
17 00
3 28
12 41
3 25
12 44
3 22
12 47
3 19
12 50
3 16
12 53
3 13
12 56
18 00
3 38
12 31
3 35
12 34
3 32
12 37
3 29
12 40
3 26
12 43
3 23
12 46
19 00
3 48
12 21
3 45
12 24
3 42
12 27
3 39
12 30
3 36
12 33
3 33
12 36
20 00
3 59
12 12
3 53
12 15
3 50
12 18
3 47
12 21
3 44
12 24
3 41
12 27
22 00
4 12
11 56
4 09
11 59
4 06
12 02
4 03
12 05
4 00
12 08
3 57
12 11
24 00
4 25
11 43
4 22
11 46
4 19
11 49
4 16
11 52
4 13
11 55
4 10
11 58
26 00
4 36
11 32
4 33
11 35
4 30
11 38
4 27
11 41
4 24
11 44
4 21
11 47
28 00
4 46
11 22
4 43
11 25
4 40
11 28
4 37
11 31
4 34
11 34
4 31
11 37
30 00
4 54
11 14
4 51
11 17
4 48
11 20
4 45
11 23
4 42
11 26
4 39
11 29
32 00
5 02
11 06
4 59
11 09
4 56
11 12
4 53
11 15
4 50
11 18
4 47
11 21
34 00
5 09
10 59
5 06
11 02
5 03
11 05
5 00
11 08
4 57
11 11
4 54
11 14
36 00
5 15
10 53
5 12
10 56
5 09
10 59
5 06
11 02
5 03
11 05
5 00
11 08
38 00
5 20
10 48
5 17
10 51
5 14
10 54
5 11
10 57
5 08
11 00
5 05
11 03
40 00
5 25
10 42
5 22
10 45
5 19
10 48
5 16
10 51
5 13
10 54
5 10
10 57
45 00
5 36
10 31
5 33
10 34
5 30
10 37
5 27
10 40
5 24
10 43
5 21
10 46
50 00
5 44
10 22
5 41
10 25
5 38
10 28
5 35
10 31
5 32
10 34
5 29
10 37
55 00
5 51
10 14
5 48
10 17
5 45
10 20
5 42
10 23
5 39
10 26
5 36
10 29
60 00
5 57
10 07
5 54
10 10
5 51
10 13
5 48
10 16
5 45
10 19
5 42
10 22
65 00
6 04
10 00
6 01
10 03
5 58
10 06
5 55
10 09
5 52
10 12
5 49
10 15
70 00
6 09
9 54
6 06
9 57
6 03
10 00
6 00
10 03
5 57
10 06
5 54
10 09
75 00
6 13
9 49
6 10
9 52
6 07
9 55
6 04
9 58
6 01
10 01
5 58
10 04
80 00
6 19
9 43
6 16
9 46
6 13
9 49
6 10
9 52
6 07
9 55
6 04
9 58
85 00
6 23
9 38
6 20
9 41
6 17
9 44
6 14
9 47
6 11
9 50
6 08
9 53
90 00
6 27
9 33
+6 24 9 36
+6 21
9 39
+6 18
9 42
+6 15
9 45
+6 12
9 48
Day of Month. Jan.
Feb. Mar. Apr
May.
June. July. Aug.
Sept. Oct. Nov. Dec.
ADDITIONAL CORE. "
FOE SUN'S ALT. lst to 15th... . +18
+15 +8 0
- 8
-13 -14 -11
-5 +3 +11 +16
16th to 31st... +17
+12 +4 -4
-11
-14 -13 - 9
-1 +7 +14 +18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction ; and for the observed altitude
of the Sun's lower limb , the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction
taking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the mam taoie.
61828°— 16-
Page 938] TABLE 47.
Longitude Factors.
F is the change in longitude due to a change of 1' in latitude.
Latitude.
Bear
0°
1°
2°
4°
6°
8°
10°
12°
Bear
ing.
ing.
0
/
/
/
/
/
/
/
/
0
1
57.29
57.30
57.32
57.43
57.61
57.85
58.17
58.57
1
2
28.64
28.64
28.65
28.71
28.79
28.92
29.08
29.28
2
3
19.08
19.08
19.09
19.13
19.19
19.27
19.38
19.51
3
4
14.30
14.30
14.31
14.34
14.38
14.44
14.52
14.62
4
5
11.43
11.43
11.44
11.46
11.49
11.54
11.61
11.69
5
6
9.51
9.52
9.52
9.54
9.57
9.61
9.66
9.73
6
7
8.14
8.15
8.15
8.16
8.19
8.22
8.27
8.33
7
8
7.12
7.12
7.12
7.13
7.15
7.18
7.22
7.27
8
10
5.67
5.67
5.68
5.69
5.70
5.73
5.76
5.80
10
12
4.71
4.71
4.71
4.72
4.73
4.75
4.78
4.81
12
14
4.01
4.01
4.01
4.02
4.03
4.05
4.07
4.10
14
16
3.49
3.49
3.49
3.50
3.51
3.52
3.54
3.56
16
18
3.08
3.08
3.08
3.08
3.10
3.11
3.13
3.15
18
20
2.75
2.75
2.75
2.75
2.76
2.77
2.79
2.81
20
22
2.47
2.47
2.48
2.48
2.49
2.50
2.51
2.53
22
24
2.25
2.25
2.25
2.25
2.26
2.27
2.28
2.30
24
26
2.05
2.05
2.05
2.05
2.06
2.07
2.08
2.10
26
28
1.88
1.88
1.88
1.88
1.89
1.90
1.91
.92
28
30
1.73
1.73
1.73
1.74
1.74
1.75
1.76
.77
30
32
1.60
1.60
1.60
.60
L61
1.62
1.63
.64
32
34
1.48
1.48
1.48
.49
1.49
1.50
1.50
.52
34
36
1.38
1.38
1.38
.38
1.38
1.39
1.40
.41
36
38
1.28
1.28
1.28
.28
1.29
1.29
1.30
.31
38
40
1.19
1.19
1.19
.19
1.20
1.20
1.21
.22
40
42
1.11
1.11
1.11
.11
1.12
1.12
1.13
.14
42
44
1.04
1.04
1.04
1.04
1.04
1.05
1.05
.06
44
46
.97
.97
.97
.97
.97
.98
.98
.99
46
48
.90
.90
.90
.90
.90
.91
.91
.92
48
50
.84
.84
.84
.84
.84
.85
.85
.86
50
52
.78
.78
.78
.78
.79
.79
.79
.80
52
54
.73
.73
.73
.73
.73
.73
.74
.74
54
56
.67
.67
.67
.68
.68
.68
.68
.69
56
58
.63
.63
.63
.63
.63
.63
.63
.64
58
60
.58
.58
.58
.58
.58
.58
.59
.59
60
62
.53
.53
.53
.53
.53
.54
.54
.54
62
64
.49
.49
.49
.49
.49
.49
.50
.50
64
66
.45
.45
.45
.45
.45 \
.45
.45
.46
66
68
.40
.40
.40
.40
.40
.41
.41
.41
68
70
.36
.36
.36
.36
.37
.37
.37
.37
70
72
.33
.33
.33
.33
.33
.33
.33
.33
72
74
.29
.29
.29
.29
.29
.29
.29
. .29
74
76
.25
.25
.25
.25
.25
.25
.25
.25,
76
78
.21
.21
.21
.21
.21
.21
.22
.22
78
80
.18
.18
.18
.18
.18
.18
.18
.18
80
81
.16
.16
.16
.16
.16
.16
.16
.16
81
82
.14
.14
.14
.14
.14
.14
.14
.14
82
83
.12
.12
.12
.12
.12
.12
.12
.13
83
84
.10
.10
.10
.10
.10
.10
.11
.11
84
85
.09
.09
.09
.09
.09
.09
.09
.09
85
86
.07
.07
.07
.07
.07
.07
.07
.07
86
87
.05
.05
.05
.05
.05
.05
.05
.05
87
88
.03
.03
.03
.03
.03
.03
.03
.04
88
89
.02
.02
.02
.02
.02
.02
.02
.02
89
90
.00
.00
.00
.00
.00
.00
.00
.00
90
0°
1°
2°
4°
6°
8°
10°
12°
Corr. to Long. = Error in Lat.xF.
TABLE 47. [Page 939
Longitude Factors.
F Is the change in longitude due to a change of 1' In latitude.
Latitude.
Bear
14°
16°
18° 30° 33°
24°
36°
38°
Bear
ing.
ing.
0
/
/
/ /
/
/ /
/
o
1
59.04
59.60
60. 24 60. 97
61.79
62.71
63.74
64.88
1
2
29.51
29.79
30. 11 30. 47
30.89
31.35
31.86
32.43
2
3
19.67
19.85
20.06
20.31
20.58
20.89
21.23
21.61
3
4
14.74
14.88
15.04
15. 22 15. 42
15.65
15. 91
16.20
4
5
11.78
11.89
12.02
12.16
12.33
12.51
12.72
12.95
5
6
9.81
9.90
10.00
10.12
10.26
10.41
10.59
10.78
6
7
8.39
8.47
8.56
8.67
8.78
8.91
9.06
9.22
7
8
7.33
7.40
7.48
7.57
7.67
7.79
7.92
8.06
8
10
5.85
5.90
5.96
6.03
6.12
6.21
6.31
6.42
10
12
4.85
4.89
4.95
5.01
5.07
5.15
5.23
5.33
13
14
4.13
4.17
4.22
4.27
4.33
4.39
4.46
4. 54 1 14
16
3. 59 3. 63
3.67
3.71
3.76
3.82
3.88
3. 95 16
18
3.17
3.20
3.24
3.28
3.32
3.37
3.42
3. 49 18
20
2.83
2.86
2. 89 2. 92
2.96
3.01
3.06
3.11
20
23
2.55
2.58
2. 60 ! 2. 63
2.67
2.71
2.75
2.80
33
24
2.32
2.34
2.36
2.39
2.42
2.46
2.50
2.54
34
26
2.11
2.13
2.16
2. 18 2. 21
2.24
2.28
2.32
36
38
1.94
1.96
1.98
2. 00 2. 03
2.06
2.09
2.13
38
30
1.78
1.80
1.82
1. 84 1. 87
.90
.93
.96
30
33
1.65
1.66
1.68
1. 70 1. 73
.75
.78
.81
33
34
1.53
1.54
. 56 1. 58
1.60
.62
.65
.68
34
36
1.42
1.43
. 45 1. 47
1.48
.51
.53
.56
36
38
1.32
1.33
. 35 1. 36
1.38
.40
.42
.45
38
40
1.23
1.24
. 25 1. 27
1.28
.30
.33
.35
40
43
1.14
1.15
. 17 1. 18
1.20
.22
.24
.26 42
44
1.07
1.08
1. 09 1. 10
1.12
.13
.15
.17 ! 44
46
1.00
1.01
1. 02 1. 03
1.04
.06
.07
.09
46
48
.93
.94
.95
.96
.97
.99
.00
.02
48
50
.87
.87
.88
.89
.91
.92
.93
.95
50
53
.80
.81
.82
.-83
.84
.85
.87
.88
53
54
.75
.76
.76
.77
.78
.79
.81
.82
54
56
.69
.70
.71
.72
.73
.74
.75
.76
56
58
.64
.65
.66
.66
.67
.68
.69
.71
58
60
.60
.60
.61
.61
.62
.63
.64
.65
60
63
.55
.55
.56
.57
.57
.58
.59
.60
63
64
.50
.51
.51
.52
.53
.53
.54
.55
64
66
.46
.46
.47
.47
.48
.49
.50
.50
66
68
.42
.42
.42
.43
.44
.44
.45
.46
68
70
.37
.38
.38
.39
.39
.40
.40
.41
70
73
.34
.34
.34
.35
.35
.36
.36
.37
73
74
.30
.30
.30
.31
.31
.31
.32
.33
74
76
.26
.26
.26
.27
.27
.27
.28
.28
76
78
.22
.22
.22
.23
.23
.23
.24
.24
78
80
.18
.18
.18
.19
.19
.19
.20
.20
80
81
.16
.16
.17
.17
.17
.17
.18
.18
81
83
.14
.15
.15
.15
.15
.15
.16
.16
83
83
.13
.13
.13
.13
.13
.13
.14
.14
83
84
.11
.11
.11
.11
.11
.11
.12
.12
84
85
.09
.09
.09
.09
.09
.10
.10
.10
85
86
.07
.07
.07
.07
.08
.08
.08
.08
86
87
.05
.05
.05
.06
.06
.06
.06
.06
87
88
.04
.04
.04
.04
.04
.04
.04
.04
88
89
.02
.02
.02
.02
.02
.02
.02
.02
89
90
.00
.00
.00
.00
.00
.00
.00
.00
90
14°
16°
18° 30°
32°
24°
26°
28°
Corr. to Long. = Error in Lat.xF.
Page 940]
TABLE 47.
Longitude Factors.
F is the change in longitude due to a change of 1' in latitude.
Latitude.
Bear
30°
33°
34°
36°
38°
40°
42°
44°
Bear
ing.
ing.
o
/
/
/
/
/
/
/
/
o
1
66.15
67.56
69.10
70.81
72.70
74.79
77.09
79.64
1
2
33.07
33.77
34.54
35.40
36.34
37.38
38.53
39.81
2
3
22.03
22.50
23.02
23.59
24.21
24.91
25.68
26.53
3
4
16.51
16.86
17.25
17.68
18.15
18.67
19.24
19.88
4
5
13.20
13.48
13.79
14.13
14.50
14.92
15.38
15.89
5
6
10.99
11.22
11.48
11.76
12.07
12.42
12.80
13.23
6
7
9.40
9.60
9.82
10.07
10.34
10.63
10.96
11.32
7
8
8.22
8.39
8.58
8.79
9.03
9.29
9.57
9.89
8
10
6.55
6.69
6.84
7.01
7.20
7.40
7.63
7.88
10
12
5.43
5.55
5.67
5.81
5.97
6.14
6.33
6.54
12
14
4.63
4.73
4.84
4.96
5 09
5.24
5.40
5.58
14
16
4.03
4.11
4.21
4.31
4.43
4.55
4.69
4.85
16
18
3.55
3.63
3.71
3.80
3.91
4.02
4.14
4.28
18
20
3.17
3.24
3.31
3.40
3.49
3.59
3.70
3.82
20
22
2.86
2.92
2.98
3.06
3.14
3.23
3.33
3.44
22
21
2.59
2.65
2.71
2.78
2.85
2.93
3.02
3.12
24
26
2.37
2.42
2.47
2.53
2.60
2.68
2.76
2.85
26
28
2.17
2.22
2.27
2.32
2.39
2.45
2.53
2.61
28
30
2.00
2.04
2.09
2.14
2.20
2.26
2.33
2.41
30
32
1.85
1.89
1.93
1.98
2.03
2.09
2.15
2.22
32
34
1.71
1.75
1.79
1.83
1.88
1.93
1.99
2.06
34
36
1.59
1.62
1.66
1.70
1.75
1.80
1.85
1.91
36
38
1.48
1.51
1.54
1.58
1.62
1.67
1.72
1.78
38
40
1.38
1.41
1.44
1. 47
1.51
1.56
1.60
1.66
40
43
1.28
1.31
1.34
1.37
1.41
1.45
1.49
1.54
42
44
1.20
1.22
1.25
1.28
1.31
1.35
1.39
1.44
44
46
1.11
1.14
1.16
1.19
1.23
1.26
1.30
1.34
46
48
1.04
1.06
1.09
1.11
1.14
1.17
1.21
1.25
48
50
.97
.99
1.01
1.04
1.06
1.09
1.13
1.17
50
52
.90
.92
.94
.97
.99
1.02
1.05
1.09
52
54
.84
.86
.88
.90
.92
.95
.98
1.01
54
56
.78
.79
.81
.83
.86
.88
.91
.94
56
58
.72
.74
.75
.77
.79-
.82
.84
.87
58
60
.67
.68
.70
.71
.73
.75
.78
.80
60
62
.61
.63
.64
.66
.67
.69
.72
.74
62
64
.56
.57
.59
.60
.62
.64
.66
.68
64
66
.51
.52
.54
.55
.56
.58
.60
.62
66
68
.47
.48
.49
.50
.51
.53
.54
.56
68
70
.42
.43
.44
.45
.46 H
^.47
.49
.51
70
72
.37
.38
.39
.40
.41
.42
.44
.45
72
74
.33
.34
.35
.35
.36
.37
.39
.40
74
76
.29
.29
.30
.31
.32
.32
.34
.35
76
78
.24
.25
.26
.26
.27
.28
.29
.29
78
80
.20
.21
.21
.22
.22
.23
.24
.24
80
81
.18
.19
.19
.20
.20
.21
.21
.22
81
82
.16
.17
.17
.17
.18
.18
.19
.19
82
83
.14
.14
.15
.15
.16
.16
.16
.17
83
84
.12
.12
.13
.13
.13
.14
.14
.15
84
85
.10
.10
.11
.11
.11
.11
.12
.12
85
86
.08
.08
.08
.09
.09
.09
.09
.10
86
87
.06
.06
.06
.06
.07
.07
.07
.07
87
88
.04
.04
.04
.04
.04
.05
.05
.05
88
89
.02
.02
.02
.02
.02
.02
.02
.02
89
90
.00
.00
.00
.00
.00
.00
.00
.00
90
30°
32°
34°
36°
38°
40°
42°
44°
Corr. to Long.=Error in Lat.XF.
TABLE 47. [Page 941
Longitude Factors.
F Is the change in longitude due to a change of 1' in latitude.
Latitude.
Bear-
46° 48°
60°
52° 54° 56°
58°
60°
Bear
ing.
ing.
o
/
/
/
/ /
/
/
/
o
1
82.47
85.62
89.13
93. 05 97. 47
102.5
108.1
114.6
1
«
41.22
42.80
44.55
46. 51 48. 72
51.21
54.04
57.27
2
3.
27.47
28.52
29.68
30.99 32.46
34.12
36.01
38.16
3
4
20.59
21.37
22.25
23.23
24.33 ! 25.57
26.99
28.60
4
5
16.45
17.08
17.78
18. 57 19. 45 20. 44
21.57
22.86
5
6
13.70
14.22
14.80
15. 45 16. 19 17. 01
17.95
19.03
6
1
11.72
12.17
12.67
13.23 | 13.86 14.56
15.37
16.29
7
8
10.24
10.63
11.07
11.56
12.11
12.72
13.43
14.23
8
10
8.16
8.48
8.82
9.21
9.65
10.14
10.70
11.34
10
12
6.77
7.03
7.32
7.64
8.00
8.41
8.88
9.41
12
14
5.77
5.99
6.24
6.51
6.82
7.17
7.57
8.02
14
16
5.02
5.21
5.42
5.66
5.93
6.24
6.58
6.97
16
18
4.43
4.60
4.79
5.00
5.24
5.50
5.81
6.15
18
20
3.95
4.11
4.27
4.46
4.67
4.91
5.19
5.49
20
22
3.56
3.70
3.85
4.02
4.21
4.43
4.67
4.95
22
24
3.23
3.36
3.49
3.65
3.82
4.02
4.24
4.49
24
26
2.95
3.06
3.19
3.33
3.49
3.66
3.87
4.10
26
28
2.71
2.81
2.93
3.05
3.20
3.36
3.55
3.76
28
30
2.49
2.59
2.69
2. 81 | 2. 95
3.10
3.27
3.46
30
32
2.30
2.39
2.49
2. 60 ! 2. 72
2.86
3.02
3.20
32
34
2.13
2.22
2.31
2.41
2.52
2.65
2.80
2.96
34
36
1.98
2.06
2.14
2. 24
2.34
2.46
2.60
2.75
36
38
1.84
1.91
1.99
2. 08
2.18
2.29
2.41
2.56
38
40
1.71
1.78
1.85
1.94
2.03
2.13
2.25
2.38
40
42
1.60
1.66
1.73
1. 80 1. 89
1.99
2.09
2.22
42
44
1.49
1.55
1.61
1.68
.76
1.85
1.95
2.07
44
46
1.39
1.44
1.50
1.57
.64
1.73
1.82
1.93
46
48
1.30
1.35
1.40
1.46
.53
1.61
1.70
1.80
48
50
1.21
1.25
1.31
1.36
.43
1.50
1.58
1.68
50
52
1.12
1.17
1.22
1.27
.33
1.40
1.47
1.56
52
54
1.05
1.09
1.13
1.18
.23
1.30
1.37
1.45
54
56
.97
1.01
1.05
1.10
.15
1.21
1.27
1.35
56
58
.90
.93
.97
1.01
.06
1.12
1.18
1.25
58
60
.83
.86
.90
.94
.98
1.03
1.09
1.15
60
62
.77
.79
.83
.86
.90
.95
1.00
1.06
62
64
.70
.73
.76
.79
.83
.87
.92
.97
64
66
.64
.66
.69
.72
.76
.79
.84
.89
66
68
.58
.60
.63
.65
.69
.72
.76
.81
68
70
.52
.54
.57
.59
.62
.65
.68
.73
70
72
.47
.49
.51
.53
.55
.58
.61
.65
72
74
.41
.43
.45
.46
.49
.51
.54
.57
74
76
.36
.37
.39
.40
.42
.45
.47
.50
76
78
.31
.32
.33
.34
.36
.38
.40
.42
78
80
.25
.26
.27
.29
.30
.31
.33
.35
80
81
.23
.24
.25
.26
.27
.28
.30
.32
81
82
.20
.21
.22
.23
.24
.25
.26
.28
82
83
.18
.18
.19
.20
.21
.22
.23
.25
83
84
.15
.16
.16
.17
.18
.19
.20
.21
84
85
.13
.13
.14
.14
.15
.16
.16
.17
85
86
.10
.10
.11
.11
.12
.12
.13
.14
86
87
.08
.08
.08
.08
.09
.09
.10
.10
87
88
.05
.05
.05
.06
.06
.06
.07
.07
88
89
.02
.03
.03
.03
.03
.03
.03
.03
89
90
.00
.00
.00
.00
.00
.00
.00
.00
90
46°
48°
50°
52°
54°
56°
58° 60°
Corr. to Long.=Error in Lat.xF.
Page 942] TABLE 48.
Latitude Factors.
f Is the change In latitude due to a change of 1' in longitude.
Latitude.
Bear
0°
1°
2°
4°
6°
8°
10°
12°
Bear-
ing.
tuff.
o
/
/
/
/
/
/
/
/
0
1
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
1
2
.03
.03
.03
.03
.03
.03
.03
.03
2
3
.05
.05
.05
.05
.05
.05
.05
.05
3
4
.07
.07
.07
.07
.07
.07
.07
.07
4
5
.09
.09
.09
.09
.09
.09
.09
.09
5
6
.11
.11
.11
.10
.10
.10
.10
.10
6
7
.12
.12
.12
.12
.12
.12
.12
.12
7
8
.14
.14
.14
.14
.14
.14
.14
.14
8
10
.18
.18
.18
.18
.18
.17
.17
.17
10
12
.21
.21
.21
.21
.21
.21
.21
.21
12
14
.25
.25
.25
.25
.25
.25
.25
.24
14
16
.29
.29
.29
.29
.28
.28
.28
.28
16
18
.32
.32
.32
.32
.32
.32
.32
.32
18
20
.36
.36
.36
.36
.36
.36
.36
.36
20
22
.40
.40
.40
.40
.40
.40
.40
.40
22
24
.44
.44
.44
.44
.44
.44
.44
.43
24
26
.49
.49
.49
.49
.49
.48
.48
.48
26
28
.53
.53
.53
.53
.53
.53
.52
.52
28
30
.58
.58
.58
.57
.57
.57
.57
.56
30
32
.63
.63
.63
.63
.62
.62
.61
.61
32
34
.68
.68
.68
.67
.67
.67
.67
.66
34
36
.72
.72
.72
.72
.72
.72
.71
.71
36
38
.78
.78
.78
.78
.78
.78
.77
.76
38
40
.84
.84
.84
.84
.83
.83
.83
.82
40
42
.90
.90
.90
.90
.89
.89
.88
.88
42
44
.96
.96
.96
.96
.96
.95
.95
.94
44
46
1.04
1.04
1.04
1.03
1.03
1.03
1.02
1.01
46
48
1.11
1.11
1.11
1.11
1.11
1.10
1.10
L09
48
50
1.19
1.19
1.19
1.19
1.19
1.18
1.17
.17
50
52
1.28
1.28
1.28
1.28
1.27
1.27
1.26
.25
52
54
1.38
1.38
1.38
1.37
1.37
1.36
1.36
.35
54
56
1.48
1.48
1.48
1.48
1.47
1.47
1.46
1.45
56
58
1.60
1.60
1.60
1.60
1.59
1.58
1.58
1.57
58
60
1.73
1.73
1.73
1.73
1.72
1.72
1.71
1.69
60
62
1.88
1.88
1.88
1.88
1.87
1.86
1.85
1.84
62
64
2.05
2.05
2.05
2.05
2.04
2.03
2.02
2.01
64
66
2.25
2.25
2.24
2.24
2.23
2.22
2.21
2.20
66
68
2.48
2.48
2.47
2.47
2.46
2.45
2.44
2.42
68
70
2.75
2.75
2.75
2.74
2.73
2.72
2.71
2.69
70
72 I 3.08
3.08
3.08
3.07
3.06
3.05
3.03
3.01
72
74 3.49
3.49
3.49
3.48
3.47
3.45
3.43
3.41
74
76 I 4.01
4.01
4.01
4.00
3.99
3.97
3.95
3.92
76
78
4.70
4.70
4.70
4.69
4.68
4.66
4.63
4.60
78
80
5.67
5.67
5.67
5.66
5.64
5.62
5.59
5.55
80
81
6.31
6.31
6.31
6.30
6.28
6.25
6.22
6.18
81
82
7.12
7.11
7.11
7.10
7.07
7.05
7.01
6.96
82
83
8.15
8.14
8.14
8.13
8.10
8.07
8.02
7.97
83
84
9.52
9.51
9.51
9.49
9.46
9.42
9.37
9.31
84
85
11.43
11.43
11.42
11.40
11.37
11.32
11.25
11.18
85
86
14.30
14.30
14.29
14.27
14.22
14.16
14.08
13.99
86
87
19.08
19.08
19.07
19.03
18.98
18.91
18.79
18.66
87 i
88
28.63
28.63
28.62
28.57
28.48
28.35
28.20
28.01
88
89
57.29
57.28
57.26
57.15
56.98
56.73
56.42
56.04
89
0°
1°
2°
4°
6°
8°
10°
12°
Cor. to Lat. = Error in Long. Xf .
TABLE 48. [Page 943
Latitude Factors.
f is the change In latitude due to a change of 1' in longitude.
Latitude.
Bear
ing.
14°
16°
18°
20°
22°
24°
26°
28°
Bear
ing.
0
/
/
/
/
/
/
/
/
0
1
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
1
2
.03
.03
.03
.03
.03
.03
.03
.03
2
3
.05
.05
.05
.05
.05
.05
.05
.05
3
4
.07
.07
.07
.07
.06
.06
.06
.06
4
5
.08
.08
.08
.08
.08
.08
.08
.08
5
6
.10
.10
.10
.10
.10
.10
.09
.09
6
7
.12
.12
.12
.12
.11
.11
.11
.11
7
8
.14
.14
.13
.13
.13
.13
.13
.12
8
10
.17
.17
.17
.17
.16
.16
.16
.16
10
12
.21
.20
.20
.20
.20
.19
.19
.19
12
14
.24
.24
.24
.23
.23
.23
.22
.22
14
16
.28
.28
.27
.27
.27
.26
.26
.25
16
18
.32
.31
.31
.30
.30
.30
.29
.29
18
20
.35
.35
.35
.34
.34
.33
.33
.32
20
22
.39
.39
.38
.38
.38
.37
.36
.36
22
24
.43
.43
.42
.42
.41
.41
.40
.39
24
26
.47
.47
.46
.46
.45
.45
.44
.43
26
28
.52
.51
.51
.50
.49
.49
.48
.47
28
30
.56
.56
.55
.54
.53
.53
.52
.51
30
32
.61
.60
.60
.59
.58
.57
.56
.55
32
34 i .65
.65
.64
.63
.63
.62
.61
.59
34
36
.70
.70
.69
.68
.68
.66
.65
.64
36
38
.76
.75
.74
.74
.72
.71
.70
.69
38
40
.81
.81
.80
.79
.78
.77
.75
.74
40
42
.88
.87
.85
.85
.83
.82
.81
.79
42
44
.93
.93
.92
.91
.89
.88
.87
.85
44
46
1.01
1.00
.99 .97
.96
.95
.93
.91
46
48
1.08
1.07
1. 06 1. 04
1.03
1.02
1.00
.98
48
50
1.16
1.15
1. 13 1. 12
1.10
1.09
.07
1.05
50
52
1.24
1.23
1. 22 1. 20
1.19
1.17
.15
1.13
52
54
1.34
1.32
1. 31 1. 29
1.28
1.26
.24
1.22
54
56
1.44
1.43
1. 41 1. 39
1.38 ! 1.35
.33
1.31
56
58
1.55
1.54
1. 52 1. 50
1.48
1.46
.44
1.41
58
60
1.68
1.67
1. 65 1. 63
1.61
1.58
1.56
1.53
60
62 1.83
1.81
1. 79 1. 77
1.74
1.72
1.69
1.66
62
64
1.99
1.97
1. 95 1. 93
1.90
1.87
1.84
1.81
64
66
2.18
2.16
2. 14 2. 11
2.08
2.05
2.02
1.98
66
68
2.40
2.38
2. 35 2. 33
2.30
2.26
2.23
2.18
68
70
2.67
2.64
2. 61 2. 58
2.55
2.51
2.47
2.43
70
72
2.99
2.96
2. 93 2. 89
2.85
2.81
2.77
2.72
72
74
3.38
3.35
3. 32 3. 28
3.23
3.19
3.14
3.08
74
76
3.89
3.86
3. 81 3. 77
3.72
3.66
3.61
3.54
76
78
4.56
4.52
4.47
4.42
4.36
4.30
4.23
4.15
78
80 5. 50
5.45
5.39
5.33
5.26
5.18
5.10
5.01
80
81
6.13
6.07
6. 01 5. 93
5.86
5.77
5.68
5.58
81
82
6.90
6.84
6.77
6.69
6.60
6.50
6.40
6.28
82
83
7.90
7.83
7.75
7.65
7.55
7.44
7.32
7.19
83
84
9.23
9.15
9.05
8.94
8.82
8.69
8.55
8.40
84
85
11.09
10.99
10.87
10.74
10.60
10.44
10.26
10.09
85
86
13.88
13.75
13.60
13.44
13.26
13.07
12.86
12.63
86
87
18.51
18.34
18.15
17.93
17.69
17.43
17.15
16.85
87
88
27.78
27.52
27.23
26.91
26.55
26.16
25.74
25.28
88
89
55.59
55.07
54.49
53. 84
53.12
52.33
51.50
50.58
89
14°
16°
18°
20°
22°
24°
26°
28°
Corr. to Lat.=Error hi Long.Xf.
Page 944]
TABLE 48.
Latitude Factors.
f Is the change In latitude due to a change of I' in longitude.
Latitude.
Bear
30°
32°
34°
36°
38°
40°
42°
44°
Bear
ing.
ing.
0
/
/
/
/
/
/
/
/
o
1
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
1
2
.03
.03
.03
.03
.03
.03
.03
.03
2
3
.05
.05
.04
.04
.04
.04
.04
.04
3
4
.06
.06
.06
.06
.06
,05
.05
.05
4
5
.08
.07
.07
.07
.07
.07
.07
.06
5
6
.09
.09
.09
.09
.08
.08
.08
.08
6
7
.11
.10
.10
.10
.10
.09
.09
.09
•7
8
.12
.12
.12
.11
.11
.11
.10
.10
8
10
.15
.15
.15
.14
.14
.14
.13
.13
10
12
.18
.18
.18
.17
.17
.16
.16
.15
12
14
.22
.21
.21
.20
.20
.19
.19
.18
14
16
.25
.24
.24
.23
.23
.22
.21
.21
16
18
.28
.28
.27
.26
.26
.25
.24
.23
18
20
.32
.31
.30
.29
.29
.28
.27
.26
20
22
.35
.34
.34
.33
.32
.31
.30
.29
22
24
.39
.38
.37
.36
.35
.34
.33
.32
24
26
.42
.41
.40
.40
.38
.37
.36
.35
26
28
.46
.45
.44
.43
.42
.41
.40
.38
28
30
.50
.49
.48
.47
.45
.44
.43
.41
30
32
.54
.53
.52
.51
.49
.48
.47
.45
32
34
.58
.57
.56
.55
.53
..52
.50
.49
34
36
.63
.62
.60
.59
.57
.56
.54
.52>
36
38
.68
.66
.65
.63
.62
.60
.58
.56
38
40
.72
.71
.69
.68
.66
.64
.63
.60
40
42
.78
.76
.75
.73
.71
.69
.67
.65
42
44
.83
.82
.80
.78
.76
.74
.72
.69
44
46
.90
.88
.86
.84
.82
.79
.77
.74
46
48
.96
.94
.92
.90
.88
.85
.83
.80
48
50
1.03
1.01
.99
.96
.94
.91
.88
.86
50
52
1.11
1.09
1.06
1.04
1.01
.98
.95
.92
52
54
1.19
1.16
1.14
1.11
.08
1.05
1.02
.99
54
56
1.28
1.26
1.23
1.20
.17
1.14
1.10
1.07
56
58
1.39
1.36
1.33
1.30
.26
1.23
1.19
1.15
58
60
1.49
1.47
1.44
1.40
.37
1.33
1.29
1.25
60
62
1.63
1.59
1.56
1.52
.48
1.44
1.40
1.35
62
64
1.78
1.74
1.70
1.66
.62
1.57
1.52
1.48
64
66
1.95
1.91
1.85
1.82
.77
1.72
1.67
1.62
66
68
2.14
2.10
2.05
2.00
1.95
1.90
1.84
1.78
68
70
2.38
2.33
2.28
2.22
2.17
2.10
2.04
1.98
70
72
2.67
2.61
2.55
2.50
2.43
2.36
2.29
2.21
72
74
3.02
2.96
2.89
2.82
2.75
2.67
2.59
2.51
74
76
3.47
3.40
3.33
3.25
3.16
3.07
2.98
2.89
76
78
4.07
3.99
3.90
3.81
3.71
3.60
3.50
3.38
78
80
4.91
4.81
4.70
4.59
4.47
4.34
4.22
4.08
80
81
5.47
5.35
5.24
5.11
4.98
4.84
4.69
4.54
81
82
6.16
6.03
5.90
5.76
5.61
5.45
5.29
5.12
82
83
7.05
6.91
6.75
6.59
6.42
6.24
6.05
5.86
83
84
8.24
8.07
7.93
7.70
7.50
7.29
7.07
6.84
84
85
9.90
9.69
9.48
9.25
9.01
8.75
8.49
8.22
85
86
12.39
12.13
11.86
11.57
11.27
10.95
10.63
10.29
86
87
16.52
16. 18
15.82
15.44
15.04
14.62
14.18
13.73
87
88
24.80
24.28
23.74
23.17
22.56
21.93
21.28
20.60
88
89
49.61
48.58
47.50
46.36
45.14
43.98
42.58
41.21
89
30°
32°
34°
36°
38°
40°
42°
44°
Corr. to Lat. = Error hi Long.Xf.
TABLE 48. [Page 945
Latitude Factors.
f Is the change in latitude due to a change of 1' in longitude.
Latitude.
Bear-
46°
48°
50°
52°
54°
5*°
68°
60°
Bear
ing.
ing.
0
/
/
/
/
/
/
/
/
0
1
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
1
2
.02
.02
.02
.02
.02
.02
.02
.02
2
3
.04
.03
.03
.03
.03
.03
.03
.03
3
4
.05
.05
.04
.04
.04
.04
.04
.03
4
5
.06
.06
.06
.05
.05
.05
.05
.04
5
6
.07
.07
.07
.06
.06
.06
.06
.05
6
7
.08
.08
.08
.08
.07
.07
.06
.06
7
8
.10
.09
.09
.08
.08
.08
.07
.07
8
10
.12
.12
.11
.11
.10
.10
.09
.09
10
12
.15
.14
.14
.13
.13
.12
.11
.11
12
14
.17
.17
.16
.15
.15
.14
.13
.12
14
16
.20
.19
.18
.18
.17
.16
.15
.14
16
18
.23
.22
.21
.20
.19
.18
.17
.16
18
20
.25
.24
.23
.22
.21
.20
.19
.18
20
22
.28
.27
.26
.25
.24
.23
.21
.20
22
24
.31
.30
.29
.27
.26
.25
.24
.22
24
26
.34
.33
.31
.30
.29
.27
.26
.24
26
28
.37
.36
.34
.33
.31
.30
.28
.27
28
30
.40
.39
.37
.36
.34
.32
.31
.29
30
32
.43
.42
.40
.38
.37
.35
.33
.31
32
34
.47
.45
.43
.41
.40
.38
.36
.34
34
36
.51
.49
.47
.45
.43
.41
.38
.36
36
38
.54
.52
.50
.48
.46
.44
.41
.39
38
40
.58
.56
.54
.52
.49
.47
.44
.42
40
42 .63
.60
.58
.56
.53
.50
.48
.45
42
44
.67
.65
.62
.60
.57
.54
.51
.48
44
46
.72
.69
.67
.64
.61
.58
.55
.52
46
48
.77
.74
.71
.68
.65
.62
.59
.56
48
50
.83
.80
.77
.73
.70
.67
.63
.60
50
52
.89
.86
.82
.79
.75
.72
.68
.64
52
54
.96
.92
.88
.85
.81
.77
.73
.69
54
56
1.03
.99
.95
.91
.87
.83
.79
.74
56
58
1.11
1.07
1.03
.99
.94
.89
.85
.80
58
60
1.20
1.16
1.11
1.07
1.02
.97
.92
.87
60
62
1.31
1.26
1.21
1.16
.11
1.05
1.00
.94
62
64
1.42
1.37
1.32
1.26
.20
1.15
1.09
1.03
64
66
1.56
1.50
1.44
1.38
.32
1.26
1.19
1.12
66
68
1.72
1.66
1.59
1.52
.45
1.38
1.31
1.24
68
70
1.91
1.84
1.77
1.69
.61
1.54
1.45
1.37
70
72
2.14
2.06
1.99
1.89
1.81
1.72
1.63
1.54
72
74
2.42
2.33
2.24
2.15
2.05
1.95
1.85
1.74
74
76
78
80
81
82
83
84
85
86
87
88
89
2.79
3.27
3.94
4.39
4.94
5.66
6.61
7.94
9.94
13.26
19.89
39.80
2.68
3.15
3.80
4.23
4.76
5.45
6.37
7.65
9.57
12.77
19.16
38.34
2.58
3.02
3.70
4.06
4.57
5.24
6.12
7.35
9.19
12.27
18.41
36.83
2.47
2.90
3.49
3.89
4.38
5.01
5.86
7.04
8.81
11.75
17.64
35.24
2.36
2.77
3.33
3.71
4.18
4.79
5.59
6.72
8.41
11.22
16.83
33.68
2.24
2.63
3.17
3.53
3.98
4.56
5.32
6.39
8.00
10.67
16.01
32.04
2.13
2.49
3.01
3.35
3.77
4.32
5.04
6.06
7.58
10.11
15.17
30.36
2.01
2.35
2.84
3.16
3.56
4.07
4.76
5.72
7.15
9.54
14.32
28.65
76
78
80
81
82
83
84
85
86
87
88
89
46°
48°
50°
52°
54°
56°
58°
60°
Corr. to Lat.=Error in Long.Xf.
Page 946] TABLE 49.
Corrections for the Observed Altitudes of the Moon's Lower Limb.
OBS. ALT.
LOWEB
LIMB.
HORIZONTAL PARALLAX.
54'
55'
56'
57'
58'
59'
60'
61'
0 1
5 30
6 OOg
630$
/ n
53 46
54 22
54 51
1 n
55 03
55 38
56 08
/ //
56 19
56 54
57 24
i it
57 36
58 11
58 40
/ //
58 53
59 28
59 57
i n
6009
6044
61 13
\ "
6127
6201
6229
i n
62 44
63 18
63 46
700
7 30
800
55 17
55 39
5558
5633
56 55
57 15
57 50
58 12
6831
5906
59 28
59 47
6022
60 44
61 03
61 38
62 00
62 19
6254
63 16
6336
64 11
64 33
64 52
830
9 00
9 30
56 15
5629
56 42
57 31
57 45
57 58
5847
5901
59 13
6003
60 16
60 29
61 19
61 33
61 45
6235
6249
63 01
6352
64 05
64 17
6508
65 20
6532
10 00
11
12
56 54
57 10
5722
58 10
58 26
5837
59 25
59 41
5952
6040
60 56
6107
6156
62 12
6223
63 11
63 27
6339
6427
64 43
64 64
65 43
6558
66 09
13
14
15
5729
57 35
5735
68 45
58 50
68 50
59 59
6004
60 04
61 14
61 18
61 18
6230
62 33
6233
6345
63 48
63 48
6500
6603
66 03
66 16
66 17
66 17
16
17
18
5733
5730
5722
58 47
6844
5836
6001
59 57
5949
61 15
61 11
61 03
62 30
6225
62 17
63 45
63 39
63 31
64 59
64 63
64 45
66 13
6607
65 59
19
20
21
57 15
57 05
56 53
5828
58 18
5806
59 41
59 31
59 18
6054
60 44
6031
6208
61 57
61 44
6321
63 10
62 66
64 35
64 23
64 09
65 49
6536
6522
22
23
24
56 40
5626
5809
5752
5738
57 20
5903
5849
5831
60 15
6000
59 42
61 28
61 12
6054
62 40
62 24
6206
6363
63 36
63 18
65 05
64 48
64 29
25
26
27
55 51
5532
55 12
5702
56 43
56 22
68 13
5753
5732
5924
59 03
5841
6036
60 14
59 51
61 47
61 25
6101
62 58
6236
62 12
64 08
63 46
63 22
28
29
30
54 51
54 28
54 04
56 00
55 37
55 13
5709
56 46
5621
68 18
57 55
6729
59 29
59 05
5838
6038
60 14
59 47
61 48
61 23
60 56
62 57
62 33
6205
31
32
33
5339
53 14
62 47
54 47
54 22
53 54
5555
5529
5501
5703
56 36
66 08
68 12
57 44
67 15
59 20
58 52
5822
6028
60 00
59 29
61 36
61 07
6036
34
35
36
52 20
51 51
51 21
53 26
52 56
52 26
54 31
54 01
63 30
5537
5506
54 35
56 44
66 12
65 41
57 60
57 18
56 46
5857
58 24
57 51
6003
59 30
5855
37
38
39
5051
•50 19
49 47
51 54
51 23
5050
52 57
52 26
51 52
54 02
53 29
5255
5507
54 33
5358
56 12
5537
55 02
57 17
66 41
56 05
58 22
57 45
5708
40
41
42
49 13
4838
48 03
50 15
49 40
49 04
51 16
50 41
6004
52 18
51 43
51 05
5321
5245
52 07
54 24
53 47
6309
5527
54 49
64 11
5630
55 60
66 12
43
44
45
47 28
46 51
46 13
4828
4751
47 12
4928
48 49
48 10
6029
49 49
4909
51 30
5049
5009
5229
51 48
51 08
63 30
52 48
5207
54 30
53 47
5306
46
47
48
4535
44 55
44 15
4633
45 53
45 13
4730
46 50
4609
4828
47 48
47 06
49 27
48 46
4803
50 26
49 43
48 59
51 24
6041
49 56
5222
51 38
5052
49
50
51
43 36
42 54
42 12
44 32
4350
4307
45 27
44 44
44 01
46 23
45 39
44 55
47 19
4634
45 50
48 15
47 30
46 44
49 11
48 25
4738
5006
49 20
4832
52
53
54
41 30
40 46
40 02
42 23
41 39
40 54
43 16
42 31
41 45
44 09
43 24
42 37
45 04
44 17
43 30
45 57
45 09
44 21
46 51
46 02
45 13
4744
4654
46 04
55
56
57
39 17
3833
37 47
4009
39 23
3837
40 59
40 13
39 26
41 50
41 02
40 14
42 42
41 53
41 04
4332
42 44
41 53
44 23
4334
42 43
45 14
44 24
4332
58
59
60
3701
36 15
3528
3750
37 03
36 15
3838
37 49
3700
39 25
38 36
37 46
40 14
39 24
3834
41 03
40 11
39 20
41 52
40 59
4006
42 39
41 46
40 52
61
62
63
34 39
3360
3302
3525
3435
33 46
36 10
35 19
3429
36 56
36 04
35 13
37 42
36 49
3557
3827
3734
36 41
39 13
38 19
37 25
39 58
39 03
3808
TABLE 49. [Page 947
Corrections for the Observed Altitudes of the Moon's Lower Limb.
OBS. ALT.
LOWEB
LDCB.
HORIZONTAL, PARALLF.X.
54'
55
56' 57' 58'
59'
6O'
61'
• r
64 '
65
66
i '•
32 13
31 23
3033
3256
32 06
31 14
3338
32 47
31 54
34 21
33 2S
3235
3506
34 11
33 17
/ n
3547
34 52
3357
/ m
3630
35 34
3438
37 13
36 16
35 19
87
9
2942
2S 51
2759
3022
29 31
28 38
31 01
30 09
29 15
31 41
30 47
29 53
32 22
31 27
3032
3301
32 06
31 10
33 41
32 45
31 48
34 21
33 24
3226
70
71
72
2707
26 15
25 23
27 46
26 52
2558
2822
27 27
2632
2859
28 04
2708
29 36
28 40
27 43
30 14
29 16
28 19
3051
29 53
2854
31 27
30 28
2928
73
74
75
24 30
23 37
22 44
2505
24 11
23 16
2538
24 43
23 47
26 12
25 16
24 19
26 46
25 49
24 53
27 21
26 22
2525
2755
26 56
25 57
2829
27 28
26 28
78
77
78
21 51
20 57
2002
2222
21 27
2032
22 52
21 56
21 00
2323
2226
21 29
23 55
22 57
21 59
24 26
23 27
22 27
24 57
23 57
2256
25 27
24 26
23 25
79
80
a
19 08
13 13
17 19
19 38
IS 41
17 45
2004
19 07
IS 10
2031
1933
1835
21 60
2001
19 02
21 27
2027
19 27
21 56
2055
19 55
2223
21 22
20 21
82
83
H
16 24
1529
1433
15 49
1553
14 57
1713
16 16
1519
1737
1540
1542
1803
1704
1605
IS 28
17 27
1627
1354
17 52
1650
19 13
13 16
17 13
•
87
13 33
12 43
11 47
14 00
13 04
12 08
14 21
13 24
12 26
14 43
13 45
12 46
1505
14 06
13 06
1527
14 27
13 26
1549
14 48
13 46
16 10
15 08
14 05
88
89
90
10 52
9 56
9 00
11 11
10 15
9 13
11 28
10 31
9 34
11 47
1049
9 50
1206
11 07
10 07
1224
11 24
10 23
12 44
11 42
10 41
13 02
11 59
1057
HDGHT or ETK CORMCTIOX.
Height in feet.
Correction.
10
4-2
42
12
4-2
24
14
4-2
06
16
+1
53
18
4-1
39
20 4-1
25
•22 +1
12
24
_i
00
28
+6
48
28
4-0
37
30
-4-0
26
35
0
00
40
-0
24
45
-0
48
50
—
08
55
—
28
60
—
47
65
—
06
70
—
24
75
41
80
58
85
-3
14
90
—3
30
96
—3
45
100
-4
00
Page 948] TABLE 49.
Corrections for the Observed Altitude of the Moon's Upper Limb.
OBS. ALT.
UPPER
LIMB.
HORIZONTAL PARALLAX.
54'
55'
56'
57'
58'
59'
60'
61'
0 /
5 30
600 g
630 5
2338
24 18
24 52
24 21
25 01
2535
25 05
25 44
26 18
25 48
26 27
27 02
26 31
27 10
27 44
27 13
27 54
28 28
27 56
2837
29 11
28 38
29 19
29 54
7 00
7 30
800
2521
25 47
2609
2604
26 30
2652
26 48
27 13
2735
2731
27 56
28 18
28 13
28 39
29 01
28 57
29 22
29 44
2940
3005
3027
30 24
30 48
31 09
830
9 00
9 30
2628
26 45
27 00
27 11
27 27
27 42
2754
28 10
2824
2837
28 53
2906
29 20
29 36
29 49
3003
30 19
3032
3046
31 02
31 15
31 28
31 44
31 57
10 00
11
12
27 10
2731
27 45
27 53
28 13
2827
2836
2855
29 10
29 19
29 38
29 52
3001
3021
3034
3044
31 03
31 16
31 27
31 46
31 58
3209
32 28
32 40
13
14
15
27 54
2759
28 01
2836
2840
2842
29 18
29 22
29 24
30 00
3005
3006
30 42
30 47
30 48
31 24
31 29
31 30
3207
32 11
32 11
32 49
32 52
32 52
16
17
18
2801
27 58
2751
28 42
2839
28 32
29 23
29 20
29 13
3004
3001
29 54
3045
30 42
3034
31 27
31 23
31 15
3209
3204
31 55
3250
32 45
3235
19
20
21
27 44
27 34
2723
2824
28 13
2803
29 05
28 54
2843
29 45
29 34
2923
3026
30 14
3002
3106
3054
30 41
31 46
31 34
31 21
32 26
32 15
3201
22
23
24
27 10
26 55
2639
27 49
27 33
27 17
2829
28 12
2756
2908
28 52
2835
29 47
29 30
29 13
3027
30 09
29 52
31 06
30 49
3031
31 45
31 27
31 10
25
26
27
26 22
2603
25 43
2700
26 40
2620
2738
27 18
26 58.
28 17
27 56
2736
2855
28 34
28 12
29 33
29 12
2849
30 11
29 49
29 26
30 48
3026
30 03
28
29
30
25 21
24 59
24 36
2558
25 35
25 11
2635
26 12
25 47
27 12
26 48
26 24
27 48
27 24
26 59
2825
28 01
2735
2903
28 37
28 10
29 39
29 12
2846
31
32
33
24 12
23 45
23 19
24 47
24 20
2353
25 22
24 55
24 27
2557
2530
2501
26 32
26 04
25 35
27 07
2639
26 09
27 43
27 14
26 43
28 18
27 48
27 17
34
35
36
22 51
22 22
21 53
23 24
2255
22 25
23 58
23 28
22 58
24 32
24 01
23 30
2505
24 34
24 02
25 39
25 07
24 34
26 12
25 40
25 07
26 45
26 12
2539
37
38
39
21 23
20 51
20 19
21 54
21 22
20 49
2226
21 53
21 20
2258
22 24
21 50
23 29
22 54
22 20
24 00
23 25
2250
24 31
23 56
23 20
25 03
24 28
23 50
40
41
42
19 46
19 11
1837
20 15
19 40
19 05
2045
20 09
1933
21 15
20 38
2001
21 45
21 06
2029
22 14
21 35
2057
22 43
22 04
21 25
23 12
2233
21 54
43
44
45
18 00
17 24
16 46
1827
1750
17 12
1855
18 17
17 38
1923
1845
1804
19 50
19 11
18 30
20 18
19 37
18 56
20 45
2004
19 22
21 13
2032
19 48
46
47
48
16 07
15 28
14 48
1633
1553
15 12
16 58
16 18
1536
17 24
16 43
16 00
17 49
17 07
16 24
18 14
1732
16 48
18 40
17 57
17 12
1905
18 21
1736
49
50
51
14 07
1326
12 44
1431
13 49
1306
14 55
14 11
13 27
15 17
14 34
13 49
15 40
14 56
14 10
16 04
15 19
14 32
1627
15 41
14 54
16 50
1603
15 15
52
53
54
1202
11 19
10 36
12 23
11 39
10 54
12 44
11 59
11 13
1305
12 19
11 32
13 25
1238
11 51
13 46
1259
12 11
14 07
13 19
1230
14 27
13 38
12 49
55
56
57
9 51
9 06
821
1009
9 23
837
1027
9 40
853
1045
9 58
9 10
11 03
10 15
9 26
11 23
10 32
9 43
11 41
10 49
9 59
11 59
11 06
10 15
58
59
60
7 35
6 48
6 00
750
702
6 13
8 05
7 17
627
821
732
6 41
8 36
7 46
6 55
8 52
801
709
9 07
8 16
723
9 22
8 30
736
61
62
63
5 12
4 23
3 35
524
4 35
3 46
537
4 48
3 57
550
5 00
4 08
604
5 12
4 19
6 17
5 23
4 30
629
535
4 40
6 42
5 46
4 51
TABLE 49. [Page 949
Corrections for the Observed Altitude of the Moon's Upper Limb.
OBS. ALT.
UPPEE
LIMB.
HORIZONTAL PARALLAX.
54'
65'
56'
57'
58'
6^
GO'
61'
o a
64
65
66
2 46
1 56
1 06
256
2 04
1 14
306
2 13
1 22
3 16
223
131
3 26
2 32
1 39
3 36
2 42
1 47
3 46
251
1 55
3 56
3 00
2 03
67
68
69
S 1
72 8
0 16
0 22
0 29
0 37
0 44
051
0 04
058
002
1 06
0 OS
0 36
1 27
2 19
3 11
4 03
0 30
1 22
2 15
3 08
401
0 24
1 17
2 11
3 05
3 59
0 17
1 11
206
3 01
3 56
0 11
1 06
2 02
2 58
3 54
1 02
158
255
352
0 57
1 54
252
3 50
0 51
1 50
2 48
3 48
3 §
75
4 55
5 49
6 43
4 56
550
6 44
4 54
549
6 44
4 52
5 48
645
4 51
5 48
6 46
4 50
548
647
4 49
548
6 48
4 47
5 47
6 48
76
77
78
737
831
9 25
739
8 34
9 29
740
8 37
933
742
8 39
936
744
8 42
9 40
745
844
9 44
747
8 47
9 48
7 49
8 50
9 51
79
80
81
10 19
11 13
12 08
10 24
11 20
12 15
10 29
11 26
12 22
10 33
11 31
1228
1038
11 37
1235
10 43
11 43
1242
10 48
11 49
1250
10 52
11 54
1257
82
83
84
13 03
13 58
1453
13 11
14 07
15 04
13 19
14 16
15 14
1327
14 25
15 23
1334
14 34
1533
13 43
14 43
15 44
13 51
14 52
1554
13 59
1501
1603
85
86
87
15 48
16 44
17 39
16 00
1657
17 53
16 11
17 09
1806
1621
17 20
18 18
1633
1732
1832
16 44
17 45
18 45
16 55
1757
1859
1706
1808
19 11
88
89
90
1835
19 31
2026
1850
19 47
20 43
19 04
2002
21 00
19 18
20 16
21 15
1932
20 31
21 31
19 46
20 47
21 48
2000
2103
22 04
20 14
21 17
2220
HEIGHT OF ErE COKEECTION.
Height in feet.
Correction.
10
+2
42
12
+1
24
14
+2
08
16
+ 1
53
18
+ 1
39
20
+1
25
22
+1
12
24
+ 1
00
26
+0
48
28
+0
37
30
+0
26
35
0
00
40
-0
24
45
-0
48
50
-1
08
55
-1
28
60
-1
47
65
-2
06
70
-2
24
75
-2
41
80
-2
58
85
-3
14
90
-3
30
95
-3
45
100
-4
00
o
UNIVERSITY OF CALIFORNIA LIBRARY
BERKELEY
Return to desk from which borrowed.
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ASTRONOMY LIBRARY
SEP 9 197
1958
NOV 3 0 1959
LD 21-100m-ll,'49(B7146sl6)476
YD
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